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Operation and control of a seismic simulator Latendresse, Vincent 1999

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OPERATION AND CONTROL OF A SEISMIC SIMULATOR by VINCENT LATENDRESSE B.A.SC. Universite de Sherbrooke, 1991 M.A.Sc. University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 1999 ©Vincent Latendresse, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Department Date A/lftrcli ^ i ^ f /^ 77 DE-6 (2/88) Abstract This dissertation deals with issues related to digitally controlled hydraulic shake tables with multi-axis degrees of motion. The recently upgraded table at the University of British Columbia was used for a variety of experiments, demonstrating a number of important issues associated with using a seismic simulator to conduct a test. Physical issues are associated with the stiffness and weight of the table, the force rating of the actuators and the capacity of the hydraulic power supply. Control issues are associated with the computer control algorithms, the configuration of analogue and digital controllers and the feedback system. As part of this study, a simplified simulation method was developed to determine the physical demands of a test sequence on a hydraulic system. The method can be efficiently applied to calculate the supply pressure drop, that results from the hydraulic actuator motions. An algorithm that removes undesirable effects of terminal velocity and displacement of a simulated earthquake of prescribed duration was introduced as part of this thesis. It proved to be a powerful tool for the preparation of earthquake time histories for simulation by a state-of-the-art controller. Post-compensation is used to limit the natural permanent drift and terminal velocity that occurs in recordings of earthquake motions. Results from a number of tests conducted at the University of British Columbia were used to demonstrate performance characteristics and limitations of shake table testing. A series of tests conducted on the table with rigidly attached weights helped calibrate the simulation model. The replication performance of the shake table was investigated with the results from test on the dynamic behaviour of telecommunication equipment racks. A 0.27 scale model of as-built bridge bent and a quarter-scale model of a steel plate shear wall building module were tested with the U.B.C. seismic simulator. These studies demonstrated the complexity of the control system and its interaction with the physical parameters of the shake table. iii Contents Page Abstract ii Contents iv List of Figures ix List of Tables xii Dedication xiii A cknowledgements xiv Chapter 1 Introduction 1 1.1 Earthquake Engineering Research 1 1.2 Shake Table Usage in Civil Engineering 3 1.3 The U B C Shake Table 9 1.4 Certain Problems Associated with Shake Table Testing 11 Chapter 2 Plan and Scope of this Thesis 14 2.1 Aims and Objectives 14 2.2 Scope 15 2.3 Organization 15 Chapter 3 Literature Review 19 3.1 Shake Table Research 19 3.2 Modern Civil Engineering Shake Tables 21 3.3 Digitally Controlled Shake Tables 27 Chapter 4 Shake Table Performance 29 4.1 Background 29 4.2 Hydraulic System Components 30 4.2.1 Hydraulic Actuators 30 4.2.2 Multi-Stage Servovalve 35 4.2.3 Hydraulic Power Supply 40 4.2.4 Accumulators 41 4.2.5 Platform 41 4.3 General System Performance 42 4.3.1 System with Rigid Payload under Sinusoidal Excitation 42 4.3.2 System with Flexible Payload under General Dynamic Excitation 46 4.4 Capabilities of a Hydraulic System 50 4.5 Flow Demands in Hydraulic System 51 4.5.1 Accumulator Flow Relation 52 4.5.2 Actuator Flow Relation 53 4.5.3 Hydraulic Power Supply Flow Relation 53 4.5.4 Flow Model 54 Chapter 5 Control of Shake Tables 57 5.1 Basic Control Elements 57 5.1.1 Servovalves and Controller 58 5.1.2 Digital Servovalves 59 5.1.3 Actuators 59 5.1.4 Load or Specimen 60 5.1.5 Signal Generator 60 5.1.6 Feedback Elements 61 5.2 Level of Digital Control 61 5.3 Multivariable Control 64 5.4 Digital Multivariable Control of Earthquake Records 70 5.4.1 Post-pulse Compensation of Strong Motion Records 71 5.5 Multi-axis Control 74 5.5.1 Control of Over Restraint 74 5.5.2 Compensation and Stabilization 76 Chapter 6 The UBC Earthquake Simulator 11 6.1 Hardware 79 6.1.1 Platform 80 6.1.2 Actuators 81 6.1.3 Hydraulic Power Supply 82 6.1.4 Accumulator 84 6.1.5 Summary of Hardware Characteristics 85 6.2 Horizontal Sinusoidal Performance Envelopes 86 6.3 Control System 88 6.3.1 VAMP 89 6.3.2 MEVCS 89 6.3.3 Digital Signal Generator 90 6.3.4 Test Article Protection Hardware (TAPS) 90 6.4 General Control Scheme 91 Chapter 7 Rigid Mass Testing 96 7.1 Background 96 7.2 Test Objectives 96 7.3 Description of the Specimen 97 7.4 Instrumentation 98 7.5 Description of Tests 99 7.5.1 Preparation of the Input Time Histories 99 7.5.2 Test Schedule 101 7.6 Results from Tests 104 7.7 Discussion of Results 105 7.7.1 Reproducibility of Results 105 7.7.2 Influence of Load 107 7.7.3 Comparison of Simulated and Measured Values 108 7.8 Summary and Conclusions 115 vi Chapter 8 Steel Shear Wall Testing us 8.1 Background 118 8.2 Test Objectives 119 8.3 Description of the Specimen 120 8.4 Instrumentation 121 8.5 Description of Tests 122 8.5.1 Preparation of the Input Time Histories 122 8.5.2 Test Schedule 123 8.6 Results from Tests 125 8.7 Discussion of Results 127 8.8 Summary and Conclusions 132 Chapter 9 Bridge Bent Testing 135 9.1 Background 135 9:2 Objectives of Tests 135 9.3 Description of the Specimen 136 9.4 Instrumentation 138 9.5 Description of Tests 139 9.5.1 Preparation of the Input Time History 139 9.5.2 Test Schedule 145 9.6 Results from Test 146 9.7 Discussion of Results 146 9.8 Summary and Conclusions 150 Chapter 10 Seismic Rated Relay Rack Testing 152 10.1 Background 152 10.2 Objectives of Tests 152 10.3 Specimen description 153 10.4 Instrumentation 154 10.5 Description of Tests 156 10.5.1 Preparation of the Input Time History 156 10.5.2 Test Schedule 160 10.6 Results from Test 162 10.7 Discussion of Results 163 10.8 Summary and Conclusions 164 Chapter 11 Summary, Conclusions and Further Research 167 Chapter 12 List of References 171 Appendix A 179 Appendix B 189 Appendix C 195 viii List of Figures Page Figure 1 -1 : The U B C shake table 10 Figure 4-1: Principal components of a shake table system 29 Figure 4-2: Simple piston arrangement 32 Figure 4-3: Total effective stiffness of actuator 33 Figure 4-4: Diagram o f a pi lot stage spool/sleeve assembly 37 Figure 4-5: Force velocity diagram for servovalve-actuator system 39 Figure 4-6: Performance envelope plot of an seismic simulator 44 Figure 4-7: Simple shake table/specimen system 47 Figure 4-8: Forces acting on actuator 48 Figure 4-9: Schematic representation of f low model 56 Figure 5-1: Basic control elements of a seismic simulator 58 Figure 5-2: Analog and digital transducer output 62 Figure 5-3: Systems with different levels of digital control 63 Figure 5-4: Mult ivariable control systems 67 Figure 5-5: Example of compensation post-pulses 71 Figure 5-6: Six degrees of freedom of a r igid mass 75 Figure 6-1: Possible configurations of the shake table at U B C 78 Figure 6-2: V iew of actuator wi th flapper/nozzle type servovalve 82 Figure 6-3: V iew of actuator w i th a voice-coil servovalve 83 Figure 6-4: Hydraulic power supply 84 Figure 6-5: Performance envelopes for longitudinal axis of motion 87 Figure 6-6: Performance envelopes for transverse axis of motion 88 Figure 6-7: Control scheme of U.B.C. simulator 92 Figure 6-8: Control frequency bands 93 Figure 6-9: Spectral density matrix 94 Figure 6-10: Structure of multivariable impedance fi le 95 Figure 7-1: Rigid mass specimen on shake table 98 Figure 7-2: Measured longitudinal acceleration of shake table during sine test (number 21) 100 Figure 7-3: Measured longitudinal displacement of shake table during sine test (number 21) 100 Figure 7-4: Measured longitudinal acceleration of shake table during Joshua test (number 24) 101 ix Figui •e 7-5: Measured longitudinal displacement of shake table during Joshua test (number 24) 102 Figui •e 7-6: Measured longitudinal acceleration of shake table during V E R T E Q I I test (number 25) 102 Figui 'e 7-7: Measured longitudinal displacement of shake table during V E R T E Q I I test (number 25) 103 Figui •e 7-8: Measured supply pressure time history for V E R T E Q I I test 25 106 Figui •e 7-9: Measured supply pressure drop for three consecutive tests (run number 28) 106 Figui •e 7-10: Three 3 Hz test sequences with different loads (tests number 9, 15, 21) 108 Figui •e 7-11: Pressure loss of a 3 Hz test sequence (test number 21) 111 Figui 'e 7-12: Pressure loss of a V E R T E Q I I test sequence (test number 25) 111 Figui 'e 7-13: Force demands of a 3 Hz test sequence (test number 21) 112 Figui 'e 7-14: Force demands of a V E R T E Q I I test sequence (test number 25) 112 Figui re 7-15: Capacity and demand for typical Sine test (test number 21) 114 Figui re 7-16: Capacity and demand for typical V E R T E Q I I test (test number 25) 114 Figui re 7-17: Recorded and measured pressure drop for l imit test (test #23) 115 Figui re 7-18: Comparison of recorded demand and capacity for l imi t test (test #23) 115 Figui re 8-1: Steel plate shear wall system viewed in the longitudinal direction 121 Figui re 8-2: Recorded table acceleration for run number 28 126 Figui re 8-3: Typical recording of storey acceleration for run number 28 126 Figui re 8-4: Recorded acceleration of the table with significant frequency noise 128 Figui re 8-5: Normalized fourier spectrum of signal wi th noise 129 Figu re 8-6: Dampers added on second story panel 129 Figu re 8-7: Recorded table acceleration of Tarzana replication test (run #30) 130 Figu re 8-8: Normalized fourier spectra of Tarzana replication test 130 Figu re 8-9: Comparison of force requirements for test run 28 131 Figu re 8-10: Comparison of force requirement for test run 29 131 Figu re 8-11: Demand and capacity of table during the test run 28 133 Figu re 8-12: Demand and capacity of the table during test run 29 133 Figu re 9-1: View of concrete bent specimen 137 Figu re 9-2: Joshua earthquake record with time increment of 0.02 sec (original) 141 Figu re 9-3: Joshua earthquake record wi th time increment of 0.01 sec (compressed) 142 Figu re 9-4: Joshua earthquake record wi th time increment of 0.006 sec (compressed) 143 Figu re 9-5: Recorded table acceleration from test number 7 147 Figu re 9-6: Recorded table displacement f rom test 7 147 Figu re 9-7: Recorded top o f specimen acceleration from test 7 148 Figui re 9-8: Peak displacement and acceleration errors for init ial test sequences 148 Figui re 9-9: Peak displacement and acceleration errors for second set of test sequences 149 Figui re 9-10: Calculated demand and capacity for highest amplitude bent test 150 Figui re 10-1: Components of relay racks 154 Figui re 10-2: 48 cm and 58 cm racks with obsolete equipment load 155 Figui re 10-3: Comparison of original and recorded acceleration waveforms 158 Figui re 10-4: Comparison of Fourier spectrum of the recorded and original waveform 158 X Figure 10-5: Comparison of calculated response spectrum 159 Figure 10-6: Comparison of original and replicated displacement traces 160 Figure 10-7: Typical acceleration recording for sine sweep test 161 Figure 10-8: Typical displacement recording for a sine sweep test 161 Fi g U re 10-9: Calculated errors for V E R T E Q I I replication 164 Figure 10-10: Calculated demand and capacity for typical V E R T E Q I I replication 165 xi List of Tables Page Table 1 - 1 : Shake table testing facilities- North American laboratories (as of 1998) 5 Table 1-2: Shake table facilities- representative international facilities (as of 1998) 7 Table 6-1: Summary of table hardware characteristics 86 Table 7-1: Table payload during testing 97 Table 7-2: Purpose of rigid mass testing instrumentation 99 Table 7-3: Summary of rigid mass tests 103 Table 8-1: Purpose of steel shear wall testing instrumentation 122 Table 8-2: Characteristics of time histories considered for study of steel plate shear wall 123 Table 8-3: Summary of steel plate shear wall tests 124 Table 9-1: Purpose of bridge bent testing instrumentation 138 Table 9-2: Summary of bridge bent tests 146 Table 10-1: Purpose of B C Tel testing instrumentation 155 Table 10-2: Summary of BC Tel testing 161 xii To Ullr xiii = Acknowledgements First I would like to thank my parents, Hubert and Solange Latendresse, and my friends who supported me during all my studies. I am obliged to my supervisor, Dr. Carlos E. Ventura, for his assistance, and also the chance he gave me to work on such a project. I would like to thank the members of my various examination committees; Dr. Donald L. Anderson, Dr. Ricardo O. Foschi, Dr. Helmut G.L. Prion, and Dr. Sheldon Cherry for their interest and guidance in my studies. I would like to kindly thank Mr. Robert C. Tauscher, the president of TEAM Corporation, and all the members of TEAM Corporation who aided in this project. A very special thanks to Mr. Klaus L. Cappel, designer and analyst, for his gracious help and many constructive technical comments. I am indebted to Mr. Howard R. Nichol, electronics technician, for his full and capable backing during all the projects mentioned in this thesis and many more. I gratefully acknowledge Mr. Robert Postgate, the rest of the machine shop, computer and secretarial staff of Civil Engineering for their many helpful suggestions and services during my years at that department. I would like to acknowledge the financial support of the Natural Science and Engineering Research Council (NSERC). xiv CHAPTER 1 Introduction 1.1 E a r t h q u a k e E n g i n e e r i n g R e s e a r c h Earthquakes are one of the most destructive forces of nature. They can, in a few seconds, destroy or damage buildings, bridges, and other civil engineering structures. Worst of all, they can kill, injure and render homeless a whole population. John Milne^, one of pioneers of modern seismology, realized that recording and reproducing earthquake motions could benefit scientific research. The motions could be analysed, measured and reproduced once they were recorded. This information could then be used to better the understanding of earthquake effects on structures. Earthquake engineering research has improved since this unrefined start, but the economic and human costs of a major quake are still linked with the strengths and weakness of structures. The 1989 Loma Prieta and 1994 Northridge earthquakes in California caused hundreds of deaths and a total economic loss exceeding 50 billion (U.S.) dollars. The 1995 Kobe or Great Ffanshin earthquake in Japan resulted in damage estimated at 200 billion dollars, 1% of Japan's gross national product, and casualties exceeded 5000. All these regions are expected to experience the effects of much larger ground motions^ 1 Chapter 1 Earthquake Engineering Research The proper use of engineering principles can reduce fatalities and the economic loss that an earthquake incurs. These principles have been developed, in the case of seismic engineering, through observation of actual damage to structures and testing of models. Unlike other types of engineers, civil engineers rarely proof-test their structures .