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Dynamic characteristics of a 30 storey building during construction detected from ambient vibration measurements Schuster, Norman David 1994

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DYNAMIC CHARACTERISTICS OF A 30 STOREY BUILDING DURINGCONSTRUCTION DETECTED FROM AMBIENT VIBRATION MEASUREMENTSbyNORMAN DAVID SCHUSTERHonours B.A.Sc., The University of Waterloo, 1992A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Civil EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1994© Norman David Schuster, 1994In presenting this thesis in partial fulfillment of therequirements for an advanced degree at the University of BritishColumbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission forextensive copying of this thesis for scholarly purposes may begranted by the head of my department or by his or herrepresentatives. It is understood that copying or publication ofthis thesis for financial gain shall not be allowed without mywritten permission.Department of CIVIL N6iIE4rThe University of British ColumbiaVancouver, CanadaDate (o ect4ABSTRACTThe dynamic response of building structures to earthquakes has become an issue in the provinceof British Columbia because of increased awareness of the seismic hazard in this region. Whilethere is a great deal of knowledge about structural dynamics, the majority of this knowledge isbased on uniform structures. Hence, there is concern about extrapolating these results to thebehaviour of nonuniform building which emerge from current architectural trends. The focus ofthis study was to monitor and to quantify the dynamic characteristics of a 30 storey, reinforcedconcrete building during its construction. This building is representative of the type ofconstruction in Vancouver, B .C. and is therefore a useful case study. In addition, the lateralforce resisting system in this structure is uniform in plan and elevation while the distribution ofstorey mass is asymmetrical due to its geometry as well as a major setback at one corner.Dynamic characteristics were determined by analyzing ambient vibrations of the structure.These vibrations were acquired and processed using a testing system developed at the Universityof British Columbia (Department of Civil Engineering). Several computer programs weredeveloped during this project to complement the existing software.The objectives of this study included determining mode shapes and periods, determining theeffect of architectural components, assessing base motion, and assessing the manner of the core’sdeformation. In addition, a dynamic analysis was performed to assess the accuracy of modelingtechniques. Finally, some aspects of current building codes were assessed.Ambient vibration testing methods proved very practical and useful. Torsional motion andmodal coupling were found to be very significant, while little motion was detected at the base ofthis building. Natural frequencies decreased and tended to converge as the building heightincreased. Architectural components did not significantly influence the dynamic characteristics.The dynamic behaviour of this building could be accurately represented using dynamic analysis.Finally, the building code provisions considered in this study appear to be appropriate.UTABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS iiiLIST OF TABLES ixLIST OF FIGURES xiACKNOWLEDGMENTS xviiDEDICATION xviiiCHAPTER 1 iNTRODUCTION 11.1 Overview Of Project 11.2 Current Research 31.3 Scope And Objectives Of This Study 41.4 Outline Of Thesis 5CHAPTER 2 BACKGROUND ON SIGNAL ANALYSIS 62.1 Ambient Vibration Testing 62.1.1 Ambient Vibrations 62.1.2 Prerequisites For Ambient Vibration Analysis 62.1.3 Formulations 72.1.4 Implementation 92.2 Signal Processing Functions Used In This Study 102.2.1 Spectral Density Functions 102.2.1.1 Cross-Spectral Density Function 112.2.1.2 Power Spectral Density Function 112.2.1.3 Coherence Function 112.2.1.4 Transfer Function 122.2.1.5 Averaged Normalized Power Spectral Density Function 122.2.1.6 Potential Modal Ratio Function 132.2.2 Modal Assurance Criterium (MAC) 142.2.3 Signal Processing Software 142.2.4 Problems Associated With Digital Data 142.2.4.1 Resolution 152.2.4.2 Aliasing 152.2.4.3 Leakage And Time Windows 172.3 Closing Remarks 18111CHAPTER 3 DESCRIPTION OF BUILDING .203.1 General Description Of City Tower 203.1.1 Overview 203.1.2 Storey Referencing Convention 213.2 Structural System 223.3 The Tower During Construction 263.4 Closing Remarks 26CHAPTER 4 AMBIENT VIBRATION TESTS 324.1 Ambient Vibration Equipment Used For This Study 324.1.1 The Hybrid Bridge Evaluation System 324.1.2 Adapting The HBES For Building Ambient Vibration Tests 334.1.3 Modifications To Data Acquisition Program 354.1.4 Checking Time History Records 354.2 Overall Objectives And Testing Procedures 414.2.1 General Test Objectives 414.2.2 Deciding The Sensor Locations 414.2.3 Typical Testing Procedure 434.3 Specific Details Of The City Tower Tests 464.3.1 Overview 464.3.2 CT1O - 10 Levels Completed 474.3.2.1 Measurement Objectives 474.3.2.2 Setup 484.3.2.3 Test Evaluation 484.3.3 CT15 - 15 Levels Completed 494.3.3.1 Measurement Objectives 494.3.3.2 Setup 494.3.3.3 Test Evaluation 504.3.4 CT2O - 20 Levels Completed 514.3.4.1 Measurement Objectives 514.3.4.2 Setup 514.3.4.3 Test Evaluation 524.3.5 CT25 - 25 Levels Completed 544.3.5.1 Measurement Objectives 544.3.5.2 Setup 544.3.5.3 Test Evaluation 544.3.6 CT32 - 32 Levels Completed 554.3.6.1 Measurement Objectives 554.3.6.2 Setup 554.3.6.3 Test Evaluation 554.3.7 CTTC - Tower Completed 564.3.7.1 Measurement Objectives 564.3.7.2 Sensor Locations and Setup 564.3.7.3 Test Evaluation 58iv4.4 Error Analysis .584.4.1 Alias Check 584.4.2 Collocation Measurement 594.4.3 Random And Bias Errors 60CHAPTER 5 AMBIENT VIBRATION ANALYSIS RESULTS 615.1 Method For Detecting Mode Shapes And Frequencies 615.1.1 Determining Natural Frequencies 615.1.2 Determining Mode Shapes 635.1.3 Typical Mode Shapes 645.1.3.1 Mode Shape Appearance 645.1.3.2 Importance Of Reference Sensors 645.1.3.3 Importance Of Signal Resolution 665.1.4 Development Of SLAVE 675.1.5 Development Of MAC 685.2 Mode Shapes From Individual Tests 705.2.1 Mode Shape Naming Conventions 705.2.2 Ten Levels Of The Tower Completed (CT1O) 705.2.3 Fifteen Levels Of The Tower Completed (CT15) 725.2.4 Twenty Levels Of The Tower Completed (CT2O) 745.2.4.1 Mode Shapes 745.2.4.2 Modal Interference Between Modes EW•2 And T•2 765.2.5 Twenty-Five Levels Of The Tower Completed (CT25) 785.2.6 All Thirty-Two Levels Of The Tower Completed (CT32) 805.2.7 Evolution Of The Mode Shape 825.2.8BaseMotion 825.2.9 Tower Completed (CTTC) 845.2.9.1 Lateral Modes 845.2.9.2 Core Deformation And Vertical Modes 855.3 Modal Frequencies 885.3.1 Modal Frequencies And Frequency Ratios 885.3.2 Frequency Trends 895.4 Effect Of Architectural Components 905.4.1 Effect On Frequency 905.4.2 Effect On Mode shapes 905.4.3 Effect On Damping 915.4.3.1 Sensitivity Analysis 915.4.3.2 Comparison Of Bare Structure And Finished Building 95CHAPTER 6 DYNAMIC ANALYSIS OF THE BUILDING 976.1 Computer Analysis 976.1.1 Choice Of Dynamic Analysis Packages 976.1.2 Calibration Of The Base Model 976.1.3 Comparison Of Analytical And Experimental Frequencies 1006.1.4 Comparison Of Analytical And Experimental Mode Shapes 1026.1.4.1 Comparison Based On A MAC Analysis 102v6.1.4.2 Comparison Based On Overlaying Mode ShapeComponents 1046.2 Design Considerations 1066.2.1 Design Frequencies 1066.2.2 Response Spectra And Seismic Demands 107CONCLUSIONS 111RECOMMENDATIONS FOR FUTURE RESEARCH 113NOMENCLATURE 114ABBREVIATIONS 115REFERENCES 116APPENDIX A DETAILS OF AMBIENT VIBRATION SURVEYS 120A. 1 Building Instrumentation 120A.2 Exact Sensor Locations And Conditioning Details 120A.2. 1 Ambient Vibration Measurements 120A.2.2 Sensor Locations 120APPENDIX B AMBIENT VIBRATION DATA ACQUISITION SOFTWARE (AVDA) -OPERATING INSTRUCTIONS 133B.lOverview 133B.1.1 Description 133B. 1.2 Revisions To AVTEST 133B. 1.2.1 Data Saturation Check 134B. 1.2.2 Check For Existing Filenames And Remaining DiskSpace 134B. 1.2.3 Addition Of Sounds Corresponding To CertainOperations 134B. 1.2.4 Increased Channel Capacity And Increased Size Of DataArrays 135B.1.2.5 Flexible Sensor Calibration 135B.2 Installation And System Requirements 136B.3 Program Execution 136B.3.1 Rurming The Program 136B.3.2 Command Line Arguments 139B.3.2.1 Nyquist Frequency (Freq) 139B.3.2.2 Number Of Points To Acquire (NumPts) 139B.3.2.3 Number Of Channels (NumChan) 140B.3.2.4 Global Gain (GGain) 140B.3.2.5 Calibration Options (Calib) 142B.3.2.6 Allowable Number Of Consecutive Saturation Points(Sat) 142viB.3.2.7 Filename Prefix (Filename).143B.3.3 Memory Considerations 143B.3.4 Output File Format 144B.4 Typical Testing Procedure 145B.5 Routine To Read “BBB” Files 146APPENDIX C AMBIENT VIBRATION TIME HISTORY PLOTfER SOFTWARE FORHP LASERJET III PRINTERS (HPPLOT) - OPERATINGINSTRUCTIONS 149C. 1 Description 149C.2 Installation And System Requirements 150C.3 Program Execution 150C.3.1 Running The Program 150C.3.2 Command Line Arguments 151C.3.2.1 Destination (dest) 151C.3.2.2 Filename Prefix (datafile) 152C.3.2.3 Number Of Files (nt) 152C.3.2.4 Calibration Flag (cal) 152C.3.2.5 Filter Setting (filter) 152C.3.2.6 Attenuation Setting(s) (att) 152C.3.2.7 Filename With Plot Labels (labelfile) 153C.3.2.8 Warning Flag (warnings) 153C.3.3 Example Of Generating Plots With A BATch File 154APPENDIX D SLAVE NODE GENERATOR SOFTWARE (SLAVE) - OPERATINGINSTRUCTIONS AND DOCUMENTATION 157D. 1 Description 157D.2 Installation And System Requirements 157D.3 Program Execution 157D.3.1 Requirements And Restrictions 157D.3.2 Running The Program 158D.3.2 Command Line Arguments 158D.3.2.1 Filename (mputFile) 159D.3.2.2 Options (flags) 159D.3.2.3 Rigid Body Rotation Cutoff (thetaCutOff) 160D.3.3 Input File 160D.3.4 Example 161D.4 Formulation 164D.4. 1 Requirements 164D.4.2 Nomenclature 164D.4.3 Two-Dimensional Formulation 164D.4.3.1 XXYY Formulation - Utilizing 4 Measurements 165D.4.3.2 XXY Formulation - Utilizing 3 Measurements 166viiD.4.3.3 XYY Formulation - Utilizing 3 Measurements 167D.4.4 Three-Dimensional Formulation 168D.5 Computer Algorithm Considerations 169APPENDIX E MODAL ASSURANCE CRITERIUM SOFTWARE (MAC) -OPERATING INSTRUCTIONS 172E. 1 Description 172E.2 Installation And System Requirements 172E.3 Program Execution 172E.3.l Running The Program 172E.3.2 Supported Mode Shape Formats 173E.3.2.1 ETABS Mode Shape (EIG) 174E.3.2.2 Slave Mode Shape (SMS) 174E.3.2.3 Analytical Mode Shape (AMS) 175E.3.2.4 Experimental Mode Shape (XMS) 176E.3.3 Example 176APPENDIX F ERROR ANALYSIS 182APPENDIX G POWER SPECTRAL DENSITY PLOTS 193APPENDIX H COMPARISON OF ANALYTICAL AND EXPERIMENTAL RESULTS 201viiiLIST OF TABLESTable 3.1. Specified Concrete Strengths 24Table 3.2. Specified Design Loads 24Table 5.1. Vibration mode shape designations 70Table 5.2. Nodal points expressed as a percent of the building’s height 82Table 5.3. Frequencies (Hz) for City Tower from 5 stages in its construction 88Table 5.4. Frequencies ratios for City Tower from 5 stages in its construction 89Table 5.5. Modal frequencies from CT32 and CTTC 90Table 6.1. MAC values (percentage) between experimental and analytical mode shapes 103Table 6.2. Comparison of measured and design periods for the building 107Table A. 1. CT1O FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 124Table A.2. CT15 FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 124Table A.3. CT2O FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 125Table A.4. CT25 FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 125Table A.5. CT32 FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 126Table A.6. CTTC FBA setups and locations, conditioning and sampling details, VISUALNodal coordinates 126Table B.1. AVDA versions and compile dates 133Table E.1. Corresponding storey labels required for the MAC analysis 177Table H. 1. Comparison of experimental and analytical frequencies for 10 levels of thebuilding completed (CT1O) 202Table H.2. Comparison of experimental and analytical frequencies for 15 levels of thebuilding completed (CT15) 202Table H.3. Comparison of experimental and analytical frequencies for 20 levels of thebuilding completed (CT2O) 202ixTable H.4. Comparison of experimental and analytical frequencies for 25 levels of thebuilding completed (CT25) 203Table H.5. Comparison of experimental and analytical frequencies for 32 levels of thebuilding completed (CT32) 203xLIST OF FIGURESFigure 2.1.Figure 2.2.Figure 2.3.Figure 3.1.Figure 3.2.Figure 3.3.Figure 3.4.Figure 3.5.Figure 3.6.Figure 3.7.Figure 3.8.Figure 3.9.Figure 3.10.Figure 3.11.Figure 3.12.Figure 3.13.Figure 3.14.Figure 4.1.Figure 4.2.Figure 4.3.Figure 4.4.Digitized sine waves sampled at 40 Hz 16Sine wave with a frequency of 22 Hz and its digital representation (sampled at40 Hz) and the resulting alias waveform 17Plot of two sine waves. Plot (a) shows a sine wave which fits perfectly withinthe analysis window of period T. Plot (b) shows a sine wave which has aslope and magnitude discontinuity at its ends while plot (c) shows the samewaveform after being multiplied by a Hanning window 19South-East Elevation of City Crest Tower 21Typical floor plan of City Tower 22Typical detail of diagonal reinforcing in the core headers 23Schematic of footings supporting the building core, columns, and retainingwalls. (Footings on the interior are shown with dotted lines) 25City Tower following the completion of Level 10 27City Tower following the completion of Level 15 27City Tower following the completion of Level 20 28City Tower following the completion of Level 25 28City Tower following completion of the structure 29City Tower with all of the architectural components installed 29Shoring detail which supports the level above it as the concrete is curing 30Platform used when pulling up cables to the top floor (left) and the cranetower which passes through the concrete floors (background right) 30Typical floor before the installation of architectural components 31Typical floor with galvanized steel stud walls prior to the installation ofdrywall 31Software hierarchy for data acquisition and analysis 35Ambient vibration time histories with signal drift in channels 5 and 7 37Ambient vibration time histories with signal contamination in channels 3, 4 and8 38Ambient vibration time histories showing dominant torsional response 39xiFigure 4.5. Ambient vibration time histories showing dominant translational response 40Figure 4.6. Typical sensor layout for the roving sensors used in the first building test 43Figure 4.7. Schematic of the data acquisition equipment 44Figure 4.8. Data acquisition equipment (taken during the CT25 test) 45Figure 4.9. Two FBA-l 1 accelerometers in position during data acquisition 45Figure 4.10. Building response during man excited test in the NS direction 53Figure 5.1. Averaged normalized power spectral densities for parallel signals in the NS andEW directions (response of the building when its structure was completed) 62Figure 5.2. Typical floor plan showing sensor locations, slave motion locations, and linesused to represent the floors in the mode shapes presented below 64Figure 5.3. Orthographic and top views of two mode shapes which have identicalfrequencies but were reduced with respect to different reference sensors 65Figure 5.4. Distortion created when animating experimental mode shapes 67Figure 5.5. NS translational mode shapes - with and without slave nodes 69Figure 5.6. Vibration mode shapes in each principal direction of the building, andcorresponding frequencies (periods) following the completion of 10 levels 71Figure 5.7. First three vibration mode shapes in each principal direction of the building,and corresponding frequencies (periods) following the completion of 15levels 73Figure 5.8. Lower vibration mode shapes in each principal direction of the building, andcorresponding frequencies (periods) following the completion of 20 levels 75Figure 5.9. Modal interference between second EW translational mode and secondtorsional mode 77Figure 5.10. Lower vibration mode shapes in each principal direction of the building, andcorresponding frequencies (periods) following the completion of 25 levels 79Figure 5.11. First four vibration mode shapes in each principal direction of the building,and corresponding frequencies (periods) for the bare structure (32 levels) 81Figure 5.12. Evolution of the second vibration modes in each principal direction of thebuilding, and corresponding frequencies (periods) 83Figure 5.13. Typical floor plan showing sensor locations, slave motion locations, and linesused to represent the floors in the mode shapes presented below 84Figure 5.14. First four vibration mode shapes in each principal direction of the building,and corresponding frequencies (periods) of the finished building (CTTC) 86xiiFigure 5.15. First four vibration mode shapes of the building core, in each principaldirection of the building, and corresponding frequencies (periods) of thefinished building (CTTC) 87Figure 5.16. Frequency trends for the tower during its construction phase 89Figure 5.17. Damping estimates for 2 signals in the NS direction using differentresolutions and windows 93Figure 5.18. Damping estimates for 2 signals in the EW direction using differentresolutions and windows 93Figure 5.19. Damping estimates for 4 signals in the NS and EW directions (torsion) usingdifferent resolutions and windows 94Figure 5.20. Damping estimates for one signal in the NS direction using individualsegments, mean, and different resolutions (no window) 94Figure 5.21. Modal damping comparison between the bare structure and structure witharchitectural components in place 95Figure 6.1. ETABS model of the building with all 32 levels 98Figure 6.2. Experimental versus analytical frequencies 101Figure 6.3. Dominant components of the fundamental mode shapes for the base model(CT32) 104Figure 6.4. Comparison of experimental () and analytical ( ) mode shape componentsfor the second torsional mode 105Figure 6.5. Spectral Acceleration curves from the NBCC and UBC building codes. Alsoshown are periods for the EW and NS directions obtained from 0measurements, code equations (0 NBCC and UBC) and D dynamicanalysis 109Figure 6.6. Base shears and overturning moments for the building, during its constructionphase, determined using procedure outlined in the NBCC (R=3.5) 110Figure A. 1. Instrumentation of the building for the first ambient vibration survey; 10 levelscompleted (CT1O) 121Figure A.2. Instrumentation of the building for the second ambient vibration survey; 15levels completed (CT15) 121Figure A.3. Instrumentation of the building for the third ambient vibration survey; 20levels completed (CT2O) 122Figure A.4. Instrumentation of the building for the fourth ambient vibration survey; 25levels completed (CT25) 122xiiiFigure A.5.Figure A.6.Figure A.7.Figure B.1.Figure B.2.Figure B.3.Figure C.1.Figure C.2.Figure D.1.Figure D.2.Figure E.1.Figure F.1.Figure F.2.Figure F.3.Figure F.4.Figure F.5.Figure F.6.Figure F.7.Figure F.8.Figure F.9.Instrumentation of the building for the fifth ambient vibration survey; all 32levels completed (CT32) 123Instrumentation of the building for the final ambient vibration survey; towercompleted (CTTC) 123Locations of FBA sensors during the ambient vibration measurements at CityTower 127-131Instructions displayed when AVDA is executed with no command linearguments 137Echo of the command line arguments 138A digitized sine wave and corresponding global gains 141Typical ambient vibration time history produced by HPP1ot 149Instructions displayed when HPP1ot is executed with no command lineparameters 151Message displayed when SLAVE is executed with no arguments 159Floor plan of a rectangular building with three instruments 161Message displayed when MAC is executed with no arguments 173Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #1 oriented in the NS direction 183Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #3 oriented in the NS direction 183Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #2 oriented in the EW direction 184Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #4 oriented in the EW direction 184Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #5 oriented in the EW direction 184Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #6 oriented in the vertical direction 185Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #7 oriented in the vertical direction 185Comparison of power spectral density functions of signals sampled at differentrates (40 Hz and 80 Hz) using FBA #8 oriented in the vertical direction 185Coherence functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1 186xivFigure F. 10. Coherence functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2 187Figure F.11. Frequency response functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1 188Figure F. 12. Frequency response functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2 189Figure F.13. Phase functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1 190Figure F.14. Phase functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2 191Figure G. 1. ANPSD piots for all of the lateral signals from the CT1O test. Peakscorresponding to natural frequencies are labeled with the correspondingmode 194Figure G.2. ANPSD plots for all of the lateral signals from the CT15 test. Peakscorresponding to natural frequencies are labeled with the correspondingmode 195Figure G.3. ANPSD plots for all of the lateral signals from the CT2O test. Peakscorresponding to natural frequencies are labeled with the correspondingmode 196Figure G.4. ANPSD plots for all of the lateral signals from the CT25 test. Peakscorresponding to natural frequencies are labeled with the correspondingmode 197Figure G.5. ANPSD plots for all of the lateral signals from the CT32 test. PeakscolTesponding to natural frequencies are labeled with the correspondingmode 198Figure G.6. ANPSD plots for all of the lateral signals from the CTIC test. Peakscorresponding to natural frequencies are labeled with the correspondingmode 199Figure H.l. Comparison of experimental () and analytical ( ) mode shapes forfundamental EW translational mode (EW• 1) 204Figure H.2. Comparison of experimental (0) and analytical ( ) mode shapes for secondEW translational mode (EW.2) 205Figure H.3. Comparison of experimental (0) and analytical ( ) mode shapes for thirdEW translational mode (EW•3) 206Figure H.4. Comparison of experimental (0) and analytical ( ) mode shapes for fourthEW translational mode (EW•4) 207Figure H.5. Comparison of experimental (0) and analytical ( ) mode shapes forfundamental NS translational mode (NS’l) 208Figure H.6. Comparison of experimental (0) and analytical ( ) mode shapes for secondNS translational mode (NS•2) 209xvFigure H.7. Comparison of experimental (G) and analytical ( ) mode shapes for thirdNS translational mode (NS•3) 210Figure H.8. Comparison of experimental (G) and analytical ( ) mode shapes for fourthNS translational mode (NS•4) 211Figure H.9. Comparison of experimental () and analytical ( ) mode shapes forfundamental torsional mode (T•1) 212Figure H. 10. Comparison of experimental (0) and analytical ( ) mode shapes forsecond torsional mode (T•2) 213Figure H. 11. Comparison of experimental (0) and analytical ( ) mode shapes for thirdtorsional mode (T•3) 214Figure H. 12. Comparison of experimental (0) and analytical ( ) mode shapes for fourthtorsional mode (T•4) 215xviACKNOWLEDGMENTSI would like to thank my advisor, Dr. Carlos Ventura. His experience with instrumentedbuildings and signal processing, along with his guidance and encouragement, contributed to thesuccess of this project. His assistance in all of the City Tower vibration surveys was mosthelpful. Finally, his thoughts and suggestions during his review of early drafts of this thesis, areappreciated.I am indebted to my colleague Dr. Andreas Felber. He developed the data acquisition systemand analysis software which was used in this study. He also served as my trainer; offeringinsightful guidance about ambient vibration testing and spectral analysis. He was alsoinstrumental during all of the ambient vibration surveys performed on City Tower, and his helpis appreciated. Finally his company, EDT Ltd., made some additional software programsavailable for use in this study.I would also like to thank those people involved with the City Crest Tower development. Mr.Don Ho of Trans City Properties Ltd. permitted the vibration measurements of his building. Mr.John Pao of Bogdonov Pao Associates Ltd. encouraged this study. He also provided contractdrawings of the building and participated in the first test at City Tower. Mr. Jim Desroches, alsoof Bogdonov Pao Associates Ltd., was my liaison. Finally, the cooperation and assistance of Mr.Vince Kehoe, of Ledcor Industries, was very helpful to the preparation and execution of all thetests which were performed at City Tower.The financial support of the Natural Science and Engineering Research Council (N.S.E.R.C.) ofCanada is gratefully acknowledged. This includes a Postgraduate Scholarship as well asResearch and Equipment Grants. The grants were used to augment the dynamic testingequipment at UBC as well as finance my attendance at EERI conferences (held in Los Angeles,California and Chicago, illinois) to present research papers based on my research.I would like to thank Mr. Howard Nichol, earthquake lab technician, for maintaining andexplaining several components of the data acquisition system.I would also like to thank all of the other people from UBC who provided invaluable assistanceduring the field tests. These people include Dr. Helmut Prion; graduate students Steve Yee,Rhonda Steinke, Tom Schmalz, Mike Baraka, Isabelle Villemure, and Markus Seethaler; andundergraduate student Aloysius Fekete.Finally, I would like to thank Dr. P. Adebar and Dr. R. Foschi who, along with Dr. Ventura,reviewed the first draft of this thesis.xviiyxviiiCHAPTER 1INTRODUCTIONThis chapter presents an overview of this research project. A general description of the problemis discussed in the first section (1.1). This is followed by a literature review (1.2). The nextsection describes the scope and objectives of this study (1.3). An outline of this thesis ispresented at the end of this chapter ( 1.4).11 OVERVIEW OF PROJECTMost civil engineering structures (buildings, bridges, etc.) are prototypes. Hence, an evaluationof a structure’s behaviour prior to or even decades after its construction is based on mathematicalanalysis as well as engineering judgment and experience with similar types of structures. Inrecent years, the dynamic response of a structure during an earthquake has become a concern inthe province of British Columbia (B.C.). In this case, a dynamic analysis of the structure isperformed in order to predict its capacity to given seismic demands. This type of analysis is verysensitive to changes in a system’s parameters; these being stiffness, damping, and mass.Moreover, the spatial distribution of these parameters, complicated by a structure’s interactionwith the soil upon which it rests, makes this task very difficult.There has been a great deal of research in the area of structural dynamics and the behaviour ofbuilding systems. However, the majority of this research has focused on uniform buildings; i.e.buildings with rectangular shaped floor plans as well as regular and symmetrical layouts of theload bearing walls and columns. In contrast, current trends in architecture have produced veryimaginative and oddly shaped buildings. Consequently, there is concern about extrapolating thebehaviour of a uniform building to the behaviour of one of these modern buildings.While fundamental engineering principles can be applied in the analysis of these modernbuildings, there is a need to verify that predictions of building response determined through suchapplications are accurate. One method to verify the accuracy of these predictions is to measure1the vibrations of the structure, and by using signal processing methods, determine the dynamiccharacteristics of the structure. These characteristics can then be compared to those determinedusing analytical models.A very popular method of determining dynamic characteristics is to analyze ambient vibrationsof the building. These types of vibration result from wind, traffic on neighbouring streets, peoplemoving about in the building, etc. For this study, an ambient vibration data acquisition andanalysis system at the University of British Columbia was available to perform thesemeasurements.The focus of this study was on the dynamic behaviour of a high-rise building, called City Tower,which is located in Vancouver, B.C. This behaviour was quantified by recording and analyzingambient vibrations of the structure. This was a very interesting case study for a number ofreasons. First, the dynamic characteristics were determined at selected points in time during thebuilding’s construction. Thus, the evolution of this behaviour as the structural system isassembled up to the point in time when all of the architectural components are installed wasmonitored. Second, the asymmetrical distribution of storey mass in this structure created someinteresting torsional effects in the vibration mode shapes. Moreover, the effect of two majorsetbacks along the height of this building was considered.As mentioned, this ambient vibration survey was conducted as the building was beingconstructed. Specifically, measurements were taken at the building following the completion of10, 15, 20, 25, and 32 levels during a 5 month period from January to June 1993. A finalmeasurement was conducted in October 1993 when all of the major architectural componentswere in place.21.2 CURRENT RESEARCHThe analysis of ambient vibration measurements of a wide variety of engineering structures hasbeen documented over the last few decades. A few studies from 1982 to present are discussedbelow.Four high-rise buildings located in New York City were recently tested by Gavin, Grossman, etal. (1992) using ambient and wind induced vibrations. This study focused on the response of tallflat-plate buildings representative of the construction in this region. Although the number ofmeasurement points in these building was rather low, several vibration mode shapes andfrequencies along with estimates of damping ratios were determined. The scope of this researchwas similar to the project discussed in this thesis. In particular, the type of construction of thesebuildings is similar to that of the building being studied in this research project. In addition, oneof these buildings was tested prior to the installation of architectural components. The latterbuilding was scheduled to be tested once it was finished.Three different structures were successfully tested in Germany using ambient vibrationmeasurements (Luz, 1992). These structures include a 12 storey office building (located atStuttgart University) along with a church tower and a single span railway bridge. Thefundamental vibration modes and several higher vibration modes were determined, along withtheir corresponding frequencies, for all of these structures. This effectively demonstrated theversatility of ambient vibration testing.Ambient vibration measurements, along with strong motion vibration measurements from severalearthquakes, were used to study several buildings on the west coast of the United States. Onestudy involved a six storey building which contained strong motion instrumentation provided bythe California Division of Mines and Geology (Pardoen, 1983). In another study, five multistorey buildings in seismically active regions in San Francisco, California and Seattle,Washington, were tested by Neuss, Maison, and Bouwkamp (1983). In yet another study, fivedifferent buildings which experienced the ground motions of the Loma Prieta earthquake3(October 17, 1989) were studied by Marshall, Phan, and celebi (1994). In the latter study,comparisons were made between results obtained from ambient vibration measurements (usingthe existing strong motion instrumentation in the buildings) with the results obtained fromanalyzing the strong motion records.An ambient vibration study was also conducted on several buildings in Vancouver by To andCherry (1982). In this study, three identical buildings (Gage Residence) at the University ofBritish Columbia were tested for comparison. In addition, the modal properties of threebuildings located in downtown Vancouver, namely the Harbour Centre Building, and the IBMand Toronto Dominion Bank Towers, were also determined.Considering the wide spread use of ambient vibration measurements to successfully determinedynamic characteristics of buildings, it was decided that this method of testing would be used tostudy City Tower.1.3 SCOPE AND OBJECTIVES OF THIS STUDYThe objective of this investigation was to monitor and to quantify the dynamic characteristics ofa multi-storey building whose structural system was representative of the type found indowntown Vancouver. The dynamic characteristics of interest were vibration mode shapes andcorresponding periods in the three principal directions (torsional and two translational) of thebuilding.In addition to modal properties, several other aspects of the building’s dynamic behaviour werestudied. These include the effect of non-structural components, motion at the base of thebuilding, and core deformations during the vibration mode shapes. The effect of non-structuralcomponents was determined based on differences in frequencies and vibration mode shapes aswell as changes in damping ratios.Following the experimental analysis, a dynamic modal analysis was performed on 5 models ofthe building corresponding to the construction stages where ambient vibration measurements4were taken. The objective of the dynamic analysis was to calibrate the models so that theresulting frequencies (periods) and mode shapes corresponded to those obtained experimentally.This would demonstrate the accuracy of state-of-the-art modeling techniques. Experimental andanalytical periods determined from this study were also compared with periods obtained from thedynamic analysis used to design the building, as well as periods obtained using expressions intwo building design codes. In addition, calculations of base shear and overturning momentswere also made.While several aspects of this building can be studied, only the topics mentioned above form thescope of this research. This limitation was due to time constraints. Moreover, other aspects ofthis building’s behaviour can always be explored in the future.1.4 OUTLINE OF THESISThis thesis is comprised of six chapters and eight appendices. The second chapter presentsbackground information on signal analysis. Chapter Three describes the high-rise buildingstudied. The next two chapters discuss the ambient vibration tests and the results obtained fromthe analysis of the collected data. The last chapter presents the results from the dynamic analysisof the building. Finally, conclusions and recommendations for future research are presented.Appendix A includes details of the ambient vibration tests and instrumentation. Appendices Bthrough E contain descriptions and operating instructions of several software programs that weredeveloped through the course of this research. Appendices F and G show plots of several signalprocessing functions determined from the experimental data. The plots in Appendix F were usedto assess the performance of the instruments which recorded the building’s vibrations. The plotsin Appendix G were used to detect natural frequencies. Finally, Appendix, H contains selectedresults from the dynamic analysis of the building.5CHAPTER 2BACKGROUND ON SIGNAL ANALYSISThis chapter presents an overview of ambient vibration theory (2. 1) as well as a discussion ofthe signal processing functions which were used in this study (2.2).2.1 AMBIENT VIBRATION TESTING2.1.1 AMBIENT VIBRATIONSA popular method for determining modal frequencies and shapes of a structure is by analyzing itsambient vibrations. This method is favoured over forced-vibration testing for several reasons.First, it is very economical. Second, several of the vibrational modes are excited and can bedetected from a single measurement using signal processing methods. Third, there is thepossibility that forced-vibrations could damage the structure. The disadvantage of using ambientvibrations to determine modal characteristics is that improper data collection and analysis canlead to erroneous conclusions. Also, damping ratios cannot be determined reliably.Ambient vibrations can be characterized as a random process combined with a deterministicsignal. The former can be attributed to the response of the structure during its normal modes ofvibration, while the latter can be attributed to the randomness of the environmental excitation aswell as noise present in the signal (Diehl, 1991; Luz, 1992). The basis of using these vibrationsto determine dynamic characteristics of a structural system is presented below.2.1.2 PREREQUISITES FOR AMBIENT VIBRATION ANALYSISThe method used to analyze ambient vibration time histories has several prerequisites. For thismethod of analysis, the structural system under consideration must have the following attributes:(1) The process being measured is stationary(2) The system behaves linearly(3) Vibration modes of interest are significantly excited(4) Vibration modes are well separated and lightly damped(5) Structure is classically damped6Stationary simply means that the process being studied (in this case the ambient vibrations of thestructure) is independent of time. Thus, measurements of the process can be made at any point intime, and the results obtained from analyzing these measurements will be the same. In additionto being stationary, the structure must behave as a linear system. In other words, the response ofthe system to a series of forces is equivalent to the superposition of the response of the system toeach individual force.The remaining three prerequisites ensure that meaningful information can be derived from thespectral analysis functions. First, in order to detect a modal frequency and its correspondingmode shape from the ambient vibrations, its contribution must be present in the measured timehistories. Second, ambient vibration theory presumes that the response at a natural frequency isdominated by the corresponding mode shape. Furthermore, frequencies and mode shapes canonly be isolated provided there is sufficient separation between them in the frequency domain.Lightly damped systems tend to have very narrow spikes in their spectra thus facilitating thisrequirement. Finally, classically damped implies that the resulting mode shape values are real,and therefore the signals from two degrees of freedom are either perfectly in-phase or perfectlyout-of-phase at a natural frequency. This avoids the problem of interpreting complex valuedmode shapes.In general, the prerequisites described above were met while analyzing the ambient vibrationmeasurements taken at City Tower.2.1.3 FORMULATIONSThe basis of ambient vibration theory begins with the solution of the multi-degree of freedomequation of motion. The displacement response for an n degree of freedom system, in terms ofits modal components, is given by Equation 2.1.{x(t)} ={41}a(t)+fØ2}a, (t)+. . .+f}a(t) (2.1)This particular equation is based on the assumption that the displacement response of the7structure in the time domain, x(t), can be expressed as a summation of correspondmg productsbetween the system’s time invariant, vibration mode shape, , and a time varying amplitudefunction, a(t). This is a fundamental basis of several dynamic formulations which can be foundin several text books (see for example Clough and Penzien, 1975, or Humar, 1990).Transforming Equation 2.1 into the frequency domain gives:{X(o)} ={1}H, (co)P1(co)+.. .+f,, }H (w)P(w) (2.2)Note that the modal amplitude is now expressed as the product of the frequency responsefunction, H(w), and the Fourier transform of the excitation, P(w). The correspondingacceleration response is given by Equation 2.3.=w2{{1}H(w)Pj(o)+. . .+{Ø}H (w)P (o)](2 3)Now consider the acceleration response at the ith degree-of-freedom of the structure which isgiven by the following equation:o) =2[1H(o)Pw +.. +1H(co)P(o)] (2.4)Using the basis that modal frequencies are well separated and modal damping is small, then itfollows that the response of the system at a natural frequency is dominated by the correspondingmode of vibration. Therefore, the acceleration response at the jth natural frequency, O)j, can becan be approximated as:X(co) (2.5)Finally, if two acceleration records are obtained simultaneously at locations a and b, then modalratios can be estimated using:Xa (cod) COJ2 PjaB’ (a )P3 (w,) —Xb(o) —— Jb (2.6)In order to assemble vibration mode shapes, all that is necessary is to obtain a series of vibration8measurements at different locations of the structure, and calculate modal ratios with respect to acommon measurement. This is analogous to the method used to calculate mode shapes in anEigenvalue analysis (Clough and Penzien, 1975).2.1.4 IMPLEMENTATIONIn order to assemble the mode shape using the method described in the previous section, it isnecessary to have two sets of sensors: reference sensors and roving sensors. The referencesensors are located at a point in the structure which contains information about the vibrationmode shapes of interest; and they remain in this location during the entire test. The rovingsensors are systematically placed at other locations in the structure where a component of thevibration mode shape is desired. After each measurement, the roving sensors are relocated todifferent locations. This continues until all of the measurements have been taken.Since the modal ratios are calculated as the ratio between the reference sensor and the rovingsensor, it is essential that the reference sensor is not located at a node in the vibration modeshapes of interest. This is unavoidable in some situations, and therefore it is necessary to useseveral reference sensors located at different locations and orientations in order to obtaininformation about different mode shapes. In this way some of the mode shapes can be detectedwith respect to (w.r.t.) one of the reference sensors, while the other mode shapes can be detectedw.r.t. another reference sensor. For the City Tower tests, 4 reference sensors (2 pairs oriented inthe north and east directions) were located on the top floor of the building while 4 roving sensorswere systematically located on the floor below. These locations are discussed further in Chapters4 and 5 as well as Appendix A.92.2 SIGNAL PROCESSING FUNCTIONS USED IN THIS STUDYAll of the ambient vibration data collected in this study was analyzed using signal processingfunctions. This involved transforming the acceleration time histories into the frequency domain,and then generating certain functions to locate frequencies (periods) and mode shapes. Some ofthe more useful functions used to relate one signal to another signal include the cross-spectraldensity function, power-spectral density function, coherence function, and transfer function.These functions and their significance are discussed in the sections below.It should be noted that the ambient vibration acceleration time histories collected during thisstudy are actually expressed as voltage, not acceleration. However, no conversion is necessarysince most of the signal processing functions involve a ratio thereby producing a dimensionlessquantity, and also since the sensitivities of each of the sensors used for the vibrationmeasurements are practically the same. For those functions which do not involve adimensionless quantity, the magnitude is incorrect. However, only the overall shapes of thesefunctions, not the magnitude, was of interest in this study.2.2.1 SPECTRAL DENSITY FUNCTIONSThe functions described below are based on statistical principles of a random process. Inaddition, these functions assume single-input-single-output (SISO) behaviour of the systemunder consideration. Thus one signal is assumed to be the input (in this case the signal from thereference sensor) while the other signal is assumed to be the output (in this case the signal fromthe roving sensor).This section only provides highlights of the spectral density functions that were used in thisstudy. A more detailed discussion of random vibrations is made by Newland (1975). A moredetailed discussion of signal processing and spectral analysis is made by Bendat and Piersol(1992).102.2.1.1 Cross-Spectral Density FunctionThe cross-spectral density function, G(f), is a measure of the amount of energy in two signals.One definition of this function is given by Equation 2.7.G(f)=X(f)X(f) (2.7)Note that this function is the product of the complex conjugate of the Fourier transform of the thsignal, X (f), and the Fourier transform of the jth signal, X1 (f). While this function was notused directly in the analysis of the ambient vibration measurements, it is the basis of severalother functions which were used. These functions are discussed below.2.2.1.2 Power Spectral Density FunctionThe power spectral density (PSD) or autospectral density function, G11(f), is a special case of thecross-spectral density function (Equation 2.7) where i=j The PSD is given by Equation 2.8.G(f) = X(f)X (f) (2.8)The PSD is a measure of the frequency distribution of the mean square value of the data. Thisfunction was used to detect possible locations of natural frequencies of the system beingmeasured. These locations colTespond to peaks or spikes in the PSD function.2.2.1.3 Coherence FunctionThe coherence function, 2’ (f), is a measure of correlation between two signals at a givenfrequency, Equation 2.9. It is also an indication of the amount of noise present in two signals.Coherence values (at a particular frequency) of unity or close to it indicate good correlationbetween the two signals, while values of zero or close to it indicate either poor correlation or thatexcessive noise is present in the signal.G.. (f)2(2.9)U 11(f)G(f)11Note that the coherence function combines the information obtained from both the cross-spectraldensity function and the power spectral density function. This function is used whendetermining the authenticity of mode shapes at a particular frequency.2.2.1.4 Transfer FunctionAnalogous to the modal ratio function (Equation 2.6) is the transferJunction,T1/f). Thisfunction is given by the signal ratio of a roving sensor and a reference sensor, Equation 2.10.T..(f)== j*(f)(f)=(2.10)X(f) X(f)X(f) G(f)Note that the transfer function can be expressed as the ratio between the cross-spectral densityfunction and the power spectral density function of the reference sensor’s signal. This functioncan also be expressed in terms of its modulus, /f), and its phase angle, E4(f), which is oftenreferred to as a phase function. These expressions are given by Equation 2.11.(2.lla)(f)= i1na[Tu(f)fl(2.llb)real[T1(f)] ,jThe modulus, Equation 2.11 a, is used to determine where high and low relative response occursbetween the two signals. The phase angle, Equation 2.1 ib, is used to determine whether the twosignals are in-phase (0° apart) or out-of-phase (180° apart). These two components of thetransfer function are the basis of the potential modal ratio functions (discussed in §2.2.1.6) whichare used to assemble and determine the location and shape of vibration modes.2.2.1.5 Averaged Normalized Power Spectral Density FunctionThe process of reviewing PSD functions in order to determine natural frequencies becomes verytime consuming when several records are involved. In order to accelerate this review, a utilityfunction was developed by Felber (1993) which would take a set of related PSD functions,12normalize them, and then average them. This weighs all of the PSD functions evenly so that theentire frequency distribution of the structure, in the frequency range of interest, can be seen in asingle plot. This function, which is called an averaged normalizedpower spectral density(ANPSD)fitnction, is given by:ANPSD(fk) = k=n (2.12)1 m=1 Gjj(fk)Iwhere / is the number of PSD functions, and n is the number of points in the PSD array.2.2.1.6 Potential Modal Ratio FunctionTraditional methods of analyzing ambient vibration records involve checking PSD functionsalong with phase functions and coherence for individual pairs of signals. This is a very timeconsuming task, especially if there are several records involved. To greatly accelerate thisprocedure, a utility function was developed by Felber (1993) which would incorporate themagnitude and phase information obtained from the transfer function, with the correlationinformation obtained from the coherence function. This function, called the potential modalratio (PMR) fiLnction,M1(f), is given by Equation 2.13.M (f) = TIJ (f). PW (f)• CW (f)where1 O°O(f)OPW(f)= —1l8O°—OO(f)l° (2.13)0 otherwiseIi ‘v2<..(f)<1CW..(f)= ‘C Thij —otherwiseThis function is simply the modulus of the transfer function multiplied by a phase window and acoherence window. Phase and coherence is checked by specifying cutoff values, If the signal ata given frequency is within a certain phase, O, and is above a specified value of coherence, y,its value is passed through. Otherwise its value is automatically set to zero.13These functions are later used to assemble mode shapes. Thus a mode shape can beauthenticated simply by inspecting it. The coherence and phase need not be checked separatelysince they have been incorporated into this mode shape.2.2.2 MODAL ASSURANCE CRITERIUM (MAC)Comparisons are often made between the shape of two vibration modes. One method to correlatethese two shapes is a modal assurance criterium or MAC (Ewins, 1984), Equation 2.14.[{a}T{4)x}12MAC(a,x) = (2.14){{øa}T{øa}][{øx}T{x}]Note that this function is similar to the coherence function. As with the coherence function,values near unity indicate good correlation while values near zero indicate poor correlation. Amatrix of MAC values can be assembled to compare two sets of mode shapes obtainedexperimentally and/or analytically.2.2.3 SIGNAL PROCESSING SOFTWAREAll of the ambient vibration data which was collected in this study was processed using threesoftware packaged called ULTRA, VISUAL, and P2. ULTRA was developed at the Universityof British Columbia specifically for processing ambient vibration records (Felber, 1993). Thisprogram calculates all of the functions described above and can be used to process severalrecords quickly and efficiently. A companion program, called VISUAL, was developedsimultaneously with ULTRA (Felber 1993). VISUAL is used to animate and visualize potentialmode shapes based on PMR functions created by ULTRA. Finally, the program P2 (EDT Ltd.,1993) was used to generate ANPSD functions.2.2.4 PROBLEMS ASSOCIATED WITH DIGITAL DATASome problems arise when continuous (analog) signals are represented by discrete points (digitaldata). Three common problems include data resolution, aliasing, and leakage.142.2.4.1 ResolutionResolution refers to the intervals between discrete points. In the case of a digitized time history,the resolution, At, is given by the inverse of the sampling rate. In the case of a time historywhich has been transformed into the frequency domain, the resolution, Af, is given by theinverse of the time history’s duration, T. The time resolution determines the threshold offrequencies which can be determined from the time history. The frequency resolution affects theprecision of the frequency values.To illustrate the effect of signal resolution, consider the plots shown in Figure 2.1. This figureshows three sine waves with frequencies of 6, 12, and 18 Hz which have been digitized using asampling rate of 40 Hz. As shown, as the frequency of the sine wave increases, the quality of thedigitized signal degrades since there are less discrete points representing the time signal.In general, reliable values of frequency (and corresponding vibration mode shapes) can bedetected up to one quarter of the sampling frequency. Frequencies above this value are moredifficult to detect and the quality of the corresponding mode shapes degrades with increasingfrequency. Examples of this can be seen in the mode shapes presented in Chapter 5.2.2.4.2 AliasingAs discussed in the previous section, as the frequency component of the waveform increases, thedigital representation of the waveform degrades. This degradation continues to the point wherethe representation becomes misleading. This point corresponds to the highest frequency that canbe resolved from a discrete time history; which is equal to one half of the sampling frequency.This frequency is often referred to as the Nyquist or cutoff frequency, and can be expressed as:f =..L (2.15)2Atwhere At is the sampling interval, and f is the Nyquist frequency.15‘If =6HzI-;\s4c4//N\j7øø\\///x%i\——— digitized time signal - continuous time signal-1.5.o o.i 0.2 0.3 0.4 0.5Time (sec)1.5If12Hz I0— digitized time signal continuous time signal-1.5-0 0.1 0.2 0.3 0.4 0.5Time (sec)I= 18Hz—0—---— digitized time signal continuous time signal-1.5- I I I I0 0.1 0,2 0.3 0.4 0.5Time (sec)Figure 2.1. Digitized sine waves sampled at 40 Hz.If the signal being measured contains a frequency component greater than the Nyquist frequencythen, in the process of digitizing this signal, a false low-frequency waveform, called an alias, willbe produced which differs from the true analog signal. The frequency of the alias can be16determined using Equation 2.16.fa = 2mf — f; f > f, m = 1,2,... such that fa <f (2.16)where fa is the alias frequency and f is the true frequency.For example, if a sampling frequency of 40 Hz (f = 20 Hz) is used, and there is a frequencycomponent of 22 Hz in the time signal, then the latter frequency will appear as an alias with afrequency of 18 Hz. Note that frequency components of 62 Hz and 102 Hz will also appear as analias with a frequency of 18 Hz. An illustration of the aliasing effect is shown in Figure 2.2.This figure shows a sine wave with a frequency of 22 Hz along with its digitized representation(sampled at 40 Hz) and the resulting alias waveform.21-2Time (sec)Figure 2.2. Sine wave with a frequency of 22 Hz and its digital representation (sampled at 40Hz) and the resulting alias waveform.To eliminate aliasing during the data acquisition process, low pass filters were used to screen outhigher frequencies. In this study, data was acquired using a sampling rate of 40 Hz (f0 = 20 Hz)with a low pass filter of 12.5 Hz with the exception of some special measurements.2.2.4.3 Leakage And Time WindowsThe discrete Fourier transform (DFT), which is used to generate the signal processing functionsdescribed above, is only valid for periodic signals. In order to use the DFT, the time signals are17treated as periodic signals, with a period equal to its duration, T. However, the time signals arenot periodic in general. Consequently, abrupt transitions (see Figure 2.3) between the end of thetime signal and the beginning of the time signal can cause a leakage effect. This effect producesextraneous frequency components in the signal processing functions. These extraneouscomponents may be incorrectly interpreted as belonging to the system being studied.One method to suppress leakage is to multiply the discrete time signal by a time window whichtapers the signal to allow a more gradual entrance and exit. This product is performed before thesignal is transformed into the frequency domain.Several time windows are available. However, one window which often produces very goodresults for analyzing ambient vibration data is the Hanning window (Daily, Riley, andMcConnell, 1993). An expression for the Hanning window is given by Equation 2.17.I!(i_cos- OtTwh(t)=l2 T)0 otherwise (2.17)An illustration of applying this window is shown in Figure 2.3. Figure 2.3b shows adiscontinuous waveform which will cause leakage when it is transformed into the frequencydomain. Figure 2.3c shows the same waveform after it has been multiplied by a Hanningwindow. Note that the Hanning window has transformed this waveform into a continuous signal.The Hanmng window was used exclusively when processing the ambient vibration records.2.3 CLOSING REMARKSThis chapter presented an overview of ambient vibration theory as well as signal processingfunctions which were used to analyze the ambient vibration records in this study. In addition,problems associated with digital data were addressed. Chapter 5 describes the method wherebydynamic characteristics of the building were determined using all of the functions just described.The next two chapters describe the building which was tested as well as the ambient vibrationsurveys.181Figure 2.3. Plot of two sine waves. Plot (a) shows a sine wave which fits perfectly within theanalysis window of period T. Plot (b) shows a sine wave which has a slope andmagnitude discontinuity at its ends while plot (c) shows the same waveform afterbeing multiplied by a Hanning window.ci)j(a)U--12I”—10 1Period, T1-(b)n0 1 2Period, T1-(c)o-10 1 2Period, T19CHAPTER 3DESCRIPTION OF BUILDINGThis chapter describes the high-rise building which was studied. The first section (3. 1) containsa general description, while the second section (3.2) contains a more detailed description of thestructural system. The third section (3.3) presents photographs of the building during the timethat the ambient vibration measurements were made.3.1 GENERAL DESCRIPTION OF CITY TOWER3.1.1 OVERVIEWThe building under consideration is a thirty storey, high-rise residential tower located indowntown Vancouver (Figure 3.1). This building is representative of the type constructed in thisregion. On the east side of the tower is a two storey townhouse linked to the tower by twopedestrian bridges. On the north side of the tower is a terrace extending from the second floor.This terrace is monolithically linked to the tower via the floor slab. An underground parkinggarage, consisting of 6 staggered levels, is located beneath the tower and the townhouses. Thebuilding contains 136 residential units (including those in the townhouse), a weight room andparty room opening onto the ten-ace, and also commercial space on the ground floor.The building is 85 m (279 ft.) in height from ground level. The parking levels are locatedbeneath ground level with a depth of 9.4 m (31 ft.). The first storey is 4 m (13 ft.) in heightwhile the other storeys are 2.6 m (8.7 ft.) high. The residential floors on levels 3 through 10 areapproximately 600 m2 (6,000 ft2) in area, reducing to about 500 m2 (5,000 ft2) on levels 11through 25. The remaining upper level areas are reduced further. The parking levels are about1100 m2 (12,000 ft2) each.The building was designed by the architectural firm Baker McGarva Hart Inc. with structuralconsultants Bogdonov Pao Associates; both of Vancouver B.C. Construction of the tower began20in autumn 1992 and was completed in January 1994.Figure 3.1. South-East Elevation of City Crest Tower.3.1.2 STOREY REFERENCING CONVENTIONSome clarification is required regarding references (in this thesis) to the storeys and levels in thisbuilding. There are actually 31 storeys in this building including the mechanical penthouse.This corresponds to 32 levels from the ground floor to the roof. Ambient vibration tests at thebuilding are referenced with respect to the number of levels which were completed at thebuilding at the time the test was performed. For instance, CTJS refers to the test which was21performed when 14 storeys or 15 levels of the building were completed.3.2 STRUCTURAL SYSTEMThis building is a reinforced concrete structure consisting of inegular shaped flat plate slabs, acentrally located rectangular core, and several columns along the perimeter of each floor. Thecolumns and core, in general, are continuous throughout the height of the tower. A typical floorplan of the building is shown in Figure 3.2.Ao 5 10 15mI •i• •Ii0 10 20 30 40 50ft.The core houses the corridor leading to the residential units, the elevator shaft and stair wells, aswell as mechanical and electrical conduits. It is the primary lateral force resisting element of thisstructure. The core measures 10.3 m by 7.6 m (34 ft. by 25 ft.) in plan while the wall thicknessvaries from 450 mm (18”) at the bottom gradually reducing to 350 mm (14”) at the top floors.The core headers were designed as coupling beams with diagonal reinforcing for energyabsorption (a typical detail is shown in Figure 3.3). The base of the core is designed to yield firstforming a plastic hinge in this region.Figure 3.2. Typical floor plan of City Tower.220LFigure 3.3. Typical detail of diagonal reinforcing in the core headers.The floor slabs are 190 mm (7.5”) thick, and about 28.3m by 24.7m (93 ft. by 81 ft.) in length.There is a major setback at the South-East (SE) corner of Level 10, as well as several minorsetbacks at the top of the building above Level 25. These set backs can be seen in figure 3.1.There are twelve columns along the perimeter of Levels 3 to 9. These consists of five 1.8 m by0.3 m (6 ft. by 1 ft.) columns and seven 0.6m (2 ft.) square columns. The number of columnsreduces to ten at Level 10 due to the setback. Above Level 10, the SE corner of the slab issupported by a wall projecting from the core. The primary function of the columns (and the wallat the SE corner) is to carry gravity loads. Specified concrete strengths for all of the buildingcomponents are summarized in Table 3.1.3-4”23Table 3.1. Specified Concrete Strengths.(Bogdonov Pao Associates Ltd., 1992, Drawing S-i)The foundation of this building is bearing on reasonably stiff glacial till (specified bearingcapacity: 480 MPa). The footings consist of several pad footings for the core and columns, and astrip footing for the parking level retaining walls. The footing for the core is 3.1 m (7 ft.) thickwith dimensions 16.2 m (53 ft.) by 12.8 m (42 ft.). The dimensions of the column footings varybetween 2.4 m (8 ft.) square to 4.3 m square (14 ft.). The strip footing is 0.6m (2 ft.) in breadth.A schematic of the footings is shown in Figure 3.4.The structure was designed in accordance with Vancouver Building By-Law 6134, CAN/CSAS413-87 for parking structures, and the Canadian reinforced concrete design standard CSACAN3-A23.3-M84. Specified gravity loads are summarized in Table 3.2. A dynamic analysiswas also performed by the structural designers to estimate the fundamental periods of thestructure as well as to understand the torsional behaviour resulting from the stepped floors.Table 3.2. Specified Design Loads.(Bogdonov Pao Associates Ltd., 1992, Drawing 5-1)Specified Design Loads Live Load Dead LoadkPa (psf) kPa (psf)roof snow load based on ground snow load of 1.6 (34) variesplus rain load of 0.3 (6.3) -A. parking slabs 2.4 (50) -B. firetruck access 12 (250) variesC. assembly areas and ground floor 4.8 (100) variesD. residential areas 1.9 (40) 1.0 (20)Description Strength• footings and walls (excluding core) 25 MPa• tower core Levels P6 - 5 25 MPaLevels 6 - 32 30 MPa• suspended slab & beams, retaining walls 30 MPa• columns Levels P6 - 4 25 MPaLevels 5 - 9 30 MPaLevels 10 - 19 35 MPaLevels 20 - 32 40 MPa• surfaces subject to de-icing slats 35 MPa• all other concrete 20 MPa• reinforcing steel grade 40024(suqpnopqiiiu&oqsaniouiuuosuiioo)SJJ1Muiuwiipui‘suurnjoo‘aioouIpJInquii.joddnssuioojjoo1nuqojI______________________________________________________________________________________________________________________________________________________LI101__IIIL_1II—IIIIrIiiElIIIIIIiiiI___L_1IIIIL_JdflffiIjji .1________________________________________________L1ll_____-_j_________________________________o———.LI0IirIiiIIIIIIiiII1,1iiL___II__jIdL1I——-I;iIIDu_jIII --I L.......L.-I3.3 THE TOWER DURING CONSTRUCTIONThis section presents several photographs of the tower during construction. The first six figures(3.5 through 3.10) show an elevation view of the building at the six points in time when theambient vibration measurements were taken 1• Note that as the building’s structure is assembled,architectural components are already being installed on the lower storeys. The remainingphotographs show details of the building during construction. Figure 3.11 shows the shoringused to support the upper concrete floor slab as it was being poured and as it cured. Thisassemblage caused both floors to move as a rigid body in the experimental mode shapes. Figure3.12 shows a portion of the platform projecting from the side of the building. This platform wasused when lifting the cables used during the ambient vibration measurements. Also shown inthis photograph is the lift located at the North-West (NW) corner of the building. In addition, thecrane shaft, which typically pierced about 10 floors before reaching the top of the building, isshown on the right side of this photo. Figures 3.13 and 3.14 show a typical floor before and afterthe stud walls and additional components were installed.3.4 CLOSING REMARKSThis chapter introduced the building which was the focus of this study. In the next chapter, theambient vibration tests which were performed at this building are described.1The photograph of the building when the structure was completed is an exception. The latter was taken about 6weeks after the structure was finished, or about 4 weeks after the corresponding ambient vibration test.26Figure3.5.CityTowerfollowingthecompletionofLevel10.Figure3.6.CityTowerfollowingthecompletionofLevel15.L’J00Figure3.7.CityTowerfollowingthecompletionofLevel20.Figure3.8.CityTowerfollowingthecompletionofLevel25.L’JFigure3.9.CityTowerfollowingcompletionofthestructure.Figure3.10.CityTowerwithallofthearchitecturalcomponentsinstalled.Figure 3.12. Platform used when pulling up cables to the top floor (left) and the crane towerwhich passes through the concrete floors (background right).Figure 3.11. Detail of shoring which supports the level above it as the concrete is curing.30Figure 3.14. Typical floor with galvanized steel stud walls prior to the installation of drywall.Figure 3.13. Typical floor before the installation of architectural components.31CHAPTER 4AMBIENT VIBRATION TESTSThis chapter presents an overview of the ambient vibration tests. The first section (4. 