^ The prototypes of electrical and mechanical equipment are usually put through rigorous testing before they are produced. This type of testing is precluded for civil engineering structures, since these are large and not mass produced. Civil engineers must rely on experience, testing and computer models to predict the performance of structures under various loads [ 5 ] [ 6 ]. Engineers tend to be conservative in their design because of uncertainties in the seismic behaviour of structures. Testing generates data that can be used to improve state-of-practice building methods. Even small improvements in design and construction techniques will have a large impact on the capital investments made on new structures. Research can provide more earthquake-resistant and cost-effective designs. The retrofit and rehabilitation techniques used to repair structures or enhance their seismic performance also need validation. Cost-effective retrofit and rehabilitation schemes can make, massive investments in the existing structures after a seismic event unnecessary while reducing the probability of injury or death from disasters. Numerous techniques have been developed to research the structural response to earthquake motions^: • shake table testing, • reaction-wall testing, 2 Chapter 1 Shake Table Usage in Civil Engineering • prototype testing using existing structures, • buried high-explosive excitation testing, • instrumentation of existing structures. All of these methods have advantages, disadvantages and applications in earthquake engineering research. This thesis will concentrate on shake table testing. Excellent reviews of the capabilities and limitations of the other types of testing are included in the referenced m a t e r i a l ^ ™ . In this document the terms shake table and seismic simulator are used interchangeably. In the practical jargon used in the high performance hydraulic field these terms are equivalent, so both are used in this thesis to lighten the text. 1.2 S h a k e T a b l e U s a g e in C i v i l E n g i n e e r i n g Shake table testing, as mentioned in the previous section, is not the only way to simulate the effects of earthquakes on structures. However, it does have certain advantages over the other testing techniques. Shake table testing is the most realistic way to simulate earthquake motions in a controlled environment. Test articles can be subjected to both historical and artificial ground motions very easily. The amplitude of these input vibrations can be controlled. This is crucial in the study of structural elements sensitive to rate of loading. Shake table tests can be employed to study the behaviour of systems too complex to model 3 Chapter 1 Shake Table Usage in Civil Engineering mathematically. The effects of material non-linearities on the overall, or global, response of structures can observed from the point of initial damage to that of structural failure. Tests can also provide information on the behaviour of structural components such as connections. Shake tables are the only means to properly simulate inertia force on distributed mass systems in a laboratory environment. This capability is critical in the study of hydro-dynamic effects on dams and of the effects of inertia forces on tall structures. One disadvantage of shake table testing is the inability to model realistically the effects of soil-structure interaction, because of payload limitations. Furthermore, full-scale structural specimens would be too large and heavy for any of the existing tables. Finally, the total stroke of a table can also limit its capabilities to simulate historical earthquakes. The field of investigation which is addressed by shake table testing can be divided into two main classes: qualification testing, and research and development testing. Qualification testing is usually executed to test the capabilities of mechanical or electrical equipment to withstand a prescribed motion. The nuclear and telecommunication industry use this type of test to verify the adequacy of their systems. In most cases, the equipment is just given a "pass or fail" evaluation. Any excursion into the non-linear range of behaviour is generally regarded as unnecessary. The construction of this type of equipment is usually complex; therefore, the behaviour of a mathematical model is rarely compared to the test results. Research and development testing is usually executed by universities and government 4 Chapter 1 Shake Table Usage in Civil Engineering organizations. Finite element models used for the design of structures have to be calibrated with test data. There are a number of variables in modelling structural behaviour which sometimes need to be verified: the amount of modal damping, non-linear behaviour, boundary conditions, impacts. Shake table tests have also been key to the acceptance of new seismic design concepts such as: base isolation, active structural control and passive energy-dissipating devices. They are also needed to characterize special phenomena like: fluid structure interaction and dynamic buckling of tanks^ 7-"-8^9-"^ "-6-'. Shake tables have been used in earthquake engineering for many years. The size and capacity of shake tables vary tremendously. Some are made for small scale testing, while others like the 15m X 15m Tadotsu Island table in Japan can carry 1000 ton specimens. A list (in alphabetical order) of the major shake table facilities in North America is included in Table 1-1. Similarly, a list of the major international shake table facilities is included in Table 1-2^10^7l As can be noted from these lists, only a few facilities can simulate the effects of earthquake motions on large to full-scale structures. Institution State/Prov-ince Pay-load [ton] Size [mXm] DOF Freq. Range [Hz] Stroke [m] Velocity [m/s] ANCO Colorado 1.8 1.56 dia. 6 0-40 0.1 2.3 Arizona State University Arizona N.A.a 3 X 3 N.A. N.A. N.A. N.A. CERL Illinois 60 3.7 X 3.7 6 0.1-60 0.15 0.76 Cornell University New York 2.7 2.1 X 1.5 2 hor& vert 0-50 0.076 0.8 Drexel University Pennsylva-nia 0.41 1.2X1.8 1 0-2,000 0.006 N.A. Table 1-1: Shake table testing facilities- North American laboratories (as of 1998) 5 Chapter 1 Shake Table Usage in Civil Engineering Institution State/Prov-ince Pay-load [ton] Size [mXm] DOF Freq. Range [Hz] Stroke [m] Velocity [m/s] EERC, Univer-sity of California California 45 6.1 X6.1 6 0-20 0.152 0.635 NASA Alabama 1 3 X 4 . 5 6 2.44 0.1 Rice University Texas 0.68 1.52X1.52 1 0-75 0.076 0.89 Stanford Univer-sity California 2.2 1.5 X 1.5 1 0-50 0.032 0.635 State University of New York at Buffalo New York 20 3.7 X 3.7 5 0.1-60 0.15 0.76 Union Carbide, Oak Ridge Tennessee 7 1.83X1.83 2 hor& vert 0.1-20 0.193 0.3 University of Brit-ish Columbia British Columbia 16 3 X 3 3 or 4 0-50 0.152 0.127 University of CA at Los Angeles California 0.51 1 X 2 1 0-30 0.037 2.54 University of Cali-fornia at Irvine California 9.1 3 X 3 4 1-50 0.254 0.254 University of Cali-fornia San Diego California 35.6 3 .0X4.9 1 0-50 0.31 0.89 University of IL at Urbana-Cham-paign Illinois 4.6 3.7 X 3.7 1 0.1-50 0.051 0.381 University of Nevada at Reno Nevada 50 4.3 X 4.3 1 & 2 0.1-33 0.3 1 University of Washington Washing-ton 9 2 .4X1.8 1 0-1,000 0.038 N.A. Universite de Montreal Quebec 15 3 .4X3.4 1 0-50 0.25 0.8 Westinghouse Pennsylva-nia 3.1 3.1 X3.1 2 0-500 0.61 2.54 Wyle Alabama 72.3 6.1 X6.1 2 0-100 0.3 0.89 Wyle California 13.2 2 .4X2 .4 2 0-70 0.3 1.17 Table 1-1: Shake table testing facilities- North American laboratories (as of 1998) a. N.A.= information not available 6 Chapter 1 Shake Table Usage in Civil Engineering Institution Country Pay-load [ton] Size [mXm] DOF Freq. Range [Hz] Stroke [m] Velocity [m/s] Ansaldo Mec-canica Nucleri, Genoa Italy 7 3 .5X3 .5 2 hor& 1 vert 0.1-60 0.07 0.86 Ctr D'Etudes Nucleaires, Saclay France 100 6 X 6 2 0.01-100 0.125 0.7 Ctr D'Etudes Nucleaires, Saclay France 20 3.1 X3.8 1 0-100 0.2 1.0 ENEA, Rome Italy 10 4 X 4 2 0.5-50 0.1 0.5 HRB at KFA, Julich Germany 25 5 X 5 2 hor& 1 vert 0.1-100 0.1 0.8 Hydroproject Res Inst. Moscow Russia 50 6 X 6 3 0.1-100 0.1 0.6 I.C.C.P.D.C., lasi Romania 140 10X 10 1 N.A. N.A. N.A. I.N.C.E.R.C., Bucharest Romania 60 6 X 6 6 N.A. N.A. N.A. ISMES Italy 30 4 X 4 6 N.A. N.A. N.A. Kajima Corp.Tokyo Japan 50 5 X 5 6 0.1-60 0.1 0.9 Korea Inst, of Machinery & Metal, Deajon Korea 30 4 X 4 6 0.1-50 0.2 0.75 Kumagai-Gumi Corp, Tsukuba Japan 70 5 X 5 6 0.1-70 0.08 0.6 LNEC, Lisbon Portugal 60 5 X 5 3 N.A. N.A. N.A. Mitsubishi Japan 100 6 X 6 3 N.A. a N.A. N.A. Nat'l Tech Univ., Athens Greece 10 4 X 4 6 0.1-100 0.1 0.89 NRC for Disaster Prevention, Tsu-kuba Japan 500 1 5 X 1 5 1 hor& 1 vert 0-50 0.03 0.37 Nuclear Power Eng Test, Tadotsu Japan 1,000 15X 15 1 hor& 1 vert 0-30 0.2 0.75 Table 1-2: Shake table facilities- representative international facilities (as of 1998) 7 Chapter 1 Shake Table Usage in Civil Engineering Institution Country Pay-load [ton] Size [mXm] DOF Freq. Range [Hz] Stroke [m] Velocity [m/s] Russia Russia 1,760 3 0 X 3 0 1 hor& 1 vert 0-50 0.152 N.A. SOPEMEA, Velizy France' 10 3 X 3 2 N.A. N.A. N.A. The NCR on Earthquake Eng., Taipei Taiwan 30 5 X 5 6 0.1-50 0.08 0.6 Tonji University, Shanghai China 15 4 X 4 2 0.1-50 0.10 1.0 Univ. of Kiril & Metodji, Skopje Macedonia 40 5 X 5 2 hor& 1 vert 0.1-30 0.125 0.64 Univ. of Mexico, Mexico City Mexico 20 4 .5X2 .5 1 0.1-50 0.051 0.381 University of Bris-tol England 15 3 X 3 6 0-100 0.3 0.6 Wtr Cons. & Hydro Pwr Res. Ints., Beijing China 25 5 X 5 2 hor& 1 vert 0.1-120 0.025 0.40 Table 1-2: Shake table facilities- representative international facilities (as of 1998) a. N.A. = information not available There are a number of limitations associated with using reduced-scale models on shake tables. Reduced-scale models cannot reliably reproduce some of the non-linear behaviour expected in full-scale structures such as brittle failure of steel connections and bond-slip of reinforced bars in concrete construction. The complex interaction of structural components with windows, non-bearing walls and other parts of buildings needs to be modelled on large-scale specimens. A initiative in the North American research community is being formed to promote large-scale testing of structures with shake tables and other methods to eliminate questions concerning scale effects'1 ^ l 3 ! . This would require the construction of several new testing facilities and the upgrade of existing ones. b Chapter 1 The U B C Shake Table The ideal shake table would be able to generate a desired dynamic excitation without it being distorted. Since all systems have physical limitations, this is rarely the case. Specimen weight, actuator capacity and stroke, finite hydraulic power, friction in the system and other factors limit the range and amplitude of the possible motions of a seismic simulator. These limits are set by the facility's hardware and control system. Many of these limitations have been observed through the years at different sites around the world. The addition of new digital controllers, bigger pumps, actuators with more responsive servo valves and longer stroke have helped to minimize these problems. However, these changes have made shake tables expensive and complex to operate. 1.3 T h e U B C S h a k e T a b l e The seismic simulator facility at the University of British Columbia was built in 1977. The funding for this project came from the Natural Sciences and Engineering Research Council (NSERC). The seismic simulator system included a single actuator that made the replication of one degree of freedom of motion possible. The controller was completely analog. The 3m X 3m aluminium platform was installed into a pit which permitted level access from the laboratory floor to the top of the table. A photo of the present day laboratory is shown on Figure 1-1. During the 1970's and 80's the simulator was used to investigate a large number of earthquake related problems. It was used to study the dynamic behaviour of model piles'12-', seismic forces on submerged structures'1and equipment isolation systems'14 .^ Passive energy 9 Chapter 1 The U B C Shake Table Figure 1-1: The UBC shake table devices'-15^ as well as a base isolation mechanisms^16! w e r e developed at U B C and tested on the table. Several other projects were conducted at the laboratory. At the start of the 1990's the structural dynamics group of the Civil Engineering Department concluded that the addition of several degrees of freedom of motion to the simulator would increase dramatically its testing capabilities. The technology associated with the control of electro-hydraulics had advanced a great deal over the proceedings two decades. These advances could also benefit the U B C researchers. The seismic simulator facility underwent a major upgrade in 1994-95. The main source of funding for this project came from B.C. Hydro, the science council of BC and the Department of Civil Engineering. This project included adding a number of hydraulic actuators in order to increase the possible number of degrees of freedom the table could replicate and also to 10 Chapter 1 Certain Problems Associated with Shake Table Testing modify the control system. The existing hydraulic power supply and platform were used without major modifications. These new actuators literally added new dimensions to the testing performed at the laboratory. The effects of multiple direction of motions on specimens could be studied. The drawback for this particular system was that actuator demands on the power system could lead to a deterioration of the expected performance. The original hydraulic power supply had been sized to provide flow for one actuator. The addition of four new actuators made large supply pressure drops possible, limiting the amount of force that could be delivered to the specimen. At the time of the upgrade the effect of the additional actuators on the system could not be reliably gauged. The other major modification to the system was the replacement of the single variable analog control system by a three variable digital feedback control system. This new technology provided the researchers with a system that could replicate earthquake motions more reliably. Test sequences could be repeated time after time almost identically with very little difference between the desired and recorded motions. 1.4 C e r t a i n P r o b l e m s A s s o c i a t e d w i t h S h a k e T a b l e T e s t i n g As with all highly complex testing systems, theoretical performance limits can be calculated, but these can only be taken as approximations due to the large number of unknowns that affect the performance of a prototype system. Some of these unknowns in a hydraulic shake table 11 Chapter 1 Certain Problems Associated with Shake Table Testing system are: (i) accurate knowledge of pressure loss in the pump and hose system, (ii) instrumentation noise, (iii) effects of loading on the performance of the actuators, etc. To gain insight into the true system performance, it was proposed that a series of performance and experimental tests be conducted. Analog control has historically been used in civil engineering shake tables. This technique had limitations, since the controllers had to be adjusted for every test in order to take into account the effect of different specimens. With digital control, the input signal to the actuators can be modified by the control algorithm, to take into account the interaction of the specimen with the system. Multi-variable control is hard to achieve with analog systems since a large number of operational amplifiers have to be adjusted in order to calculate the corrective feedback signal. This type of control can also be better implemented with digital control algorithms. More accurate and complex feedback schemes can also be implemented with digital control. The calculations associated with efficient multi-axis, multi-variable digital control are however still too time-consuming to allow for real-time compensation of input time histories. The use of digital control brings added flexibility to the upgraded system, but also new demands. The use of digital shaker control has historically been limited to linear non-destructive testing. This type of control has been applied in seismic qualification tests for nuclear power plant equipment, aerospace research, and automotive engineering, but rarely, if at all, in the field of structural dynamics. The active control of building vibrations is one exception to this. Digital control is used extensively in this field, but control algorithms in this research area are created to limit structural response, not to reproduce desired motions. The 12 Chapter 1 Certain Problems Associated with Shake Table Testing control strategies employed are therefore quite different. The performance of digital feedback control, when applied to the testing of large structures that enter the non-linear behaviour range, has never been investigated. Furthermore, the control system's performance determines the size and type of the experiments that can be conducted on a shake table. The control methodology used to command the system has to be fully understood and adapted to meet the expectations of non-linear dynamic testing. For this thesis, a simulation technique was developed. It calculates the flow demands associated with the replication of any acceleration time history. This algorithm will provide information on the capacity of a shake table and the demands of the test conducted on it. This will help researchers to determine if their test specimen is too large or heavy. A compensation algorithm was also devised to help prepare time histories for simulation by a digital three variable controller. Other issues associated with shake table testing will also be discussed. This will provide the reader with an understanding of certain problems associated with shake table testing. 