1) dealswith the data acquisition system which was used, and modifications which were made to itthroughout this study. The next section (4.2) lists the general testing objectives and the sensorlocations. The following section (4.3) contains a critique of each of the 6 tests which wereperformed at the building. The final section (4.4) presents an error assessment of the collecteddata.4.1 AMBIENT VIBRATION EQUIPMENT USED FOR THIS STUDY4.1.1 THE HYBRID BRIDGE EVALUATION SYSTEMDuring the course of his graduate studies towards a doctorate degree in Civil Engineering, Felberassembled and developed a data acquisition and analysis system that could be used for vibrationmeasurements and system identification of bridge structures. This system was named the HybridBridge Evaluation System (HBES). The aim of his research was to develop a system whichcould do this evaluation quickly and inexpensively.The need for such a system arose from current economic trends. At present, existing bridges arebeing maintained and/or retrofitted for increased traffic demands as well as for strengtheningthem to withstand seismic loads. A retrofit process begins with an evaluation of the existingstructure. Evaluations are usually based on an analytical model which is used to predict thebehaviour and possible damage arising from a seismic event (or any other loading which needs tobe considered). These models, in turn, are based on geometric properties obtained from olddrawings as well as material properties obtained from core specimens at key locations in thestructure. In addition, several assumptions need to be made about the soil on which the bridgesupports rest as well as any interaction or composite action which occurs between separate spansor components of the bridge. Since this results in a certain amount of uncertainty, there is a need32to verify that these models are accurate. This would lead to increased confidence in the resultsderived from these analyses.Modal properties of a bridge can be determined by measuring its vibrations when it is subjectedto some form of excitement. One method of exciting the bridge is to use a forced input such as asinusoidal force created by an eccentric mass shaker. This method has the advantage of excitinga single mode of the structure at a given frequency. In addition, good estimates of damping canbe obtained from measuring the resulting vibrations. The disadvantages of this method is that itis expensive, and it is usually not convenient to shut down a bridge for an extended period toperform this type of test. An alternative to forced vibration measurements is to simply measureambient vibrations. This has several advantages. First, these types of vibrations were providedby the traffic using the bridge as well as other sources. Second, the bridge did not need to beshut down to perform these tests. Finally, the measurements could be conducted at any time.One problem with vibration measurements is the amount of time required to process the data.This activity could take anywhere from several weeks to several months to complete. Therefore,Felber also developed a software package, called ULTRA, which could be used for manual orautomatic reduction of the ambient vibration records. In this way, data could be analyzedimmediately in the field to check the quality of the data and also to obtain some preliminaryresults. In addition to this, measurements could be repeated or sensor arrangements modified ifthe measured data did not meet the test objectives. So instead of taking several months toprocess the data, the data was already processed and preliminary results obtained, the same daythat the test was performed. Additional and more detailed analyses could be carried out later.For a more detailed discussion of the development of this system, see Felber (1993).4.1.2 ADAPTING THE HBES FOR BUILDING AMBIENT VIBRATION TESTSThe HBES had been used successfully to test the Colquitz River bridge near Victoria, B.C. aswell as a wharf located in Squamish, B.C. Also, an ambient vibration survey of the33Queensborough bridge, located in New Westminster B.C., was already underway at the onset ofthe City Tower study.Because of the success using this system, it was decided to use it to perform an ambient vibrationsurvey of City Tower. Practically no modification to the HBES was necessary. However, as thetests progressed, several hardware and software components were added to the system toaccommodate both the tests and subsequent analysis of the building’s ambient vibrations.With the addition of several new cables with lengths of 150 m (500’) and 300 m (1000’), cablespools had to be constructed and wired so that they could be located away from the dataacquisition equipment and connected to the system using a patch cable. It was also necessary tobuild stands to support these spools as the cable was being wound and unwound.Several computer programs were also developed throughout this study. The first program wasdeveloped to plot the ambient vibration time histories so that they could be inspected prior toperforming detailed analyses. This program, called HPPLOT, is discussed in §4.1.4 and inAppendix C. Revisions were also made to the data acquisition program, AVTEST, and anenhanced version of it, called AVDA, was developed. Details of these revisions appear in §4.1.3and in Appendix B. Two other programs were developed for data analysis. One of theseprograms, named SLAVE, was used to enhance the three dimensional appearance of the modeshapes. The other program, called MAC, was used to perform a modal correlation analysisbetween analytical mode shapes and experimental mode shapes. The latter two programs arediscussed in Chapter 5 and in Appendices D and E, respectively. All of these programs areintended to complement the existing software. To illustrate, a software hierarchy is shown inFigure 4.1. This figure shows which files serve as input files to the respective programs andwhich files serve as output files. The file types are designated by their extension while arrowsdenote input/output behaviour.344.1.3 MODIFICATIONS TO DATA ACQUISITION PROGRAMLEGENDThroughout this study, revisions were made to improve the data acquisition program namedAVDA (formerly AVTEST). These modifications helped improve the quality of the recordeddata and also increased the automation of the system. Details of these revisions, and operatinginstructions, can be found in Appendix B.4.1.4 CHECKING TIME HISTORY RECORDSDue to electrical anomalies, noise, and forces unknown, the ambient vibration time historiesacquired with this system are occasionally susceptible to drift and contamination. In order tocheck for electronic drift, spikes, or shorts occurring in one or several channels, a program wasdeveloped which would plot the time histories of each channel, for each data segment, on thecomputer programdeveloped by the authorcomputer programdeveloped by othersI i input/output fileFigure 4.1. Software hierarchy for data acquisition and analysis.35same page. This allowed a comparison between all of the signals that had been recordedsimultaneously. Two examples of signal drift and also signal contamination are shown inFigures 4.2 and 4.3, respectively. As can be seen in Figure 4.2, channels 5 and 7 show anexcessive level of electronic drift while the other channels show normal vibrations of thestructure. Also, channel 6 shows a slight offset from zero which could indicate that the sensorwas not balanced correctly or that this instrument was tilted during the measurement. Figure 4.3shows an example of signal contamination. Channels 3, 4, and 8 show an unidentified anomalyin the signals while the other channels show normal response. By inspecting the time histories inthis manner, the user can decide which records need to be corrected, and which records areunreliable.While this program was originally developed to check the quality data, it can also be used toinspect the vibration behaviour of the structure being tested. Figure 4.4 shows a set of recordsfrom one setup at City Tower. Channels 1 through 4 were located on the same floor; channels 1and 2 are oriented in the North-South (NS) direction while channels 3 and 4 are oriented in theEast-West (EW) direction. Since identical vibrations can be seen in these 4 channels, it followsthat the building is vibrating in a torsional mode. In this case, these vibrations correspond to thefundamental torsional mode (f=l .504 Hz, T=0.665 s). Another example is shown in Figure 4.5where translational motion was evident. In this figure, the sensor arrangement for the first fourchannels is identical to the arrangement described above. At 45-55 seconds into themeasurement, the NS fundamental mode (f=l.543 Hz, T=0.648 s) was dominant in the records.This is indicated by the high amplitude, sinusoidal vibrations in channels 1 and 2 and lowamplitude vibrations in channels 3 and 4. At 80-100 seconds into the measurement, the EWfundamental mode (f=l.875 Hz, T=0.533 s) becomes dominant. Vibration associated with thismode was detected in the same manner as the NS fundamental mode except that the highamplitude vibrations occur in channels 3 and 4 while low amplitude vibration occurs in channels1 and 2. This type of behaviour confirms that fundamental modes usually dominate the responseof a building structure. Operating instructions for this program can be found in Appendix C.36Filename:Ir’rr’ikI-rAI...+iii.-IAmphtudeAttenuat)on:0dBINyquietFrequency:20HzISement#,nnni.j-iOui.ower.v,OtIOflP%muIenLviuraLlonsIFllter:12.5HzIMar28.1993of—CL.J’.J7(peakvalueofeachsegmentshowninparentheses)IKejthlayGaIn:5I10:57:16—+14<Reference>Levl19-cou’mnbaseatNWcornerNORTHPositive+0.39)c1(-0.31)-1.4,+1.4<Reference>Level19-columnbasestNEcorner;NORTHPoshive+0.43)2(0.5 +1.4<Reference>Lvel19-olumnbaseatNWcorner;EASTPos)tive+0.40)30.0..,.................•.+1.4<Refernce>Lval19olumnbaseatSWcorner;WESTPositive+0.46)4+14rr.Lv’elO9-+0:2)...CI)(-0.69)-1.4,+1.4Lo.iel09-cblumnbakeatNEorner;NORTHPositive+0.26).60.0____________________________________(-0.55):.Level09columnbaseatNWcornerEASTPosihve+1.4’’Lvel09-boiumnbseatSWcorner;EASTPositive+0.321‘-80.0________(-0.44) 05101520253035404550556065707580859095100(voltsltimelsocl(-0.67)-0.8.+0.8+0.34)(-0.28)-0.8,+0.21)IAmplitud.Att.nun:0dNyquistFr.qu.noy20HzIS.gm.ntlFilenemrICT32-CoreMotionAmbientVibrationsct32c3I(peekvalueofeachsegmentshownInparentheses)KithlevGdn:510:56:327ot8(-0.34)-0.8+0.8+0.32)<Ref.r.no.>Le,el29-flooreimiddleocore,weltside;EASTPosdvTj..vel1-‘floàratofwetside;NORTHPtlv0,01 2 3 4 5 6 7 8•‘Level21’-flooreimiddleofcore,wstside;EASTPoshive00---——(-0.17)-0.8,,..—.‘....,....,....,....,....,...,....,....,....,-.-.,.-..,....‘+0.8’’.Reterenc’e>Level’29-fiooatmiddIofcore,’westsid;UPPoshive...............-......+0.8‘‘‘,‘1ev.!14-flooramiddleocore,wstilde;EASTPos’itlve+0.36)(-0.41)-0.8+0.8‘Level01-flooreimiddleocore,westside;EASTPoshive+0.32)0.0(-0.35)-0.8,+0,8’Lovel’21-flooatmiddlofcore,’westsid;UPPoshive+0.27)0o::it-11Liii1TrrlflI-(-0.21) 0•S-(volts)It)lb202bJO354045505550time(eec!55707580859095100[Ffenama:CT25-GlobalTowerMotionAmbientVibrationsAmplitudeAttenuation:6dBNyquistFrequency:20Hzsegianti—CV(peakvalueofeach.epmentshownInparenthase.)(eIthlevGaIn:518:19:54I+2.0+2.00)0.0RIiIII11thIilUIflhIII1AAAAAAII2 3 4<Reference>Level24-co’umnbaseatNWorner;NORTHPostlvoAAAAAU.AAAAA( UAA(-2.00)-2.0_____________+2.0’+1 .90)0.0(-1.84)-2.0,V“J V)”iw‘g’yyVV VVVbIIMlN1iti)ll)I!l1IIil-<Referónce>Loyal24-columnbaéoat8orner;NORTHPositiveAAAiiti.AiliiAAA!!11VV1I11VP‘W+2.0+2.00)JLikiLi[ILIJrjtIJuIi<Reference>Level24.âolumnbaseatNWcorner;EASTPositiveUiiA.k.51..-L1.i.5AIAA,I’-.AkA<Reference>Lvel24-bolumnbaseatSWcorner;EASTPositive1AAA6J1LA.ALAR.iak.A.AhaA,k.a..t(-2.00)’+2.0’+028)5(-0.25)-2.0,+2.0’+0.18)60.0(-0.20)+2.O’40.15)1,vLevel)‘6-NWornarofboreatbaseofwall;UPPositive7 8(-0.12)+0.13)LevelP6-NEcornerofcoreatbaseofwell;UPPositive(-0.11)-2.00IvoltsiLevelP6-SEéornarofcoreatbaseofwell;UPPositive510152025303540455055time(sac)LevelP6-SWöornerofóoreatbaseofwall;UPPositive6065707580859095100Filename:Ct15151+0.4’+0.22)11-0.21)+0.19)(-0.16)-0.4,+0.4+0.21)(-0.23)-0.4.+0.4+0.19)(-0.20)+0.4’[+0.22)(-0.23)-0.4,+0.4’(+0.19)(-0.19)-0.4.+0.4+0.21)(-0.26).04+0.4+0.19)(-0.33) 0IvoitsiCityTower-CT15-Level15IAnwIItudeAttenuBHZFeb21.1993ISeament#(peakvalueofeach.eq9ntshownInp.lentheeee!-G19I12:11:048of8,‘rferenoe(evoIi4):NWorner.NoRTHpos)tIveref,r.noe(IeveI’14):NEoorn.r,NORTHposItiveTn•ri‘‘‘‘‘‘‘‘‘‘‘r.f.renc.(j.vel14):NWcornerEASTpo.It)v.2 4 5 6 8‘refernc.(.vl14):SWcorner.EASTpositive—-;.-;.,:-I..l14(oiitopofcbl):NWorner,NORTHpostive-‘‘14(ntopofNEorne.NORTHpotive‘‘‘level14(‘ontopof’col.):NWcorner.EASTpositive‘‘‘‘14onoj,of’cl):Wcor,orEAST’ptive510152025303540455055tim.IeecJ60657075808590961004.2 OVERALL OBJECTIVES AND TESTING PROCEDURES4.2.1 GENERAL TEST OBJECTIVESThe primary objective of this study was to determine changes in dynamic characteristics of ahigh-rise building as construction progressed; based on ambient vibration measurements of thestructure. The dynamic characteristics of interest were the vibration mode shapes along with thecorresponding modal periods (frequencies). These modal properties are typically required in anytype of dynamic analysis. Modal periods are an indication as to which modes will be excited bythe dominant frequencies of the time-varying load under consideration, while the mode shapesindicate deformations of the structure which create stresses in its members.There were some other objectives in addition to obtaining modal characteristics. The secondobjective was to assess foundation motion at ambient vibration levels. This was done bymeasuring the rocking motion of the base of the core’ and also lateral motion at ground level andat the lowest parking levels (P5 and P6). The effect of architectural components on thebuilding’s vibration characteristics was also of interest. This was determined by making acomparison between the bare structure and the structure with all of the major architecturalcomponents installed. Comparisons were based on changes in periods, mode shapes anddamping. Another objective was to measure vertical core motion in order to assess the nature ofits deformation; i.e., shear or flexure.4.2.2 DECIDING THE SENSOR LOCATIONSWith the exception of some special measurements (which will be discussed in §4.3), only lateralmotion of each floor of the building was of interest. Moreover, only the global behaviour wouldbe studied. Local vibrations of the columns or floors was not of interest.1The core is resting on a 2.1 m (7 ft.) thick pad footing which is independent of the footings supporting theperimeter columns as well as the parking stnicture retaining walls41The location of the sensors were very important for a number of reasons. First, since this entirestudy was comparative in nature, it was decided that the sensors would be placed in the samelocation for each of the six tests. Also, because the sensors would be mounted using anchorbolts, it was desirable to choose a location where the bolts could remain in place until all of thetests were completed2,and in a location which did not interfere too much with the constructionprocess. Of course, the most important consideration was that the sensors should be placed inlocations such that modal information could be extracted from the vibration records. Also, tomaintain quality control, the same sensor layout for the roving sensors (i.e. sensors which wererelocated from setup to setup) was used on each floor to minimize the chance of error whenreconnecting the sensors to the cables after each move.When deciding the sensor locations, two documents were consulted (A.S.C. S2, 1990; Rojahnand Matthiesen, 1977). Both of these documents provide guidelines for placing a limited numberof sensors in a building structure. A review of California Strong Motion InstrumentationProgram (CSMIP) documents which showed the sensor layout of several instrumented high-risebuildings in California, U.S.A. also proved helpful (CSMIP, 1989). With this information, thesensor layout shown in Figure 4.6 was chosen. In this figure, the arrows indicate the positiveorientation of the accelerometer sensors. This sensor arrangement could be used quite effectivelyto isolate translational and torsional motion of each floor in both the North-South (NS) and East-West (EW) directions. Following the first test however, the location of the 4th sensor waschanged to the NW corner in order to improve the appearance of the resulting mode shapes (see§4.3.3 for more information).The location of the reference sensors (i.e. sensors which remain in the same location throughoutthe test) also had to be decided. As discussed in §2.1.4, the reference sensors must be situatedwherever there are antinodes in the vibration modes of interest. The top floor of the building was2several of these bolts had to be replaced from test to test since they were removed by workers whenever itmterfered with their work.42chosen for this purpose where four sensors were positioned using the same layout as the rovingsensors. This provided a redundant measurement in each of the two principal directions.The sensor layouts will be discussed in more detail in §4.3. Specific details can also be found inAppendix A.A4.2.3 TYPICAL TESTING PROCEDUREBefore the measurements could begin, the cable used to connect the sensors to the dataacquisition equipment had to be laid out. Following this, the data acquisition station was set upwhile the reference sensors were installed and connected. While a preliminary measurement wastaken to verify that the equipment was working correctly, the remaining four roving sensors wereinstalled and connected. Following each measurement, the roving sensors were systematicallylocated from floor to floor until the test was completed.A schematic of the data acquisition system is shown in Figure 4.7. A photograph of the dataacquisition equipment is shown in Figure 4.8. Acceleration measurements were obtained using 8Kinemetrics force balanced accelerometers (model FBA- 11). A typical sensor arrangement isshown in Figure 4.9. Several lengths of cable were available to connect the sensors to the signalconditioner. These cables included: 5-90m (300’), 2-150m (500’), and 4-300m (1000’) as wellas several shorter cables which served as patch cables for the longer cables. The signalFigure 4.6 Typical sensor layout for the roving sensors used in the first building test.43conditioner is a Kinemetrics model containing 8 cards (model AM-31) which were used to filterand amplify the signals. Conditioned signals could be monitored on a 2 channel Zonic spectrumanalyzer or digitized and stored on disk via a Keithley 575 analog-to-digital (AiD) converter.Two PC computers were also included in this setup. The data acquisition computer, a Compaqportable with an Intel 80286 processor, was dedicated to acquiring the ambient vibration records.In between measurements, the data files from the previous setup were transferred to the dataanalysis computer using a commercial software package called LapLink. This second computerwas a PC with an Intel 80486DX processor. This arrangement allowed data to be collected onone computer while the second, and faster, computer could be used to process the data in-situ tocheck its quality as well as to perform some preliminary analyses. Once the data had beenchecked, the roving sensors could be relocated to the next floor and the next setup recorded.data analysis computer(PC 80486DX)--b-b-b-,-b-bdata acquisition computer(Compaq portable 286)Figure 4.7. Schematic of the data acquisition equipment.EZZZ:1A1lFDA-liBA-1iconditioneramplificationandfilteringanalog to digitalconverter44Figure 4.9. Two FBA- 11 accelerometers in position during data acquisition.Figure 4.8. Data acquisition equipment (taken during the CT25 test).a._w454.3 SPECIFIC DETAILS OF THE CITY TOWER TESTS4.3.1 OVERVIEWSuccessful ambient vibration surveys require a great deal of planning. The schedule of the CityTower surveys was critical since tests were to be conducted following the completion of every 5storeys. Therefore it was necessary to follow the contractor’s progress very closely. At the onsetof construction, each floor was completed in about 5 working days, but this rate was lateraccelerated to 4 working days. Once the required number of storeys were in place,measurements were taken during the following weekend.The first step in the planning of every test was to visit the City Tower construction site. Twovisits were made - one about 5 days before the test, and a second visit one day before the test.The purpose of the first visit was to inspect the building and the surrounding site in order todetermine where to place the data acquisition equipment (hereafter referred to as the station),where and how the cables would be laid out, and identify any restrictions which would hamperthe test. The purpose of the second visit was to obtain keys from the contractor in order to gainaccess to the site, and to install anchor bolts wherever the sensors would be located. The lattertask helped speed up the test and also helped the crew when positioning the sensors.A crew was necessary for these surveys to help with all of the physical work involved. The sizeof these crews varied from test to test and it was found that a 5 member crew worked best for thebuilding surveys. The crew was typically made up of professors, graduate and undergraduatestudents, and engineers.One of the most time consuming task of these surveys is unwinding and laying out the cables.Therefore, it is very important to plan this task so that it may be done as efficiently as possible.The location of the station is another consideration. Since wailcie-tailcies were used forcommunication, it was necessary to have a clear communication path between the station and thecrew on the upper floors who were in charge of relocating the sensors from setup to setup.46The sensors were usually mounted on aluminum plates which were fastened to the concrete floor(or wall in some situations) using the anchor bolts. A different strategy for fastening these plateswas necessary for the last test (CTTC) since ceramic tiles and carpet had been installed over theconcrete floors. For the tiled surfaces, the plates were fastened using double sided carpet tape.This worked very well though it was sometimes difficult to remove the plate afterwards. Specialplates were assembled for situation where the sensors needed to be positioned on a carpetedsurface. Three 5mm (3/16”) bolts were attached to these plates in order to act as feet. In thisway, the weight of the plate was concentrated at the tips of these bolts which were in contact, asclose as possible, to the building structure3.Measurements typically began at the top of the building. Roving sensors were systematicallyplaced on the levels to be measured as the crew worked its way down the building. This orderwas reversed for the last test, CTTC, since cables had to be lowered from the top of the buildingrather than pulling them up from the ground.The testing procedure changed and was improved from test to test. Highlights and methodologyfrom the individual tests are discussed in the sections which follow.4.3.2 CT1O -10 LEVELS COMPLETED4.3.2.1 Measurement ObjectivesThe objectives of this test were to obtain:• lateral mode shapes and periods• torsional mode shapes and periods• assess effect of discontinuities• assess rocking of foundation3Th1s method of fastening the sensors was tested prior to the test using a collocation measurement in order to ensurethat reliable measurements could be made.474.3.2.2 SetupThe first test of this study took place on Saturday, January 16, 1993. At this point in time, the10th floor had just been cast a few days before. This floor was being supported by the floorbelow it (Level 9) with shoring and jack-posts while the concrete was curing.The station was located on Level 9 for a number of reasons. First, since only 8 cables wereavailable at this point in time (2-15m, 2-30m and 4-90m), the station had to be situated veryclose to the reference sensors so that they could be connected to the signal conditioner using theshort cables. Also, since this floor was heated (for curing the concrete in the winter), it provideda comfortable location for conducting the measurements and data analyses.The reference sensors were mounted on the side of the columns about 500mm (20”) from thesoffit of Level 10. The roving sensors were systematically placed on all floors; beginning withLevel 9. The 90m cables used to connect to the roving sensors was passed through a hole in theconcrete floor to Level 8 where they were unwound. From here, these cables were droppedbetween the stairways since it was open all the way to Level 1.Specific sensor locations and signal conditioning information can be found in Appendix A.4.3.2.3 Test EvaluationBeing the first test, it was perhaps the most difficult for a number of reasons. First, constructionworkers who were on site that day interfered with the test. Curious workers stopped by thestation several times to see what was going on. Some other workers were curious enough todismantle one of the accelerometers. Fortunately, the sensor was not damaged. In addition tothis, a concrete grinder was being operated that day which may have banded the frequency rangeof the excitation. This is undesirable for an ambient study.Another problem was the location of the station. Although the lift was available in the morningto transport all of our equipment to the 9th floor, it was not available at the end of the test.48Therefore all of the equipment had to be carried down 9 flights of stairs. Also, since there weretwo flights of stairs, the generator used to power the data acquisition equipment was accidentallyleft behind on one of the landings. It had to be retrieved the following morning.As far as the test was concerned, it was found that Level 9 and 10 moved together as aconsequence of the shoring which was supporting Level 10. Hence it was not necessary toinstrument the top floor. Instead, positioning the reference sensors at the base of the columns onLevel 9 would have sufficed.In future tests, it was decided that the station would be situated at or near ground level. Also, thelocation of the reference sensors would be mounted on the floor one level below the level whichhad just been cast. Finally, the test would take place on a Sunday when there were no workers atthe site.4.3.3 CT15 -15 LEVELS COMPLETED4.3.3.1 Measurement ObjectivesThe objectives of this test were:• obtain at least three vibration modes and frequencies in the three principal directions.• position the sensors to provide improved mode shapes, and better measurement of base“rocking”.4.3.3.2 SetupThe second test of this study took place on Sunday, February 21, 1993. At this point in time, the15th floor had just been cast 2 days before. This floor was being supported by the floor below it(Level 14) with shoring and jack-posts while the concrete was curing.This test was performed in sequence with two tests at the Queensborough bridge. Hence, thestation was located at ground level in a cube van which housed the station during the bridge tests.The addition of 2-150m (500’) cables and 4-300m (1000’) cables to the equipment made itfeasible to install the reference sensors at the 14th level.49The sensor layout was similar to the previous test with the following changes. First, the FBAlocated at the south-west (SW) corner, which was oriented in the NS direction, was relocated tothe north-west (NW) corner. This was done to improve the definition of the vibration modeshapes. Second, in order to enhance the base-motion analysis, two of the reference sensors wererelocated to the building core for two of the setups. In addition, sensor #6 was moved to insidethe core on Level P6 and oriented vertically to improve the observed motion of the core rocking.Finally, due to time constraints, only every other floor was measured during this test.As with the previous test, cables were passed through the opening between the stairways. Someof the other cable, as an experiment, was pulled up to the 14th floor from the outside of thebuilding. The test proceeded as before. Measurements were made starting at the undergroundparking level, and then progressively on every second floor beginning with Level 15.Specific sensor locations and signal conditioning information can be found in Appendix A.4.3.3.3 Test EvaluationThe biggest criticism of this test was that the cables got severely tangled as they were broughtdown from the 14th floor. In addition to this, the 150 m cables had to be completely unwoundand laid out in the alley neighbouring the building site. In contrast, the cable which had beenpulled up to the upper floors from the outside of the building was collected very easily andefficiently.As far as the test was concerned, Level 14 proved to be a good location for the reference sensors.In addition, Level 14 and Level 15 moved together. It was found that the sensors which wererelocated to the building core for two of the setups did not enhance the base motion analysis.Therefore, this procedure was not used again. The quality of the signals appeared to be betterthan those of the previous test. It is believed that this can be attributed to a better location of thereference sensors, and the absence of construction activity during the measurements.This test introduced several refinements which would be used in the tests which followed. First,50the reference sensors would be positioned on the level just below the floor which had just beenpoured as they were in this test. Further, it was clear that the two floors at the top of the buildingmoved together, and therefore the motion of the highest floor was not measured in subsequenttests. Second, Sunday proved to be a good day to conduct these tests since all construction at thesite had ceased. Third, the cables would be pulled up from the outside of the building (asopposed to the inside) in future tests. In addition, male plugs would be added to the 1 50m cablesso that they did not need to be unwound completely in order to use them4.4.3.4 CT2O -20 LEVELS COMPLETED4.3.4.1 Measurement ObjectivesThe objectives of this test were:• obtain at least three vibration modes and frequencies in the three principal directions.• perform man-excited vibration measurements• high-frequency vertical measurement (for soil-structure interaction analysis)4.3.4.2 SetupThe third test of this study took place on Sunday, March 28, 1993. At this point in time, the 20thfloor and the core walls above this level were in place. Level 20 was still being supported fromthe 19th level with shoring.In this test, the reference sensors were located on Level 19. Roving sensors were positioned onevery other floor beginning with Level 17. The station was located in one of the finished roomsat ground level. Two platforms which projected out from the side of the building, one on thenorth side of the building and one on the south side, facilitated pulling the cable up from theground. The cable spools were positioned at ground level. Thus, as the cable was lowered fromfloor to floor throughout the day, the slack could be wound up. By the time the cable reached theground, it was all wound up and could be placed back onto the truck since it was no longer4This type of connection had already been implemented in two of the four 300 m cables at that time.51needed.Man excited tests of the building were also performed. The building was excited by two crewmembers, located on the top floor, who were rocking back and forth with the same period as thebuilding’s NS fundamental period (1.07 s). A sample of the building’s response is shown inFigure 4.10. In this figure, channels 1 and 2 show the response of the structure due to the manexcitement while channels 3 and 4 show normal ambient vibrations. As can be seen, the crewmembers were able to amplify the motion of the structure 5 times above ambient levels. Alsonote the beating effect caused by a slight difference between the building’s period and the periodof the excitation.The sensor layout was similar to the previous test with the following changes. First, referencesensor #4 was accidentally oriented in the opposite direction. In addition to this, the referencesensors remained in the same location for the entire test (unlike CT1 5 where two of them wererelocated to inside the core).Specific sensor locations and signal conditioning information can be found in Appendix A.4.3.4.3 Test EvaluationThis test went very well. The only problems encountered had to do with drift and shorts in someof the signals. It was later found that this may have been caused by one of the crew membersdisturbing the connection between a patch cable and one of the 300 m cable spools.In future tests, it was decided to follow the same procedure as this test since it worked very well.Also, any contact with the cable during the measurements was avoided in order to prevent shortsin the signals.52.w-—-ir—i---rA ti AilkA A AA A AA AA AA AA AAAA A AAA A A AAAAA!H•11 9 C’.) C C,, CDUItIQ CD 0 CD Cl)-I.CD z cD CI AIAAMAAAAAAAAAAAAAAAI.(-Q.34-2.0.+20o.oW%M*.--_—:<Reference>Lv&1-oIumnbseatSWcorner;WESTPositive(.041)-2.0. 0I’o(tsl455055time(sad4.3.5 CT25 -25 LEVELS COMPLETED4.3.5.1 Measurement ObjectivesThe objectives of this test were:• obtain at least four vibration modes and frequencies in the three principal directions.• high-frequency vertical measurement (for soil-structure interaction analysis)4.3.5.2 SetupThe fourth test of this study took place on Sunday, April 25, 1993. At this point in time, the 25thfloor and the core walls above this level were in place. Level 25 was still being supported fromthe 24th level with shoring.The sensor layout was similar to the previous test except that sensor #4 was oriented in the eastdirection as it should have been in the previous test. The station was located on the second floor.Specific sensor locations and signal conditioning information can be found in Appendix A.4.3.5.3 Test EvaluationThis was perhaps the best test. Everything went smoothly. The only problems encountered hadto do with shorts in some of the signals. In addition to this, most of the signals recorded fromsensor #4 appeared to be contaminated. However, since this was a redundant reference sensor, itwas not a concern.It was decided that the procedure followed in this test was excellent and should be used in thefollowing test.544.3.6 CT32 -32 LEVELS COMPLETED4.3.6.1 Measurement ObjectivesThe objectives of this test were:• obtain at least four vibration modes and frequencies in the three principal directions.• sensor collocation measurement• measure core deformation• diaphragm motion of a typical floor4.3.6.2 SetupThe fifth test of this study took place during the weekend of June 5-6, 1993. At this point intime, the entire structure had been completed. Level 32 had been cast about 2 weeks before.The sensor layout and procedure was the same as the previous test with some additional setups.The motion of the crane was measured since at the time it was believed that it was interactingwith the building. A special measurement was also conducted on Level 27 in order to estimatedamping. Some additional sensor setups were planned. However, as will be discussed shortly,the data collected from these setups was unreliable.Specific sensor locations and signal conditioning information can be found in Appendix A.4.3.6.3 Test EvaluationThis test did not run as smoothly as the previous test but was nevertheless done well. The qualityof the data collected on the first day of the test was good with the exception of some drift andcontamination in some of the channels. The quality of the data collected on the second day,though, was poor. The majority of the signals were contaminated by an unknown source (seeFigure 4.3). This contamination may have been caused by a high voltage power cable which ranup to the crane from the second floor where the station was located. Consequently, all of themeasurements made on this day were considered unreliable.554.3.7 CTTC - TOWER COMPLETED4.3.7.1 Measurement ObjectivesThe measurements collected during the final test were made primarily to assess the contributionof non-structural elements to the dynamic behaviour of the building. Specific objectives were asfollows:• Determine frequencies of the finished building and acquire sufficient data to assemblepartial vibration mode shapes to properly categorize these frequencies.• Estimate damping for the first two vibration modes in each principle direction.• Take vertical measurements around the perimeter of the building core in order to determinehow the core is deforming (shear and/or flexure)5. As a bonus, axial modes of vibrationmay also be determined using these measurements.• Take two measurements of a representative setup, one at 40 Hz, and the other at 80 Hz todetermine if any aliases are being created in the 0-20 Hz range.• Take a collocation measurement to assess the signal variance between reference and rovingsensors.The analytical result for the last two objectives are discussed in §4.4.4.3.7.2 Sensor Locations and SetupThe final test of this study took place on Wednesday, October 27, 1993. At this point in time, allof the major architectural components had been installed. Suites up to the 25th floor had beenfinished while the floors above it were currently being finished.Several factors influenced the location of the sensors. First, based on the analysis of the past 5tests, it was concluded that only 2 orthogonal reference sensors (located at the top of thebuilding) were required to generate the mode shapes instead of 4. Second, due to increasedconfidence in the program named SLAVE (see Chapter 5) , it was decided that only 3 lateral5This measurement was attempted during the second day of the previous test (CT32), but as discussed, the majorityof the data collected on that day was contaminated by an unknown source rendering it unreliable. Therefore, this isa second attempt to gather this information.56measurements were required on each floor; one in the north direction (NS) and two in the eastdirection (EW). The remaining 3 sensors were available to simultaneously take verticalmeasurement of the core. This arrangement of sensors (2 lateral reference, 3 laterallfloor, 3vertical at core) was preferred since the same setup would be used on each floor therebyminimizing the chance of error. Also, to accommodate workers on Level 29, the referencesensors were placed on Level 30; not Level 29 as originally planned.Based on the results from the last test, excellent spectra which contained spikes from eachvibration mode of interest could be obtained on Level 17 and Level 19. It was also desirable toobtain mode shapes to verify that these spikes were genuine. There were also implementationconstraints since the majority of the building was closed off and since the elevator was onlyoperating during week days. Given these requirements, it was decided to set up the dataacquisition equipment on Level 29. Cables could then be lowered from Level 28 to the sensorslocated on the floors below. It was decided to only instrument half of the building; beginningwith Level 17 (to generate spectra for comparisons) and then every third floor above this level (togenerate mode shapes). This was done to reduce the time required to conduct the test, andbecause only the top portion of the mode shape was necessary for the purpose of identification(based on results from CT32).For the measurements used to estimate damping, the same sensor arrangement as CT32 wasused, except that reference sensors 1, 3, and 4 had to be located on Level 30 to accommodate theworkers on Level 29.The collocation measurement simply involved placing all the sensors on a single plate (in thesame direction and orientation) and then taking a measurement as usual. It was expected thateach sensor should record the same signal.Specific sensor locations and signal conditioning information can be found in Appendix A.574.3.7.3 Test EvaluationWhile this test only had about half of the setups as the previous tests, a great deal of informationwas obtained. The procedure and sensor layout was optimal and proved to be very effective ingenerating the required dynamic characteristics of the building. Indeed, this setup isrecommended in future studies of buildings with a similar configuration.4.4 ERROR ANALYSISA scientific study is incomplete without some mention of error. One source of error results in thedigitization process whereby aliasing is introduced. To check for this, two measurements weretaken using the same sensor setup at different sampling rates. Another source of error is causedby different sensitivities in the sensors. To quantify this, a collocation measurements was takenwhereby all the sensors were aligned in the same direction and orientation. Finally, bias andrandom errors are also introduced in the signal processing functions. These three sources oferrors are discussed in the following sections. The measurements associated with aliasing andsensor sensitivities were made during the last ambient vibration test, CTTC.4.4.1 ALIAS CHECKBased on the results from the CT32 test, Level 17 proved to be a good location to conduct thismeasurement since contributions from all the modes of interest appear in spectra generated at thislevel. Two measurements were made using the standard setup (see Figure A.7s) - one using asampling rate of 40 Hz and the second using a sampling rate of 80 Hz6. For comparison, theportion of the spectra ranging from 0 - 20 Hz were plotted together. The portion of the spectraranging from 20 - 40 Hz for the data sampled at 80 Hz was plotted in reverse order (i.e. from 40 -20 Hz from left to right). Plotting the data in this manner allowed coincidental spikes to beeasily found. According to these plots, there did not appear to be any folded frequencies for thelateral signals (see Figures F. 1 through F.5). The vertical signals, however, show a significant6Note that these sampling rates correspond to Nyquist frequencies of 20 Hz and 40 Hz respectively.58spike around 21.5 Hz with a corresponding alias at 18.5 Hz (see Figures F.6 through F.8). Thereare also two other significant spikes around 37 Hz - one of which coincides with the spikeassociated with the second torsional mode. However, it is unlikely that the spike around 3 Hz isan alias since it has already been shown to correspond to the second torsional mode, and sincethe spikes at 37 Hz is much higher than the low-pass filter used (25 Hz7). In any event, thesealiases do not affect the frequencies determined throughout the analysis, and therefore thesefrequencies were considered to be genuine.4.4.2 COLLOCATION MEASUREMENTSince the basis of the vibration mode shapes (determined in this analysis) is a transfer functionbetween a given signal and a reference signal, it is important that all of the sensors respond in asimilar manner. In order to check this a collocation measurement was conducted. Thus thesensors should be measuring the same motion. Coherence functions (CF), Phase functions (PF),and Frequency Response functions (FRF) were generated for the roving sensors (Number 3, 4, 5,6, 7, and 8) relative to the reference sensors (Number 1 and 2) (figures appear in Appendix F).The Coherence functions (Figures F.9 and F. 10) showed an overall value of unity except for adrop off below 0.5 Hz. The only other exceptions were sensors 5 and 6 which showed ananomaly between 2 to 3 Hz. However, these anomalies correspond to a valley in the PSDfunctions and is therefore of no concern. Also, since the lowest mode is at 0.55 Hz, the drop offis also of no consequence.The Phase functions (Figures F. 13 and F. 14) showed an overall variance of roughly ±3°. In asimilar manner to the CF, there is a jump just below 0.5 Hz as well as an anomaly with sensors 5and 6 in the same frequency region as before (2 to 3 Hz). Sensor #4 shows a significant drift upto ±10°. In any event, a phase cut-off of 20° was used when generating the PMR functions, andtherefore these phase variances are within tolerance.71n retrospect, a low-pass filter of 12.5 Hz should have been used as was used for the measurement sampled at 40Hz.59Finally, the frequency response functions (Figures P.11 and P.12) show a drop off below 0.5 Hz,an overall value of unity in the range 0.5 to 9 Hz, and a gradual drop off up to 20 Hz. Since thetrend in these functions is similar, generating ratios (as is done with a transfer function) betweenthem should not produce any major errors. Furthermore, the frequency range of interest isbetween 0.5 to 10.5 Hz which is in the unity range - therefore, the effects of the gradual drop isof no concern anyway.4.4.3 RANDOM AND BIAS ERRORSBoth the Power Spectral Density (PSD) function and the Coherence function (CF) have bias andrandom errors which are a consequence of averaging the spectra in the frequency domain. Biaserror refers to the variance in frequency while random error refers to the variance in the value ofthe function at a given frequency.As mentioned in Chapter 2, the correct magnitude of the PSD was not of interest in this study.Therefore, neither was the random error. However, the bias error is of concern since PSD plotswere used to locate natural frequencies. Bias errors in the PSD functions ranged from -2% to-33%. This means that a frequency determined from this plot could be lower than the actualfrequency by as much as 33%. This error was evident since in some cases the mode shape wasfound at a frequency which was greater than the corresponding peak in the PSD.The bias error for the coherence function is undefined. The corresponding random error is afunction of frequency, and due to resolution problems, it can become very high (Bendat andPiersol, 1992). This was the case in this study. Coherence between the reference sensors andsome of the roving sensors, at some levels in the building, was found to be surprisingly low.Since there was sufficient foreknowledge of the mode shapes being detected, coherence wasgenerally ignored when reviewing the mode shapes. This was done by using a coherence cutoffof zero in the potential modal ratio functions.60CHAPTER 5AMBIENT VIBRATION ANALYSIS RESULTSThis chapter presents the analytical results of the ambient vibration records. The first section(5. 1) presents the method whereby modal frequencies and the corresponding mode shapes weredetermined. This is followed by a discussion of the mode shapes (5.2) and a discussion offrequency ratios and frequency trends (5.3). The last sections deal with the effect ofarchitectural components (5.4).5.1 METHOD FOR DETECTING MODE SHAPES AND FREQUENCIESThe following subsections discuss the procedure followed when determining the dynamiccharacteristics of City Tower. The signal processing functions mentioned herein are discussed inmore depth in Chapter 2.5.1.1 DETERMINING NATURAL FREQUENCIESPrior to any detailed analysis, all of the records were plotted using HPPLOT to visually inspectand assess the quality of the signals. Signals containing excessive signal drift were conditionedto improve their quality before they were used in the analysis. In some cases, some signals werecontaminated and were not considered reliable. Such records were discarded from furtheranalysis.Natural frequencies were determined by generating averaged power spectral densities (PSD) ofeach signal. Peaks in this function may correspond to natural frequencies or may indicate that anatural frequency is within the vicinity. Therefore, the corresponding frequency of each of thesepeaks were noted and later verified when the associated mode shapes were reviewed.Since there was a pair of sensors oriented in both the NS and EW directions of each floor,translational and torsional motion could be enhanced by combining these signals. In order toaccelerate this process, a program called P2 (EDT Ltd., 1993) was used to generate averaged61I0 1 2 3 4 5 6 7 8 9 10Frequency [Hz](b) Signals in East-West Directionadded subtractednormalizedpower spectral density (ANPSD) functions. Thus, an overview of the frequencycontent of the structural system could be viewed in a single plot. ANPSD functions from thefifth test (CT32) are shown in Figure 5.1.1001010.11001)110.10.01Figure 5.1. Averaged normalized power spectral densities for parallel signals in the NS and EWdirections (response of the building when its structure was completed).The two ANPSD functions shown in Figure 5.1 were created using pairs of sensors in the NS andEW directions respectively. These pairs of signals were combined before the transformation. Ascan be seen, by adding two parallel signals (as shown by the solid line), peaks associated withtranslational motion are enhanced while peaks associated with rotational motion are diminished.The reverse is true when the same two signals are subtracted (as shown by the dashed line).These plots also give indications of modal coupling (i.e., vibration modes which have bothtranslational and rotational motion). The second torsional mode (f 3.65 Hz) is a good exampleof this behaviour. This modal coupling can be attributed to the asymmetrical distribution of the0 1 2 3 4 5 6 7 8 9 10Frequency [Hz]62storey mass of the tower. ANPSD plots from all of the tests can be found in Appendix G.5.1.2 DETERMINING MODE SHAPESOnce possible values of the natural frequencies have been determined, the next step was togenerate and inspect the corresponding mode shapes. The procedure was as follows. First,potential modal ratio (PMR) values were generated for all of the signals with respect to the fourreference sensors1 using the program ULTRA. Second, these values were assembled intodeflection shapes which were animated and viewed from a variety of angles using a companioncomputer program called VISUAL. By viewing the deflection shape at or near a frequencydetermined from an ANPSD, the frequency was either verified as a frequency of the structure ordiscarded. In the former case, the deflection shape was verified as being a vibration mode shapewhile the frequency was verified as being a natural frequency. Both of these modal propertieswere then categorized depending on the dominant component of the mode shape (translational,torsional, etc.).There was a lot of judgment involved when verifying modal properties in this manner.Deflection shapes which were smooth were accepted while those which were erratic wererejected. Some foreknowledge of the building’s mode shapes also proved helpful. In particular,the fundamental mode shapes, along with its harmonics in sequential order, were expected. Forinstance, if (for a given direction) a fundamental and a third mode was located, then it followedthat there must be a second mode located between these two modes. Moreover, the mode shapeswere typical of those described in structural dynamic text books (dough and Penzien, 1975;Humar, 1990).One observation that was made when reviewing higher mode shapes (those higher than thesecond mode shape) was that sometimes the well defined mode shape had a frequency which was1Only two reference sensors were used in the final test, CTTC63slightly higher than the corresponding peak obtained from the ANPSD plots. This can beattributed to bias errors in the PSD functions.5.1.3 TYPICAL MODE SHAPES5.1.3.1 Mode Shape AppearanceIn order to simplify the appearance of the mode shapes, each floor in the building is representedby either a quadrilateral or a triangle as shown in Figure 5.2. The vertices of the trianglesrepresent the sensor locations. This simplification should be kept in mind when looking at themode shapes.terrace (at level 2 only) A—+ measured motion (accelerometer)generated motion (slave)vertical motion (base only)——- mode shape outlinesetback at level 10o 5 10 15m0 10 20 30 40 5Oft.Figure 5.2. Typical floor plan showing sensor locations, slave motion locations, and lines usedto represent the floors in the mode shapes presented below.5.1.3.2 Importance Of Reference SensorsThe choice of reference sensor proved to be very important when creating the mode shapes sinceeach reference sensor contained different components of these modes. For instance, a referencesensor oriented in the NS direction produced very smooth NS translational modes and torsionalmodes, but produced very erratic EW translational modes. It is likely that this reference sensor• _ _ _ _ _ — —— — — — —64contained very low or zero amplitude motion in the EW direction at the frequenciescorresponding to the EW translational modes. Therefore, when the transfer functions werecalculated, the resulting values were very large thereby producing the erratic displacement of themode shape. Thus, some mode shapes could only be obtained using one of the reference sensorswhile the other mode shapes had to be obtained by using one of the other reference sensors -even if the reference sensors were parallel.An excellent example of the importance of reference sensor locations arose while studying anincident of modal interference (this phenomenon is discussed in more depth in §5.2.4.2). In thiscase, two completely different mode shapes, with identical frequencies, were produced by usingtwo different, but parallel, reference sensors. These two mode shapes are shown in Figure 5.3.Figure 5.3. Orthographic and top views of two mode shapes which have identical frequenciesbut were reduced with respect to different reference sensorsNESWNESWNE NESW NWreference signalNW cornerSWreference signalSW corner65The mode shape on the left was reduced w.r.t. the reference sensor located at the NW corner ofthe building while the mode shape on the right was reduced w.r.t. the reference sensor located atthe SW corner of the building. The mode shape on the left shows a superposition of atranslational and a torsional mode shape with closely spaced frequencies. In contrast, the modeshape on the right only shows the translational mode. It is likely that the reference sensor locatedat the NW corner contained information about both the translational and torsional modes whilethe reference sensor located at the SE corner only contained information about the sametranslational mode. Thus, the translational mode could be isolated by using one reference sensorbut could not be isolated by using the other one. In this case, both of these reference sensorshelped identify this interesting phenomenon.Overall, the two reference sensors (oriented in the NS and EW directions) located at the NWcorner of the building were used to find the majority of the mode shapes discussed in this thesis.In some cases though, it was necessary to use the other reference sensors to find the remainingmode shapes. This demonstrates the value of having redundant reference sensors.5.1.3.3 Importance Of Signal ResolutionA significant factor affecting the quality of the mode shapes was the Nyquist frequency andresolution of the PMR functions. The Nyquist frequency defines the threshold of the frequencyrange. It was found that good quality mode shapes could be resolved in the range of zero to onehalf of the Nyquist frequency; which is consistent with previous studies (Ewins, 1984). Modeshapes with frequencies outside of this range tended to be very crude. Consequently, modeshapes in this range are more difficult to locate and categorize with any certainty. Theappearance of the mode shapes can also be improved by using a lower resolution when averagingthe signals. A lower resolution means that more averages are used when generating the PMRfunctions. This tends to smooth the function but at the cost of increasing the frequencyresolution. For this study, mode shapes with frequencies below 10 Hz were reported withconfidence while those above this frequency were often considered questionable. Generally, a66medium resolution (16 averages, Af = 0.156 Hz) was used when generating ANPSD functionswhile a low resolution (32 averages, Af = 0.3 12 Hz) was used when generating the PMRfunctions.5.1.4 DEVELOPMENT OF SLAVEOne limitation of VISUAL is that it can only animate displacements which have been measuredat a particular point of motion (POM). For City Tower, this represents 4 POMs per floor.Consequently, there was an inherent distortion in the mode shapes since motion at other pointson the floor were not being animated. This distortion is illustrated in Figure 5.4. This figureshows translational motion of each floor as depicted by the mode shapes. If translational motionoccurs in the NS direction (Figure 5.4c), points A and B move (since they were instrumented)while point C remains fixed thus distorting the shape of the triangle. A similar distortion occursfor translational motion in the EW direction (Figure 5.4b). Here, points A and C move whilepoint B remains fixed. It was not too difficult categorizing the lower mode shapes with this typeof distortion. However, the higher modes became impossible to categorize due to modalcoupling. Since all of the higher modes had rotational components, torsional modes could not bedistinguished from translational modes.A(a) typical floor plan of building showing sensor layout and orientation (denoted by arrows). (b)distortion created by motion associated with (b) east-west translation and (c) north-south translation.Figure 5.4. Distortion created when animating experimental mode shapes(a)67To deal with this problem, it was decided to calculate the motion at other points on the floor bytreating each floor as a rigid body and then interpolating from the PMR values derived from theambient vibration records. Fortunately, the mathematical formulation for this process had beendeveloped previously (çelebi, et al., 1987). These formulations were later implemented in acomputer program called SLAVE. Specific formulations as well as instructions for using thisprogram can be found in Appendix D.Excellent results were obtained using the program SLAVE. As an example, consider the modeshapes shown in Figure 5.5. This figure shows orthographic and top views of the first three NStranslational mode shapes (from CT25). The mode shapes at the top show vibrational motionwith just the measured POMs (master nodes) while the mode shapes at the bottom show thevibrational motion with both the master and the slave nodes included in the plot.As can be seen, the first and second modes in the top of Figure 5.5 can be categorized easilydespite the distortion. However, it is unclear how the third mode shape should be categorized.Even the top view of the third mode did not provide sufficient information. Now, once the slavenodes have been generated and appended to the mode shape, a much clearer picture is formed.The distortion has been eliminated from all of the modes. Furthermore, the third mode shape cannow be categorized with confidence. In this case, the third mode is in fact a translational modewith a rotational component (modal coupling). The program SLAVE was essential forenhancing and properly categorizing all of the mode shapes described in the following section.5.1.5 DEVELOPMENT OF MACA portion of this study was concerned with correlating mode shapes based on a MAC analysis(see Chapter 2). To facilitate this analysis, a program was developed to compute the correlationcoefficient between two sets of mode shapes which were obtained either experimentally oranalytically. Details of this program as well as operating instructions can be found in AppendixE.680 ct C) C C C C I-.C C C C)viewfromtopviewfromNWcornerL1 z5.2 MODE SHAPES FROM INDIVIDUAL TESTSThis section presents all of the experimental mode shapes which were obtained from this study.The evolution of the building’s dynamic behaviour is also discussed based on these vibrationmodes.5.2.1 MODE SHAPE NAMING CONVENTIONSThe following conventions are used when referring to specific mode shapes:Table 5.1. Vibration mode shape designations.designation descriptionNS•1, NS•2, ... translational mode with dominant components in the north-south (NS)direction and corresponding order - i.e. fundamental, second, third, etc.EW• 1, EW•2, ... translational mode with dominant components in the east-west (EW)direction and corresponding order - i.e. fundamental, second, third, etc.T•1, T•2, ... torsional mode and corresponding orderA•1, A•2, ... axial mode and corresponding order5.2.2 TEN LEVELS OF THE TOWER COMPLETED (CT1O)At this stage in the building’s construction, 10 levels of the building were completedcorresponding to a height of 25.1 m (82.3 ft.). Five vibration mode shapes were obtained fromthe ambient vibration records. These mode shapes, along with their corresponding frequencies(periods) are shown in Figure 5.6. In this figure, Levels 1 through 10, and the lowest parkinglevel P6 of the building, are depicted in these mode shapes. Unlike the fundamental modes, thequality of the second modes was not very good. Moreover, the second EW translational modecould not be found with certainty due to a lack of definition.The fundamental frequencies were very high. However, the building was also much stiffer thana typical building of this height since its core was designed for a 30 storey building, not a 9storey building.The mode shapes tend to be very directional with no evidence of modal coupling. The nodal70TjCD a CDCCDCD cICC’) CDCC’)CD o-tOCD IN 9 L) 00 Cl) 00 00 N 9 C Cl)LJcit N C C Cl)VibrationModeShapeCategoryTorsionalNSTranslationEWTranslation(E.Elevation)(E.Elevation)(N.Elevation)C N)UtC N C CfJda:—.t-1’-0 0Ipoint for the second modes were located between the 7th and 8th floor (approximately 74% ofthe building’s height). There did not appear to be any significant rocking motion of the core.Also, the absence of lateral motion at the ground floor indicates no significant embedment effect;i.e. there is no significant difference between the motion at the ground floor and the motion at thebase of the building. This can be attributed to the stiffening effect of the surrounding soil as wellas the parking structure which the tower connects to at this level. The setback at level 2 as wellas the tall first storey do not appear to affect the vibration modes at all.5.2.3 FIFTEEN LEVELS OF THE TOWER COMPLETED (CT15)At this stage in the building’s construction, 15 levels of the building were completedcorresponding to a height of 38.3 m (125.7 ft.). Nine vibration mode shapes were obtained fromthe ambient vibration records. These mode shapes, along with their corresponding frequencies(periods) are shown in Figure 5.7. In this figure, only every other floor is depicted with theexception of levels 2 and 14 as well as level P6. The definition of these modes shapes are betterthan those from the previous test. This was attributed to the relocation of the reference sensors,and that no construction was taking place at the building during the ambient vibrationmeasurements.There was a drop in all of the building’s frequencies, compared with the previous test, due to theaddition of five storeys. Specifically, there was a 40% drop in the translational modalfrequencies and a 30% drop in the torsional modal frequencies.Overall, the mode shapes tend to be directional though modal coupling is noticeable in the modesNS•2, NS•3, and EW•3. This coupling can be attributed to the setback located at the SE cornerof level 10 which introduces a significant redistribution of the floor mass. The nodal point forthe second modes is located at the 11th floor (approximately 72% of the building’s height) whilethe nodal points for the third modes are located at the 7th and 13th floors (approximately 45%and 86% of the building’s height, respectively). Rocking motion of the core is evident in modeEW•2 but is not evident in the other modes. Also, the embedment effect discussed in the72VibrationModeShapeCategoryrjTorsional(E.Elevation)North-SouthTranslation(E.Elevation)East-WestTranslation(N.Elevation)CtL1èo00LJNNN,-.__CDCDC 0000()cjCfJCl)C I!00t’J.CçjCCNNN‘B‘BCD zCDCD—00- 00NNN()CCCbCD00‘.C c)Cl)Cl)Cl)previous section is not present in these modes. The setbacks at Level 2, along with the tall firststorey, do not appear to affect the vibration modes at all.5.2.4 TWENTY LEVELS OF THE TOWER COMPLETED (CT2O)5.2.4.1 Mode ShapesAt this stage in the building’s construction, 20 levels of the building and the core above Level 20were completed. This corresponded to a height of 54.2 m (177.7 ft.). Ten vibration mode shapeswere obtained from the ambient vibration records that were collected during this test. Thesemode shapes, along with their corresponding frequencies (periods) are shown in Figure 5.8. Inthis figure, only every other floor is depicted with the exception of level 2 and level P6. Thedefinition of these mode shapes is excellent, though a loss of definition can be seen in some ofthe higher modes (such as EW•3, EW•4 and T•3).There was a drop in all of the building’s frequencies, compared with the previous test, due to theaddition of another five storeys. Specifically, there was a 40%, 30% and 25% drop in the EWtranslational, NS translational, and torsional modal frequencies, respectively.As can be seen, the modal coupling in all of the higher translational modes is becoming morepronounced. This demonstrates that the setback at the corner of level 10 has an important effecton the vibration characteristics of this structure. The nodal point for the second modes arelocated at the 15th floor (approximately 71% of the building’s height) while the nodal points forthe third modes are located around the 10th and 17th floors (approximately 46% and 80% of thebuilding’s height respectively). Although the definition of the mode EW•4 is quite crude, thenodal points for this mode appear to be located at the 6th, 11th, and 17th floors (approximately27%, 51%, and 80% of the building’s height respectively). There did not appear to be anyevidence of rocking motion of the core in any of these mode shapes. At this point, it seemedclear that the setback at Level 2, along with the tall first storey, are not significant factors in thebuilding’s vibrational behaviour. In contrast, the setback at Level 10 was a very important74VibrationModeShapeCategoryTorsional(E.Elevation)C cc U) 00 N C ON -J C’)North-SouthTranslation(E.Elevation)East-WestTranslation(N.Elevation)L%JN_9 00 U) C/)LMcc N 9 (A LN) C’) (A C 00 N 9 00 C/) ‘.0 C U) N 9 C/)CD Lit !zoCnCD-e 0<0-‘-t‘-a.pCD 0 toCD0-tO a CDt’CtP CDCD • 0 0-CDCnPs..-’C)0-eCt‘-a.I-.t-e9.0-CD no00t+J0-tt00taE.CDt 0-N 9 L%JC/)A LitONN 9 ‘.0 C/)00 “a t) N 9 C/)C C U)‘.0N 9 C C C/)t) U)!thJ\W{00 cc C ON N 9 C (A U) C/)attribute since it had introduced significant torsional motion to almost all of the vibration modes.5.2.4.2 Modal Interference Between Modes EW•2 And T•2One of the most interesting observations made in this study was an incident of modalinterference (Thomson, 1993). This involves the superposition of motion between modes whichhave closely spaced frequencies (periods).This type of behaviour was found during the analysis of the data collected during the CT2O test.In this case, the motion of the second EW translational mode (f=5. 16 Hz, T=O.194 s) and thesecond torsional mode (f=5.51 Hz, T=O.181 s) were combined, resulting in the mode shapeshown in Figure 5.9. At first glance, the EW translational mode appeared to be the secondtorsional mode; rotating about an axis located at the SW corner of the building. However, thisdid not make sense since the second torsional mode had already been located, and since therewas no structural element located at the SW corner which would cause this type of rotation.Upon closer inspection, it was surmised that if translational and rotational motion from thesecond EW translational mode and the second torsional mode, respectively, were combined asshown in Figure 5.9c, lateral motion (EW direction) would be increased at the NW corner andeliminated at the SW corner. This indeed was the case. The combination of motion justdescribed can be seen clearly by looking at the top view of the mode shape (Figure 5.9b).Similar behaviour was observed for the corresponding torsional mode (Figure 5.9d). In this casethe EW motion at the NW corner has been eliminated while the EW motion at the SW corner hasbeen increased.76NE‘SW(I)Second Torsional Mode (coupled with second EW Translational Mode)Second EW translational mode shape: (a) viewed from the north-west corner, (b) viewed from thetop of the building, (c) probable superposition with second torsional mode (top view)Second torsional mode shape: (d) viewed from the north-west corner, (e) viewed from the top ofthe building, (t) probable superposition with second torsional mode (top view)Figure 5.9. Modal interference between second EW translational mode and second torsionalmode.SW NE‘SNW SWN(c)Second EW Translational Mode (coupled with second Torsional Mode)NE7’N;NW SW(e)775.2.5 TWENTY-FIVE LEVELS OF THE TOWER COMPLETED (CT25)At this stage in the building’s construction, 25 levels of the building and the core above Level 25were completed. This corresponded to a height of 67.4 m (221.0 ft.). Ten vibration mode shapeswere obtained from the ambient vibration records that were collected during this test. Thesemode shapes, along with their conesponding frequencies (periods) are shown in Figure 5.10. Inthis figure, only every other floor is depicted with the exception of level 2 and level P6. Also,level 23 was not instrumented due to time constraints, and since measurements on this floor werenot essential for determining the modal characteristics for this particular test.There was a drop in all of the building’s frequencies, compared with the previous test, due to theaddition of another five storeys. Specifically, there was a 25% drop in the translational modalfrequencies and a 20% drop in the torsional modal frequencies.At this stage in the building’s construction, the rotational component of the translational modeshad increased in magnitude relative to the previous test. However, other aspects of the building’sdynamic behaviour did not change from the previous test. There was still evidence of nosignificant embedment effect, and the structural configuration at the ground floor of the building(tall first storey, and setback at level 2) do not affect the dynamic behaviour. Also, there was noevidence of rocking at the base of the core. The nodal point for each of the second translationalmodes is located around the 19th floor (approximately 73% of the building’s height) while thenodal point for the second torsional mode is located at the 17th floor (approximately 65% of thebuilding’s height). Note that there is a noticeable shift in the nodal point of the torsional mode atthis stage. As for the other modes, the nodal points for the third modes are located around the11th and 21st floors (approximately 41% and 80% of the building’s height, respectively). Thenodal points for the mode NS•4 are located at the 8th, 16th, and 23rd floors (approximately 29%,61%, and 88% of the building’s height, respectively).78VibrationModeShapeCategoryTorsional(E.Elevation)North-SouthTranslationEast-WestTranslation(E.Elevation)(N.Elevation)0 0 N LN)t’JCl)i )- C SM — 000r—No c0< CD cl)0n D c-0-“s 4)0b(A$o(.e3px NCDt0-“CD0Ocl)Cj)_LN)—t%)00t-CD°ci,Cl)—:L0 t‘—,-JONAUIeE_0S°NNCDF-’92CD—.—0ON2t)0E)Cl)—U So‘CE.Li1k)Z(AqQN.<0CDa9 00 (A ‘C N ON Cl) cc (A N 9 to Cl) 00 to 00 N 9 (J3 Cl)it;.—--yto U)Ia‘4,5.2.6 ALL THIRTY-TWO LEVELS OF THE TOWER COMPLETED (CT32)At this stage in the building’s construction, the entire structure (32 levels) was completed. Thiscorresponded to a height of 83.2 m (273.0 ft.). Twelve vibration mode shapes were obtainedfrom the ambient vibration records that were collected during this test. These mode shapes,along with their corresponding frequencies (periods) are shown in Figure 5.11. In this Figure,only every other floor is depicted with the exception of level 2 as well as level P6. Also, level 31was not instrumented since these measurement were not required, and level 3 was notinstrumented since that level was inaccessible during the test.All of the mode shapes are very well defined with the exception of the mode EW•4. Here themode shape is quite crude. There also appears to be considerable lateral movement at the groundfloor in this mode. However, this can be attributed to either the crudeness of the mode shape orthat the amplitude of this vibration mode is minute. In other words, the amplitude of this mode isthe same as the amplitude of the ground motion in all of the other mode shapes.There was a consistent drop in all of the building’s frequencies, compared with the previous test,due to the addition of another seven storeys. Specifically, there was a 25% drop in thetranslational modal frequencies and a 20% drop in the torsional modal frequencies.There had been little change in the building’s dynamic behaviour compared to the previous test.The nodal point for the second modes is located around the 23rd floor (approximately 71% of thebuilding’s height) and the 19th floor (approximately 59% of the building’s height) for thetranslational and torsional modes, respectively. The nodal points for the third modes are locatedaround the 16th and 26th floors (approximately 49% and 81% of the building’s height,respectively). Finally, the nodal points for the fourth modes are located at the 10th, 19th, and27th floors (approximately 30%, 59%, and 84% of the building’s height, respectively).80VibrationModeShapeCategoryGO C p-iCD Sn- o-o‘-i’i-0 p t< -ia‘ CGO CD CC aCDCDZct,00CDCl)J riDtS.0CDa C,) C -I tDOno ,-‘ t) CD <C CD Cl).9S000C,)C (SiN C Ca)0000N 9 t%)C (SICl)UIN 9 l.i) Cl)‘L UC’Cl)C 0000Torsional(E.Elevation)North-SouthTranslation(E.Elevation)East-West Translation(N.Elevation)ii—e’9ThElTIE9 0\ :t 91 Irt00N C C’Cl) (SIN 9 LN)-J a Cl) 9’ C (Si(SiN 9 C’ LI’Cl)00(SiL’JN 9 C’ Cl)i:—tIQHIIiIiirMS!!inrEE±.n=cEED*%---r41>?9’I,tecCtss-NfltA’)I/4I.’