13 CHAPTER 2 Plan and Scope of this Thesis 2.1 A i m s a n d O b j e c t i v e s The aims of this study are: • To gain testing experience using the newly improved U B C seismic simula-tor facility. • To assess the operational limits and devise means to predict shake table response to different applications. • To understand and adapt the concepts associated with digital feedback con-trol to this particular application. At the outset of this project, most of the specific details of how to achieve these objectives had not been developed. The first task was to get the simulator back on-line after the retrofit and learn how to adapt the new technology, then, through a number of scheduled tests, to elaborate techniques useful to researchers. These experiments shed light on a number of practical issues that had to be addressed in order to make the simulator work in an acceptable fashion. The final yields of this thesis reflect these concerns. The original aims of the project were therefore achieved, with a number of solutions developed from the questions and needs of researchers. These solutions became the contributions of the author to the current state of knowledge. They can be summarized as follows: 14 Chapter 2 Scope • The development of a simple simulation technique to gauge the operational limitations of a civil engineering seismic simulator. • The development of an efficient compensation technique to allow the use of historical earthquake records by a three variable digital feedback control system. • The accumulation and adaptation of information about prototype testing, instrumentation of test specimens and control of a digital system. 2.2 S c o p e This thesis will cover the subjects of hydraulic power control, instrumentation, and digital feedback control techniques, as used in civil engineering shake table tests. The amount of information on each of these subjects in the general field of knowledge is quite extensive, but very few documents, as will be mentioned in the literature survey, are appropriate for utilization in this particular field of testing. This thesis therefore does not try to be the ultimate reference in any of these specific subjects, but a general reference that can be used by engineers, technicians, and others that are involved in dynamic testing of large specimens. 2.3 O r g a n i z a t i o n This thesis covers the main topics of interest in the field of civil engineering seismic simulator testing. Although there exists a wealth of information on the results of previous tests conducted on such simulators, there is very little in the literature on performance capabilities of shake tables and the design of simulator experiments. Certain aspects of the performance of seismic simulators are of great interest to experimenters; for instance how large can the 15 Chapter 2 Organization specimen be, or what maximum force output can be expected from an actuator. This study will address these concerns, with a review of basic hydraulics and a general overview of system operation. It would be impossible to cover all the possible test types that can be executed on a simulator, but through a number of case studies the author intends intend to address the principal concerns that appear repeatedly in an experiment. The body of this thesis is divided into three parts. The first is a literature review; the second discusses the general performance of a digital earthquake simulator; the third part looks at the planning and execution of structural engineering tests on a shake table using a series of case studies. The first part consist of only one chapter giving a brief literature review of the use of shake tables for testing models of civil engineering structures. It also discusses the advent of digital control in seismic simulator facilities. It references a number of sources and gives the reader a short background on dynamic testing. The second part consists of three chapters on the general subject of hydraulic systems and their use in earthquake signal replication. Chapter 4 deals with the general hydraulic system components and general system dynamics. It has been included since the experimenters that come in contact with these types of systems are not generally familiar with the discipline of fluid power control. The limitations of such systems in reproducing transient signals is elaborated upon. This last objective is of particular interest for earthquake replication testing. The chapter includes a description of the major components of a shake table, their interaction 16 Chapter 2 Organization during a test and their general physical limitations. A description of the simulation method developed as part of this thesis is also included. It calculates the operational limits of most shake table. Chapter 5 describes the control of shake tables. The type of control systems used in shake table are detailed. Since digital control techniques are now an integral part of any leading-edge simulator, the concept of level of digital control is discussed. A classification method developed as part of this thesis is used to illustrate different examples. A detailed explanation of a new post-compensation pulse calculation method, introduced in this thesis, is also included. This algorithm solves problems associated with three-variable digital control. Chapter 6 illustrates the different elements of the previous chapter, using a case study of the UBC earthquake simulator. The major components of this particular facility are described, and its design and measured capabilities documented. The control algorithm that calculates the digital drive signal from the feedback measurements is summarized. The third part of the thesis is composed of four chapters and consists of descriptions of tests conducted at the U B C simulator. Through these accounts, several of the notions developed in the previous chapters are illustrated with practical case studies. All these chapters are structured in the same fashion, and relate in different levels of detail the concepts developed in the second part of the thesis. It should be noted that the author actively participated in all aspects of these tests. He collaborated with the researchers involved in these projects in the design, instrumentation and testing the various specimens. He was also instrumental in Chapter 2 Organization selecting the time histories used for testing and the processing of the recorded test data. Chapter 7 discusses the characterisation of the U.B.C. simulator through rigid mass testing. Several steel plates were attached to the shake table top and shaken with sinusoidal and transient signals to provide calibration data for the simulation model developed in Chapter 4. Chapter 8 discusses the testing of a steel plate shear wall specimen. In this case study the force limits of the simulator are demonstrated. The full capacity of the actuator was needed to force the specimen into non-linear behaviour and provided an example of high force requirement testing. Chapter 9 describes the testing of a scale model of an actual bridge bent located in Vancouver. This test illustrates the basic requirements of prototype testing for civil engineering shake tables. The scaling and compensation of test histories for use in a three-variable control simulator are detailed along with several other notions developed in Chapter 5. Chapter 10 discusses the testing of a telecommunication equipment rack. In this test, a time history provided in a standard protocol had to be replicated as exactly as possible. Certain physical limitations of the simulator hampered this process and some compromises had to be made. This chapter describes these adjustments and illustrates the control concepts associated with them. Chapter 11 concludes and summarizes the text. A complete list of references is also included. 10 CHAPTER 3 Literature Review 3.1 S h a k e T a b l e R e s e a r c h Earthquake simulators have been used extensively to reproduce the effects of ground motions on structures. John Milne, one the pioneers of seismology, used a crude railway truck shake table at Tokyo University. He investigated the effects of base excitation on buildings at the end of the last century^. At the start of this century, researchers used pendulums and unbalanced flywheels to actuate motion simulators. These reproduce different types of excitation on soil samples and models of tall buildings. However, it was only in the last 30 years that attention was paid to the development of suitable tables for earthquake simulation. The Experimental Institute for Models and Structures (ISMES) in Bergamo, Italy, was one of the first institutions to use modern technology to simulate the effects of vibration on models in the 1950's. A steel platform measuring approximately 3m by 4m could be excited by three different vibration-generating units. This table was used to test models of dams situated in Italy, Japan, Yugoslavia, the U.S.A. and Mexico. A replica of the Pirelli building, located in Milan, was also subjected to base excitation^17^18l In the 1960's, a number of vibration generating units were used to actuate shake tables. The 19 Chapter 3 Shake Table Research Electric Power Development Company of Tokyo built a 5m by 5m table in 1960 for studies on dams. It was driven either vertically or horizontally, by using an eccentric rotating mass drive^. The University of Chile put a table into service in 1965 that operated on a cam follower principle. A rotating disc with a seismograph cut edge actuated the table with the help of a lever system^. The National Laboratory of Civil Engineering in Lisbon, Portugal was reported in 1965 to have a shake table actuated with an electromagnetic shaker'211 The same type of shake table was also installed at ISMES in Bergamo'22^. These simulators could by controlled either by a sine wave generator or a random voltage generator. The latter could be used to drive test models with random vibrations of a constant spectral density. The ISMES table could also use magnetic tape recordings of real earthquakes as drive signals. All these early systems greatly helped to advance earthquake engineering research. They were the first machines that could adequately reproduce the effects of base motion on structures. Researchers could record and analyse results from scale model testing. However, these systems did have limitations. The eccentric mass vibration generators could not reproduce earthquake motions. The cam follower systems could not reproduce signals very accurately. Electromagnetic shaker-driven tables are still being used today, but also have several limitations. They cannot develop the power required to move heavy specimens, and are severely limited in their displacement stroke. This restricts their use in the testing of large scale models of civil engineering structures, which require high power output at low frequency. 20 Chapter 3 Modern Civil Engineering Shake Tables In the late sixties, a number of shake tables, 3m by 3m and larger, were designed^23l These simulators needed a power source that could subject nearly full-scale models to earthquake motions. Closed loop electrohydraulic systems were the only economically and technically feasible drive method. These systems do not have a large operating frequency range but they can produce large force outputs at high velocity with large displacement stroke. Electrohydraulic drives are still to this day the most popular way to actuate civil engineering shake tables. 3.2 M o d e r n C i v i l E n g i n e e r i n g S h a k e T a b l e s The use of the shake tables for testing models of civil engineering structures is well documented and there are a large number of papers and reports in the literature about the results of these investigations. There is considerably less literature on shake table facilities and the control system that drives them. A notable exception is the University of California at Berkeley's shake table, on which there is an abundance of information. Other good sources of information are the Institute of Environmental Sciences reports and proceedings, which contain a large amount of information about linear digital control of shake tables, and the proceedings of the World Conferences on Earthquake Engineering. Japan has at the present, the greatest number of large-scale shake tables in the world. These facilities include the large simulators at Tadotsu and the National Research Centre (NRC) for Disaster Prevention, Tsukuba. A number of other medium size state-of-the-art simulators have also been built in the last decade. The Kajima Corporation and the Kumagai-Gumi 21 Chapter 3 Modern Civil Engineering Shake Tables Corporation both operate 5m by 5m, six degree-of-freedom tables. The Mitsubishi Corporation operates a large 6m by 6m table with a payload capacity of 100 tons. These simulators are primarily used to study the seismic performance of new types of structural systems. In Japan, private construction companies are quite active in seismic research and have developed, along with the government, specific technology for use in shake table facilities'41^. For more information on these tables, see Table 1-2 on page 7. The Japanese large-scale earthquake simulator program was put into high gear after the 1973 oil crisis. At this time, laws were enacted to promote the use of nuclear power in Japan. The public had apprehensions about the earthquake resistance of complicated systems like a nuclear power plant. The government therefore decided to conduct large-scale proving tests of the most critical components of the facilities. These tests required very large high-power shake tables since the specimens were near full-scale containment vessels used in the reactor core. In 1975, funding for such simulator systems was appropriated by the government. This posed a number of technical problems since special actuators, high-flow servo valves and pump systems had to be designed. The Nuclear Power Engineering Centre (NUPEC) was established in 1976. The construction of the Tadotsu large-scale high-performance seismic simulator was completed in July 1982[24^25^. Its platform measures 15m by 15m and it can test models weighing 1,000 tons. Over twenty three experiments have been conducted on this platform since its construction. The primary design concern for this facility was that near full-scale specimens could be tested in it. The accuracy of replication of earthquake motions was therefore a secondary consideration'26 .^ 22 Chapter 3 Modern Civil Engineering Shake Tables European researchers have over the last decades been quite active in earthquake engineering research. As noted in the previous section, the Italians and Portuguese were pioneers in the field of shake table testing. This involvement of the Europeans in seismic research has only grown during the past years. Recently, a consortium of five major shake table laboratories in Europe was formed. The European Consortium of Earthquake Shaking Tables (ECOEST) includes these research groups • Laboratory of Earthquake Engineering, National Technical University, Ath-ens, Greece • Earthquake Engineering Research Centre, University of Bristol, UK ISMES, Bergamo, Italy • C3ES, (Centro de Estudos Especiais de Engenharia Sismica), LNEC, Lis-bon, Portugal. This consortium was formed to accomplish a pre-normative research programme in support of EuroCode 8. A number of experimental projects were devised to investigate priority design topics. The experimental work included shake table testing of infield frames, of scaled reinforced concrete frames designed for different ductility demands, and of scaled bridge models using three shaking tables in order to simulate asynchronous input motions^28l A comparative assessment of the shake tables of ECOEST was performed to insure that results obtained from different sites were comparable. Because of the distinctions in the facilities, direct comparisons were difficult. Each site has very different hardware, software, control systems and performance characteristics. A performance review of each site was 23 Chapter 3 Modern Civil Engineering Shake Tables therefore accomplished using two standard flexible test specimens. These specimens were designed and built in Bristol and were shipped between the facilities. These adaptable test articles had adjustable mass and variable natural frequency. A test methodology was devised, based on comprehensive set of tests performed on the tables in Athens and Bristol. A frequency response function test and time history reproduction tests were included in the performance evaluation. Both types were used on the flexible specimens and rigid payload. The single variable digital control algorithms, set-up for best match either on acceleration or displacement, performed well during these linear tests. A good match between acquired and achieved displacement and acceleration was observed. A non-linear test article is currently being developed. It will allow the table control systems to be tested repetitively under more severe load conditions'29^. The French operate a large seismic research facility, Tamaris, in Saclay near Paris. It contains several shake tables of different sizes, including the Azalee 6m by 6m platform. This laboratory is working on many projects including testing of piping technology and electrical equipment^ 30-'. The Institute of Earthquake Engineering and Engineering Seismology at the University of "Kiril and Metodij", Skopje, Republic of Macedonia, operates a large-scale shake table. The Institute has been involved in seismic research since 1965. The biaxial 5m by 5m simulator is controlled by an analog three-variable control system. At low frequencies, the system provides control in respect to displacement, while for higher frequencies in respect to acceleration'31^32^. The U.C. Berkeley shake table performance is extensively covered in a series of articles that 24 Chapter 3 Modern Civil Engineering Shake Tables span the table's life from the stage of conception to the present. These references describe the table size, capabilities and limitations'-33-'. It was noticed early on that a significant amount of geometric coupling and table-specimen interaction was present and that these limited the performance of the table. A number of tests were performed, and used to describe the simulator's dynamic performance. The resonant frequency of the oil columns for both of the major directions of movement and transmissibility for the foundation were investigated [34] [35] ^ t m e s a m e t j m e a computer model of a shake table was developed to analytically reproduce the experimental behaviour of these systems'36 .