—4—zN ir’uiNP11WIC b____Cl)a5.2.7 EVOLUTION OF THE MODE SHAPEIt is worthwhile examining all of the mode shapes as they evolved throughout the constructionprocess. The first point worth mentioning is that modal coupling became significant after thesetback was introduced at level 10. Moreover, the resulting torsional effects became morepronounced as the building became higher. The second point worth mentioning is that theoverall proportion of these mode shapes tended to be the same. For comparison, the nodal points(expressed as a proportion of the building height) were tabulated, and can be found in Table 5.2.Although there are some variations, in general the nodal points occurred at the same point in thestructure. There is also the shift in the nodal point for the second torsional mode encounteredduring the CT25 and CT32 tests. As another comparison, all of the second modes were tabulatedand are shown in Figure 5.12. As can be seen, the mode shapes maintain the same proportionduring its evolution.Table 5.2. Nodal points expressed as a percent of the building’s heightTest 2nd mode 3rd mode 4th modeCT1O 74CT15 72 45, 86CT2O 71 46,80 27, 51, 80CT25 73 (65)* 41, 80 29, 61, 88CT32 71 (59)* 49, 81 30, 59, 84* torsional mode5.2.8 BASE MOTIONBased solely on the mode shapes, there did not appear to be any significant movement at the baseof this structure. The only rocking motion (of the core) appeared in a single mode shape (CT15,mode EW•2). Also, there was no significant lateral motion associated with the parking levels(i.e. those levels below ground level). This behaviour can probably be attributed to the suddenincrease in stiffness as the tower frames into the parking structure and the neighbouringtownhouses.82VibrationModeShapeCategoryTorsional(E.Elevation)North-SouthTranslation(E. Elevation)East-WestTranslation(N.Elevation)- 000c00NN? C-0Ca C,,zi!1iThsLfl—]\!tII00rj tn C I •Ln C 00 N 9 0000N 9 -a-C N p C,, p 00 C.,—a(I’N 9C L1C,,-Jz C I EU’N 9 C,,4—C C,,ITh\\5.2.9 TOWER COMPLETED (CTTC)Two aspects of the vibration mode shapes were investigated during this test. First, lateral motionof each instrumented floor was determined for comparison with the previous test (CT32).Second, vertical (and interpolated lateral motion) of the core was determined in order toinvestigate the manner in which the core deforms. Since a different sensor layout was used inthis test, the lines used to represent each floor and the core in the resulting mode shapes areslightly different from the other tests. For reference, sensor locations and mode shape outlinesfor these mode shapes are shown in Figure 5.13.—4 measured motion (accelerometer)v generated motion (slave)vertical motion (core only)mode shape outlineAo 5 10 15r0 10 20 30 40 5Oft,Lateral Modal Outline Core Motion Modal OutlineFigure 5.13. Typical floor plan showing sensor locations, slave motion locations, and lines usedto represent the floors in the mode shapes presented below.5.2.9.1 Lateral ModesAt this stage in the building’s construction, the majority of the building was finished. All of themajor architectural components such as glazing and partition walls were in place. Since theprimary objective of this test was to compare frequency shifts due to the addition of thearchitectural components, only 5 storeys were instrumented in order to assemble partial modeshapes. These partial mode shapes were sufficient to verify the modal frequencies. Twelve84lateral vibration mode shapes were obtained from the ambient vibration records that werecollected during this test. These mode shapes, along with their corresponding frequencies(periods) are shown in Figure 5.14. In this figure, only 5 levels are depicted, namely levels 17,20, 23, 26, and 29.The analysis showed that there was little or no change in the modal frequencies when comparedwith those from the last test (CT32). In addition, the shape of the vibration modes did notchange; at least not the portion which was measured in this test. This is based on a MACanalysis between the mode shapes obtained from CT32 and the mode shapes obtained from thistest.5.2.9.2 Core Deformation And Vertical ModesThe core modal displacements are shown in Figure 5.15. According to these mode shapes, thecore deforms primarily in flexure during the translational modes but there is no significantvertical core displacement associated with torsional modes. An interesting aspect of the first andsecond translational mode shapes is that the upper half of the building remains straight whileflexure occurs in the lower half. The latter is based on comparisons between analytical andexperimental mode shapes. This type of modal behaviour makes sense since less energy isrequired to deform the core in this way and since less energy is associated with the lower modesof vibration.Although determination of modes dominant in the vertical direction of this structure was beyondthe scope of this study, an attempt was made to locate some of these modes based on the verticalmeasurements of the core. Only a single axial mode could be found. This mode is included inFigure 5.15. As shown, all three corners of the core move in parallel and in phase. This type ofmotion suggests that this is the fundamental axial mode shape of the structure. However, sinceonly a portion of the structure was measured, it is possible that this could be the second axialmode of the structure.85Vibration Mode Shape Number29 _26c,o___231_H>2017/_______CD0.644 Hz (1.552 s) 2.930 Hz (0.341 s) 6.523 Hz (0.153 s) 10.469 Hz (0.096 s)1c Cc__ __ __&)_0.547 Hz (1.828 s) 2.266Hz (0.441 s) 4.883 Hz (0.205 s) 7.461 Hz (0.134 s)—7CC’)CF-’1.289 Hz (0.776 s) 3.633 Hz (0.275 s) 6.055 Hz (0.165 s) 8.906 Hz (0.112 s)Figure 5.14. First four vibration mode shapes in each principal direction of the building,and corresponding frequencies (periods) of the finished building (CTTC).(Only the top half of the building is shown in these mode shapes).86Vibration Mode Shape Number290C10.644 Hz (1.552 s) 2.930 Hz (0.341 s) 6.523 Hz (0.153 s) 10.469 Hz (0.096 s)C0“Co-C’-,Uto 0.547 Hz (1.828 s) 2.266Hz (0.441 s) 4.883 Hz (0.205 s) 7.461 Hz (0.134 s)tC0-ICM‘.40H_____1.289 Hz (0.776 s) 3.633 Hz (0.275 s) 6.055 Hz (0.165 s) 8.906 Hz (0.112 s)C00C’)4:8.164 Hz (0.122 s)Figure 5.15. First four vibration mode shapes of the building core, in each principal direction of thebuilding; and corresponding frequencies (periods) of the finished building (CTTC).(Only the top half of the building is shown in these mode shapes.875.3 MODAL FREQUENCIESThis section presents all of the experimentally obtained frequencies and how they changed as thebuilding was being constructed.5.3.1 MODAL FREQUENCIES AND FREQUENCY RATIOSTabulated frequencies and frequency ratios appear in Tables 5.3 and 5.4 respectively. As to beexpected, the modal frequencies decreased as the building increased in both height and mass.Modal frequency ratios between the higher modes and the corresponding fundamental modewere found to be consistent from test to test. Also, the overall sequence of these ratios tended tobe 4-9-14, 4.5-10.5-16, and 3-5-7 for the NS translational, EW translational, and torsionaldirections respectively. Note that all of the numbers are equally spaced for each sequence(namely 5, 6, and 2 for the aforementioned directions). The higher spacing for the EWtranslational modes, compared with the spacing for the NS translational modes, can be attributedto the higher lateral stiffness in the EW direction.Table 5.3 Frequencies (Hz) for City Tower from 5 stages in its construction.corresponding CT1O CT15 CT2O CT25 CT32mode shapeNS•l 2.62 1.56 0.94 0.70 0.55NS•2 9.69 6.25 4.10 3.05 2.30NS•3 10.70 8.24 6.25 4.88NS•4 7.54EW•1 3.13 1.88 1.17 0.86 0.64EW•2 8.63 5.16 3.95 2.93EW•3 10.04 8.83 6.86EW•4 18.91 10.49T•1 3.91 2.58 1.91 1.48 1.29T•2 10.47 7.77 5.51 4.45 3.65T•3 11.88 9.02 7.58 6.05T•4 8.6588Table 5.4. Frequencies ratios for City Tower from 5 stages in its construction.modal frequency ratio CT1O CT15 CT2O - CT25 CT32NS•2INS•1 3.7 4.0 4.4 4.3 4.2NS•3/NS•1 6.8 8.8 8.9 8.9NS•4INS•1 13.8EW•2/EW•1 4.6 4.4 4.6 4.5EW•3/EW•1 8.6 10.3 10.6EW•4/EW•1 16.1 16.3T•2/T•1 2.7 3.0 2.9 3.0 2.8T•3/T•1 4.6 4.7 5.1 4.7T•4/T•1 6.75.3.2 FREQUENCY TRENDSTrends for the modal frequencies were estimated by plotting the frequencies in Table 5.3 againstthe storey height of the building. This plot is shown in Figure 5.16. As can be seen, the changein frequency for both translational and torsional modes follow a similar trend. Furthermore,translational modal frequencies appear to be more sensitive to building height than torsionalmodal frequencies. Worth noting is the cross-over between the second EW translationalfrequencies and the second torsional frequencies. The intersection around 19 storeys coincideswith the modal interference described previously in §5.2.4.2.12 -11 —10 -9-‘ 8-7-6-4-Z 3-2-1—0--. modesmodesI I I I I I I I I I I I I I I I I I I I I I I I I9 10 11 12 13 14 15 16 17 18 19 ) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Number of Levels CompletedFigure 5.16. Frequency trends for the tower during its construction phase.895.4 EFFECT OF ARCHITECTURAL COMPONENTSOne of the objectives of this study was to compare the dynamic characteristics of a bare structurewith those of a structure with architectural components (such as drywall, cladding, and glazing)attached. This comparison was based on the mode shapes and frequencies (periods) as well as onestimates of damping obtained from the last two tests (CT32 and CTTC).5.4.1 EFFECT ON FREQUENCYThe modal frequencies from the tests CT32 and CTIC are compared in Table 5.5. As can beseen, there has been little or no change in the modal frequencies. The only significant shiftsoccurred in the higher modes of vibration. These modes involve more complex deformationsthan the lower modes, therefore it makes sense that the architectural components would affectthem during low amplitude vibration.Table 5.5. Modal frequencies from CT32 and CTTCmode shape CT32 CTIC changedesignation (Hz) (Hz) (%)NS•l 0.547 0.547 -EW•l 0.644 0.664 3.1T•1 1.289 1.289 -NS•2 2.305 2.266 -1.7EW•2 2.930 2.930 -T•2 3.652 3.633 -0.5NS•3 4.883 4.883 -T•3 6.055 6.055 -EW•3 6.856 6.523 -4.9NS•4 7.539 7.461 -1.0T•4 8.652 8.906 2.9EW•4 10.488 10.469 -0.25.4.2 EFFECT ON MODE SHAPESAs mentioned earlier, the mode shapes themselves did not change with the addition ofarchitectural components. A MAC analysis showed excellent correlation between thecorresponding mode shapes obtained from the CT32 test (the bare structure) and from the CTIC90test (the finished structure). Note that this comparison is somewhat incomplete since only theupper portion of the building’s mode shape was available for this comparison.5.4.3 EFFECT ON DAMPINGDamping estimates derived from ambient vibration measurements are generally unreliablebecause of large errors due to time windows as well as digitization and noise present in the timesignal (Brownjohn, 1988). Other studies have shown that damping levels are force dependentand are typically inconsistent during low amplitude vibrations (Okauchi, Miyata, et al., 1992).Moreover, damping levels under ambient conditions tend to be lower than damping levels understrong motion (Marshall, Phan, and celebi, 1994). Therefore, the actual values of dampingdetermined from ambient vibrations appear to have little meaning. Furthermore, they certainlyshould not be used to predict structural behaviour under extreme loads such as earthquakes andhurricanes.Despite all of the negative conclusions documented about damping estimates from ambientvibrations, an attempt to estimate damping for the lower 6 modes was made anyway. This wasdone for completeness, and also with the hope that a qualitative comparison could be madebetween the structure with and without architectural components installed. Measurements takenfor the purpose of estimating damping were made on level 27 using a lower sampling rate (20Hz) than was used for the other measurements (40 Hz). A level closer to the base of the buildingwould have been preferred. However, this was not feasible since architectural components hadalready been installed on the lower floors at the time of the CT32 test.5.4.3.1 Sensitivity AnalysisThe method used to estimate the damping level was the bandwidth method (dough and Penzien,1975) using an averaged PSD function for each of the four measurements made on Level 27.However, several considerations had to be made. The first consideration was whether or not toapply a time window to the signal before transforming it to the frequency domain (as was usually91done). For instance, a Hanning window, compared with a rectangular window, tends to inflatethe width of the spikes in the frequency domain thereby causing an increase in the calculatedvalue of damping. The second consideration involved choosing the frequency resolution ornumber of averages to be used when calculating the PSD functions. The smoothing whichresults from several averages may also widen the width of the spike as well as reduce the heightof the spike. Both of these factors would increase the calculated value of the damping using theband-width method.In order to quantify the sensitivity of calculated damping values, several combinations ofwindows (rectangular and Hanning) and resolutions (high, medium, low, and very low)2wereused. In addition to this, estimates were made using individual segments from one record(cttcdl05). The results of this exercise are summarized in Figures 5.17 through 5.20. The firstthree figures (5.17, 5.18, and 5.19) show comparisons of damping estimates for the first andsecond vibration modes. The last of these figures (5.20) show damping estimates for a singlerecord only.Figures 5.17, 5.18, and 5.19 consistently show that damping estimates increase as the resolutiondecreases, and that there is a considerable variation in the damping values (damping estimatesranged from 1% to 5% for NS•1, 0.5% to 3% for EW•1, and 0.2% to 1.7% for T•l). Dampingestimates also increased when a Hanning window was used.Damping estimates were also made based on eight individual data segments from a singlechannel. The arithmetic mean of these values was also calculated. These values were comparedto the values determined from averaging in the frequency domain. A summary is shown inFigure 5.20. As can be seen, damping values are consistent from data segment to data segmentexcept for the mode NS• 1 which shows some variation. The arithmetic mean appears to produce2These are the designations used in the program ULTRA’ which was used for this analysis. High, medium, low,and very low correspond to 8, 16, 32, and 64 averages respectively.92modetype& number/channel!(window)very lowmediumm jVhighresolutionFigure 5.18. Damping estimates for 2 signals in the EW direction using different resolutions andwindows.G)CuCo)C.)CECuCl) ‘- •— -= rC U) - L()VCl) • •C (I)C CCresolutionmode type & number! channel I(window)Figure 5.17. Damping estimates for 2 signals in the NS direction using different resolutions andwindows.‘S0)Cu4-CcD.2C0.ECuvery low931.8%1.6%1.4%1.2%1.0%0.8%0.6%0.4%0.2%0.0%Q(oco• 1__-__ • ‘— —.-._ • ,_-— .mode type & number I channel I (window) — .,... c.iFigure 5.19. Damping estimates for 4 signals in the NS and LW directions (torsion) usingdifferent resolutions and windoWS.4.0%01.0%0.5% A0.0%Segment number! mean 18,16,32,64averagesLNS.lT’l7 NS•2T’2‘5a,. ‘-0EresolutionDamping (percent ofcritical)a) t, za)EMode designationFigure 5.20. Damping estimates for one signal in the NS direction using individual segmentSmean, and different resolutions (no window).94a good estimate. Estimates based on a high resolution produced results which were similar to themean except for the mode NS•1. There was considerable variation in damping estimates basedon lower resolutions (values ranged from 0.3% to 3.6% for NS•1 and 0.1% to 1.3% for NS.2).Based on these results, it is clear that damping values are very difficult to quantify accurately.However, one conclusion that can be drawn from these figures (especially Figure 5.19 whichshows damping estimates for the torsional modes) is that for a given window and resolution, theresults are quite uniform. Therefore, it seemed reasonable that relative comparisons could bemade between damping levels.5.4.3.2 Comparison Of Bare Structure And Finished BuildingUsing the basis that relative comparisons of damping values could be made (as discussed in theprevious section), it was decided to compare damping estimates from the CTTC test and theprevious test, CT32, using a rectangular window, and a high resolution. The results appear inFigure 5.21.Figure 5.21. Modal damping comparison between the bare structure and structure witharchitectural components in place.1.2%1.0%.C.)C.) r. C)fll,4— ‘i.O/U00.6%0.4%0.2%0.0%CT32D crrcNS• 1HiNS•2 EW•1 EW•2 T•1Vibration mode shape designationEl1T•295According to this figure, the addition of architectural components to the structure results in amodest increase in damping of the fundamental NS translational mode (from 0.4% to 1%) as wellas the second EW translational mode (from 0.14% to 0.17%). The remaining modes showed adecrease in damping (from 0.8% to 0.5% for the mode EW•1 as well as a 0.15% drop in theother). These shifts in damping are quite small. Moreover, in light of all of the errors associatedwith damping estimates from ambient vibration records, one can conclude that there has been nosignificant change in the damping levels with the addition of the architectural components.However, this conclusion is based on ambient levels of vibration, and should not be extrapolatedto high amplitude vibrations induced in the structure by a seismic event. In the latter case, it isbelieved that architectural components will contribute to dissipating energy (i.e. damping) if thestructure undergoes large displacements.96CHAPTER 6DYNAMIC ANALYSIS OF THE BUILDINGThis chapter presents a discussion of dynamic analyses of the building (6. 1). In addition,design considerations based on the results of this study are also discussed (6.2).6.1 COMPUTER ANALYSISTo complete this study, a dynamic analysis of the building was performed. This was done todetermine if the building’s dynamic characteristics could be accurately represented by ananalytical model.6.1.1 CHOICE OF DYNAMIC ANALYSIS PACKAGESThe program ETABS (CSI Ltd. 1992) was chosen for this analysis for two reasons. First, it isspecialized for the analysis of building systems. Second, this software package is commonlyused for design by engineering consultants, and thus serves as a useful benchmark.6.1.2 CALIBRATION OF THE BASE MODELA very precise model of the building, with 32 levels and the parking levels in place, was createdusing information from the contract drawings of this building (Bogdonov Pao Associates Ltd.,Baker McGarva Hart Inc.). The objective of developing this model was to calibrate it such thatits frequencies (periods) and mode shapes, obtained through dynamic analysis, corresponded tothe experimental results. Several revisions and adjustments were made to the model in order tosatisfy this objective.The calibrated (base) model of City Tower corresponding to the CT32 test is shown in Figure6.1. A detailed description of this model is given below.97Figure 6.1. ETABS model of the building with all 32 levels.98The core was modeled as an assemblage of shear panels; taking into account all door and wallopenings. The stiffness of these panels was represented by using the same wall thicknessesspecified on the drawings (ranging from 450mm (18”) at the base to 350 mm (14”) at the top)along with the secant stiffness (based on specified values of f’ - see Table 3.1) to represent theconcrete. Shear panels were also used to model the parking level retaining walls.Columns were modeled as stick elements accounting for all geometric and material properties.Stairways were modeled as X-bracing. Vertical soil stiffness was modeled by providing anadditional storey at the base of the building. Columns and shear walls were extended to thisstorey and their properties appropriately modified to model the soil. Lateral and torsionalsprings, representing the soil, were added to the parking levels acting through the centre of massof the core.The floor slabs were not modeled directly since an intrinsic assumption in ETABS is that theseslabs behave as rigid diaphragms. However, the distribution of floor mass was meticulouslyaccounted for. A density of 24 kN/m3was used to model the weight/mass of all of the reinforcedconcrete in this building.About 20 revisions, which included modifications and adjustments to the model, were madebefore the model was calibrated satisfactorily. The revisions which significantly affected themodal properties are as follows. First, the addition of the header beams properly modeled thetorsional stiffness of the core. Second, the addition of both the retaining walls and lateral soilsprings to the parking storeys also helped improve the match of both the frequencies and theshape of the vibration modes. Finally, the upper storeys (above Level 25) were found to be tooheavy. Reducing the reinforced concrete density from 24 kN/m3 to 20 kN/m3 at these levelsimproved the values of the analytical fundamental frequencies (which were too low prior to thischange). This change reflects the lower steel percentage in the core1 above Level 25. The1Note that the density of steel (7850 kg/rn3)is over 3 times the density of concrete (2430 kg/rn3). Therefore areduction in the steel percentage also reduces the overall density of the reinforced concrete.99revisions to this model which did not significantly affect the modal properties include thestairway (acting as cross-bracing) and a torsional spring, representing soil stiffness, applied at theparking levels.Once the base model (all 32 levels) was calibrated, 4 other models of the building were createdcorresponding to the state of the building at the time of the other ambient vibration tests (CT1O,CT15, CT2O, and CT25). These models were created simply by taking the base model andremoving the upper storeys such that the number of storeys in the model was the same as thenumber of storeys in the building at the time of the aforementioned tests. It was found (throughdynamic analysis) that these other models accurately represented the dynamic behaviour of thebuilding, at the corresponding stage in its construction, without further modifications.The results of the original calibration and subsequent modeling of the building at other stages inits construction are discussed in the following sections.6.1.3 COMPARISON OF ANALYTICAL AND EXPERIMENTAL FREQUENCIESComparisons between corresponding analytical and experimental frequencies (for all 5 models)were based on percentage differences, and also by plotting these frequencies against each other.In terms of differences between analytical and experimental frequencies, it was found that mostof the corresponding frequencies were within 5% of each other. The remaining frequenciesdiffered by as much as 24%. Tabulated frequency comparisons can be found in Appendix H.Plots of experimental versus analytical frequencies were also made for comparison; these appearin Figure 6.2. In these plots, the closer each point comes to the diagonal, the better thecorrespondence of the analytical frequency to the experimental frequency. Since most of thesepoints came very close to this line, it was concluded that there was very good correspondence.100—/////T.- - - EW• - -ONS.1 — —E2_t-zrcTio========::frNS•3/I:: -----(Ns.2 --o 1 2 3 4 5 6 7 8 9 101112Experimental Frequency (Hz)10Nci0. 3 ——<101211Nc)4Figure 6.2. Experimental versus analytical frequencies.I /19T.2NS.3A1211Ncici). 4<10:j .CEW.2]4 T.2- — — ——s.‘F/: c•---Hl—1211N40 1 2 3 4 5 6 7 8 9 101112Experimental Frequency (Hz)0 1 2 3 4 5 6 7 8 9101112Experimental Frequency (Hz)EEEEEEEEE]ELE,EW3——- - -/----— —— NS•2012345Experimental6 7 8 9 101112Frequency (Hz)11/T[ A—j EW•——— - .3 —) Ns.34EWNS•2T•1 CT320 1 2 3 4 5 6 7 8 9 10Experimental Frequency (Hz)1016.1.4 COMPARISON OF ANALYTICAL AND EXPERIMENTAL MODE SHAPESWhile frequencies are an important measure of dynamic response, vibration mode shapes areperhaps more important since they determine the deformation of the structure. Thesedeformations induce strains and stresses in the structural members. Therefore, it is important thatthese vibration mode shapes are properly represented by an analytical model.Experimental mode shapes were generated relative to the center of rotation of each instrumentedfloor using the programs SLAVE and MAC. This was done so that direct comparisons could bemade with the mode shapes produced by ETABS2. Comparisons were made based on a MACanalysis and also by overlaying the mode shapes on a plot.6.1.4.1 Comparison Based On A MAC AnalysisMAC values were generated between analytical and experimental mode shapes. These valuesare shown in Table 6.1. Overall, the dominant components of the corresponding first and secondmode shapes were well correlated (MAC values of 99% and 100%) while the corresponding thirdand fourth mode shapes showed moderate correlation (MAC values of 81% to 91%). Thesevalues are shown in bold in Table 6.1.Care had to be taken when interpreting MAC values. In particular, it was found that sometimesexperimental and analytical fundamental modes (NS translation, EW translation, and torsional)were all well correlated to each other. For example, the analytical mode EW• 1 shows goodcorrelation with the experimental modes NS• 1, EW• 1, and T• 1 (from Table 6.1 a, MAC valuesare 98%, 100%, and 95%, respectively). Though this result was puzzling at first, it was laterrealized that this made sense since the shape of each of these vibration modes was similar.Therefore, it followed that the correlation between the dominant component of these modeshapes should be quite good. An example of similarities in mode shape components is shown in2The mode shapes produced by ETABS consists of two translational and a single rotational component of each floorat the centre of mass of that floor.102Figure 6.3. In this figure, the dominant component of the analytical fundamental modes areplotted. As can be seen, the shape of the translational modes are virtually identical while theshape of the torsional mode (rotations) is similar to the others.Table 6.1. MAC values (percentage) between experimental and analytical mode shapes.(a) EW component (ex eriinental modes along the top; analytical modes alon the left side)A’X NS.l NS’2 NS’3 NS.4NS•1 84 1 35 11 89 20 7 4 76 37 0 0T’l T.2 T•3 T.41.98 5 13 8 100 2 3 5 95 12 0 0T•1 91 17 10 19 92 1 13 2 89 8 6 3NS•2 4 12 53 4 2 89 10 1 9 69 1 0EW*2 1 12 69 1 1 100 3 0 0 92 1 0T.2 2 13 80 4 4 97 6 2 0 95 0 2NS•3 1 14 34 19 1 58 18 1 0 62 42 5T.3 0 2 4 66 0 5 82 0 0 2 81 25EW•3 0 1 15 74 1 13 89 1 0 8 79 11NS.4 0 1 12 69 1 14 81 0 0 8 72 22T.4 1 0 10 2 1 0 6 67 0 1 4 56EW4 1 1 24 18 3 1 15 90 0 2 8 56(b) NS component (ex erimental modes along the top; anal ,tical modes alon the left side)A\X NS.1 NS.2 NS’3 NS.4 EWl EW 2 EW 3 EW’4 T 1 T 2 T3 T 4NS 1 99 2 0 5 89 5 3 5 88 10 5 3EW•1 72 18 0 1 69 6 9 9 42 3 0 0T.1 20 55 0 5 13 16 6 2 49 54 2 11NS2 1 100 0 0 0 56 7 1 14 69 7 0EW.2 1 73 19 1 0 41 1 1 9 38 3 0T.2 0 77 22 5 0 41 8 9 11 79 39 3NS4 1 9 91 0 0 5 36 17 6 27 81 0T•3 1 12 85 5 0 9 20 16 6 30 86 8EW•3 4 1 18 85 3 9 17 10 1 6 34 81NS 4 4 1 10 92 3 7 29 9 0 4 22 82T.4 5 2 17 74 5 10 12 7 1 6 36 85EW•4 3 2 0 1 6 10 4 8 2 0 3 14(c) rotational component (experimental modes along the top; analytical modes along the left side)A\X NS 1 NS.2 NS.3 NS.4 EW 1 EW.2 EW•3 EW•4 T.1 T’Z T3 T.4NS.l 70 17 1 1 92 0 0 6 99 1 0 1EW.l 64 28 3 1 89 2 0 5 97 6 0 1T’l 70 19 2 1 93 0 1 7 100 2 0 1NS•2 7 94 24 3 15 75 8 3 19 88 3 0EW.2 1 81 30 2 0 95 12 0 0 97 6 0T. 0 82 14 1 1 84 2 0 1 99 0 0NS.3 1 31 98 13 1 40 71 6 3 19 86 2T. 0 12 89 6 0 25 76 1 1 6 94 0EW.3 6 1 0 72 7 3 8 32 2 0 1 90NS.4 3 17 68 78 2 13 31 31 2 10 57 55T4 2 1 14 84 4 0 0 13 2 0 12 81EW.4 10 9 12 33 3 2 14 87 3 3 9 301031.2501.000E0.7500.5000.2500.000Figure 6.3. Dominant components of the fundamental mode shapes for the base model (CT32).6.1.4.2 Comparison Based On Overlaying Mode Shape ComponentsExperimental and analytical mode shapes were normalized such that the displacement at the topstorey was equal to unity. Each component of the normalized mode shapes were then plotted forcomparison. This proved to be a good method. A typical set of these plots is shown in Figure6.4. This figure shows the components for both the analytical mode shape (shown by the solidline) and the experimental mode shape (shown by the diamonds) for the second torsional modeof the base model (CT32). In this example, there is a very good match for all three components.Overall, the dominant component of the corresponding vibration mode shapes matched verywell. In some cases, one or two of the other components also matched really well. In the othercases, the match was not that good. All of the comparative plots for the base model, CT32, canbe found in Appendix H.Based on the results of the MAC analysis and the comparison described above, it was concludedthat the calibrated analytical models have represented the dynamic characteristics of the actualbuilding very well.-5 0 5 10 15 20 25 30 35Level Number1041.500• 1.0000.5000-0.500-1.000-51.5001.0000.5000.000-0.500-1.000-1.500Level NumberFigure 6.4. Comparison of experimental (G) and analytical ( ) mode shape components forthe second torsional mode.1.5001.000j 0.5000.000E -0.500-1.000Translational DOF (EW)00. ii. liii • I... • I... • I... • I. ii. I... • I in in-5 0 5 10 15 20 25 30 35Level Number000Translational DOF (NS)0i•..I....I....I....I....I•••.I.•..I.•.•0 5 10 15 20 25 30 35Level NumberRotational DOFi•••I...•I••••Ir•••I•••.I•...I....I.••.-5 0 5 10 15 20 25 30 351056.2 DESIGN CONSIDERATIONSResults obtained in this study were also used to assess some aspects of building codes. In thissection, periods estimated using code formulae are presented. In addition, seismic demand onthe building at each stage in its construction, based on code response spectra, are also discussed.6.2.1 DESIGN FREQUENCiESCivil engineering structures are usually prototypes, and therefore prediction of its behaviour bothstatically and dynamically must be estimated based on fundamental engineering principles alongwith experience. In the case of City Tower, a dynamic analysis was performed by the structuralconsultants (Bogdonov Pao Ltd.) in order to understand the torsional behaviour of this building.This analysis was performed using the software package ETABS. However, unlike the modelwhich was developed in this study, the design model was more simplified since the purpose wasto determine an envelope of seismic loads.Periods obtained during the design process along with the periods obtained experimentally areshown in Table 6.2. Also shown are periods, T, calculated using expressions in both theNational Building Code of Canada (NBCC) (NRC, 1990) and the Uniform Building Code (UBC,1991). The expression from the NBCC is given by Equation 6.1:T=O.09/i(6.1)where h is the height of the building (in metres) measured from its base, and D is the dimensionof the wall (in metres) which constitutes the main lateral load-resisting system in the directionparallel to the applied forces. The expression from the UBC is given by Equation 6.2:T =where0.1C=—== (6.2)A =Ae[0.2+[PJ ]; -0.9106where h is the height of the building (in feet), Ae is the minimum cross-sectional shear area atthe first storey (in ft2), and De is the wall length which is oriented parallel to the applied forces(in feet).Table 6.2. Comnarison of measured and design periods for the building.Mode NS Translation EW Translation TorsionMeasured Design Measured Design Measured Design- 2.310s - 1.767s - 1.000s1 1.828 S 2.719s 1.552 S 2.335 s” 0.776 s -1.891s** - 1.616s** - -2 0.434 0.505 0.341 0.402 0.274 0.3343 0.205 0.242 0.146 0.202 0.165 -*Jcc *UBCIn general, the design periods tended to be longer than those which were measured. However,this is to be expected since the design periods represent the structural response during anearthquake, while the measured periods represent the structural response during ambientconditions. Also worth noting is that the period calculated using the formula in the UBC camevery close to the measured periods.6.2.2 RESPONSE SPECTRA AND SEISMIC DEMANDSAnother consideration in the design process of the structure is its response if an earthquakeshould occur during its construction. This is a consideration which is often overlooked since thetime period over which the construction occurs is quite short relative to the life of the structure.Usually only the loads which act on the structure as a result of the construction process (such asthe shoring shown in Figure 3.14) are accounted for.To illustrate seismic demands of City Tower as it was being constructed, fundamental(translational) periods for both the NS and EW directions of the building were plotted with theircorresponding location on design “spectra” from both the NBCC and UBC. These spectra werenormalized for Vancouver3.In addition, the fundamental periods estimated from the dynamicfor NBCC “spectra”: v=0.2, Za=Zv, F=1; for UBC “spectra”: seismic zone = 2b, S=1107analysis and the code equations were also included in this plot which is shown in Figure 6.5.According to this plot, it appears that the seismic demand on City Tower, in terms of spectralacceleration, was very high at the onset of construction but gradually decreased as the buildingwas erected. In addition to this, the seismic demand corresponding to the periods obtainedexperimentally, analytically, or by using the code equations are similar.Quantifying seismic demand in terms of spectral acceleration, though, is very misleading. Inparticular, while there is a high spectral acceleration early on in construction, only a portion ofthe total building mass is present. Therefore, the actualforce acting on the structure is about thesame. In order to demonstrate this, base shear and overturning moments were calculated inaccordance with clause 4.1.9.1 of the NBCC. This was done using the fundamental translationalperiods obtained from the five ambient vibration tests at City Tower. The results appear inFigure 6.6. In this figure, the base shear is shown by the bars while the overturning moments areshown by the lines. As can be seen, the seismic demand in terms of base shear is constantthroughout the construction phase. The overturning moment, however, increases as the buildingincreases in both height and weight. Overall, it would appear the seismic demand on thestructure during its construction phase is either lower or equal to the demand corresponding tothe finished structure.One final note should be made about the proximity of the frequencies as the building wasconstructed. As can be seen in either Table 5.3 or Figure 5.16, as the height of the buildingincreases, frequencies corresponding to the higher modes come very close to the fundamentalfrequencies. Therefore, it is likely that these modes will get excited thereby contributing to thedynamic response of the structure during an earthquake. This confirms a provision in the NBCCwhereby a portion of the lateral loads is concentrated at the top of the structure (NBCC clause4.1.9.1(13)) to account for the contribution of higher modes.1080.7 -SEISMIC RESPONSEFACTORS PERIODS0.6-_______NBCC 0 ExperimentalL)05- UBC C Dynamir.-)N 0.4-cAnalysis0.3-z0.2-——c0.1-EW DIRECTION0.0—-0.0 0.2 0,4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0Period (sec)0.7-SEISMIC RESPONSE PERIODSFACTORS0.6 -NBCC Experimental0.5- Dynami0.4-0.3-— —c2 0.2-———————_——a—0.1-NS DIRECTION0.0- I• I• I•1•1•1• 1•1•1•1•1• 1•1•1•-0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0Period (sec)Figure 6.5. Spectral Acceleration curves from the NBCC and UBC building codes. Also shownare periods for the EW and NS directions obtained from 0 measurements, codeequations (0 NBCC and UBC) and C dynamic analysis.10910000- -1000008000- -- 80000> 6000- •- -60000 ‘C- -40000-20000C- 0Stage in Building’s ConstructionFigure 66. Base shears and overturning moments for the building, during its construction phase,determined using procedure outlined in the NBCC (R=3.5).—0——— M-EWF0 M-NS_______________2000 -CT1O CT15 CT2O CT25 CT32110CONCLUSlIONSA number of conclusions can be drawn from the results of this investigation. These have beengrouped into four sections; namely Ambient Vibration Testing, General Dynamic Behaviour,Special Dynamic Behaviour, and Analytical Analysis.AMBIENT VIBRATION TESTING• Determining dynamic characteristics of a building using ambient vibrations and signalprocessing functions is a very practical and useful method.• Reliable estimates of damping are very difficult, if not impossible, to obtain from ambientvibration records.GENERAL DYNAMIC BEHAVIOUR• Asymmetry in building mass distribution can lead to significant rotational motion and modalcoupling. Therefore, the dynamic consequences of setbacks should be carefully considered inthe design of a building.• The shape of the vibration modes remain invariant with the increase in building height.• Modal frequencies decrease with increase in building height and mass (obviously). In addition,the spacing of the frequencies corresponding to the higher modes and the fundamental modesdecreases as the building height increases. Also, translational modal frequencies are moresensitive to changes in height compared with torsional modal frequencies.SPECIAL DYNAMIC BEHAVIOURThe following conclusions are limited to the type of building considered herein. Moreover, thebehaviour described below is for low amplitude vibrations. This behaviour may change duringhigh amplitude vibrations.• Architectural components do not appear to affect the frequency of vibration or the shape of thevibration modes. In addition, there is no significant changes in damping levels during ambientlevels of vibration.• The building core, which is often referred to as a shear wall, deforms in flexure duringtranslational modes of vibration. There in no vertical motion of the core associated with thetorsional modes of vibration.• There is no significant base motion associated with this building. This can be attributed to theunderlying soil which is very stiff as well as the stiffening effect created by the underground111parking structure.ANALYTICAL ANALYSIS• The dynamic behaviour of this building, in terms of frequencies and mode shapes, can beaccurately represented using dynamic analysis.• The expressions for estimating fundamental translational periods in building codes such as theNBCC and UBC appear to be reasonable for low levels of vibration.• The calculated base shear and overturning moments for this building, during its constructionphase, do not exceed those expected during its service life. Therefore, assessing these demandson a building of this type, during its (short) construction phase, does not seem warranted as partof the design process.112RECOMMENDATIONS FOR FUTURERESEARCHWhile this project explored many aspects of the dynamic response of this building, there areseveral additional aspects worth studying. First, an analysis of the soil-structure interaction ofthis building could be performed using appropriate signal processing methods. Second, furtherrefinements could be made to the ETABS analytical model to improve the correlation betweenthe analytical and experimental mode shapes and corresponding periods. Finally, a more detaileddynamic analysis could be performed using the ETABS models. In particular, stressdistributions throughout the structure, resulting from a design earthquake, could be studied.Further, this analysis could be repeated using simplified models of the building to determinewhat level of detail is warranted in this type of analysis.In future ambient vibration studies of buildings with configurations similar to City Tower, thesensor layout used for the last test, CTI’C, is recommended. A great deal of information wasobtained using this setup, and in conjunction with the software program SLAVE, well refinedmode shapes were obtained. In addition, the length of the measurements (data segments) shouldbe increased to improve the resolution and reduce the bias and random errors associated with thesignal processing functions.It would be interesting to conduct another ambient vibration survey of City Tower several yearsfrom now to determine if there have been any significant changes in its dynamic behaviour.However, this may be difficult to implement since public reaction to a “dynamic test” may beunfavourable.Finally, VISUAL could be modified to incorporate the slave node generator routine used in theprogram SLAVE. This would make the analysis of building mode shapes more efficient in termsof time and computer disk space.113NOMENCLATURECW(f) coherence windowf frequency (Hz)f Nyquist frequency (Hz)Af frequency resolution/increment (Hz)G(f) power spectral (autospectral) density functionH(o) transfer functionI-s segment length (points)M(f) potential modal ratio functionP(w), {P()) loading function in the frequency domain - single component and vectorPW(f) phase windowt time (sec)At time increment (seconds)T period (seconds)T(f) transfer functionx(t), { x(t) } displacement response in the time domain - single component and vectorX(o), {X(c)) displacement response in the frequency domain - single component and vectorX*(o), {X*(0)} complex conjugate of the displacement response - single component andvectorX(w), [X(cD)} acceleration response in the frequency domain - single component and vectory(t) modal amplitude in the time domain0, { 4} time invariant mode shape - single component and vectormodulus of the transfer function, T(f)y2(f) coherence function9(f) phase functionradial frequency (equal to 2irf) (radians/s)114ABBREVIATIONSANPSD Averaged Normalized Power Spectral DensityASD Autospectral DensityAV Ambient VibrationCF Coherence FunctionCSMIP California Strong Motion Instrumentation ProgramCT1O City Tower ambient vibration test - 10 levels completedCT1 5 City Tower ambient vibration test - 15 levels completedCT2O City Tower ambient vibration test - 20 levels completedCT25 City Tower ambient vibration test - 25 levels completedCT32 City Tower ambient vibration test - 32 levels completedCTI’C City Tower ambient vibration test - Tower CompletedEW East-West (direction)FBA Force-Balance-AccelerometerFRF Frequency Response FunctionHBES Hybrid Bridge Evaluation SystemNBCC National Building Code of CanadaNS North-South (direction)PF Phase FunctionPMR Potential Modal RatioPSD Power Spectral DensitySISO Single Input Single OutputTF Transfer FunctionUBC Uniform Building Code (or University of British Columbia)w.r.t With Respect To115REFERENCESAccredited Standards Committee S2, Mechanical Shock And Vibration. (1990) AmericanNational Standard - Vibration OfBuildings - Guidelines For The Measurement OfVibrations And Evaluation OfTheir Effects On Buildings (ANSI S2.47-1990), New York,U.S.A.Baker McGarva Hart Inc. (1992) City Tower, 1155 Homer Street, Vancouver, B.C.Architectural Contract Drawings (A1.01-A10.02). Vancouver, B.C., Canada.Bendat, J.S., Piersol, A.G. (1993) Engineering Applications of Correlation and SpectralAnalysis, Second Edition. John Wiley and Sons, Inc., New York, U.S.A.Binstock, A., Babcock, D.P., and Luse, M. (1991) HP LaserJet Programming. AddisonWesley, Don Mills, Ontario, Canada.Bogdonov Pao Associates Ltd. (1992) City Tower, 1155 Homer Street, Vancouver, B.C.Structural Contract Drawings (S1-S21). Vancouver, B.C., Canada.Borland International Incorporated. (1991-92) Borland C++ Version 3.1. Scotts Valley,California, U.S.A.Brownjohn, J.M.W. (1988) Assessment Of Structural Integrity By Dynamic Measurements.Ph.D. Thesis, University of Bristol, United Kingdom.celebi, M., Safak, A. et al. (1987) Integrated Instrumentation Plan For Assessing The SeismicResponse OfStructures - A Review Of The Current USGS Program. USGS Circular 947.California, U.S.A.Clough, R.W. and Penzien, J. (1975) Dynamics of Structures. McGraw Hill, New York,U.S.A.CSI, Ltd. (1992) ETABS Three Dimensional Analysis of Building Systems - Users Manual.Computers and Structures, Inc., Berkeley, California, U.S.A.Dally, J.W., Riley, W.F., and McConnell, K.G. (1993) Instrumentation For EngineeringMeasurements, 2nd Edition. John Wiley and Sons, Inc., New York, U.S.A.Diehl, J. (1991) Ambient Vibration Survey: Application, Theory AndAnalytical Techniques.Application Note #3. Kinemetrics Systems, Pasadena California, U.S.A.EDT Ltd. (1994) U2, V2, and P2, Manual Version 2.0. Experimental Dynamic InvestigationsLtd., Vancouver, B.C., Canada.Ewins, D.J. (1984) Modal Testing: Theory and Practice. John Wiley and Sons Inc., NewYork, U.S.A.Felber, A.J. (1993) Development Of A Hybrid Bridge Evaluation System. Ph.D. thesis,University of British Columbia, Canada.116Hewlett-Packard Company. (1990) HP PCL 5 Printer Language Technical ReferenceManual. (HP Part #33459-90903).Humar, J.L. (1990) Dynamics of Structures. Prentice Hall, New Jersey, U.S.A.KDAC 500. (1989) Keithley KDAC500 Data Acquisition and Control Software (Document#501-915-01 Rev. C; Software: KDAC500IB Version 1.4, P/N: 500-886; IBIN-AInterface card: Document # 501-910-01 Rev. C). Keithley Instruments Inc., Cleveland,Ohio, U.S.A.Keithley 575. (1989) Model 575 Measurement and Control System (Document # 575-901-01Rev. C). Keithley Instruments Inc., Cleveland, Ohio, U.S.A.Kernighan, B.W. and Ritchie, D.M. (1988) The C Programming Language, 2nd Edition.Prentice Hall, New Jersey, U.S.A.Luz, E. (1992) Experimental Modal Analysis Using Ambient Vibration. International JournalOf Analytical And Experimental Modal Analysis (v7 nl pp.29-39).Marshall, R.D., Phan, L.T., and celebi, M. (1994) Full-Scale Measurement OfBuildingResponse To Ambient Vibration And The Loma Preita Earthquake. Fifth U.S. NationalConference on Earthquake Engineering Proceedings (Volume II, pp. 66 1-670).Microsoft Corporation. (1991) Microsoft MS-DOS User’s Guide and Reference - OperatingSystem 5.0.Newland, D.E. (1975) An Introduction to Random Vibrations and Spectral Analysis.Longman Group Ltd., New York, U.S.A.NRC (1990) National Building Code Of Canada. Associate Committee Of The NationalBuilding Code, National Research Council Of Canada, Ottawa.Okauchi, I., Miyata, T., Tatsumi, M. and Kiyota, R. (1992). Dynamic Field Tests and Studies onVibration Characteristics ofLong Span Suspension Bridges. ISCE Journal ofStructural Engineering and Earthquake Engineering, 9 (pp. 89-100).Pardoen, G.C. (1983) Ambient Vibration Test Results Of The Imperial County ServicesBuilding. Bulletin Of The Seismological Society Of America (Volume 73, No. 6, pp.1895-1902).Rojahn, C. and Matthiesen, M. (1977) Earthquake Response And Instrumentation OfBuildings.Journal Of The Technical Councils of ASCE.Shakal, A., Huang, M., Reichle, M., Ventura, C., Cao, T., Sherburne, R., Savage, M., Darragh,R., and Petersen, C. (1989) Csmip Strong-Motion Records From The Santa CruzMountains (Lomna Prieta), California Earthquake Of 17 October 1989. Report # OSMS89-06. California Department of Conservation, Division of Mines and Geology, Officeof Strong Motion studies.Stroustrup, B. (1993) The C++ Programming Language, 2nd Edition. Addison Wesley,New York, U.S.A.117To, Ngok-Ming (1982) The Determination Of Structural Dynamic Properties Of ThreeBuildings In Vancouver, B.C., From Ambient Vibration Surveys. M.A.Sc. thesis,University of British Columbia, Canada.UBC (1991) Uniform Building Code. International Conference of Building Officials,Whittier, California, U.S.A.1186TTAPPENDIX ADETAILS OF AMBIENT VIBRATION SURVEYSThis appendix shows the exact location of each sensor for each of the six City Tower ambientvibration surveys. In addition, filenames, attenuation and filter settings on the signal conditioner,and the nodes corresponding to the VISUAL input files are presented.A.1 BUILDING INSTRUMENTATIONFigures A. 1 to A.6 show the south elevation of the building at the particular stage in constructionwhen the ambient vibration measurements were taken. Instrumentation on all of the floors whereambient vibration measurements were taken, is shown in these figures. In addition to this, floorelevations (relative to the ground floor) of each level are also shown.A.2 EXACT SENSOR LOCATIONS AND CONDITIONING DETAILSA.2.1 AMBIENT VIBRATION MEASUREMENTSSpecific details about the measurements are summarized in tables A. 1 through A.6. These tableslist each floor which was measured, along with the filename containing the ambient vibrationdata (in *.bbb format) and conditioning details (attenuation and filters). Each channel numberhas been cross-referenced with the node number used in the structure file used to assemble andanimate the mode shapes in the program VISUAL.A.2.2 SENSOR LOCATIONSEach of the sensor setups is cross-referenced with figure A.7. The latter figure shows the exactlocations and orientations of all of the setups described in the aforementioned tables.120The following legend applies to figures A. 1 through A.6.LEGEND+ POSITIVE orientation of FDA -horizontalPOSITIVE orientation of FDA -out of plane of pagePOSITIVE orientation of FDA -into plane of page() FDA number & location0 FDA number & additionallocation on same floorfloor elevation (m) elevation (It)15 +38.30 +125.6714 +35.66 +117.0013 *33.02 +108.3312 +30.38 +99.6711 +27.74 +91.0010 +2510 +82.339 +22.45 +73.678 +19.81 +65.007 +17.17 +56.336 +14.53 +47.675 +11.89 +39.004 +9.25 +30.333 +5.60 +21.672 +3.96 +1 3.00I.I1:.:j [.1II.!J1Ik!IL®IL®III.. I IIILcIII Ii1 I_______________________I II.!i]II I[I.1;)ii_iLF’1 0.00 0.00P1&P2j]______1I°1 l1.) P5II P6Figure A. 1. Instrumentation of thebuilding for the first ambient vibrationsurvey; 10 levels completed (CT10).-9.40 -30.83Figure A.2. Instrumentation of thebuilding for the second ambient vibrationsurvey; 15 levels completed (CT15).121floor elevation (m) elevation (ft)26 +67.36 +221.0025 +64.72 +21 2.3324 +62.08 +203.6723 +195.0022 +56.79 +1 86.3321 +54.15 +177.6720 +51.51 +169.0019 *48.87 +1 60.3318 +46.23 +151.6717 +143.0016 +40.94 +1 34.3315 +38.30 +125.6714 +35.66 +117.0013 +33.02 *108.3312 ÷30.38 +99.6711 +27.74 +91.0010 +25.10 +82.339 +22.45 +73.678 +19.81 +65.007 +1 7.17 *56.336 +1 4.53 +47.675 +11.89 +39.004 +9.25 +30.333 +6.60 *21.672 ÷3.96 +13.00iiri .1..III I IHñ H41H.11Hi[iI [.1 ILIIII I1[1[.111[1E.I.IIIIIIiiIIIII ,I [. I III :lii8II:1 II4H1.1II1Ij I.U1III1 0.00 0.00P1 & P2P3 & P4IIp5195 -Q fl -30.83Figure A.3. Instmmentation of thebuilding for the third ambient vibrationsurvey; 20 levels completed (CT2O).__IFigure A.4. Instrumentation of thebuilding for the fourth ambient vibrationsurvey; 25 levels completed (CT25).12232 .83.21 .273.0031 *80.57 +264.3330 +255.6729+75.29 +247.0028+72.64 +238.3327 +70.00 +229.6726 +67.36 +221.0025+64.72 +21 2.3324 +62.08 +203.6723 +195.0022 +56.79 +1 86.3321 +54i5 +177.6720+51.51 +1 69.0019 +48.87 +1 60.3318+46.23 +151.6717 +143.0016 +40.94 +1 34.3315 +38.30 +125.6714 +35.66 +117.0013 +33.02 +108.3312+30.38 .99.6711 +27.74 +91.0010+25.10 +82.339 +22.45 +73.678+1 9.81 +66.007 *1 7.17 .56.336+1 4.53 +47.675 .11.89 .39.004.9.25 .30.333+6.60 *21.872 +3.95 +13.00______________________________[I____ ___[.1___________ ____________ ____________ ____________ _ __ _____________________ __ __ __ __ __ __ __ __ __ __ __ __ _____________________ __ __ _______ ____________________I._ _ _‘VII 1:1:1V.._Uii_[1II..II [:1I [I1 0.00 0.00____IIII.1II I II.Figure A.6. Instrumentation of thebuilding for the final ambient vibrationsurvey; tower completed (CTTC).P51.1 P6 -9.40 -30.83I(8)l(craneul Ifloor elevation (m) elevation (ft)L!: Hii1III .j.I1ri[1.fl[L®[)[i[1ITiII III II.]..1.. ..Ij. IVI IIFigure AS. Instmmentation of thebuilding for the fifth ambient vibrationsurvey; all 32 levels completed (CT32).123HCDH•T1Ci)CD(7,0C,C,0017ZI-3CDcmHC.,CDC.,I0CD-4a)01.C.I\)-CCDCDO- (0gggg-C)QC)C)C)C)——-—.0—. O-=.)CD e-a) CD rS)I’.)I’.)rs,a)CS)a)CS)?6)rS)r.r.)(TI010101(71010101nCflbi.!0::::‘ ..0 3000033CDCO-= -8- 00C)CDCDCDCD00-— Coopc8 :c-.’3 :‘__—J3.j)0oCD-Jz;5.a)00--DID)a) (DID 0CO -a)a) —I--—-a—--—--—C.)3CD3-0- CDCDm --ci -II.C.) 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Locations of FBA sensors during the ambient vibration measurements at City Tower.©-ii0.2a0 -JeveiTLCT1O • roving sensorsLEGENDE FBA location & mountNA.— POSITIVE orientation of FBA -horizontalPOSITIVE orientation of FBA -vertical0 FBA number & location0 5 10 20 30 40 50 ft. A number & additionalIi] location on same floor](a) Level P51P6CT1O• roving sensorsQ setup [ph] []setup [pv]12750—JI1ffff’___L>JS L>L_087(c) Level 2 (d) Levels 3-9CT10 roving sensors CTI 0 • reference sensors (Level 9 only)CT1O • roving sensorsI —0 I0 0ED01 :EI—J(e)Level P5/P6_____(f) Level 1_____CT15 • roving sensors CT15 • roving sensorsCT2O• roving sensors CT2O• roving sensorsCT25 • roving sensorsCT32• roving sensorso setup [ph] []setup [pv]128©-—J0__IuffuPIIED0:N1_____(g) Level 1____(h) Level 2CT25 • roving sensors CT1 5 • roving sensorsCT32 roving sensors CT2O • roving sensorsCT25 • roving sensorsCT32 • roving sensors00 0I—JIIU- L[uP’8(i)Level2 ICT32 • roving sensors (setup TH) (j) Levels 3-9CT15 roving sensorsCT2O • roving sensorsCT25 • roving sensorsCT32 • roving sensors129(o) Level 29CT32 • reference sensors(k) Level 14CT1 5 • reference sensors (setup PV,PH)JQCT1 5 • reference sensorsCT1 5 • roving sensors (placed on top of columns)(1) Levels 11-25CT15 • roving sensorsCT2O • roving sensorsCT25 roving sensorsCT32 • roving sensors(m) Level 19• reference sensors(n) Level 24CT25 • reference sensors(p) Level 32CT32 • roving sensors130_jJ 67 0(q) Levels 27/30 (r) Levels 29/30CT32 • crane measurements CTTC • setup Dl0__(_____collocation plate4____(s) Levels 17-26 (t) Level 29CTTC • roving sensors CTTC • roving sensorsCTTC • collocation setup__L°(u) Level 30CTTC • reference sensors131t€:jAPPENDIX BAMBIENT VIBRATION DATA ACQUISITIONSOFTWARE (AVDA) - OPERATING INSTRUCTIONSB.1 OVERVIEWB.1.1 DESCRIPTIONThe software program AVTEST is one of the original components of the HBES software. Itsfunction is to instruct the Keithley analog-to-digital (A/D) converter to sample data at a specifiedrate while plotting the channels real time on the screen. It also extracts this data and stores it onthe hard drive of the field computer. During the course of this research, this program hasundergone several revisions to enhance its capabilities and to improve quality control whenacquiring data.B.1.2 REVISIONS TO AVTESTModifications to the AVTEST source code were performed using a Borland C/C++ compiler(Borland International Inc., 1992) along with the library provided by the Keithley 500/B software(KDAC, 1989). All routines are written in C (Kernighan & Ritchie, 1988). Newer versions ofthe program were named AVDA - an acronym for Ambient Vibration Data Acquisition.Table B.1 lists all versions of AVDA which were released during 1992-1994. Following thistable is a description of all enhancements which were made to this program.Table B.1. AVDA versions and compile dates.Program Name Program Version Compile Date/TimeAVTest 0.1 07-09-92 ll:02aAVDA 0.2 06-03-93 l2:2lpAVDA 0.2.1 10-25-93 l2:44pAVDA 0.3 11-26-93 10:21aAVDA 0.3.1 02-07-94 ll:47aAVDA 0.3.2 03-23-94 4:OlpAVDA 0.3.3 04-09-94 l2:35pAVDA 0.413 04-29-94 l2:l7pAVDA 0.4.1 05-31-94 ll:31aAVDA 1.0 l5-lO-9412:34p133AVTEST and subsequent versions of AVDA were used extensively in several ambient andimpact vibration studies. Through this use, several limitations of the program were identifiedand subsequent improvements were made to the program modules.B.1.2.1 Data Saturation CheckOne modification involved adding a routine that would check each individual segment forsaturation (i.e. clipping) prior to storing it on disk (ver. 0.2). If any saturation was detected, all ofthe data collected in that particular segment would be discarded automatically and the acquisitionrepeated. In some cases though, the data segments saturated at the beginning of the acquisitionand the user had to wait for the program to collect the entire segment - and then discard it. Thisrepresented a waste of valuable time. To improve this, an option was added which would allowthe user to discard the segment manually (ver. 0.413). This modification provided automated andimproved quality control over the collected data.B.1.2.2 Check For Existing Filenames And Remaining Disk SpaceIn another revision of the program, a routine was added which would check whether or not thename of a data file was already in use, and if so, to warn the operator (ver. 0.2.1). In addition tothis, the available hard disk space was checked to ensure that all of the data could be stored onthe disk during the program’s execution (ver. 0.3). These modifications were added since thesemistakes occurred frequently; leading to loss of time and data.B.1.2.3 Addition Of Sounds Corresponding To Certain OperationsAnother modification involved providing feedback as the program performed its variousoperations (ver. 0.2). This was done by associating unique sounds to these operations. Theseinclude such actions as calibration, accepting and rejecting a segment (manually orautomatically), an input error if a filename was already in use or if there was insufficient diskspace or memory, and finally notification that all of the data had been collected. Thus theoperator could concentrate on other activities unless he/she hears a sound requiring his/her134attention.B.1.2.4 Increased Channel Capacity And Increased Size Of Data ArraysThe introduction of impact testing into the dynamic testing program at UBC prompted the needto rewire the A/D converter so that 16 channels of data could be acquired instead of only 8channels. Consequently, AVDA also had to be modified to account for this change’ (ver. 0.3).Also, since higher sampling rates would be used, memory had to be increased. This was done byusing far data routines in AVDA for dynamically allocated memory as well as modifying aparameter in the BATch file k. bat. The latter parameter is described in more detail in §B .3.3.Along with increasing the number of data acquisition channels, the size of the data segments wasincreased. Hence, beginning with version 0.32, the length of each data segment has beenembedded in the output file header. This was a missing piece of information in the file headersand was necessary since segment lengths could now be larger than the default value of 4096.These files are still compatible with the program ULTRA. The details of the output file headerappear in §B.3.4.B.1.2.5 Flexible Sensor CalibrationYet another modification involved providing alternative sensor calibration options. Instead ofcalibrating before and after collecting the data, or not at all, the operator has the option ofcalibrating before and/or after (ver. 0.4B) and/or can simply monitor the signals without storingthe data on disk (ver. 0.4.1).The final version of this program, which was released along with this thesis, was version 1.0. A1This in an important change and the operator should note that versions of AVTEST and AVDA prior to this version(0.3) WILL NOT WORK CORRECTLY since they assume that the Keithley A/D converter is wired for 8 channels,NOT 16 (as was the case at the time of this writing).21n version 0.3, the segment length defaulted to the maximum allowable segment length. As of version 0.3.1, thesegment length is the smaller of this number and the number of points to be acquired.135copy of the program source code and executable files are available from the computer graphicslab of the Civil Engineering Department.B.2 INSTALLATION AND SYSTEM REQUIREMENTSThis program should run on any PC computer with a 80286 processor or higher, a CGA monitor,and at least 20 Mb of hard disk space (for storing the data files). In addition to this, an IBIN-Ainterface card which communicates with the Keithley 575 A/D converter must be installed in thecomputer and properly configured (see the documentation provided with the card for furtherinfonnation).This program works correctly with MS-DOS 5.0 and will probably work with other versions aswell. The system configuration should be kept simple, and it is very important that theWindows extension SMARTDRV.EXE is not installed since it interferes with the samplinginterrupts.This program works well in conjunction with the DOS utility DOSKEY (see a DOS 5.0 manualfor details). This utility retrieves previous command lines thus eliminating the need to retype allof the input parameters at the DOS prompt. Usually, most of these parameters remain the samethroughout the test. Also, the parameters which change more frequently, such as the filename,appear at the end of the parameter list so that they can be readily modified.The files AVDA.EXE, AVDA.TBL and K.BAT must be copied into the directory containing theKeithley drivers. For more information of the installation of the latter drivers, refer to theKeithley 500/B documentation.B.3 PROGRAM EXECUTIONB.3.1 RUNNING THE PROGRAMPrior to executing AVDA, the memory resident program K500.EXE must be executed. Thelatter program sets up its own kernel in memory and then executes other programs including136AVDA (see the Keithley 500/B documentation for further information). This task is facilitatedby using a BATch file called k.bat. This BATch file takes several arguments. The first argumentis the name of the data acquisition program (in this case AVDA). The remaining arguments arepassed on to AVDA. In other words, to run the program, type the following at the DOS prompt:k avda <argl> <arg2>The arguments (arg 1, arg2, etc.) are described in the following section (B .3.2). if no argumentsare specified, the program version and a descriptive list of the arguments is displayed on thescreen as shown in Figure B. 1. If all of the arguments are valid, then they will be echoed to thescreen prior to acquiring the data. This allows the user to verify the parameters beforeproceeding. Warning messages, if any, will also be displayed.UBC Civil Ambient Vibration Data Acquisition Program — Version 1.016 Channel Interactive — October 1994written by N. Schuster, A. Felber, and S. YeeAVDA Freq NumPts NuinChan GGain Calib Sat filenameFreq : Nyquist Frequency [Hz] (0.1—1000)NuinPts : Total number of Points in k (1,2,4,8,16,32,64,128)NuinChan : Number of Channels to be Sampled (1-16)GGain : Global gain (1,2,5,10)Calib : calibration: <b> before, <a> after, <m> monitor, <n> noneSat : allowable consecutive saturation points per segment (0—1024)——> specify —1 to disable saturation check routinefilename : filename prefix for storageFigure B.l. Instructions displayed when AVDA is executed with no command line arguments.For example, if the following line is entered at the DOS prompt:k avda 20 32 8 5 ba 2 beerOlthen the screen shown in Figure B.2 will appear when AVDA is executed.At this point, the user can proceed or terminate the program if any of the parameters areincorrect, if the user chooses to proceed, then the program will do the following:(a) if a BEFORE calibration was specified:• acquire and store data for the sensor calibrations before the test• scan all channels afterwards so that the user can set the attenuation levels137(b) if a MONITOR calibration was specified• acquire and display data from each sensor (no data is stored on disk)• scan all channels afterwards so that the user can set the attenuation levels(c) acquire the data• collect as many segments as necessary• check each segment for saturation (if requested)• store the data on disk(d) if an AFTER calibration was specified:• acquire and store data for calibrations after the testWhile acquiring the data (step “c” above), the user can press <ESC>3followed by <R> tomanually reject the segment. Alternatively, after pressing <ESC>, the user can press <X> toterminate the program prematurely4.UBC Civil Ambient Vibration Data Acquisition Program — Version 1.016 Channel Interactive — October 1994written by N. Schuster, A. Felber, and S. YeeNyquist Frequency 20.00 HzTotal Number of Points 32768Number of Channels 8Global Gain 5Calibration BEFORE AFTERAllowable Consecutive Saturation Points 2Filename Prefix : beerOlDisk Space Required (bytes) 1228800Available Disk Space (bytes) 12345678Available KEITHLEY memory per channel 12762Available CORE memory per channel 45964Segment Length : 8192Number of Segments : 4Duration of Measurement : 0:13:39Press any key to proceed or ‘X’ to terminateFigure B.2. Echo of the command line arguments.3Pressmg the ESC key is necessary in order to interrupt the real-tune graphing routine (GRAPHRT). Note that thisdoesn’t interrupt the sampling routine (BGREAD) which will continue in the background until it is fmished or untilthe user presses the <R> or the <X> key.4Before exiting, AVDA will warn the user if the length of the data array which is already stored on disk is not apower of 2. It will also try to update the “Number of Points” field in the output file header to reflect the actualnumber of data points saved on disk.138B.3.2 COMMAND LINE ARGUMENTSThe following list is a detailed description of each parameter which must be specified on thecommand line.B.3.2.1 Nyquist Frequency (Freq)The Nyquist frequency, represents the maximum frequency that can be resolved from thedata. This determines the sampling rate that the program will use when acquiring the data; itsvalue is equal to twice the Nyquist frequency. Legal values of the Nyquist frequency must be inthe range of 0.1 to 1000 Hz, though an upper limit of 100 Hz is recommended for slowermachines such as the portable Compaq II.B.3.2.2 Number Of Points To Acquire (NumPts)This is the total number of points (in kilobytes) that the program will collect for each chatinel.This number is specified using one of the index numbers shown in the following table.Index Number of points____________per channel1 10242 20484 40968 819216 1638432 3276864 65536128 131072Due to DOS memory limitations, the data arrays for all of the channels being sampled must becollected in one or more data segments of equal length. The length of these segments depends onhow much memory has been allocated by the K500.EXE module as well as the number ofchannels being sampled. AVDA determines the maximum feasible segment length prior toacquiring the data, and displays this value in the screen echo (see Figure B.2). Typical segment139lengths, L5, include 4096, 8192, and 16384 points.Note that the segment length and the Nyquist frequency affect the frequency resolution of thedata. The frequency resolution, Af, can be determined as follows:LFor example, the frequency resolution for a 4096 point segment with a corresponding Nyquistfrequency of 20 Hz is equal to 2*20/4096 0.00976 Hz.B.3.2.3 Number Of Channels (NumChan)This is the number of channels to be sampled by the AID converter. This number must be in therange of 1-16. At the time of this writing, channels 1 through 8 are used for digitizing the signalsfrom the Kinemetrics signal conditioner while the remaining channels receive input from the 8BNC connectors on the Keithley A/D converter.B.3.2.4 Global Gain (GGain)The Keithley 575 AID converter transforms the analog signals into 16 bit integer values. Thiscorresponds to a resolution of 216 or 65536 steps, which are used to represent the shape of thetime signal. In order to optimize the signal resolution, a global gain is applied to the incomingsignal. Note that the global gain defines the threshold of the time signal; which is numericallyequal to ±10/(GlobalGain).Legal values of global gains are shown in the following table:sensor output voltage global gain(V)±1 105±5 2±10 15AVDA limits the segment lengths to 16384. This is due to the fact that the Keithley routines do not allow arrayslarger than 32767 points.140To illustrate this process, consider the plots shown in Figure B.3. This figure shows a sine wavewith an amplitude of 2 volts which has been digitized using the four possible global gains. Ascan be seen, the signal resolution improves with increasing global gains. However, the globalgain must be chosen to avoid clipping the signals. In this case, a global gain of 10 clips the sinewave while a global gain of 5 is the optimal gain that should be used to represent the signal. Forthe FBA-l 1 accelerometers, a global gain of 5 is typical.