^ This model could then be used to determine the capabilities of seismic simulators in general. After this initial period of measuring the dynamic characteristics of the table no other investigations were conducted until the late 1980's. In 1988, a second series of tests was conducted to determine the shaking table-structure interaction effects^37!. This interaction was studied using three different types of loading namely: (i) bare table, (ii) with three large concrete blocks, and (iii) a large steel structure with a high centre of gravity. The results of these tests were used to identify the properties of the simulator, to compare the desired input time histories with the experimental ones, and also to compare the desired and experimental response spectra. This preliminary work was expanded into a full doctoral thesis published in 1991 on the subject of shake table-structure interaction^38]. The author of this thesis developed a number of uni-directional and bi-directional linear single degree-of-freedom (SDOF) systems to reproduce the recorded motion of the table. This exercise yielded good matches and one of the conclusions was that a table-specimen system can be represented by a simple dynamic model. This facility has recently undergone a major upgrade, which was completed in June 1996. A number of new actuators were added to convert the table from a biaxial to a triaxial simulator. The size of the 25 Chapter 3 Modern Civil Engineering Shake Tables accumulator banks that help the shake table sustain velocity in time of peak demand was increased approximately sevenfold and the control system was modified from a single variable feedback system to a three variable feedback system'39]. The reference text also mentioned a number of new projects to be investigated by the university staff, but no results except from a small performance test were included. As mentioned earlier, not many other facilities have covered their work as well as Berkeley. Other large American facilities with shake tables have published only a few papers on their shake tables'40]. These works describe the general features of the installations and not the performance of the systems as such. A study of the U.B.C. Earthquake simulator's performance was done in 1981'42]. This thesis developed a theoretical model of the different parts of the facility, in order to obtain an understanding of the behaviour of the shake table under operational conditions. This work provides a good reference on how the table used to behave, but, with the recent upgrade of the system, many of parameters of the study have changed. Therefore this work is of limited value at the present time. Control problems of large civil engineering shake tables have been discussed extensively over the years. A series of articles underline the major problems with this type of simulation'43]'44]'45]'46]. A number of conclusions can be drawn from these publications. Control problems become more apparent as specimen mass and eccentricity increase, or when one of the specimen resonant frequencies is close to the table's oil column resonant frequency. 26 Chapter 3 Digitally Controlled Shake Tables Off-line compensation could be used to increase test accuracy. More complex and efficient control algorithms can be implemented with the use of digital feedback control. 3.3 D i g i t a l l y C o n t r o l l e d S h a k e T a b l e s The idea of using digital control techniques in shake table systems is not new. The U.S. military and aerospace industry have been using these techniques for a number of years. It started in 1970 when the ground work for the use of digital control was laid out'47!. The early papers on this subject describe the implementation of such systems but not their practical use. In the mid 1970's, literature about real systems that use digital control began to appear'48-"49!'50!, e a r i y approach used a simple correction technique on the recorded response spectrum to compensate the initial drive history of the system. This yielded good results, but the method was cumbersome due to the limited computer power of the time. The experiments were limited to non-destructive testing of equipment and transport vehicles. Some seismic qualification testing was done on nuclear power plant equipment, but the test specimens were never pushed beyond the elastic limit. The focus of this particular research group shifted after this period to other topics of interest like aerospace testing. Therefore no other references to seismic testing were found after 1976. However, the development of digital control did not stop at this point, and there are many references that trace the advances in this field. With the advent of more powerful computers, the control algorithms have become more complex'51!'52!. The compensation techniques are now better able to take into account the resonance of a system, the interaction of the table-specimen, etc.'53!. 27 Chapter 3 Digitally Controlled Shake Tables Some European seismic simulators are now equipped with digital controllers but the control programs have not been used with great success when the specimen exhibits non-linear behaviour '5 4^. Recently, some tests on linear specimens using new digital control techniques have been quite successful'29 .^ The recently built single-axis shake table at Ecole Poly technique in Montreal has used digital control techniques with success ' 5 5 ^ 5 6 l A number of the iteration techniques and control algorithms were used on a steel frame that could be modified to produce linear or non-linear characteristics under the same excitation level without changing its dynamic characteristics. A performance indicator based on the acceleration response spectra was also developed to gauge the differences between the different control techniques. Three-variable control was used, along with an adaptable digital filter or an iterative test procedure. The available literature does not mention whether these schemes involve off-line or time domain compensation. The system has been reported to perform well when using the basic three variable technique, and it was this approach that proved the most stable in the frequency band of interest. The iterative procedure worked better if a full amplitude test was used to calibrate the algorithm, which can often prove to be a problem in civil engineering destructive testing. But again, this test and the ones recently conducted at the University of British Columbia[57] are rare examples of control programs being used to extrapolate the specimen behaviour into the non-linear behaviour range, since historically most of the experiments were non-destructive. 23 CHAPTER 4 Shake Table Performance 4.1 B a c k g r o u n d This chapter will review the basic components of a hydraulic shake table. Figure 4-1 shows a schematic diagram of the principal components of such a system.The hardware components used in a simulator system have some performance limitations which affect the overall operation of the shake table. The following sections discuss the limitations of several of the hydraulic components: actuator stroke, flow limitations in servovalves and flow capabilities of hydraulic power supplies. Servovalve J Actuator Accumulator Controller Command Signal Feedback Platform Figure 4-1: Principal components of a shake table system 29 Chapter 4 Hydraulic System Components The dynamic characteristics of the test payload also affect the performance of a motion simulator. Therefore, the performance limits of a simulator with rigid payload under sinusoidal excitation is also reviewed in this chapter. The relations between different components of the test are examined. This investigation leads to the formulation of mathematical equations from which a simplified simulation method is developed. This algorithm simulates the hydraulic fluid flows in a shake table system. The method is used to determine the operational limits of a seismic simulator loaded with a flexible payload undergoing general dynamic excitation. 4.2 H y d r a u l i c S y s t e m C o m p o n e n t s This section will review the basic components of a hydraulic shake table: the actuator, the servovalve, the power supply, the accumulators and the platform. Their function in the system is described. The basic dynamic characteristics of a simulator system are discussed. 4.2.1 Hydraulic Actuators Hydraulic actuators are often used to power civil engineering shake tables for several reasons. Hydraulic systems offer quick response time and high drive stiffness, both of which facilitate their control. The heat generated from the movement of parts is continuously transferred away, and mechanical parts are lubricated by hydraulic fluid. This saves wear and tear and cuts down on maintenance. The level of forces that can be delivered by hydraulic actuators exceeds those that can be produced by electric motors since fluid power systems are not limited by the magnetic saturation effect of ferromagnetic materials. By contrast, hydraulic 30 Chapter 4 Hydraulic System Components actuators use the power of pressurized fluid and, since very high pressure (in the order of 2 kN/cm2) can be used, they can produce large forces with relatively small components. The actuators used in most civil engineering applications are double-acting linear hydraulic actuators. There are two main components in this type of actuator: the actuator stage and the servovalve. The actuator is the part of the cylinder that generates the force needed to move the shake table and specimen. The force generated is proportional to the pressure in the system and the area of the actuator stage chamber (F = Pressure xArea). Thus an actuator with an actuator-stage area of 80 cm2 and a supply pressure of 2 kN/cm2 would be able to produce a maximum force of 160 kN. This maximum force output of an actuator is also referred to as the "blockedforce rating". In many applications, hydraulic fluid is considered incompressible. This is only an approximation, since trapped hydraulic fluid will always compress a small amount when pressurized. This compressibility has negligible effects when lightly loaded, slow moving systems are used. It is not the case for fast acting, heavily loaded seismic simulators. The hydraulic stiffness of the actuator depends mainly on the volume of the actuator chambers, the area of the piston and the bulk modulus of the hydraulic fluid' 5 8^ 5 9^ 4 2!. Figure 4-2 illustrates a simple piston arrangement. The hydraulic stiffness of this arrangement can be calculated with the following equations: 31 Chapter 4 Hydraulic System Components y Area of Piston ( A ) Figure 4-2: Simple piston arrangement AV = yA where: AV _ Ay V ~ V V V F = PA = (5 A2y K H Eq. 4-1 V K A V P P y-Hydraulic Stiffness Area of piston Volume of the trapped fluid Bulk modulus of the fluid Pressure Axial displacement 32 Chapter A Hydraulic System Components Since there are two chambers in a typical hydraulic actuator; the stiffness of the two volumes of fluid have to be considered when calculating the total effective stiffness. Figure 4-3 illustrates this situation. Figure 4-3: Total effective stiffness of actuator The system on the left of the figure shows the two chambers of the actuator and their associated stiffness. The two springs are linked together by the piston rod which is connected to the test mass. The system on the right represents a simple oscillating mass system; it is the analytical equivalent of the system on the left. The springs in both systems are considered to be in a parallel arrangement. The stiffness of two springs in a parallel arrangement can be added to calculate the total effective stiffness. Equation 4-2 illustrates this relation: Kt = Kx+ K2 Eq. 4-2 where: Kt: Total effective stiffness Kx: Stiffness of chamber 1 = p\42/Vj K2: Stiffness of chamber 2 = p\4 V V 2 33 Chapter 4- Hydraulic System Components The system on the right side of Figure 4-3 also represents a Single-Degree-of-Freedom system (SDOF). The undamped natural frequency of vibration of such a system can be calculated with Equation 4-3 [ 6 0 ]. Eq. 4-3 where: oo: Natural frequency of vibration M: Mass of payload The natural frequency of vibration is an important dynamic characteristic of an SDOF system. The dynamic behaviour of such a system can explain some physical limitations of actuators used in seismic simulators. When the frequency of operation of an actuator is close to its natural frequency of vibration (co), then control problems can arise. The mass-spring system will go into resonance; since damping is generally low in an actuator, large amplification of motion can be expected. When the frequency of operation is high compared to co, then the response of the actuator/payload system approaches zero. The compressibility of the fluid trapped in the actuator becomes a problem. Increasing flow is required to raise the pressure of the compressible fluid sufficiently to achieve the desired acceleration'61 \ A modern digital controller can typically control a system up to its natural frequency of resonance. Coherence between the desired and measured output is generally good several octaves above the natural frequency. Chapter 4 Hydraulic System Components Some control problems have been encountered when the frequency of operation is one third of the oil-column frequency^62\ At this rate of motion, the system may excite the oil-column frequency which corresponds to the third harmonic of the input motion frequency. These control problems can generally be minimized by careful tuning of the system. The defining characteristics of actuators are their blocked-force rating and the hydraulic stiffness of the actuator. 4.2.2 Multi-Stage Servovalve The servovalve controls the flow of hydraulic fluid to the actuator stage. Its purpose is to transform the electrical drive signal produced by the controller, the command signal, into hydraulic fluid flow that fills the actuator stage chambers. A multi-stage servovalve, which is the type commonly used in high-performance hydraulic applications, uses several servovalves in series to drive the actuator. Each of these servovalves is considered a stage. Every stage in a hydraulic actuator uses the output of the previous stage as input. A photo of a flapper/nozzle type actuator is shown in Figure 6-2 on page 82, and a photo of a voice coil type actuator is shown on Figure 6-3 on page 83. These two types of servovalve-actuator combinations have been the overwhelming choice for shake table applications since they offer fast response times to the control signal and good linearity. The two principal types of first stages used in engineering applications are the flapper/nozzle and the voice coil valves. These two types of stages differ in the method that they use to 35 Chapter A Hydraulic System Components transform the electrical signal into motion. The flapper/nozzle type uses a small torque motor to move the first spool assembly whereas the voice coil uses a magnetic field and a magnet to do the same task. The pilot valve provides hydraulic fluid to the slave valve which, in turn, controls the flow of fluid to the actuator stage. The hydraulic spool valve stages all function in the same way. A diagram of a pilot stage spool/sleeve assembly is shown in Figure 4-4. The spools block port openings in the sleeve assembly that supply hydraulic fluid. The first spool assembly in a multi-stage servohydraulic valve is moved by the torque motor or the voice coil depending on the valve type. Which ports are blocked by the lands depends on the position of the spool in the sleeve. The movement of the lands and shaft directs the flow of fluid to the slave valve section of the servovalve. Multi-stage servovalves use the measured response signal to correct the input signal. An electric current produced by a transducer is amplified and used as feedback to the valve controller. This stabilizes the actuator since environmental variables, such as temperature, hydraulic fluid viscosity and load, can be compensated for automatically. There are several types of control schemes used by valve controllers: position, velocity, acceleration or force. Analogue or digital hardware can be used to combine the feedback signals. Using a combination of control schemes generally provides better control of the actuator over a larger frequency band. The electric feedback signal can also be amplified or corrected to compensate for mechanical non-linearity of the actuator, such as valve imperfections. 