—GlobalGain: 15--5 -Figure B.3. A digitized sine wave and corresponding global gains.05-10 05 1 15 2 25 3 35 4 4.5 5 55 6time250 05 1 15 2 2.5 3 35 4 45 5 55 6timeci)C-25ci)C0 05 1 15 2 25 3 35 4 45 5 5.5 6timeI I I I I I I0 05 1 15 2 25 3 35 4 45 5 55 6time141B.3.2.5 Calibration Options (Calib)This option is used to ensure that all of the Kinemetrics FBA- 11 sensors are properly connectedto the signal conditioner and are functioning colTectly. Calibrations can be performed beforesampling, after sampling, or not at all. These calibration records are also stored to disk using thefile naming convention discussed in §B.3.2.7. The correct procedure for sensor calibration isdiscussed in §B .4. An alternative to calibration is to use the MONITOR option. This is similarto the calibration option except that the data is not stored on disk.The calibration options are activated by specifying one or more of the parameters summarized inthe table below. If more than one parameter is used, then they should be specified as a singlestring. For example if the user wants to calibrate before and after sampling the data, he/sheshould specify “ba” or “ab” for the calibration option.option parameter program actionBEFORE b sample and save calibration data before data samplingAFTER a sample and save calibration data after data samplingMONITOR m sample and display each channel before data samplingNONE n data sampling onlyB.3.2.6 Allowable Number Of Consecutive Saturation Points (Sat)After each data segment is acquired, and prior to storing the data onto disk, the program checkseach data array to ensure that no clipping has occurred. Clipping occurs if the signal amplitudewas higher than the threshold set by the global gain (see §B.3.2.4 for details). If clipping hasoccurred in any of the channels, then all of the data segments are discarded and the measurementrepeated. Because of time constraints, several rejections might be undesirable. Therefore, if theuser is willing to tolerate some saturation points, he/she may specify the number of consecutivepoints that will be ignored by this routine.Legal values of Sat must be in the range of 0-1024. Values of 0 or 1 provide good qualitycontrol of data though values of up to 5 have been used in some bridge tests. This routine canalso be disabled by specifying a negative one (-1) for the Sat parameter. The latter option can142help accelerate the data acquisition process.B.3.2.7 Filename Prefix (Filename)This program uses the DOS filename convention which consists of 8 characters with a 3character extension. Due to this limitation, the first 6 characters (the filename prefix) of thesefilenames are specified by the user while the remaining two characters are used by AVDA tospecify the type of file being created as well as the channel number. The extension appended tothe filename is “.bbb”. This filename convention is illustrated below:optional prefix extensionprefix__.bbbfile type: 1 L channel numbera = after calibration (in hex)b = before calibration0= data fileNote that since only one character is available to specify the channel number, hex (base 16)notation is used. A conversion table from decimal to hex is shown below.channel# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16label 1 2 3 4 5 6 7 8 9 A B C D E F 0B.3.3 MEMORY CONSIDERATIONSAs discussed in §B.3.1, AVDA is executed from another program, K500.EXE, which sets up itsown kernel in RAM for video and for data arrays. The memory available for data arrays createdby the Keithley 500 routines depends on a parameter specified in a BATch file named k.bat. Thecontents of this file are shown below for reference:echo offif exist %1 goto run_itif exist %1.com %O %1.com %2 %3 %4 %5 %6 %7 %8 %9if exist %1.exe %O %1.exe %2 %3 %4 %5 %6 %7 %8 %9run_itK500 -m 12800 -c AVDA -q %1 %2 %3 %4 %5 %6 %7 %8 %9143Lines 2-4 appends the appropriate extension to the data acquisition program so that the K500program can execute it correctly. The last line executes the K500 program. The -m 12800parameters shown on the last line instructs the Keithley software to allocate 12800 16-bytememory segments for use as data arrays. This number limits the length of the data arrays whichcan be collected before it is stored on disk and the memory purged. The user can optimize theamount of space used for data arrays by adjusting this number. However, the size of this arrayalso reduces the amount of memory available for use by AVDA. To facilitate optimizing thisnumber, AVDA displays the size of these data arrays (in terms of the number of data pointswhich can be stored in memory for a given number of channels). These values can be seen in theecho screen shown in Figure B.2. Adjustments should only be made to the number following “-m”. The other parameters should NOT be modified.B.3.4 OUTPUT FILE FORMATAll of the output files are stored in binary format. The data (in units of volts) is preceded by aheader which identifies the file and includes all pertinent information. Specific details of this fileare given below. A routine for reading these data files appears in §B.5.file content (in sequence) variable type length (bytes)identification string char 42reserved long 4segment length (points) long 4sampling interval (sec) float 4number of sampled points, N long 4channel number (on Keithley) int 2global gain int 2filename char 80site (currently not used) char 80setup (currently not used) char 80year int 2day char 1month char 1hour unsigned char 1minute unsigned char 1second unsigned char 1data points float 4 * N144B.4 TYPICAL TESTING PROCEDUREA typical setup procedure is as follows:1. Verify connections between Keithley, signal conditioner, and data acquisition computer2. Turn power switches to ON for all of the aforementioned equipment3. Install the sensors at selected locations4. Balance the sensors (if necessary)5. Connect cables between sensors and signal conditioner6. Set the signal conditioner to TEST7.Run AVDA (from the KE1THLEY directory) and verify the input parameters8. If calibrating:(a) set attenuation to 66dB and filters to OUT for all channels(b) press any key to begin sampling(c) after a short BEEP, the operator should turn the key on the signal conditioner from TESTto CALIBRATE.(d) after approximately 1 second, the key should be turned from CALIBRATE to NATURALFREQUENCY and should remain in this position until calibration is complete.(e) once all of the data is acquired 6, inspect the individual calibration records for eachchannel, as they are displayed one by one, to ensure that the sensors are workingcorrectly.(I) turn the key on the signal conditioner back to TEST(g) once all of the records have been displayed, the user has the option of repeating thecalibration, or proceeding. If any of the sensors are not functioning, the problem can beremedied before proceeding.9. Set attenuation and filters for recording10. Proceed with the data acquisition11. If calibrating after the data acquisition, repeat the procedure described in step #8.12. Transfer data files to data analysis computer13. Inspect recorded time histories using ULTRA (for quality control)14. Relocate roving sensors to the next setup.15. Repeat steps 3-14 until the test is finished.If the user wishes to use the MONITOR option in lieu of calibration, the signal conditioner6calibrations are sampled at 600 Hz and 2048 points are collected; this has a duration of 3.4 sec145should be plugged in and the key on the conditioner should be set to OPERATE before any ofthe sensors are moved. This ensures that the filter cards are not overloaded by the movement ofthe sensors as they are being relocated.For further information about calibrating and balancing the FBA- 11 accelerometers, see theoperating instructions (Kinemetrics FBA- 11).B.5 ROUTINE TO READ “BBB” FILESThe following is a generic routine (written in C) for reading the binary files created by AVDA.The source code can be modified by the user to suit the application.#include<stdio. h>#include<stdlib.h>#include<string. h>#include<dos. h>void ReadBBBFile( char *name );1* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *1void ReadBBBFile( char *name ){FILE *fp; 7* file pointer to *.bbb file */long reserved; 7* reserved for future use */long segLen; 1* segment length */long N; 7* total number of pointsmt n; /* Keithley channel numbermt mag; /* global amplitude gainchar filename[80]; /* filename - embedded in data */char site[80]; 7* site *7char setup[80]; 7* setup *7char id[50]; /* identification string *7float del; 7* time increment *7struct date d; 7* date structure *7struct time t; 7* time structure *7long 7* counter *7mt 7* segment number (counter) *7float *data; 7* data array *7mt ns; 7* number of segments *7fpos_t filePos; 7* file position *7const char BBBldentifier[] = “Karg Weissbier ist das beste in der Welt’;7* open file *7if( (fp = fopen( name, “r”) == NULL ){printf(”Error opening input file -- Terminating Program\n” );exit( EXIT_SUCCESS);}1467* header *7printf( “Reading header information.. .\n” );fread( id, sizeof(char), 42, fp );if( strcmp( hi, BBBldentifier ) != 0 ){printf(”Invalid file format! -- Terminating Program\n” );exit(EXIT_SUCCESS);}fread( &reserved, sizeof(long), 1, fp );fread( &segLen, sizeof(long), 1, fp );fread( &del, sizeof(float), 1, fp );fread( &N, sizeof(long), 1, fp );fread( &n, sizeof(int), 1, fp );fread( &mag, sizeof(int), 1, fp );fread( filename, sizeof(char), 80, fp );fread( site, sizeof(char), 80, fp );fread( setup, sizeof(char), 80, fp );fread( &(d.da_year), sizeof(int), 1, fp );fread( &(d.da_day), sizeof(char), 1, fp );fread( &(d.da_mon), sizeof(char), 1, fp );fread( &(t.ti_hour), sizeof(unsigned char), 1, fp );fread( &(t.ti_min), sizeof(unsigned char), 1, fp );fread( &(t.ti_sec), sizeof(unsigned char), 1, fp );/* sort out segment length */if( reserved != 0L )segLen = 4096L; 7* default value (pre 0.3 version of AVDA) *7segLen ( segLen > N ) ? N segLen;ns = N/segLen;7* data *7data = (float *)cal[oc( N, sizeof(float) );{printf(”Memory allocation error! -- Terminating Program\n” );exit( EXIT_SUCCESS);}for( j 0; j < ns; j-i-+ ){prtntf(”segment #%d\n”, j+1);fread( &(data[j*segLen]), sizeof(float), segLen, fp );}7** > insert user code here <*/}1478171(-0.23)+0.4’÷0.19)0.0(-0.19)+0.4’÷0.21)a.oA(0.28)+0.4’0.19)8 oo(.0.33).__j -O40(voholAPPENDIX CAMBIENT VIBRATION TIME HISTORY PLOTTERSOFTWARE FOR HP LASERJET III PRINTERS(HPPLOT) - OPERATING INSTRUCTIONSC.1 DESCRIPTIONThe program HPP1ot is used to plot the ambient vibration and calibration records produced bythe program AVDA (see Appendix B). Its function is to plot all of the channels on the samepage for comparison. Thus the user is able to visually determine if any anomalies or signalcontamination has occurred in one or more of the channels before any data analysis is done. Asample output created by this program is shown in Figure C. 1.Filename:flft.r:12.5 Hz I Feb 21. I S.nentSct1515 I City Tower - CT15 - Level 15 IxotIfd.va1o 121104 8 ot 8Ipeib web,. of .aoh eeametit shown In aer.nth.s.ot÷0.4 refenutO. Onad 14) NW óonnen. NOI)TH poiNv.+ 0.22)ut.l hi .1:. AA AAAAA.LL.l.H...1234567(-0.21)+-:::: I I I I I I I I I reneJIo.o.vd’14:Nomen,Nrn1HpoeAtiv.(-0.1(+0.21)I I I I I I- II I I I I I Ir.fe4no.Ie14i:SVoamer.ASTpaeeemIIIIIiii:.i.iIIIi+0.22)14 (on tap of oaIj: NW carnen, N&(TH,._th. ,i., .L.iIihi(Ai(IAli liLl.II.ill.1’ “ IIpI9II (‘TT ‘II ‘‘I.vd 14(49 top of 4.1): N! darner, N0TH p.iIdW, . . . .bond 14 (on tsp e(caIJ: NW aarner. EAST paddw.. ‘I - .. .11 IhI . .,,.. - -. .hIIlI1lIlllIIi.,......hiii,.i...91 ‘)1 1(1’ I’TT)1’,iiI,Ii j.,tIevd 14 (on top afoot.): SW namer. EAST poeebwii LIIillii........time (eon)Figure C. 1. Typical ambient vibration time history produced by HPP1ot.149The header contains several information about the data files. These include the filename prefix,an optional title, conditioning information, the time at which the data was collected, and thesegment number. Each plot contains the channel number, peak values for that particular channel(shown in parentheses), an optional label, and finally the time signal itself. All of the plots arescaled according to the peak value of all of the channels shown on that page.C.2 INSTALLATION AND SYSTEM REQUIREMENTSThis program should run on any PC computer with a 80286 processor or higher. Also, since thisprogram sends printing instructions directly to the printer, it must be used with a printer whichsupports Hewlett Packard’s printer control language PCL5 (Hewlett-Packard Company, 1990)such as a HP LaserJet Ill.This program can be copied into any directory and executed from any other directory providedthere is a path to it.C.3 PROGRAM EXECUTIONC.3.1 RUNNING THE PROGRAMTo run the program, several parameters must be specified on the command line. A list of theseparameters will be displayed by executing the program without any arguments, i.e. by typingHPP <enter>at the DOS prompt. By doing so, the screen shown in Figure C.2 will appear.The speed of this program depends on the speed of the computer, and more importantly, thespeed of the parallel port (which connects the computer to the printer). It takes about 5 minutesto generate the plots for a typical setup, but it takes about one hour’ for a LaserJet Ill to print the1 This is based on 8 data files containing 32768 data points, 2 sets of calibration files, executed on a PC computerwith an 80486DX processor150entire setup. Since this is such a long period of time, and since there are usually several setups,this program is best used over night since the printer and the computer must be dedicated to thetask. A BATch file can be created to execute the program with all the necessary parameters (see§C.3.3 for an example).-U- D D — iL BBB Time History File Plotter 1.0H — — i t (requires HP/PCL5 based laser printer)Please specify the following parameters when executing this program:HPP dest datafile nf [cal] [filter] [att] [labelfile] [warnings]dest = destination for printer commands (either PRN or a file)datafile = first 6 characters of ‘BBB” files to be plottednf = the number of ‘BBB files to be plotted[cal] = calibration flag’ —> 0 = print; 1 = don’t print; default = 1[filter] = filter setting on signal conditioner [Hz][att] = attenuation setting on signal conditioner [dB]; if multiplevalues, use: att_1,seg_1,seg_m;att_2,seg_m-i-1,seg_n...[labelfile] = file containing “header” title, and individual plot titles[warnings] = warnings “flag’ —> 0 = display; 1 suppress; default = 0ex.1 (minimum) HPP pm corona 8ex.2 (multi att. values) HPP ipti corona 8 0 12.5 12,1,1;18,2,8ex.3 (file dest.; label file) HPP myFile.ext corona 8 0 12.5 12 corona.hppFigure C.2. Instructions displayed when HPP1ot is executed with no command line parameters.C.3.2 COMMAND LINE ARGUMENTSThe following is a detailed description of each parameter. Note that only the first fourparameters are required and that the rest are optional.C.3.2.1 Destination (dest)This is the destination of the printer commands. If “pm” or “ipti” is specified, the printercommands will be sent directly to the printer. If the name of a file is specified (name andextension arbitrary), the printer commands will be written to that file. However, the user shouldnote that these files take up a lot of disk space (over 5 megabytes2). To later print this file, enter2Th1s is based on 8 data files containing 32768 data points and 2 sets of calibration files151the following command at the DOS prompt:copy filename.ext pmwhere “filename.ext” is the name of the file previously specified. DO NOT print this file usingthe DOS utility PRINT since it interferes with the PCL instructions.C.3.2.2 Filename Prefix (datafile)This is the file prefix of the “BBB” files; i.e. the characters which precede the “labels” which areappended to the file (01, 02, a 1, b 1, ...) during data acquisition.eg. to print the files “ctlOO9Ol.bbb”, “ct100902.bbb”, etc. use “ctlOO9”eg. to print the files “test0l.bbb”, “test02.bbb”, etc. use “test”C.3.2.3 Number Of Files (ut)This is the number of files which make up the setup.C.3.2.4 Calibration Flag (cal)If the user wishes to print the calibration files, a zero (i.e. “0”) should be specified, otherwiseunity (i.e. “1”) should be specified. This argument is optional and defaults to “1”.C.3.2.5 Filter Setting (filter)This is the filter setting that was used on the signal conditioner (Hz) during data acquisition.This number appears in the header of each page (except calibration which defaults to “OUT”). Ifno value is specified, “N/A” (not available) is displayed instead. A negative one (i.e. “-1”) canalso be specified to indicate that this value is unavailable.C.3.2.6 Attenuation Setting(s) (aft)This is the attenuation setting on the signal conditioner (dB). This number appears in the headerof each page (except calibration which defaults to “66”). If no value is specified, “N/A” (not152available) is displayed instead. A negative one (i.e. “-1”) can also be specified to indicate thatthis value is unavailable.The program assumes that this setting is the same for all the files. However, if the attenuationwas changed in between segments, these different values can be specified using the followingformat:all_i, seg_l, seg_m; att2, seg_m+1, seg_n [,att_3,...JFor example, if segments 1 and 2 were attenuated at 12 dB while segments 3 to 8 were attenuatedat 18 dB, specify the following:12, 1,2; 18,3, 8DO NOT SEPARATE THE NUMBERS WITH ANY SPACES!C.3.2.7 Filename With Plot Labels (labelfile)If the user wishes to add a custom label to the header as well as individual plots, he/she mayspecify the name of an ASCII file (name and extension arbitrary) which contains the followingstrings (max. 80 characters):<title appearing in header><label of plot #1><label of plot #2><label of plot #nf>The first string appears in the header while the other strings appear in the top right corner of thecorresponding plot (right-justified).C.3.2.8 Warning Flag (warnings)If the program is unable to locate any of the files specified on the command line, it wifi prompt153the user as to whether it should continue or stop. If the program is being used in a BATch file,this intenuption could be very inconvenient.To suppress these warnings, specify a “1”. By default, these messages are displayed.C.3.3 EXAMPLE OF GENERATING PLOTS WITH A BATCH FILESuppose all eleven data files from the CT 15 test are to be plotted. Further, it is desired that allthe relevant conditioning information appear in the header, and that each plot is to contain a labeldescribing the location of each sensor. To accomplish this, follow these steps:1) With the information from Table A.2 (see Appendix A), create a BATch file called“CT15...HPP.BAT” which contains the following lines:Note that this BATch file executes HPP1ot along with the required parameters to satisfy the taskdescribed above. Also, the label files have the same name as the filename prefix for thecorresponding file (for consistency). Finally, all warnings from the program are to be suppressedso that such warnings do not interrupt the BATch job.2) Create the label files following the format described in §C.2.7. To illustrate, the contents ofthe label file “CT151 l.HPP” is shown below:hpp pm ctl5pv 8 0 12.5 0 ctl5pv.hpp 1hpp pm ctl5ph 8 0 12.5 0 ctl5ph.hpp 1hpp pm ct1515 8 0 12.5 6,1,1;18,2,8 ct1515.hpp 1hpp pm ct1513 8 0 12.5 12 ct1513.hpp 1hpp pm ctl5ll 8 0 12.5 18 ctl5ll.hpp 1hpp pm ct1509 8 0 12.5 12 ct1509.hpp 1hpp pm ct1507 8 0 12.5 18 ct1507.hpp 1hpp pm ct1505 8 0 12.5 12 ct1505.hpp 1hpp pm ct1503 8 0 12.5 12 ctl503.hpp 1hpp pm ct1502 8 0 12.5 12 ct1502.hpp 1hpp pm ctl5Ol 8 0 12.5 12 ctlSOl.hpp 1CT15 - City<Reference><Reference><Reference><Reference>Level 11 -Level 11 -Level 11 -Level 11 -TowerLevelLevelLevelLevelcolumncolumncolumncolumn- Ambient Vibration Measurements14 - column base at NW corner; NORTH Positive14 - column base at NE corner; NORTH Positive14 - column base at NW corner; EAST Positive14 - column base at. SW corner; EAST Positivebase at NW corner; NORTH Positivebase at NE corner; NORTH Positivebase at NW corner; EAST Positivebase at SW corner; EAST Positive154The first line will appear in the header; the second line will appear in the top right corner of theplot for channel 1; the third line will appear in the top right corner of the plot for channel 2; andso on.3) Copy all of the BBB files from the CT15 test to the same directory on the computer’sharddrive which contains the BATch file and label files described above.4) Turn on the printer and ensure that there is sufficient paper and toner. In this case 1 l*(8+2) or110 sheets will be required to plot all of the time histories.5) Finally, execute the BATch file by typing the following at the DOS prompt:ctl5_hpp <return>This wifi execute the instructions in the BATch file, and if all goes well, in approximately 11hours, all of the data files from the CT15 test will be plotted.155156APPENDIX DSLAVE NODE GENERATOR SOFTWARE (SLAVE) -OPERATING INSTRUCTIONS AND DOCUMENTATIOND.1 DESCRIPTIONIn some cases, the measured motions of each floor provide an incomplete picture of thebuilding’s vibration mode. In order to improve this, motion at other points on the floor isinterpolated by treating each floor as a rigid body, and then using the measured components ofthe mode shapes (master nodes) to calculate corresponding motion at these slave nodes.D.2 INSTALLATION AND SYSTEM REQUIREMENTSThis program was written in C++ (Stroustrup, 1993) and compiled with a Borland C++ 3.1compiler. The program should run on any PC computer with a 80386 processor (with an 80387FPU) or higher, and at least 1Mb of memory.The program can be copied into any directory and executed from any other directory providedthere is a path to it.D.3 PROGRAM EXECUTIOND.3.1 REQUIREMENTS AND RESTRICTIONSThis program uses the potential modal ratio files (*.mod) created by the program ULTRA asmaster files to interpolate for unmeasured points of motion (POM) which are refened to as slavenodes. The output files are created using the *.mod format so that the companion program,VISUAL, can use them. There are several prerequisites:(1) The coordinates of the master nodes must not have identical x or y coordinateseg.xl = (50, 100); x2 (60, 80) <---- OKxl = (50, 100); x2 = (50, 80) <---- unacceptablexl = (51, 100); x2 = (50, 80) <---- OK157As shown above, the user can get around this restriction by slightly offsetting the coordinates(since the motion probably doesn’t vary that much anyway)(2) A minimum of 3 master files is required and must be of the following combinations:XXY - 2 in the x direction, 1 in the y directionXYY - 1 in the x direction, 2 in the y directionXXYY - 2 in the x direction, 2 m the y directionXXYZZZ - 2 in the x direction, 1 in the y direction, 3 in the z directionAlso, the *mod files should have the same attributes (same reference sensor, same resolution,same coherence cutoff, etc.). SLAVE will check to see that these requirements are met, but ifnecessary these verifications can be suppressed by entering the appropriate code on the commandline.(3) the underlying assumption of this program is that the inputted motion are those of a rigidbody (or at least they can be treated as such).D.3.2 RUNNING THE PROGRAMTo run the program, several parameters must be specified on the command line. A list of theseparameters will be displayed by executing the program without any arguments, i.e. by typing:SLAVE <enter>at the DOS prompt. By doing so, the message shown in Figure D. 1 will be displayed on thescreen.D.3.2 COMMAND LINE ARGUMENTSThe following is a detailed description of each parameter. Note that only the first parameter isrequired while the rest are optional.1586ciiisuoidosoqjsuojnuuoj(cj)juuoTsuunp-oMIqItTMO01A14suoiidoiqioajjoinosjdiduiooiuopslulodjoiqwnuiudwooiuopuuoinjosiXunbijarudwooluopjjjonoauaiqociduiooiuopsuis_oouaijaiardwooluopuopdispuopdo:shxoJJojsuondosujspjqisandmooITJ1ow1ndijnonndoiournuiiodqIlonilsu!U1oisflq1‘(siusouaijiIUa1jJTpsqDns)siopqSITUTsJIoumrd1nupTOAqJOUopqOTqM5JTJp0urSfl01Sq5TMiSflT41ji‘1SJTJsuondouwJoJdJLIA5ruaLq(sv’n)suodOzztucjUTpqiospSTJTjS1IJOI1UU0JqJUTTpuuiuiootpU0U0TSUIXsiqiAjiodsIOU0nqU0TSUIXqIA1qpnoqsIIOUWUJJIfldU[qiJoUflUSisiq(jJrnJ?JJ)UJ1UI!UZtUSIUOUJnJ1ouqnA&PIflDXs3AV’ISuqApAiqdsipiuan1(o6—o)JJ04fl0uooi.&poqpi:sijuoornApoqio—[i]IflUIOJ“!SJ4Uids—[s]Inw.IoJUisijue—[p]AAXXesn—[x]jjonosqdidrnoouop—[d]suTodjoqumuoJl3drnoocuop—[u]uonIoeIAounbjoiduioocuop—[j]jjonoouxooodwooUop—[a]suiseouejioadrnoacuop—[i]:)Jou!o°iuporneTuspjO{MJTads(Als,uoisualxo)S[TWOpopouOIVUISUiUi14UoOijcnduiU\[JJO1flJWIfl][xsdujpcn:sIJ]ounnduTAvis0T—(cw)UOTSJAP4UJ04’qO—‘‘°DpoegI.ilI..1I..1I..1I..1AV‘1SIIIII’‘II’‘II’‘II’‘Ifollows:option descriptionx use XXYY formulation exclusivelyd allow dual entries in formulaes allow split entries in formulaer create rigid body motion fileThe x option instructs the program to use the XXYY formulation exclusively (see §D.4 for moreinformation). A dual entry means that either both x motions are non-zero while the y motion(s)are zero (at a particular frequency) or vice versa. A split entry means that only a single x andsingle y measurement are non-zero.Finally, the user can specify an r to instruct the program to output the rigid body motions (RBM)at a specified centre of rotation so that comparative studies can be done with analytical modeshapes generated by a program such as ETABS (see Appendix E for further information). In thiscase, the RBM files will be created instead of the *.mod files.D.3.2.3 Rigid Body Rotation Cutoff (THETACUTOFF)The XXY and XYY formulations check to see if the rotation of the rigid body does not exceedthis value (typically 70-80° is specified - default is 90°). See the formulations section for furtherdetails.D.3.3 INPUT FILEThe input file is an ASCII file whose name should have the extension “sly”. The format of thisfile is as follows:n filename.str Eilename.messlaveFilena.rne_1 xcr ycr zcr mn mn2 mr3 [mr4j [mr5) [mr6]slaveFilename_2 . .slaveFilename_n . .All of these parameters are described below.160n The number of slave files to be generated.filename.strfilename.mesSLAVE uses the nodal coordinates specified in a structure file’ whengenerating the slave nodes. Note that the coordinates of the slave nodes mustalso be included in this file.SLAVE uses the direction cosines from a measurement file’ to determine thedirection of the motion. These direction cosines are cross-referenced with thenodal coordinates in the structure file. Note that the direction cosines andcorresponding filename of the slave node files must also be included in thisfile. Also the direction cosines must be either unity (±1) or zero (0) i.e. themotion must occur along the X or the Y axis.slaveFilename_# The name of the output slave file (or RBM file)ccr I ycr I zcr These are the x, y, and z coordinates of the centre of rotation. These mustcorrespond to the coordinate system used in the structure file.mr# These are the name of the master files (*.mod). A combination of 3, 4, or 6filenames may be listed, and they need not be in any particular order.Note that if the next slaveFilename in the list has the same centre of rotation and master files asthe preceding slaveFilename, then these parameters do not need to be specified.D.3.4 EXAMPLEY4w4-NSFigure D.2. Floor plan of a rectangular building with three instruments.1See the VISUAL documentation in Felber, 1993.2340+C.O.R.¶1—x161To illustrate the use of this program, consider a building with rectangular floors as shown above.The corners are located at nodes 0,1,2,3 while sensors are located at nodes 4 and 5. Motion inthe X and Y direction were measured at 4 while only Y direction motion is measured at 5. Also,the origin is taken to be at the bottom left corner while the centre of rotation (COR) is located inthe centre of the floor. To generate the motion of each corner of the floor, the following filesmust be prepared:structure file (sainple.str)Structure File Sample200 -200 200 -20060 0.0 0.0 20.01 100.0 0.0 20.02 100.0 70.0 20.03 0.0 70.0 20.04 0.0 35.0 20.05 100.0 36.0 20.0401122330Note that the y coordinates of nodes 4 and 5 have been slightly offset in order to satisfy one ofthe restrictions discussed in §D.3.1measurementfile (sample.mes)Measurement File Sample114eo4e 4 1 0 04no4e 4 0 1 05eo4e 5 1 0 0Oeo4es 0 1 0 0Ono4es 0 0 1 0leo4es 1 1 0 0lno4es 1 0 1 0Zeo4es 2 1 0 0Zno4es 2 0 1 03eo4es3 1003no4es 3 0 1 0162slave inputfile (sarnple.slv)8 sample sampleOeo4es 50.0 35.0 0.0 4eo4e 4no4e 5eo4eOno4esleo4eslno4esZeo4esZno4es3eo4es3no4esThe modal files 4eo4e.mod , 4no4e.mod and Seo4e.mod must already exist (created usingULTRA).After the program has been executed, the following files will be created:Oeo4es.modOno4es.modleo4es.modlno4es.mod2eo4es.mod2no4es.mod3eo4es.mod3no4es.modThese files can be used like regular *.mod files. Also, when animating the mode shapes, it isntnecessary to use the original (master) mod files unless desired. If, in the above example, the userspecified that rigid body motion (RBM) files were to be generated, the following files (withcorresponding filenames) will be created instead.Oeo4es.rbmOno4es.rbmleo4es.rbm1 no4es.rbm2eo4es.rbm2no4es.rbm3eo4es.rbm3no4es.rbmThe RBM files contains formulation information in the header. This is followed by tabulatedrigid body motions; along with corresponding frequencies.163D.4 FORMULATIONThe objective of this formulation is to develop expressions which can be used to calculate motionat other points of a floor in a building which has been instrumented.D.4.1 REQUIREMENTSThe following formulation has been adapted from celebi, Safak, et al. (1987). The sensorlocations should be positioned with the following considerations(1) sensor locations should not lie on a straight line.(2) directions of the sensors should not all be parallel(3) all sensor directions should not intersect at one point.D.4.2 NOMENCLATUREThe nomenclature is consistent with that of celebi, Safak, et al. (1987). The relevant variablesare listed here:xi, y, z Cartesian coordinates of point iu,, u, u displacement of point i in the x, y, and z directions, respectivelyu0, u,0,u0, rigid-body translations in the x, y, and z directions, respectivelye ,e,, e rotation about the x, y, and z axis, respectivelyD.4.3 TWO-DIMENSIONAL FORMULATIONThe basis of the following formulae are two equations which describe the displacement of point iin the x and y directions. These equations are:u =u,0 +x(cosO—1)—y(sinO) (D.la)U),, =u0 +y(cosO—l)+x1(sinO) (D.lb)In these equations, u j and u1 represent motion of the master nodes while u0 and u0 representthe motion of the floor at its centre of rotation. It is the latter two variables which must be solved164for. For this exercise, it will be assumed that 4 measurements have been made. Two of thesemeasurements are aligned with the positive x direction while the other two are aligned with thepositive y direction. Further, it is also assumed that none of the sensor share the same Cartesiancoordinates. With this basis, Equation D. 1 can be rewritten for these four measurements:u1=u0+x(cos—1)—ysinO) (D.2)ux2 = uxo+x2(cosO—1)—y2(sinO) (D.3)u3=u0+y(cosO—1)+x3(sinO) (D.4)uy4 =uyo+y4(cosO —1)+x4(sinO) (D.5)This can also be written in matrix notation by treating the trigonometric expressions as distinctvariables (even though one can be derived from the other):ux1 1 0 x1 —y1ux2 — 1 0 x2 —y2D6u,3 — 0 1 y3 x3 (cos6—1)( . )u4 0 1 y4 x4 sinOSince there are only three unknowns, only three of Equations D.2 to D.5 are required. However,if the trigonometric expressions are treated as distinct variables (as they were with Equation D.6),then all 4 equations can be used. Both of these treatments are used in the formulations presentedbelow.D.4.3.1 XXYY Formulation - Utilizing 4 MeasurementsSubtracting Equation D.3 from Equation D.2 and subtracting Equation D.5 from Equation D.4gives:I3=(cosO—l)—asinO (D.7)/3=(cosO—1)+asinO (D.8)where165a — — ))2 /3 = —x—x1_x2 xa= X3 — x4 R= Uy3 —y i’yy3—y4 y3—y4Subtracting Equation D.7 from Equation D.8 gives:sinO=1 (D.9)+ aThe other trigonometric term can be solved for using the identity(cosO_l)=g1_5f 2O—1 (D.1O)The rigid body translations can then be solved for by realTanging Equation D. 1.Finally, the displacement of the slave POM can be found by using Equation D. 1 after substitutingthe rigid body translation and rotation and the slave node’s Cartesian coordinates.D.4.3.2 XXY Formulation - Utilizing 3 MeasurementsSubtracting Equation D.3 from Equation D.2 gives:f3 =(cosO—1)—asinO (D.7)wherea— — /3 — —x— 1 — x1 —x2Two identities need to be introduced at this time; these being:sin2=2tan(D.lla)1+ tan2 4cos2=1tan(D.llb)1+ tan2or166(cos2—1)=—2tan2.(D.llc)1+ tan2By letting 2 = O and substituting Equations D. 1 la and D. 1 ic into Equation D.7, and thenrearranging gives:—2a ±ga2_13(13+2)tan4?=(/3+2)(12)Upon substituting Equations D.lla and D. 1 lc into Equation D.7, a quadratic is created with anextraneous root. The correct root can be determined in a computer algorithm (as will bediscussed in §D.5).The trigonometric terms can now be solved for by substituting Equation D. 12 into both EquationD. 1 la and Equation D. 1 ic. The rigid body translations can then be solved for by rearrangingEquation D.1.Finally, the displacement of the slave POM can be found by using Equation D. 1 after substitutingthe rigid body translation and rotation and the slave node’s Cartesian coordinates.D.4.3.3 XYY Formulation - Utilizing 3 MeasurementsThe following formulation is similar to that of the previous section except now two of the signalsare in the y direction as opposed to the x direction.Subtracting Equation D.5 from Equation D.4 gives:J3=(cosO—1)+asinO2 (D.8)whereaX34/3Uy3Uy4y—y3_y4 YThe identities introduced in the previous section are also used here. As before, by letting 2 =167and substituting Equations D. 1 la and D. 1 ic into Equation D.8, and then rearranging gives:+2a ±ga2_13(13+2)tan4=(/3+2)(D.13)As with the XXY formulation, an extraneous root is created. The correct root can be determinedin a computer algorithm (as will be discussed in §B.5).The trigonometric terms can now be solved for by substituting Equation D. 13 into both EquationD. 