36 Chapter 4 Hydraulic System Components Pilot Valve Section P R P Figure 4-4: Diagram of a pilot stage spool/sleeve assembly (Courtesy TEAM Corp.) Several factors limit the performance of the servovalve-actuator system'62^58!. Most are directly attributable to the servovalve. It controls the complex interface between the electrical command signal and the hydraulic fluid flow. The spool opening of the slave valve section of the servovalve, in conjunction with the external load and supply pressure, determines the amount of oil flow to the actuator stage chambers. The full value of the supply pressure is available to the servovalve. When no load is present in the system, the maximum velocity can then be developed by the servovalve-actuator system. If the actuator is constrained, then no flow is required to produce motion. In this situation, maximum pressure differential can be developed across the actuator chambers. This generates the maximum force output. 37 Chapter 4 Hydraulic System Components If the system is operating in a situation between these two extreme conditions, some design equations have been developed to predict the performance of the servovalve-actuator system. Equation 4-4 relates the maximum force that an actuator can produce'63^64!'58]. This value depends on the maximum force output, the desired velocity, maximum velocity and spool valve opening. Equation 4-5 is used to calculate the maximum velocity with maximum effective pressure drop. Normally, the servovalve pressure drop is assumed to be a third of the supply pressure. F = (signV) • Fmax • (1 - (\ • - ^ Y ) Eq. 4-4 with: Vmax = Eq. 4-5 where: Vel: Velocity Vmax :Maximum velocity Fmax :Blocked force rating a: Servovalve spool opening (1 equals 100% open) k: Servovalve flow rating A : Area of actuator Ps: Supply pressure Pd: Servovalve pressure drop These two equations were used to plot the graph in Figure 4-5. The supply pressure was taken to be equal to 1990 N/cm2; the servovalve pressure drop as a third of the supply pressure; the blocked force rating calculated with an piston area of A=521cm2; the servovalve spool Z>8 Chapter 4 Hydraulic System Components opening was assumed to be 100%. The calculated force-limit curve cannot be exceeded at any time during a test sequence. A simple sinusoidal excitation would produce an elliptic load path like the one shown on the figure. For this type of loading, the maximum performance of the servovalve is developed when the load ellipse comes into contact with the maximum load curve. The peak dynamic force available to the system is limited to 95% of the blocked (maximum) force rating. This value is typically called the dynamic force rating. Figure 4-5: Force velocity diagram for servovalve-actuator system The defining characteristics of servovalves are their peak flow rating. 39 Chapter 4 Hydraulic System Components 4.2.3 Hydraulic Power Supply The hydraulic power supply provides regulated pressure and hydraulic fluid flow to the actuators and accumulators of the system. It is usually designed to furnish the average flow requirements of a system. A pressure-compensated variable-flow pump will provide a constant pressure to the system without generating large amounts of heat when the system is at rest. When the servovalves are operating at near zero position, the flow from the pump will reduce to near zero. This is a possible disadvantage in a fast acting system like a shake table since it will take a certain time for the pump to react to a demand from the servovalves. This is why a typical seismic simulator uses accumulators to accommodate the surges in hydraulic fluid flow demand. The pump also needs sufficient power to produce the maximum rated flow at the normal operating pressure. If the motor driving the pump is not large enough, peak flow cannot be produced. Equation 4-6 relates this requirement. When the pump operates at a regulated pressure, the supply flow will increase as the power requirements increase. A photo of a typical hydraulic supply is shown on Figure 6-4 on page 84. Power = Flow • Pressure Eq. 4-6 The defining characteristics of these types of pumps are their supply pressure, usually 2 kN/ cm2, their flow rating (usually given in litres per minute), and power. 40 Chapter 4 4.2.4 Accumulators Hydraulic System Components These devices have a varied role in hydraulic systems. They serve to regulate the pressure surges in hydraulic systems, to filter out the pulsation effects of the pump, and to increase the dynamic stability of the system. Often, though, their primary purpose in shake table systems is to store hydraulic power in order to reduce peak demands on the pump. Only one of the numerous types of accumulators will be discussed here: the gas-loaded bladder accumulator. The accumulator usually contains a gas-filled bladder housed in a metal canister. It is generally connected to the main supply line. Under normal operating conditions the canister half-fills with hydraulic fluid, which compresses the trapped bladder of gas and effectively stores fluid energy. This bladder expands if the operating pressure in the supply line falls below the normal pressure. This released fluid supplies surges in demand and reduces line pressure fluctuations. The volume of the canister is finite; therefore an accumulator can only help maintain the desired flow for a limited time. The defining characteristics of these gas-loaded accumulators are their volume and pressure rating. 4.2.5 Platform The platform is the structure onto which the specimens are attached. The main design concern for platforms is their mass and stiffness. They should be very stiff so that they do not deflect under service, thus introducing unwanted frequencies. Their weight should be kept to a minimum since the more the table weighs, the more power is required to move it. Actuators 41 Chapter 4 G e n e r a l S y s t e m P e r f o r m a n c e have a finite amount of force output. The more force that is required to move the platform, the less power is available to excite the specimen. A heavier table has some advantages in systems with vertical actuators under lateral excitation. The weight of the platform lowers the combined centre of gravity of the table-specimen system. A table-specimen system with a high combined centre of gravity can generate large overturning moment when excited with relatively low base input acceleration. This overturning moment, if large enough, can overpower the vertical actuators. This can lead to unsafe situations. A system with a low centre of gravity does not experience this problem as much. A number of materials have been used to construct platforms: concrete, steel, aluminium, magnesium, etc. The optimal choice of a construction material for a platform depends greatly on its size and the maximum force output of the actuators that move it, and the desired natural frequencies of the bare table. The defining characteristics of a table are, therefore, its mass and stiffness. 4.3 G e n e r a l S y s t e m P e r f o r m a n c e 4.3.1 System with Rigid Payload under Sinusoidal Excitation There are physical limitations to the motions that a shake table may undergo. These limitations are created by the hardware used in the system. At lower frquency, the stroke 42 Chapter 4 General System Performance limitations of the actuator control the intensity of the generated motions. The peak pump flow or the servovalve flow capacity control the intermediate frequencies, since they limit the peak velocity the simulator can attain. The force limitations of the actuators limit the acceleration that can be produced at higher frequencies. The assumptions of sinusoidal motion and rigid payload are normally used to calculate the typical performance envelope of a seismic simulator. Sine motion replications are considered long duration tests, the contribution of the accumulators can be ignored. The accumulators are designed to provide hydraulic fluid for peak flow demands not constant flow demands. See "Accumulators" on page 41. This simplifies the calculation of the performance envelop considerably[65][62]. The theoretical motion restrictions can be represented on a log-log plot. Figure 4-6 shows a velocity versus frequency graph with such an axis scaling. The advantage of this type of diagram is, that lines of • constant displacements are lines parallel to the diagonal from left/down to right up, • constant velocities are horizontal lines, • constant accelerations are lines parallel to the diagonal from left/up to right/ down. It should be clarified here that these plots are log-log diagrams and not the traditional tripartite plot commonly used in earthquake engineering. Since the two axis have different scaling, the 43 Chapter 4 General System Performance e limit I I I ! , I'M I Ij;} i LLLL 0.1 0.5 1 5 10 50 100 Frequency (Hz) Figure 4-6: Performance envelope plot of an seismic simulator diagonal lines are not at 45°, as in the case of the tripartite plots. This is not the conventional method of plotting these graphs, but in the case of seismic simulator performance curves this method presents the pertinent information in a clear way. The performance diagrams for a simulator system would include at least one performance curve for each axis of motion. The stroke limit of a particular axis of motion can be represented by a constant displacement line. The velocity limits, imposed by the flow limits of the servovalve or power supply, can be represented by a constant velocity line. The force 44 Velocity limit Fore i^t.J. Li. : & U' Point of maximum power output AO Frequency of oil column resonance cf/ cx-Chapter Ar General System Performance limits, assuming rigid payload, can be represented by a constant acceleration line. There are other factors that limit the performance of a simulator system. The pump must have enough power to supply the flow of hydraulic fluid at operating pressure. This relation is presented in Equation 4-6 on page 40. The point of maximum power output, shown in Figure 4-6, represents a noteworthy operating situation. The power demands on the pump, during operation at the conditions described by this point, are at their maximum. If pump power is not large enough, the amplitude of the simulated motions will not be sustained. The hydraulic stiffness of the oil column in an actuator will also limit the performance of a simulator. At frequencies of operation above the oil column frequency, a modern digital control system should be used to control a hydraulic simulator. See "Hydraulic Actuators" on page 30. The performance limits of a simulator over the frequency of the oil column will not be shown in this document. This frequency is well over the operating range of most civil engineering tests. However, in the case that a researcher would like to operate the system over this frequency, the attenuation of the input motion due to the compliance of the oil column should be considered. The force velocity diagram of a particular servovalve illustrates another performance limit of the simulator system. The load ellipse of a sinusoidal motion, shown in Figure 4-5 on page 39, cannot exceed the curve calculated with Equation 4-4 on page 38. The performance of a typical multi-stage servovalve limits the dynamic force output of an actuator to 95% of the blocked force rating. See "Multi-Stage Servovalve" on page 35. The maximum velocity an 4 5 Chapter 4 General System Performance actuator-servovalve system can attain is also limited by the available supply pressure and payload. Other factors, such as the presence of mechanical resonant frequencies, electrical noise, foundation compliance, etc, can limit the performance of a seismic simulator in any type of testing. These limiting factors are not usually considered when constructing a sinusoidal motion performance envelope. 4.3.2 System with Flexible Payload under General Dynamic Excitation In this section, the effects of placing a Single Degree Of Freedom (SDOF) structure and other systems on a simulator will be analysed. Figure 4-7 shows a schematic view of a Multi-Degree-Of-Freedom (MDOF) shake table/specimen system. This model is limited to horizontal movement. The frequency of the replicated motions is assumed low compared to the natural frequency of vibration of the oil column trapped in the actuator. The actuator compliance is, therefore, neglected. In the previous section, the model of the actuator/payload was a SDOF system. The payload of the system is now no longer rigid, so that the seismic simulator model transforms into a MDOF system. The simulator platform and the specimen become a coupled dynamic system. The actuator is represented by an external force applied to the system. The inertia forces generated by the movement of the table and the base shear created by the specimen are equilibrated by the force of the actuator. Equation 4-7 and 4-8 are the governing equations of motion for this MDOF system 46 Chapter 4 General System Performance M c r K r ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ O Figure 4-7: Simple shake table/specimen system Mtxt + C(xt-x) + K(xt-x) = Fa Eq. 4-7 M'x-C{xt-x)-K(xt-x) = 0 Eq. 4-8 where: C: K: xt: x: Mass of table Damping coefficient of the specimen Stiffness coefficient of the specimen Actuator force Absolute table displacement Absolute specimen displacement Some insight into the operational requirements of shake tables can be gained by looking closely at these basic equations. The actuator has to produce enough force to move the rigidly attached mass of the table and counteract the base shear produced by the specimen. This force, as mentioned earlier, is directly proportional to the hydraulic system pressure. The force 4 7 Chapter 4 General 5ystem Performance generated by the specimen at its base is a variable that depends on the input time history, and its value is needed to verify whether the capacity limits of the actuator have been surpassed. The SDOF specimen could be replaced by any number of other systems since only the base shear time history is required to check the limit conditions. This simplifies the analysis of this problem considerably because it reduces the problem to the situation illustrated by Figure 4-8. M A I N S T A G E v VE A , 1 P< ®— I t a GUI |—GD Pa T P L A T F O R M 3L I ! I S E R V O V A L V E Figure 4-8: Forces acting on actuator In this representation, the base shear caused by the specimen is replaced by an external force acting on the platform, and the main internal workings of the actuator, namely the main stage and the servovalve, are schematically depicted. Considering this example, the total actuator force equation can be established. This equation also includes the force required to overcome the piston seal friction force. 43 Chapter 4 General System Performance F = Mt x xt + Ve + Fs Eq. 4-9 where: F: Total actuator force Ve: Specimen base shear Fs: Seal friction force. These variables will be used later: Ps: Supply pressure Pt: Tank pressure This equation represents the force demand on the system. The power delivered by the actuator serves both to move the platform itself and the specimen and to break the seal force. It is produced by the internal workings of the cylinder. The total force balance equation of the system can be formulated as such: PXAX = P2A2 + F Eq. 4-10 where: Al A2 Chamber one pressure Chamber two pressure Chamber one area Chamber two area By manipulating Equation 4-10 and making the assumption that A = A, = A2, which is true 49 Chapter 4 for most high performance actuators, it transforms to: F = (Pl-P2)xAx§ Capabilities of a Hydraulic System Eq. 4-11 where, the factor: (j): Linear supply pressure reduction factor, has been introduced to account for a supply pressure drop in the servovalve, a linear correction factor has been applied to the equation. By applying this linear factor, a particular case can be evaluated by setting = P and P2 = Pt in Equation 4-11. Normally, in the initial design stage of an hydraulic simulator, a value of 66% is used for (j) ^ 6 6 \ The performance testing of an actual seismic simulator is described in the following chapters. When evaluating the performance of this existing system, a value of 90% was used. 4.4 C a p a b i l i t i e s o f a H y d r a u l i c S y s t e m In the previous section, the value of force that an actuator can deliver was shown to be directly proportional to the amount of the supply pressure. In a hydraulic system powered by a pressure-compensated hydraulic pump, the supply pressure is supposed to be constant, and only the flow should vary. This assumption is not always true since, in times of rapid movement, the flow from the pump might not be enough to supply the surges in demand from the actuator. This problem is usually compounded by the long hoses that connect the actuator and the pump. As discussed in previous sections, hydraulic fluid is not really incompressible. Because 50 Chapter 4 Flow Demands in Hydraulic System of the large volume of trapped fluid present in the supply line, an additional flow is required to raise the pressure to that needed to produce the commanded acceleration. The accumulators that are attached to the supply hoses are designed to minimize this situation, but, in certain cases, the demands are sufficiently large and/or sustained for a long enough period to significantly lower the supply pressure. In this event, the capability of the system to produce force is lowered. The dynamics of a real hydraulic system are quite complex, and a full simulation is beyond the scope of this thesis. An approximate simulation method that uses only simple system characteristics was developed. It calculates the system supply pressure at all times and, hence, the maximum force output of any actuator in the system. 4.5 F l o w D e m a n d s in H y d r a u l i c S y s t e m In this section, the individual flow-pressure characteristics of each of the major hydraulic elements will be quantified and used to link the different parts of the system simulation'67^58^59l To simplify the derivations, certain assumptions need to be made: • The compressibility of the hydraulic fluid is neglected. • The hydraulic fluid exchanges in the system are considered to be made under isothermal conditions (constant temperature) conditions, except in the accumulators. • Supply lines are considered big enough to accommodate all the transfers of hydraulic fluid. 51 Chapter 4 Flow Demands in Hydraulic System • Supply line dynamics are not considered. The variable of interest in this simulation is the system pressure; therefore, the analysis will concentrate on the pressure-controlling elements of the system: the accumulators. By accounting for all the hydraulic flow sources and demands in a system, the supply pressure can be calculated. 4.5.1 Accumulator Flow Relation The total bladder volume is considered a critical parameter since an increase or decrease in its value will signify that the pressure of the system is fluctuating as well. The accumulators in the system will be modelled using the following equation'66^: ^ l ^ ' 4 = P2V24 Eq.4-12 where: Pj: Initial pressure V]\ Initial volume P2: Final pressure V2: Final volume This formulation reflects the fact that, unlike the hydraulic fluid exchanges in the system, the bladder volume changes are adiabatic. The trapped volume of the bladders contained in the system can be calculated at any time since it needs to be compliant with the volume changes in the hydraulic fluid (incompressible fluid assumption). 52 Chapter 4 4.5.2 Actuator Flow Relation Flow Demands in Hydraulic System The actuator flow requirement can be linked to its instantaneous velocity. The flow requirement to move the main stage during a certain time is formulated as: Qa = \x\xA Eq.4-13 The absolute value of the velocity must be taken since the flow requirements of an actuator are always positive. For a system with multiple actuators, the flow demands of each can be calculated and summed to generate the total actuator flow for the system. A certain amount of flow is linked to leakage within the actuator. The seals between the two main stage chambers cannot completely prevent the migration of fluid between them. This situation is not entirely unwelcome since it provides a certain amount of damping and stability to the actuator and reduces the amount of friction that needs to be overcome. There is also a certain amount of leakage flow in the servovalve. The total leakage flow will be taken as a constant in the analysis, hence: Qt = Constant Eq. 4-14 4.5.3 Hydraulic Power Supply Flow Relation The hydraulic power supply is the source of fluid flow. As stated earlier, most pumps used in these types of applications are pressure-compensated; therefore, if the system supply pressure is equal or greater than the reference operating pressure, the pumps will produce no flow. This pump flow relation is implemented in the simulation by comparing the present and reference 53 Chapter 4 Flow Demands in Hydraulic System pressure at each time increment. If the present pressure is lower than the reference pressure, the pump flow is gradually activated over a few time increments. This slight lag simulates the response time required to bring the flow up to demand level. 4.5.4 Flow Model [ 6 8 ] The complete flow model used to simulate the time variation of the supply pressure of a shake table system is illustrated in Figure 4-9. The model requires that certain parameters be initialized before the simulation starts: V0: Sum of all initial bladder volumes Qp: Flow capacity of the pump Qf Estimate of leakage flow Pmax: Operating pressure An: Area of actuators in the system x: Desired velocity of time signal to reproduce After the initialization, the following calculations are done at each time increment: 1. The instantaneous velocity for each actuator in the system is obtained. The absolute values are calculated and multiplied by their specific main-stage area to obtain the individual actuator flow. These individual flows are then summed to get the total actuator flow. Equation 4-13 on page 53 is used for this calculation. Since this flow will make the bladder volume grow, its sign is positive. 2. If the current system pressure is lower than the system operating pressure, the vir-tual pump is activated and its flow calculated. As mentioned before, a certain lag is introduced to mimic the real behaviour of the system. Since this flow will make the bladder volume diminish, its sign is negative. 54 Chapter 4 Flow Demands in Hydraulic System 3. The leakage flow is calculated. Since this flow will make the bladder volume grow, its sign is positive. 4. All the flows are summed and multiplied by the time increment of the simulation. The result is the incremental volume change for the time period of calculation. 5. This AV is added to the bladder volume of the previous time increment and yields the present bladder volume. 6. This new volume is then used to compute the value of the only unknown in Equa-tion 4-12 on page 52, the new system supply pressure. 7. The new value of the supply pressure is used to calculate the actuator force capac-ity. 8. The value of the supply pressure is multiplied by a linear reduction factor. This algorithm was applied with a Mathcad® ' 6 9^ program sheet, calibrated and used to gauge the demands of the tests presented in the third part of this thesis. The U.B.C. simulator was a good candidate to test the validity of this approach since the original hydraulic power supply could not keep up with the velocity demands of the combined actuators when performing high velocity tests. This permitted the recording of large supply pressure drops in the system with a number of excitation types which provided ample data for calibration. The results from these tests, as mentioned earlier, will be presented further in this text. 55 Chapter 4 Flow Demands in Hydraulic System CHAPTER 5 Control of Shake Tables In the previous chapter, the performance of a hydraulic system was described by the physical limitations of its elements. There was an underlying assumption that the system could accurately reproduce the desired motions. This assumption cannot always be made in a shake table system since large and heavy specimens affect the behaviour of the table. Control systems are installed to minimize this influence. This chapter will review schemes used to command shake tables. The basic control elements will be listed and described. 5.1 B a s i c C o n t r o l E l e m e n t s The basic control elements of a seismic simulator control system are as follows: • The servovalve • The servovalve controller • The actuator • The load • The control signal generator • The feedback control elements A block diagram of their interrelation is shown in Figure 5-1. 57 Chapter 5 Basic Control Elements Error Signal Forward Path Reference Signal Generator Valve C o n t r o l l e r w Servovalve w Actuator Load 7\ W w Feedback Element Feedback Path Figure 5-1: Basic control elements of a seismic simulator 5.1.1 Servovalves and Controller 8. IS) Servovalves control the flow of hydraulic fluid to the actuators. A servo valve is a precision four-way valve of which the final stage directs the flow of oil to a hydraulic actuator. A first stage converts electrical signals into spool motion (i.e. the mechanical motion of the servo valve spool). For larger size actuators, the force to move the final, or power stage requires an additional stage, a smaller four-way valve that acts as a power amplifier and directs the flow controlled by the first stage to the ends of the power stage spool'61]. Although many types of analog servovalves are used in hydraulic systems, the most common in shake table applications is either the flapper/nozzle or the voice coil. Both use multiple stages to direct the final flow to the main stage but differ in the workings of their first stage. This part of the servovalve transforms the electrical command signal into mechanical motion, moving the pilot spool/sleeve assembly. It instigates the flow of oil to the slave valve section of the servovalve, which in turn feeds the actuator stage of the actuator. These two types of servovalves are the most commonly used since they provide the system with fast response 53 Chapter 5 time and good linearity between the input and control signal. Basic Control Elements The flapper/nozzle type valve uses a torque motor linked to the pilot spool. The torque motor is basically a small mechanical arm connected to an armature that is located between two small permanent magnets. The electric command signal will magnetize the armature. By varying the current and direction of the signal, the movement of the arm and, consequently, that of the spool can be controlled. The voice coil servovalve uses a large permanent magnet and a coil of wire linked to the pilot spool to generate the initial flow of oil. It works in a way analogous to an audio speaker. The current in the coil is varied in amplitude and direction to move the spool around in the magnetic field created by the magnet. This movement instigates the flow of hydraulic fluid. 5.1.2 Digital Servovalves Digital servovalves use the same hardware to initiate the movement of the pilot stage, but a micro processor built into the valve does not need an analogue input to function. This permits direct control of the valve from a computer; and, changes to its operational characteristics can be readily made, depending on load mass, flexibility and other system parameters. 5.1.3 Actuators The actuator provides the force to move the payload. The compressibility of the hydraulic fluid, often neglected, can become an important control factor because of the large variations in loading pressures and amount of trapped fluid in the actuator stage. The hydraulic spring 5 9 Chapter 5 Basic Control Elements this creates could influence the motions of the system by attenuating the input motions. Seal friction forces and leakage are other elements that contribute to the system dynamic characteristics. 5.1.4 Load or Specimen The shake table-specimen interaction in seismic simulator tests has always been a prevalent control concern. It has been recognized for a long time that a specimen placed on the shake table can significantly affect the behaviour of the hydraulic system. This effect becomes quite prevalent in civil engineering testing since the specimen mass often surpasses the platform mass'-36^37^38^44-''-45-'. Large excursion in the non-linear behaviour range and vibrational noise generated by the test article also compound this problem. Noise pollution is often recorded by the monitoring instruments. Rattles, loose connections in attachments and falling objects distort the recorded response signal and complicate the correction of the drive signal by the feedback elements. 5.1.5 Signal Generator The signal generator transforms the reference time history into a signal that can be used by the valve controller. As with most other control elements, this device can be either digital or analog. A digital generator will output a discrete signal at given time intervals whereas the analog will output a continuous signal. Time histories created by a signal generator could include actual earthquake records, as well as single or multi-frequency histories. 60 Chapter 5 5.1.6 Feedback Elements Level of Digital Control The feedback control method employed dictates the nature of the feedback elements. A closed-loop system uses a control variable (position, velocity, acceleration or force) to correct itself .This requires that a transducer transforms the sensed measurand into an electric signal that can be used by the conditioning unit. This hardware component has the task of transforming the output from a measuring device into the input signal to the controller. The quality of the transducer and conditioning unit, as well as their capability of measuring the control variable accurately, is essential to the proper and stable operation of the feedback system. A number of ingenious devices have been invented to measure a wide range of variables. These transducers can again be divided into two classes: analog or digital. Analog transducers produce a continuous signal which is normally proportional to the measured variable. In contrast, digital transducers provide a discrete signal which varies over time increments and has a number of "steps" or resolutions. Figure 5-2 illustrates this difference. For systems under computer control, the signal from a digital transducer can be used directly, without analog to digital conversion. 5.2 L e v e l o f D i g i t a l C o n t r o l The control that experimenters have over an experiment and the shake table that drives it can determine the limits of any test. In many of the seismic simulators of today, digital hardware or computer software is used on a regular basis. At which point of the control sequence the 61 Chapter 5 Level of Digital Control Analog Transducer Digital Transducer Input (Measurand) Input (Measurand) Figure 5-2: Analog and digital transducer output digitalization process takes place, therefore, becomes an important characteristic of such a system. A simple classification method for seismic simulators was developed as part of this thesis. It helps illustrate the differences in control techniques. Closed-loop hydraulic systems with different levels of digital control are illustrated in Figure 5-3. 62 Chapter 5 Level of Digital Control Casel : single control variable, complete analog control Error Signal Reference Analog Signal Generator! Analog Controller Forward Path Analog Servovalve Actuator Load Analog Feedback Controller Analog JTransducerj Feedback Path Response te Case 2: single control variable, mixed analog and digital control Off-line Testing , _ ' System Id o Digital Signal Generator Analog Controller Analog Servovalve Actuator Load Digital \ . A Feedback D \ . Controller Analog Feedback Controller Analog [Transducer! o ci-in <o te g ' TO in te Com Case 3: single control variable, complete digital control Off-line Testing System Id Digital Signal Generator Digital w Digital w Actuator Load S FY Controller W Servovalve W Digital Feedback Controller Digital Transducer » o o_ in <o te Figure 5-3: Systems with different levels of digital control 63 Chapter 5 Multivariable Control The first system illustrated uses only analog components. The desired input, directly generated by an analog device, feeds into the servovalve controller, and only a real-time analog error compensation occurs. The second system contains both types of control elements. The reference input can be modified, based oh information gained from previous test sequences and/or system identification techniques. Real-time analog error compensation still exists, but the system can adapt the input signal to the servocontroller using off-line compensation. This gives much better control of the system to the operators. The third system uses digital control components exclusively. It can adapt its behaviour using digital feedback correction in both real-time adjustments to the servovalve and off-line compensation of the input time history. This system affords a very high level of control to experimenters. 