1 la and Equation D. 1 ic. The rigid body translations can then be solved for by rearrangingEquation D.1.Finally, the displacement of the slave POM can be found by using Equation D. 1 after substitutingthe rigid body translation and rotation and the slave node’s Cartesian coordinates.D.4.4 THREE-DIMENSIONAL FORMULATIONThe basis of the following formulae are three equations which describe the displacement of pointi in the x, y, and z directions. These equations are:= u0+x1(cosO -i-cosO —2)—y(sinO)+z(sinO) (D.14a)= +x1(sinOj+ycosO+cosO —2)—z(sinO) (D.14b)(D.14c)There are several combinations of these equations but at least 6 are required to solve for the 6unknowns. In this exercise, it will be assumed that 6 measurements have been made. Two, one,and three of these measurements are aligned with the positive x, y, and z directions, respectively.Further, it is also assumed that none of the sensor share the same Cartesian coordinates.Equation D. 14 can be rewritten for the aforementioned measurements. However, the closedformsolution is very tedious to formulate and very difficult to implement since the equations must besolved simultaneously and since several extraneous roots appear in the solution. Since the168rotations associated with building floors are small, the following approximations can be made:sinOcos 1Using the above approximations in Equation D. 14, the following six expressions can be writtenfor the aforementioned displacements:u1 = u0 — yO +z163, (D.15)u2 =—yO + zO (D.16)u3=u0+x1O—zO (D.17)u4 =u0—x1O+yO, (D.18)= u0 — xO +y19 (D.19)= — xO + yO (D.20)Equations D. 15 through D.20 can be assembled into a matrix and solved simultaneously. Thematrix equation is as follows:o i o —1 l xo yl1 0 0 0 z2 —y2 Uy0 U21 0 0 0 z3 —y3 u0 — u3o o 1 y4 —x4 0 O 0Z4o o 1 y5 —x5 0 O 0z5o 0 1 y6 X6 0 OZ 0z6D.5 COMPUTER ALGORITHM CONSIDERATIONSFor the two-dimensional formulation, the objective was to first calculate the rigid body rotationabout the center of rotation, and then use this value to calculate the rigid body translations.Because of the numeric problems associated with inverse trigonometric routines (arcsine,arccosine, etc.), the value of O was never calculated directly since it is not actually needed.In general, the XXYY formulation is stable while the other formulations can become unstable if169the correct root is not used in subsequent formulae. It was found that the extraneous root led toexcessively high rigid body rotations (somewhere in the range of 8001800). Therefore, thecorrect root can be detennined by calculating (9 and then checking to see if it is excessive (orconversely checking to see if it is a reasonable value).Another problem arises when the rigid body translations are calculated. Equations D.2 and D.3will generally give different answers for un,, and similarly, Equations D.4 and D.5 will generallygive different answers foru0. One way to deal with this is to calculate a known displacement,and then comparing it with the given displacement. The value which is closest can then be usedin subsequent calculations. This problem arises for several reasons including: (a) loss ofprecision, (b) inaccurate Cartesian coordinates of the sensors, and (c) that the structure to whichthe sensors were mounted is not a rigid diaphragm although its behavior is assumed to be similar.The three-dimensional formulation is generally stable. In the event that the matrix becomessingular, the formulation reverts to an appropriate two-dimensional formulation.170ILIAPPENDIX EMODAL ASSURANCE CRITERIUM SOFTWARE (MAC)- OPERATING INSTRUCTIONSE.1 DESCRIPTIONComparison of dynamic modal characteristics are made on the basis of both frequencies(periods) and vibration mode shapes. One method of correlating mode shapes is to perform amodal assurance critenum (MAC) analysis. This involves a formulation which has beendescribed in Chapter 2; and is reproduced here for reference (Equation E. 1).[{øa}TMAC(a,x)= E.l[{øa}T{øa }1 [{}Tf}JThis program takes two sets of mode shapes (analytical and/or experimental) and assembles amatrix of MAC values. This permits the user to correlate mode shapes which have been obtainedfrom different sources.E.2 INSTALLATION AND SYSTEM REQUIREMENTSThis program was written in C++ and compiled with a Borland C++ 3.1 compiler. The programshould run on any PC computer with a 80386 processor (with an 80387 FPU) or higher, and atleast 1Mb of memory.The program can be copied into any directory and executed from any other directory providedthere is a path to it.E.3 PROGRAM EXECUTIONE.3.1 RUNNING THE PROGRAMIn order to assemble a MAC matrix, the names of the two mode shape files as well as a name for172the output file must be specified on the command line. For assistance, executing the programwithout any arguments, i.e. by typing:MAC <enter>at the DOS prompt will display the correct sequence of these filenames as well as someadditional information (as shown in Figure E. 1).This program supports several different mode shape formats, which are described in more detailin §E.3.2. However, some of these formats (such as the ETABS *.EIG format) are saved in amore efficient format. Therefore, MAC can also be executed with only one or two of the modeshape filenames specified so that they can be translated into a better format. These translatedfiles can be used in subsequent MAC analyses.f—i DModal Assurance Criterium Analysis 1.0— — _Fi A Program by Norman SchusterMAC modeShapeFilel [modeShapeFile2] [macFilename]modeShapeFile#: mode shape filemacFilename: output file (required for MAC analysis)DO NOT include the file extension when specifying the files!supported mode shape file formats (in scanning order):Analytical (*s)Experimental (* . xms)ETABS (*.eig) (saves in *.aJns format)SLAVE (*.sms) (saves in *xms format)Figure E. 1. Message displayed when MAC is executed with no argumentsE.3.2 SUPPORTED MODE SHAPE FORMATSThis program supports several different mode shape formats. However, it will only save modeshape files in either the AMS or XMS format. Further, this program will scan for the followingextensions in this order: *J.,4S *.XMS, *.EIG, and *.SMS. For example, if there are two fileswith identical names but different extensions, such as HLENAME.EIG and FTLENAME.AMS,the file with the name FILENAME.AMS will be opened, not the other one.173E.3.2.1 ETABS Mode Shape (EIG)One application of this program was to compare experimental mode shapes with analytical modeshapes obtained from dynamic analysis using the program ETABS (CSI Ltd., 1992). Tofacilitate this process, a routine was developed which would read the ETABS *.EJG files. Thisroutine determines the number of periods and storeys in this file, and then extracts thefrequencies, storey labels, and con-esponding motion of each floor. This information is latersaved in the AMS format (see §E.3.2.3 for details).E.3.2.2 Slave Mode Shape (SMS)The ETABS mode shapes consist of only 3 degrees-of-freedom per floor (two translation and onerotation) with respect to the centre-of-mass of that floor. Since the experimental mode shapeswere not specified in this manner, a file format was developed which would transform theexperimental mode shape (of a building) into planar motion relative to the centre-of-rotation.This allowed a proper comparison between the two types of mode shapes. This process wasfacilitated by the program SLAVE (see Appendix D) which performs this transformation in theprocess of creating slave nodes.The format of this file is given below:tile_header (max. 80 characters)number_of_s toreys (NS)label_i RBM_Filename_llabel_NS REM_F ilename_NSnumber_of_frequencies (NF)freg_lfreq_NFThe file_header is for adding a description. This is followed by the number of storeys aswell as the storey labels and corresponding modal displacements specified in a RBM file. The174REM files must already exist from a previous execution of the program SLAVE. Also, thestorey labels must be identical to the corresponding storey label in the ETABS model. Finally,the number of frequencies and a list of the frequencies which correspond to the mode shapes tobe assembled are specified in the input file. These frequencies MUST correspond exactly (4decimal precision) to those in the RBM files.The mode shapes which are assembled in this process are later saved in the XMS format (see§E.3.2.4 for details).E.3.2.3 Analytical Mode Shape (AMS)This mode shape file contains all the pertinent information required for the MAC analysis. Thisconsists of the modal frequencies, and the corresponding modal displacements for each storey.The format of this file is given below:file_header (max. 80 characters)number_of_frequencies (NF)<TAB>freql <TAB>freq2 . . . <TAB>frecj_NFnumber_of_storeys (NS)label_i Ux <PAB>Ux_1 <TAB>Ux_2 . . . <TAB>Ux_NFlabel_i Uy <TAB>Uy_1 <TAB>Uy_2 . . . <TAB>Uy_NFlabel_i Qz <PAB>Qz_1 <TAB>Qz_2 . . . <TAB>Qz_NF<BLANK LINE>label_2 Ux <TAB>Ux_l <TAB>Ux2 . . . <PAB>Ux_NFlabel_NS Qz <TAB>Qz_i <TAB>Qz_2 . <TAB>Qz_NFThe file_header is for adding a description. This is followed by the number of frequencieswith the specified frequencies on the following line. Note that each frequency is preceded by a<TAB>, and that they need not be in any particular order. Following the frequencies is themodal displacements for each storey. This consists of 3 lines for each direction (translation inthe x and y directions, and rotation about the z axis). Each of these lines begins with the storeylabel (which must be identical to the corresponding storey label in the other mode shape file), thedirection (Ux, Uy, or Qz), followed by the displacement corresponding to each frequency175specified at the top of the column. Each displacement must be preceded by a <TAB>.This file can be readily imported into a spreadsheet for easy manipulation and exported just aseasily. This format is used for saving modal information obtained from an ETABS *.EJG formatfile. It can also be used to assemble other analytical mode shapes to be used in a MAC analysis.E.3.2.4 Experimental Mode Shape (XMS)This file format is identical to the AMS format. A different extension is used so that analyticalmode shapes (AMS) can be distinguished from experimental mode shapes (XMS).E.3.3 EXAMPLESuppose a comparison is to be made between analytical mode shapes obtained from usingETABS and experimental mode shapes obtained using ULTRA. The output file from ETABSwill be in the EIG format and can be used as is. The mode shape obtained from using ULTRArequires further manipulation.First, rigid-body-motion (RBM) files must be created using the program SLAVE. Thecorresponding input file for this purpose is given below.slave inputfile (ct32r52n.slv)17 ct32s ct3Zs5Zn3252nP06 0.0 0.0 0.0 04eo52n 06eo52n 04no52n 05no52n3252nL01 0.0 0.0 0.0 O7eo5Zn 09eo52n 07no52n 08no52n325ZnL0? 0.0 0.0 0.0 lOeo52n 12eo52n 10no52n llno5Zn3Z52nL05 0.0 0.0 0.0 l6eo5Zn 18eo52n 16no52n l7no5Zn3252nL07 0.0 0.0 0.0 19eo52n Zleo5Zn 19no52n 20no52n3252nL09 0.0 0.0 0.0 22eo52n 24eo52n ZZno5Zn 23no52n3252nL11 0.0 0.0 0.0 25eo52n 27eo52n 25no52n Z6no5Zn3Z52nL13 0.0 0.0 0.0 28eo52n 30eo52n Z8noS2n 29no52n3252nL15 0.0 0.0 0.0 31eo52n 33eo52n 31no52n 3Zno5Zn325?nLl7 0.0 0.0 0.0 34eo52n 36eo52n 34no52n 35no52n3252nL19 0.0 0.0 0.0 37eo52n 39eo52n 37no52n 38no52n325ZnLZ1 0.0 0.0 0.0 40eo52n 42eo52n 4Ono5Zn 41no52n3Z5ZnLZ3 0.0 0.0 0.0 43eo52n 45eo52n 43no57n 44no57n325ZnLZ5 0.0 0.0 0.0 46eo52n 48eo52n 46no57n 47no52n3252nLZ7 0.0 0.0 0.0 49eo52n 5leo5Zn 49no52n 50noSZn3252nLZ9 0.0 0.0 0.0 52eo52n 54eo52n 52no52n 53no5Zn3252nL32 0.0 0.0 0.0 55eo52n 57eo52n 55no52n 56no5Zn176The program SLAVE must then be executed by specifying this filename along with “r” in the listof options (see Appendix D for exact details of running SLAVE). After this, the RBM fileslisted in Table E. 1 will be created.Now, in order to perform the MAC analysis with the ETABS file, the corresponding storey labelsmust be specified. A list of the storey labels used in the ETABS file and the correspondingfloors which were measured experimentally are shown in the table below.Table E. 1. Corresponding storey labels required for the MAC analysis.ETABS Storey Labels Corresponding RBM FileL32 - 3Z52nL32L31L30L29 3252nL29L28L27 3252nL27L26L25 3252nL25L24L23 3252nL23L22L2i 3252nL21L20L19 3252nLi9L18L17 3252nL17L16L15 3252nLi5L13 3252nL13LiZLii 325ZnL11LiOL09 3252nLø9L08L07 3Z5ZnL07L06L05 3252nLO5L04L03L02 3Z5ZnLØZLOl 3252nLøiP0?P04P06 3252nP06The next step is to create a slave mode shape (SMS) file. The contents of this file are given177below:slave mode shape (ct32_52n.smns)City Tower - 32 Storeys17P06 3252nP06LOl 3252nL0iL02 3252nL02L05 3252nL05L07 3252nL07L09 3252nL09Lii 3252nLi1L13 3252nL13L15 3252nL15L17 3252nL17L19 3252nLi9L21 3252nL2iL23 3252nL23L25 3252nL25L27 3252nL27L29 3252nL29L32 3252nL3240.54692.30474. 88287.5391As can be seen, the storey label and the corresponding RBM file have been specified togethernear the beginning of this file. The list of storey labels and RBM files is followed by the numberof frequencies and the frequencies of the mode shapes to be assembled from the RBM files.These frequencies need not be in any particular order.Once, this file is created, the MAC analysis can be performed by typing the following at the DOSprompt:MAC ct3252n ct32d ct32d52nwhere “ct32d” is the name of the ETABS mode shape file. Following the analysis, the followingfiles will be created:ct32_52n.xmsct32d.amsct32d52n.macThe first two files contain the information derived from the original mode shape files, and can be178used again in subsequent analyses. The last file contains the MAC matrix. The contents of thisfile is shown below. Note that 4 matrices are created - one for each direction and one whichcontains the sum of all three matrices. Also, the frequencies from the first mode shape file(ct32_52e.xms) appear at the top of each column while the frequencies from the second modeshape file (ct32d.ams) appear at the beginning of each row. Furthermore, the format of this fileis such that it can be readily imported into a spreadsheet for formatting and/or furthermanipulation.MAC output file (ct32d52n.inac)Modal Assurance Criteria (MAC) Analysis(1) ct3Z_52e.xms City Tower - 32 Storeys(2) ct32d.ams CITYTOWER, VANCOUVER B.C. - CT32Dct32_52e.xms runs left to right; ct32d.cims runs top to bottomAll components0.5469 2.3047 4.8828 7.53910.4729 2.3709 0.1974 0.3675 0.15800.6205 2.2581 0.5275 0.1572 0.10311.1840 1.7152 0.8798 0.1238 0.26182.3815 0.1088 2.0465 0.7719 0.06953.2243 0.0122 1.6249 1.1772 0.03893.5687 0.0194 1.7435 1.1506 0.09884.8618 0.0182 0.5759 2.2417 0.31856.2659 0.0060 0.2937 1.7850 0.76227.3189 0.1219 0.0406 0.3143 2.30997.7835 0.0793 0.1940 0.8762 2.3945Ux component0.5469 2.3047 4.8828 7.53910.4729 0.8409 0.0093 0.3538 0.10990.6205 0.9765 0.0519 0.1269 0.07961.1840 0.9059 0.1688 0.1013 0.19422.3815 0.0435 0.1210 0.5316 0.04293.2243 0.0053 0.1211 0.6858 0.01223.5687 0.0190 0.1278 0.8028 0.04124.8618 0.0075 0.1423 0.3440 0.18636.2659 0.0001 0.0174 0.0356 0.66347.3189 0.0018 0.0116 0.1490 0.73867.7835 0.0014 0.0130 0.1162 0.6883Uy component0.5469 2.3047 4.8828 7.53910.4729 0.8275 0.0135 0.0044 0.04150.6205 0.6399 0.1978 0.0004 0.00921.1840 0.1087 0.5215 0.0004 0.05462.3815 0.0001 0.9832 0.0004 0.00111793.2243 0.0000 0.6891 0.1963 0.01093.5687 0.0000 0.7950 0.2086 0.04544.8618 0.0027 0.1189 0.9208 0.00036.2659 0.0059 0.1530 0.8573 0.04037.3189 0.0556 0.0228 0.1649 0.84697.7835 0.0510 0.0130 0.0819 0.9267Qz component0.5469 2.3047 4.8828 7.53910.4729 0.7024 0.1745 0.0092 0.00650.6205 0.6417 0.2779 0.0299 0.01431.1840 0.7006 0.1895 0.0220 0.01312.3815 0.0652 0.9423 0.2399 0.02553.2243 0.0068 0.8147 0.2950 0.01583.5687 0.0004 0.8207 0.1393 0.01234.8618 0.0080 0.3148 0.9769 0.13196.2659 0.0001 0.1233 0.8922 0.05857.3189 0.0646 0.0062 0.0004 0.72457.7835 0.0269 0.1679 0.6781 0.7795180T81APPENDIX FERROR ANALYSISThis appendix contains several signal processing plots which were used to assess the accuracy ofthe instrumentation (FBA sensors) which was used to measure the ambient vibrations of thebuilding.Figures P.1 to P.8 were used to determine if any aliasing was occurring during measurements ofthe ambient vibrations. These figures show power spectral densities (PSD) of two measurementsusing the same sensor arrangement but with different sampling rates; these being 40 Hz and 80Hz. For the PSD corresponding to the 80 Hz sampling rate, the data in the 20 to 40 Hz range wasplotted in reverse order to facilitate locating aliases.Figures F.9 to Figures F. 14 were used to compare the different sensitivities of the FBA sensors.Coherence functions, frequency response functions, and phase functions were generated todetermine variances between different sensors.1821000cuzI0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]1001010.10.01Figure F. 1. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #1 oriented in the NS direction.1000100; 10(0.0.010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.2. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #3 oriented in the NS direction.18310000.14:0.01 ••••••• t....I...,I....I . I....I . I....I....I....I .0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.3. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #2 oriented in the EW direction.100040Hz 80Hz 80Hz folded0.01 I....I...,I....I I....I I....I....I....I I....I.,.,I....0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.4. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #4 oriented in the EW direction.100010.14:0.01 I. .. . I I I. .. . I I. . . . I. . . . I. . . . I I. . .. I. . . . I.. .0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.5. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #5 oriented in the EW direction.18410040Hz 80Hz 80Hz folded010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.6. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #6 oriented in the vertical direction.10040Hz 80Hz 80Hz folded0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.7. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #7 oriented in the vertical direction.j___01234567891011121314151617181920Frequency [Hz]Figure F8. Comparison of power spectral density functions of signals sampled at different rates(40 Hz and 80 Hz) using FBA #8 oriented in the vertical direction.1850.8a)0.40020.0040020.01.00.8a)040020.01.00.8a)040 0.20.01.00.8a)0A0020.01.00.8a)0A0020.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]-air—- I ‘-—--- i iq i sit..0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]-- ——r——4—’—r—.- — .10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]i _________________________0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]— ___L--_L-_-_. — - t;_0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F.9. Coherence functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1.i Aa’ — — — —FBA#3/FBA#1.......L..._.._._.._IFBA#4/FBA#1. ..I....j_ — I.... I.... I.... I.. .1....IL:,:::z :::::: :zzz:z :::::: ::z::....i...1........ — i.”. Jflk — ..t.,.I -rI IFBA#6/FBA#1.—.-. 3 .... 3 .... 3.... .... .... 3.... — I. . . . I. . . I. . . . I. . . . I.I— I.. .1... .3.... •... I.... I I.... I.1i_i1861.00.80.60.40.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]L — — —J______________0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]( — — :--- —‘f H’-H —FBA#5/FBA#2[_j_ J_ J_____j_j_1.00.80.60.40U0.20.0Frequency [Hz]1.00.40.0FBA#7/FBA#2_J_J_ JJ_I_J_J___ , ... .. . I...0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]1.00.80.60.4c0.20.0it::.... J— •... I— L___ I I. . . . . . . . . . . . . j.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]L — — — — —j______________1.00.4u0.20.01.00.80.60.4U0.20.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20FBA#6/FBA#2[— I_ J....I.,0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]-‘-I#8/ FBA #2Figure F. 10. Coherence functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2.187t04 .......FBA#3/FBA#1[‘ 02 I0.0 II JhL1h._..L — LJ I.... I... .1.... I.... I....0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]8 rrFBA#4/FBA#1g 02i:t 0.0—I....I I....I I....I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]‘r!: = et z. zz z zti. —. jFBA#5/FBA#1[02 F—[[r.t 0.0 :..khh:_L.kJ_ JjJ_ I.... I.... I.... I.... I....0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]r-‘r- -, - H FBA#6/FBA#1[0.2 F0.0 I I. . .. . .1. . ..J .. .1.... I... .1.... I.... I....0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]OS f I .g FBA#7/FBA#1[g 02 F F Ft 0.0 J )jj_ ii i.... i.... i,.. i.,..0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]jt.1” ..FBA#8/FBA#1[g 0.2 F Ft 0,0 I I. ... .::J”’’ I I.... I I.... I....0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F. 11. Frequency response functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1.188! 1.0 ;:-4-.b*.b.-• ;;: Z; ;0.8C El. El. IZ IZLI. El El El El El. jFBA#3/FBA02t 0.0 . I....I... .1.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]!gfjFBA#4/FBA#2F 0.20.0 — I..”I....I....I....I..,,0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]1.0I jFBA#5/FBA#2020.0 — JJ_0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]a8 7. E’ 5... wI jFBA#6/FBA#2F 0.2 [ F F0.0 — JJ JJ_ I.”.I.”.I....I....I,,..0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]—I / jFBA#7/FBA#2& 02 :— ..,....._0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]i_’.3 ]FBA#8/FBA#2F 0.2 F0.0 — -n-n— .i0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F. 12. Frequency response functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2.189Figure F.13. Phase functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #1.10 - ——I IFBA#3/FBAiI10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]10 —— ——I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]‘‘ 10 — — —I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz], 101——I-—jFBA#6/FBA#1I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]108I FBA #7 I FBA #1I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]10jFBA#8/FBA#10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]190108‘:0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]8[j/FB0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]10 -0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]I ‘ F1 EE I.E I.E I.Ez0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]10 —— I IjFBA#7/FBA#2j0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]10 ——8 FBA #8 I FBA #2I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Figure F. 14. Phase functions of FBA #3,4,5,6,7, and 8 w.r.t. FBA #2.191161APPENDIX GPOWER SPECTRAL DENSITY PLOTSThis appendix contains several of the averaged normalized power spectral density (ANPSD)piots which were used to locate natural frequencies of the building. Pairs of signals, in both theNorth-South and East-West direction of the building, were added and subtracted to producespectra isolating translational and torsional motion respectively. These spectra are shown infigures G. 1 through G.6. In addition, the spikes corresponding to natural frequencies are labeledwith the corresponding vibration mode. The naming convention for these modes is explained inTable 5.1.193CDa)za)Ia)za)added - subtracted(b) Signals in the East-West direction of the buildingFigure G. 1. ANPSD plots for all of the lateral signals from the CT1O test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.added subtracted1001010.10.011001010.10.01NS•1 Tç1__________________________________________IINS•2L-0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](a) Signals in the North-South direction of the buildingEW• 1T’2I:I I I I.,._I____I._,,I...._i_,_.._.I .—.—0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]194a)Iadded - subtractedadded subtractedFigure G.2. ANPSD plots for all of the lateral signals from the CT15 test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.a)I1001010.10.011001010.10.01NS 1 T•10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](a) Signals in the North-South direction of the buildingEW • 1Til__________________________________T20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](b) Signals in the East-West direction of the building195cl0z0000z00(B) Signals in the East-West direction of the buildingFigure G.3. ANPSD plots for all of the lateral signals from the CT2O test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.added subtractedNS.1 I IN .2T2NS’311.£flII‘WI,•1I I I,...I....I....I I I....I01001010.10.011001010.10.011 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hzj(a) Signals in the North-South direction of the buildingEWe 1T’ 1added subtracted. EW.2 EW.4EW.3.1.1 I I__._I....I I..,.I....I....I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]196100ci)cDzci)Czci)added - subtractedadded subtracted0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](b) Signals in the East-West direction of the buildingFigure G.4. ANPSD plots for all of the lateral signals from the CT25 test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.NNS.2T’2kiINS.3T’31010.11001010.10.010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz]Ew.1 (a) Signals in the North-South direction of the buildingT 1EW2197100Frequency [Hz](b) Signals in the East-West direction of the buildingFigure G.5. ANPSD plots for all of the lateral signals from the CT32 test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.• 1T• 1NS2added subtractedTr2NS •3I0z1010.11001010.10.010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](a) Signals in the North-South direction of the buildingEW. 1‘T’lEW•2 added subtractedTp2EW.3....I I...,I....I....I...,I....I I....I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201981000zcz)added - subtracted0.010 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](b) Signals in the East-West direction of the buildingFigure G.6. ANPSD plots for all of the lateral signals from the CTTC test. Peaks correspondingto natural frequencies are labeled with the corresponding mode.S .1100 . T.1NS.2I....I,,..I....I,...I....I....I0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Frequency [Hz](a) Individual signals in the North-South direction of the building1000__________________________________________W. 1T 1100ci0zI199oozAPPENDIX HCOMPARISON OF ANALYTICAL ANDEXPERIMENTAL RESULTSThis appendix presents a comparison between frequencies and mode shapes obtainedexperimentally (measurements) and analytically (dynamic analysis) using the software programETABS (CSI Ltd., 1992). Tables H. 1 through H.5 compare experimental and analyticalfrequencies. Also shown in these tables are the percentage difference in these frequencies alongwith the modal direction factors corresponding to the frequencies obtained using ETABS.Figures H. 1 through H. 12 show comparisons between experimental and analytical mode shapecomponents. Each of these figures show the modal displacements for each principal direction ofthe building; namely translation in both the North-South (NS) and East-West (EW) directionsand rotation about the center of mass of each floor. In general, the match was excellent for thedominant component of the mode shape (i.e. the NS component for the NS translational modesshowed good correlation; the rotational component of the torsional modes showed goodcorrelation, etc.). In some cases the other components of the modes matched very well while inother cases, the match was poor. Due to space limitations, only the modes from the CT32 modelare shown.201Table H. 1. Comparison of experimental and analytical frequencies for 10 levels of the buildingcompleted (CT10).frequencies modal direction factors (%)mode measured ETABS difference EW NS rotationaldesignation (Hz) (Hz) (%) direction directionNS•1 2.617 2.471 -6 1 97 2EW•1 3.125 3.233 3 99 1 0T•1 3.906 3.673 -6 0 2 98NS•2 9.688 9.800 1 0 92 8T•2 10.469 10.965 5 1 8 91EW•2 13.033 99 0 1NS•3 18.043 2 33 64T•3 20.692 2 66 32Table H.2. Comparison of experimental and analytical frequencies for 15 levels of the buildingcompleted (CT15).frequencies modal direction factors (%)mode measured ETABS difference EW NS rotationaldesignation (Hz) (Hz) (%) direction directionNS•1 1.563 1.537 -2 0 98 2EW•1 1.875 2.018 8 99 0 1T•1 2.578 2.528 -2 1 2 96NS•2 6.250 5.927 -5 0 86 14T•2 7.773 7.526 -3 10 13 76EW•2 8.633 8.546 -1 89 1 9NS•3 10.703 11.694 9 1 55 45T•3 11.875 13.107 10 4 44 52Table H.3. Comparison of experimental and analytical frequencies for 20 levels of the buildingcompleted (CT2O).frequencies modal direction factors (%)mode measured ETABS difference EW NS rotationaldesignation (Hz) (Hz) (%) direction directionNS•1 0.93 8 0.997 6 0 99 1EW•1 1.172 1.310 12 99 0 1T•1 1.914 1.853 -3 1 1 98NS•2 4.102 4.046 -1 0 90 10EW•2 5.156 5.244 2 15 10 75T•2 5.508 5.787 5 84 1 14NS•3 8.242 8.449 3 1 54 45T•3 9.023 10.284 14 4 47 48EW•3 10.039 12.407 24 33 18 49202Table H.4. Comparison of experimental and analytical frequencies for 25 levels of the buildingcompleted (CT25).frequencies modal direction factors (%)mode measured ETABS difference EW NS rotationaldesignation (Hz) (Hz) (%) direction directionNS•1 0.703 0.665 -5 0 99 1EW•1 0.859 0.874 2 99 0 0T•l 1.484 1.415 -5 1 1 99NS•2 3.047 3.003 -l 0 92 8EW•2 3.945 3.988 1 41 6 53T•2 4.453 4.269 -4 58 2 39NS•3 6.250 6.135 -2 2 64 34T•3 7.578 7.696 2 9 35 56EW•3 8.828 9.473 7 28 27 45Table H.5. Comparison of experimental and analytical frequencies for 32 levels of the buildingcompleted (CT32).frequencies modal direction factors (%)mode measured ETABS difference EW NS rotationaldesignation (Hz) (Hz) (%) direction directionNS•1 0.547 0.473 -14 0 100 0EW•1 0.645 0.621 -4 100 0 0T•1 1.289 1.184 -8 0 1 99NS•2 2.305 2.382 3 1 95 4EW•2 2.930 3.224 10 92 2 7T•2 3.652 3.569 -2 7 4 89NS•3 4.883 4.862 0 1 85 13T•3 6.055 6.266 3 11 14 75EW•3 6.856 7.319 7 55 28 18NS’4 7.539 7.783 3 34 44 21T•4 8.652 9.593 11 6 27 67EW•4 10.488 10.331 -1 4 60 35203ci.)Eci.)Cl)CII)Eci)Cl)-e0Cci)Eci)Cl)-e-eC$-5 0 5 10 15 20 25 30 35Level NumberFigure H.l. Comparison of experimental (G) and analytical ( ) mode shapes for fundamentalEW translational mode (EW. 1)Translational DOF (EW).... I.... I.... I.... I.... I.... I.... I....1.2501.0000.7500.5000.2500.000-0.2505.0004.0003.0002.0001.0000.000-1.0001.5001.0000.5000.000-0.500-5 0 5 10 15 20 25 30 35Level NumberTranslational DOF....I....I....I....I....I....I....I....-5 0 5 10 15 20 25 30 35Level Number0o0 00000000000Rotational DOF000...I....I....I....I....I....I....I....2041.500Translational DOF (EW)1.0000.500Cl)0.000CE -0.500-1.000 • I . . I . I . . I . I • I . . I-5 0 5 10 15 20 25 30 35Level Number2.000Translational DOF (NS)• 1.000j)E0.000Cl)-1.000C$ -2.000-3.000-5 0 5 10 15 20 25 30 35Level Number2.000Rotational DOF_01.0000.000-1.00000-2.000-5 0 5 10 15 20 25 30 35Level NumberFigure 11.2. Comparison of experimental (0) and analytical ( ) mode shapes for second EWtranslational mode (EW•2)2051.5001.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.000-1.500Level NumberFigure H.3. Comparison of experimental (0) and analytical ( ) mode shapes for third EWtranslational mode (EW’3)Translational DOF (EW)....I....I....I....I....I....I....I....0 5 10 15 20 25 30 35Level Number-5‘1)C)CC,)CI)C,)C0Translational DOF (NS)0....I.,..I....I....I...rI....I....I....0 5 10 15 20 25 30 35Level Number0-5Rotational DOF....I....I....I....I....I....I....I....-5 0 5 10 15 20 25 30 35206C.)CC.)0ci)$ci)C.)cc•)0$Figure H.4. Comparison of experimental (G) and analytical ( )translational mode (EW•4)mode shapes for fourth EW1.5001.0000.5000.000Translational DOF (EW)0-0.500—1.000 • I . . I . . I . . I . . I . . I . . I-5 0 5 10 15 20 25 30 35Level Number10Translational DOF5.000 -0 00 0 00.000 -0 0-5.000 -00 0—10 I • I • • • • I • • • I • • I • • • • I • • I •-5 0 5 10 15 20 25 30 35Level Number1.500Rotational DOF1.000 -0.500 -0.000 --0.500 -—1.000 ....I....I....I....I...•I....I....I....-5 0 5 10 15 20 25 30 35Level Number207‘SEI).5S)cl0-5 0 5 10 15 20 25 30 35Level NumberFigure H.5. Comparison of experimental (0) and analytical ( ) mode shapes for fundamentalNS translational mode (NS•1)Translational DOF (EW)00000o000....I....I....I....I....I.... I.-5 0 5 10 15 20 25 30 35Level Number1.5001.0000.5000.000-0.5001.2501.0000.7500.5000.2500.0001.5001.0000.5000.000-0.500-1.000-1.500-5 0 5 10 15 20 25 30 35Level Number.5ci)II)rJ)0Rotational DOFrj’000- 0,....I....I....I....I....Ir...I....I....208201)C,)CI.)EC.)C,)CEC,)CELevel NumberFigure H.6. Comparison of experimental (0) and analytical ( ) mode shapes for second NStranslational mode (NS•2)Translational DOF (EW)00 00000 0000 000 00....I.... I....I.... I.... I.... I....I....-5 0 5 10 15 20 25 30 35Level Number100.000-10-201.5001.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.000Translational DOF (NS).r..I,...I....I....I....I....I..r.I....0 5 10 15 20 25 30 35Level Number-5Rotational DOF....I....I....I....I....I....I....I....0000-5 0 5 10 15 20 25 30 35209C.)-d-d0C..)c)-d0Figure H.7. Comparison of experimental ()translational mode (NS•3)and analytical ( ) mode shapes for third NS00 000 00 0Translational DOE (NS)002.000- Translational DOF (EW)0.000 --1.000 --2.000 --3.000 --4.000 --5.000 I....I....I....I.... I....I....I....-5 0 5 10 15 20 25 30 35Level Number1.5001.0000.5000.000-0.500-1.000-5 0 5 10 15 20 25 30 35Level Number1.500Rotational DOF1.0000.5000.000-0.500 --1.000 ....I....I....I....I....I....I....I....-5 0 5 10 15 20 25 30000)0)ILevel Number352101.500L0000.)- 0.500C/)0.000-0.500-1.0001.5001.0000)E0.000C-0.500-1.0001.5001.0000.5000.000C$ -0.500-1.000Figure H.8. Comparison of experimental (0) and analytical ( ) mode shapes for fourth NStranslational mode (NS•4)00Translational DOF (EW)....I....I....I....I...I....I....I....-5 0 5 10 15 20 25 30 35Level NumberTranslational DOE (NS)00II 1.1 II 1.1.1 I I III • liii III II I •I I ii.-5 0 5 10 15 20 25 30 35Level NumberRotational DOF- 00 00....I....I•••II•...I....I.••II...II..I•00-5 0 5 10 15 20 25 30 35Level Number2111.500C’,0C’,0C’,0$o00Translational DOF (EW) 00.... I.... I.... I.... I.... I.... I.... I....-5 0 5 10 15 20 25 30 35Level Number1.0000.5000.000-0.5006.0004.0002.0000.000-2.0001.5001.0000.5000.000Translational DOF (NS)000000....I....I....I....I...,I....I....I....-5 0 5 10 15 20 25 30Level Number35-5 0 5 10 15 20 25 30 35Level NumberFigure 11.9. Comparison of experimental (‘) and analytical ( ) mode shapes for fundamentaltorsional mode (T•1)2121.500ci.)UCci)Sci)UCl)CSci)Sci)C.)Cl)C$Level NumberFigure H. 10. Comparison of experimental (G) and analytical ( ) mode shapes for secondtorsional mode (T•2)000Translational DOF (EW)0....I....I..rrI....I....I....I....I....-5 0 5 10 15 20 25 30 35Level NumberTranslational DOF (NS)0....I....I....I....I....I....Ir...I..,.-5 0 5 10 15 20 25 30 35Level Number1.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.000-1.5000Rotational DOF....I....I....I....I....I....I....I....-5 0 5 10 15 20 25 30 352131.5001I)C,,EC.)CtC)0Eci)Cd)0-5 0 5 10 15 20 25 30 351.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.0001.5001.0000.5000.000-0.500-1.000Level NumberTranslational DOF (NS)....I....I....I....I....I....I....I....-5 0 5 10 15 20 25 30 35Level Number-5 0 5 10 15 20 25 30 35Level NumberFigure H. 11. Comparison of experimental (0) and analytical ( ) mode shapes for thirdtorsional mode (T•3)2141.5001.0000.5000.000-0.500-1.000-1.5001.500• 1.000E0.500cj0.0000-0.500-1.0001.5001.0000.5000.000-0.500-1.000Level NumberFigure H. 12. Comparison of experimental (0) and analytical ( ) mode shapes for fourthtorsional mode (T•4)-5 0 5 10 15 20 25 30 35Level Number0Translational DOF (NS)000....I....I....I.,.,I....I....I.r.,I....0 5 10 15 20 25 30 35Level Number0-5Rotational DOF....I....I....I....I....Ir...I....,....-1.5000-5 0 5 10 15 20 25 30 35215

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