5.3 M u l t i v a r i a b l e C o n t r o l The systems described in the previous section only used one control variable. Typical seismic simulators cannot achieve an equally high performance in a broad frequency range without using multiple control variables. A typical historical earthquake time history is in general a wide frequency band signal. It contains both low and relatively high frequencies. A single control variable does not provide enough feedback information to the controller to replicate this type of transient time signal adequately. A system using only displacement feedback would have little high frequency control. The following equations represent this case. The desired displacement plus a certain amount of error is equal to the actual position of the system. This system, since it uses only displacement 64 Chapter 5 Multivariable Control as a feedback variable, minimizes the error only in this frequency band. The actual velocity is, therefore, equal to the desired velocity plus the first derivative of the error. Since the system is not controlled by velocity, the error cannot be limited in this frequency band. Finally, the desired acceleration plus the second derivative of the error is equal to the actual system acceleration. If the displacement error on a replication test is assumed to be sinusoidal ( E = Asinco?), the resulting acceleration error, its second derivative(e = -Aco sinew), would be much larger. Thus, X = Xt + e Eq. 5-1 X = Vt + e Eq. 5-2 X = At+'i Eq. 5-3 where: X,X,X: Actual system position, velocity and acceleration Xt, Vt, At: Desired system position, velocity and acceleration e: system error The replication errors can be minimized by using several control variables. A system that uses acceleration, velocity and displacement to correct the actual motions can control its motions across a large frequency band, every section of the frequency range being controlled directly by one of the variables. Several approaches have been developed in order to use multivariable feedback techniques. Again, these can be divided into two groups: analog and digital techniques. Multivariable control scheme systems equivalent to those shown in Figure 5-3 are illustrated in Figure 5-4. 65 Chapter 5 Mul t ivar ia te Control The forward and feedback paths now use a number of measurands: acceleration, velocity and displacement. Velocity transducers are very rarely used in shake-table testing; therefore, this variable is generally derived using the other two. 66 Chapter 5 Mul t ivar ia te Control Case 1: multiple control variables, complete analog control o te Analog Signal Generator Analog Controller w Analog Servovalve w Actuator w Load i V fe W W w Analog Analog Feedback Velocity Controller Calculator Analog Acc. [transducer] Analog Displ. transducer] in SI o ci-in <u te Case 2: multiple control variables, mixed analog and digital control Acc. Off-line Testing Displ. te o o Digital Signal Generator Digital Feedback Controller System Id Acc. Displ. Analog — • Analog Controller Servovalve Actuator Load Analog Feedback Controller Analog Velocity Calculator Analog Acc. [Transducer! Analog Displ. ransducerl a o in te Acc. Case 3: multiple control variables, complete digital control Off-line Testing l : Displ. y ~"3 <J i 05 in te E o u Digital H Displ. Transducer] Figure 5-4: Multivariable control systems 67 Chapter 5 Multivariable Control The first system in Figure 5-4 depicts a totally analog system. The function generator feeds one of the control variables into the controller that must calculate, using operational amplifiers, the other two references. These histories are compared in real time to the feedback signal obtained from the transducers. A composite error signal computed from this comparison is added to the reference signal. This signal controls the servovalve. The second method uses a mix of analog and digital control elements, along with several control variables. The signal that drives the servovalve is generated using off-line compensation of the reference signal by a digital algorithm. Previous test sequences or techniques involving the characterisation of the system can both be employed to execute this compensation. During the test, the error correction occurs in much the same way as in the first case. The last illustration describes a totally digital simulator; this design would provide the operators with the most control of any of the systems considered. It permits multivariable real-time control of the servovalve, and these valves could even change their dynamic characteristics during a test sequence. Because of the high complexity and the response-time requirements of seismic testing, earthquake simulators of this type are very rare. Most seismic simulators fall into a control technique category between the two extreme cases: specifically, case 1 of Figure 5-3 and case 3 of Figure 5-4. Most have digital signal generation, but only some have digital feedback; few have digital servocontrollers and servovalves. Also, most simulators utilize one or two analog control variables for correction, but only a few use 66 Chapter" 5 Multivariable Control digital multivariable control of any form. As technology advances, systems will probably become increasingly electronic and hopefully more accurate. But, even at this point in time, the mixed approach has proven very successful for the replication of earthquake and other time signals with seismic simulators. The match between recorded and desired motion need not be perfect since experimenters always use the recorded motions for their analysis. Substantial errors could, however, cause the frequency of the excitation to shift from the desired one and, therefore, to excite the specimen in an unexpected way. The acceptable amount of error is often dictated by the nature of the test. The seismic simulator at the University of British Columbia uses a multivariable, mixed analog and digital control scheme. This subject will be discussed extensively in the next chapter. There is not much information publicly available that would permit the determination of the exact control scheme utilized at other seismic simulator facilities around the world. This is because a description of the control system is rarely included in research papers. Normally, the focus is primarily given to the experiment conducted on the simulator and not to the control system that drives it. One of the references cited describes the operating systems used at certain European facilities'29^. The shake tables at Bristol University, the National Technical University of Athens and ISMES, Bergamo, Italy, all use a mixed digital and analog multivariable control scheme. The Universite de Montreal shake table also utilizes this mixed 69 Chapter 5 scheme'56]. Digital Multivariable Control of Earthquake Records 5.4 D i g i t a l M u l t i v a r i a b l e C o n t r o l o f E a r t h q u a k e R e c o r d s Most strong-motion records are acquired by accelerometers or seismometers. There are few velocity records because seismometers usually saturate at low ground-motion level since they are mainly used for seismic micromeasurements. A recording site is rarely instrumented at the same location with velocity and acceleration transducers, and acquiring absolute displacement records of an event would be very difficult. In a seismic simulator under digital multivariable control, an algorithm must generally be used to generate the missing control variables. This poses a problem since integration and derivative algorithms require that the input data meet some basic criteria. Through some analyses of records, it was noticed that an acceleration trace that generates residual velocity or displacement presents unwanted characteristics when used in simulator control. If a system, with an analog servo controller, completes its test sequence in non-zero position, the servovalve amplifier will drive it back to that point as soon as the control signal terminates. Additionally, most control algorithms use a frequency domain operation at some point in the compensation process. Any drift in one of the control signals will usually degrade the quality of these calculations. A technique was devised as part of this thesis to insure that this would not happen, and it is developed in the next section. 70 Chapter 5 Digital Mul t i var ia te Control of Earthquake Records 5.4.1 Post-pulse Compensation of Strong Motion Records This technique uses two half-sine pulses of equal amplitude, placed at the end of the reference acceleration record, to ensure that near-zero velocity and displacement occur at the end of a test sequence. Figure 5-5 shows a representation of these pulses. T, T2 Figure 5-5: Example of compensation post-pulses Assuming that: and also: v(0 = f a(t)dt Eq. 5-4 d(t) = J v(t)dt Eq. 5-5 A: Amplitude of the acceleration pulse Tf Period of application of the first half sine T 2 : Period of application of the second half sine with initial conditions: a(0) = 0 v(0) = VQ 71 Chapter 5 Digital Mul t i var ia te Control of Earthquake Records 4(0) = D0 Equation 5-4 and 5-5 are used to calculate the residual velocity and displacement after applying the first acceleration pulse to the system with initial velocity and displacement. These equations are integrated over the interval 0 < t < T{; a(t) = A sin ((710/7:1) Eq. 5-6 with 5-4 and 5-5: 2ATX AT,/ r , D ^ = V 0 ^ ^ - ^ s i n ( H ) ) + D 0 AT2 d(Tx) = V0Tl+-^- + D0 for the interval 0 < f < T2: a(t) = -Asm((nt')/T2) Eq. 5-7 with 5-4 and 5-5: v { t ) = i z - r i T j - T v ° + — 2A = - ( ^ i - 7 : 2 ) + V 0 Eq.5-8 AT7/T7 (Tzt\ \ 2AT, *<o = -^ 1 Md-0+ v+- r1 ' + < « r ">. 72 Chapter 5 Digital Multivariable Control of Earthquake Records ^ 2 ) = ^(r? + 2 r 1 r 2 - 7 ^ ) + v 0 ( r 1 + 7'2) + z) 0 Eq.5-9 requiring v(T2) = d(T2) = 0 and using 5-8 and 5-9: 24 - ( T l - T 2 ) + V0 = 0 ^ ( r 2 + 2 r 1 r 2 - ^ ) + v 0 ( r 1 + r 2 ) + D 0 = o By substitution, Tx can be solved for: 7 C V 0 „ K 8 D 0 and also 7\ 2 ~4A ,2 ^ Eq. 5-11 To insure that Equations 5-10 and 5-11 do not yield imaginary values: K V A < — Eq.5-12 And Equations 5-10 and 5-11 must not yield a negative time period: TvT2>0 Eq. 5-13 To use this approach, the amplitude of the post-pulses needs to be chosen. A value of approximately one percent of the peak acceleration seems to meet the practical requirements, one of which is that the structure cannot be excited at the end of the test sequence by a large 73 Chapter 5 Multi-axis Control pulse of acceleration. The algorithm also determines the polarity of the first pulse, making it opposite to the last cycle of the reference time history. The calculation of Tx and T2 can proceed after these steps. The absolute value of Equation 5-11 determines which root of Equation 5-10 makes physical sense. 5.5 M u l t i - a x i s C o n t r o l The motions generated by an earthquake have several directional components. These movements can be described with the six degrees of freedom system shown in Figure 5-6. To simulate any seismic event completely, a shake table would, therefore, need to move in these six directions. Most simulators are limited to one or two of these motions. This partly has to do with the cost of the multiple actuators needed and the control problems associated with producing several synchronised motions. 5.5.1 Control of Over Restraint For several reasons, a simulator might use more than one actuator to control the motions in one degree of freedom. Besides the need for force capacity in one direction with a relatively high operational velocity, the system geometry might require multiple actuators for stability; a square table is much more stable on four legs than three. The system must be "aware" of this over-restraint, or problems could potentially arise. Actuators will conflict with each other if they are not controlled into cooperation. Most of these phenomena can be attributed to slight errors in the generated motions and the different dynamic characteristics of the cylinders. Variations between the produced and desired motion in an over-restrained system will cause 74 Chapter 5 Multi-axis Control Vertical Longitudinal Roll Yaw lateral Figure 5-6: Six degrees of freedom of a rigid mass the actuators to introduce undesirable unbalanced forces to the platform. This also reduces the loading capacity of the system. The control techniques require several measured variables (displacement, pressure) to correct the input signal to the servovalves. These specialized controllers are programmed specifically for the individual simulators. The program will vary, depending on geometry and position of actuators, and it can be executed with the help of operational amplifiers or digital circuits. The physical system will dictate the exact control solution. Even two systems identical in specifications will have at least adjustment differences, because of the small variations in fabrication of its components. 75 Chapter 5 Multi-axis Control 5.5.2 Compensation and Stabilization By using certain control concepts, we may try to address the problems caused by the geometry of the system, nonidealities of the drive, etc. The hydraulic spring created by the trapped volume of oil in the main stage of the actuator can cause some control problems. It tends to amplify or attenuate the system motions because the fluid in the chambers compresses a small amount. This extra motion makes the actuator shaft act as a pump, raising the pressure in one chamber and lowering it in the other. The use of an inner pressure feedback loop can eliminate some of the effect of the hydraulic spring. 76 CHAPTER 6 The U B C Earthquake Simulator The UBC seismic simulation facility underwent a major upgrade in 1994-95. The existing shake table was transformed from a one degree of freedom system with an analog controller to a four degree of freedom system with a digital signal generator. Four hydraulic actuators and signal amplifiers were added to the existing hardware. The hydraulic pump system originally installed was used without major modifications. The original horizontal actuator and its amplifier were preserved. The modifications were such that the four new cylinders can be placed in two different configurations, namely (i) as four vertical actuators, adding the vertical and two rotational d.o.f.'s, or (ii) as two horizontal actuators, which would add one horizontal and one rotational d.o.f. to the system, see Figure 6-1. The main horizontal direction of motion, which is produced by the old actuator, is active in all configurations. 77 Chapter <o Configuration 1H X 3V Longitudinal Vertical Roll Existing rigid links m Pitch Configuration 3H Longitudinal Lateral Yaw Figure 6-1: Possible configurations of the shake table at U B C Chapter €> Hardware The signal generating sub-system was also upgraded from an analog system to a fully digital one. The desired digital movement time histories are now generated by a workstation and passed via an ethernet link to a digital controller. This controller generates the control signals that are fed to the analog actuator amplifiers. Once a pre-test is performed, the feedback signals can be analysed by the computer system and used to correct the input signals in order to produce a modified test history. This procedure helps to minimize the effects of shake table-specimen interaction, since, with the help of the recorded signals from the pre-test, the control software can determine where in the input time histories more or less excitation is required. These modified test histories are then used for the next test run, and the desired test history can then be better replicated by the table-specimen system. The following sections will describe the laboratory and some of the hydraulic components of the shake table. This system will be simulated with the methods detailed in Chapter 4 to test the sensitivity and correctness of the approach. The system properties used in the study will be emphasized during the description. 6.1 H a r d w a r e The University of British Columbia Structural Dynamic Laboratory is 16 meters long and 11.5 meters wide. It houses the 3m by 3m shake table and provides space for construction, assembly and handling of relatively large structural models. The laboratory is equipped with a 4500 kg overhead crane for placing models and equipment on the shake table. Clearance above the table is 4.25 meters. It is equipped to record 32 channels of instrumentation 79 Chapter 6 Hardware information from a test specimen. All channels are conditioned by variable gain amplifiers and variable cut-off filters, which provide control over signal level and noise reduction. The recorded signals are fed into three separate data acquisition systems. The first is a free-standing personal computer-based data acquisition with a 16 channel, 12 bit acquisition board and program. This system provides quick access to data after a test sequence for verification. A second PC, equipped with a 32 channel, 16 bit multiplexed data acquisition system, serves as the main data logger. It uses software developed in-house to maximize acquisition speed while including many options created specifically for the facility. A third 10 channel, 16 bit dedicated computer system records the signals used in the off-line feedback calculations. 6.1.1 Platform The 3m by 3m aluminium table is fabricated from a grid of I-beams and a continuous plate as its top. These components are welded together to form a cellular construction. The beams are all of the same size, except for the four main load-carrying members which have a thicker web. A series of anchorages for specimens are also welded to the side of the beams. The shake table has a payload capacity of 16000 kg and a mass of 2043 kg. The simulation of the system will therefore use: Mt = 2043 kg where: Mt: Mass of platform 60 Chapter 6 6.1.2 Actuators Hardware The table is moved with 3 or 5 hydraulic actuators, depending on the desired motions for the experiment. The hydraulic actuators in the system are all double-acting linear actuators. The original actuator (Figure 6-2) has a flapper/nozzle type pilot stage in the analog servo valve. The actuator stage of this cylinder has an area of 80.9 cm2 and a stroke limit of ±7.6 cm. The latter value is not implicitly used in the simulation but obviously the desired test sequence cannot be reproduced if its displacement demands exceed this limit. The servovalve attached to this actuator has a flow limit of 5670 cm3/s. The newly acquired actuators (Figure 6-3) have a piston area of 45.2 cm2 and a stroke limitation of ±8.3 cm. These are equipped with analog voice coil servovalves which have a flow limit of 2290 cm3/s. As mentioned, all servos in the system are analog, therefore all of them are connected to analog feedback controllers. When a tall and heavy specimen is tested, a certain amount of analog pressure feedback serves to stabilize the system. The value of interest for the simulation are: 45.2 cm2 45.2 cm2 80.9 cm2 100 cm3/s where: A Qi--1,2,3 • leakage flow Area of the actuators of the system 61 Chapter 6 Hardware Figure 6-2: View of actuator with flapper/nozzle type servovalve 6.1.3 Hydraulic Power Supply The single power supply for the laboratory (Figure 6-4) provides regulated hydraulic pressure and flow to the servovalves and actuator. The operating pressure of the system is adjusted at approximately 1990 N/cm2. The supply will attempt to provide constant operating pressure to the servovalves during a test sequence. In certain systems like the U.B.C. simulator, the flow demands from the multiple actuators can cause this pressure to drop, since the pump cannot keep up with the flow demands. This situation reduces the potential force that the actuator stage of the cylinders can produce. The fact that high flow demand periods of a test sequence are usually linked to high force demands also becomes painfully obvious in heavy specimen testing. A peak flow of 264 l/min. or 4415 cm3/s can be generated by the U B C supply. 52 Chapter 6 Hardware Figure 6-3: View of actuator with a voice-coil servovalve Model calibration tests on the simulator after the upgrade showed that the high demands of sinusoidal testing can cause low pressure shut downs. This limits the type of testing that can be executed with the simulator. Even tests on small specimens can be impossible if the system cannot reproduce certain high flow demand test sequences. The requirements in order to conduct large velocity long duration testing are enormous because of the flow requirements. Accumulators are not meant to provide hydraulic fluid for periods of time longer than a few seconds. They cannot be used advantageously in long duration testing. The lower operating 53 Chapter 6 Hardware Figure 6-4: Hydraulic power supply range for the pressure was experimentally measured at 700 N/cm 2. The pump has 93250 Watts of power. It can therefore sustain maximum flow at operating pressure. The simulation variables linked to the pump are: Qp= 4415cm3/s /> = 1990 N/cm 2 where: Qp: Pump flow Pmax: Operating pressure of the power supply 6.1.4 Accumulator The accumulators are connected to the supply lines at several places. A l l these canisters •84 Chapter 6 Hardware contain a gas-filled bladder that expands and contracts as the supply pressure varies. One of these devices is attached to the pump, two to the supply manifold of the main actuator, and two to each of the new actuators. Only the total volume of the bladders is considered in the simulation. Half of the total canister volume is considered to equate the bladder volume at operating pressure. The value used in the simulation is: VQ= 2900 cm3 where: V 0 : Total volume of the accumulators in the system 6.1.5 Summary of Hardware Characteristics Table 6-1 summarizes the hardware characteristics of the U B C seismic simulator. 35 Chapter 6 Horizontal Sinusoidal Performance Envelopes The U B C Seismic Simulator Facility Two Configuration 1H x 3V; 4 active DOF: longitudinal, vertical, roll, pitch. 3H; 3 active DOF: longitudinal, lateral, yaw. Platform 3 x 3 m Aluminium Mass: 2043 kg Payload: 16000 kg (mass) Actuators 4 actuators with voice-coil servo valve. Area: 45.2 cm2 Stroke: ± 8.3 cm 1 actuator with flapper/nozzle servo valve Area: 80.9 cm2 Stroke: ± 7.6 cm Hydraulic Power Supply Pressure: 1990 N/cm2 Peak Flow: 246 l/min. Power: 93250 Watts Accumulators Total Volume: 2900 cm3 Table 6-1: Summary of table hardware characteristics 6.2 H o r i z o n t a l S i n u s o i d a l P e r f o r m a n c e E n v e l o p e s The performance envelopes for the U.B.C. seismic simulator were calculated with the information compiled in the previous section and plotted on a frequency versus velocity &6 Chapter Q Horizontal Sinusoidal Performance Envelopes diagram. These types of plots illustrate the performance limitations of a seismic simulator replicating sine motion with a rigid payload. For more information, see "System with Rigid Payload under Sinusoidal Excitation" on page 42. 1 0 0 , ^ y I m , I, , ~ i , , , , , I 0.1 0 .5 1 5 1 0 5 0 1 0 0 Frequency (Hz) Figure 6-5: Performance envelopes for longitudinal axis of motion Two distinct envelopes were calculated for each of the horizontal directions of motion. They are illustrated on Figure 6-5. One illustrates the bare table payload case, while the other is for the case of the table and 4000 kg of additional rigid payload. The curves are limited to an upper frequency equal to the natural frequency of vibration of the actuator-payload system. 57 Chapter <o Control 5ys tem 0 . 1 0 . 5 1 5 1 0 5 0 1 0 0 Frequency (Hz) Figure 6-6: Performance envelopes for transverse axis of motion 6.3 C o n t r o l S y s t e m The desired motions of the shake table are generated using a specialized software package provided by STI Corporation of California. This package runs on a mini main frame computer (DIGITAL VAX 4000) under the VMS operating system. The multi purpose program consists of two main parts: VAMP (Vibration Analysis Modal Package) and MEVCS (Multi Exciter Vibrational Control Software). Chapter 6 Control System 6.3.1 VAMP The VAMP subprogram can generate as well as analyse various signals'70^. It is used to generate the desired motion time histories of the shake table. It can produce various signal types like sine sweeps and import strong motion time histories from various source files. Its other function is to analyse the test results. 6.3.2 MEVCS The MEVCS subprogram is used to set the control limits for the hardware and monitor feedback signals from the transducers^ 1 .^ It is also the main link between the signal generating and manipulation software and the digital signal generator. It controls the iteration process from its replication module. The replication module is used to minimize the influence of the test specimen and the system on the desired motions of the shake table. Since the shake table has a mass that is generally comparable to the test specimen and limited force capacity, its performance is influenced by the experiment conducted on it. Therefore, the desired time histories cannot be exactly replicated by the system. This is a problem, since the desired peaks and frequency of the time histories will be distorted. To minimize this effect, the STI software corrects the original time histories, using the feedback signal to produce corrected drive signals. These drive signals are then used to conduct the next test run. The intent of this iterative procedure is to produce excitation that is closer to the desired one. This procedure will be explained in more detail in the next section. 59 Chapter 6 Control System One of the concerns in strong motion testing is that a specimen should not be altered during the pre-test procedure. Since the STI software requires feedback signals to generate a corrected signal, the test article needs to be shaken before full motion tests can be performed. The closer the pre-test excitation level is to the desired full motion level, the closer the response of the specimen should be to the expected test response. High pre-test excitation is not a problem if specimen linearity is expected, but if this is not the case, only very low amplitude runs might be acceptable. Damaging a specimen during low level testing might also jeopardize the validity of the whole test. On the other hand, if the levels of the feedback signals are not high enough, the effectiveness of the iterative procedure used by the MEVCS program to extrapolate the corrected signals could be affected. This again limits the software's capacities to produce an excitation that is close to the desired time histories. 6.3.3 Digital Signal Generator The digital signal generator is the device that actually drives the shake table during a test. Once the desired time histories are generated by the VAX computer, they are fed through an ethernet link to the generator. When the start signal is given, it generates the drive signals to the actuator amplifiers. Through its integrated data acquisition module, it also reads the signal produced by the position and acceleration transducers placed on the table. These traces can be viewed in real time on the VAX screen and retrieved for analysis after a test run. 6.3.4 Test Article Protection Hardware (TAPS) This piece of hardware is always active during a run'72]. It is setup during the pre-tests to generated a shutdown signal to the controller if certain limits are exceeded. The TAPS unit 90 Chapter & General Control Scheme capacity to react quickly to events is crucial if excessive motions are detected. This protects the hardware from breakage. 6.4 G e n e r a l C o n t r o l S c h e m e The U.B.C. seismic simulator uses a number of control concepts to direct the movements of the platform and specimen through the actuators. Most of these concepts have been generally described in Chapter 5, "Control of Shake Tables" and now will be specifically defined for this site. The system general control scheme can be illustrated by Figure 6-7. This scheme is quite similar to the one illustrated by Case 2 of Figure 5-4 on page 67. The control system uses a multivariable control algorithm which is implemented during the off-line compensation of the reference input. This compensation has two phases that are directly linked together. Initially the table/specimen system is shaken with a series of very low level sweeping sine signals or a low coherence random excitation. This characterises the initial system and the replication module calculates a frequency response function (FRF) by comparing the recorded acceleration and displacement time histories to the reference acceleration, velocity and displacement traces. The velocity is not recorded experimentally and therefore is calculated from the acceleration and displacement signals. The program applies multivariable control by separating the signals into certain frequency bands. The users choose the "widths" and "positions" of these bands during the pre-test setup; 91 Chapter 6 General Control Scheme Acc. Off-line Testing System Id ] Displ. i 1 Acc. Displ. te o Digital Signal Generator Analog Analog Actuator Load Controller w Servovalve o u Digital Feedback Controller Analog Feedback Controller Analog Acc. [Transducer! Analog Displ. [Transduced o ci-in <o te Figure 6-7: Control scheme of U.B.C. simulator Figure 6-8 illustrates this concept. The upper and lower bounds of the control bands determine the frequency range of command. This range separates further into regions, to emphasize displacement correction at low-range frequencies, velocity correction at middle-range frequencies, and acceleration correction at high-range. Every test has its characteristics and these parameters can change significantly. A test that requires high frequency excitation employs almost exclusively acceleration feedback, while an earthquake replication test requires multivariable control, since it contains low and relatively high frequencies. Specimens or attachments that pollute feedback signals with vibrational noise can be better controlled by setting these parameters adequately. This noise generally arises in the higher frequency bands; therefore, the upper bound of the control range might be lowered. Experience has shown that an acceptable level of control is exerted on a specimen if the control limits extend from half to twice the frequency of its first mode of vibration. This generalization should be used with care since special cases occur. 92 Chapter 6 General Control Scheme TO 5 E O p O U T 5 J O < >> E O P E E <D O TO 2 E O |> o o < >> E O E O P 5 JO <0 o o < 2 TS P IO E o < Frequency Figure 6-8: Control frequency bands The use of multiple actuators generates a matrix of frequency-response functions calculated from the system identification test. The dimension of this square matrix equals the number of actuators. A two actuator system would therefore be associated with a series of 2 X 2 matrices of FRFs. The main diagonal represents the autospectra of the identification test signals, while related cross spectra are located on the off-diagonal locations (see Figure 6-9). Additionally, each of the control variables generates one of these spectral density matrices, which then becomes associated with one segment of the control frequency bands. The total impedance file includes all these matrices and can be visualized in three dimensions as shown in Figure 6-10. The control program uses this file to predict the initial drive history, reference velocity and displacement from the reference acceleration trace. The multivariable control scheme implemented with this method permits control of a multiaxis seismic simulator over a wide frequency band. However, this approach has its limitations, since only certain small nonlinearities can be addressed by linear calculation techniques. Nonlinear response produces variations from test to test which are different from those observed during the low level characterisation. The MEVCS program therefore utilizes a second type of off-line feedback correction to facilitate the replication of earthquakes. 93 Chapter 6 General Control Scheme Actuator 1 Actuator 2 jo o i_ o o 3 o < s_ o TO O < Frequency Figure 6-9: Spectral density matrix The second type of off-line compensation used by the system consists of a mixed time/ frequency domain calculation. The difference between measured and desired histories is systematically reduced by this interactive and iterative procedure. The simulator shaken with the actual test sequence provides this second array of feedback signals. A comparison of the reference motions and those obtained during a low level replication test sequence permits the software to adjust the amplitude and phase of the drive histories. The calculations use the frequency domain information represented in the impedance file by sectioning the time signals into small segments that are separately convoluted with each of the spectral density matrices'-73-"-74-'. These matrices are again linked to each other through the control frequency band separation that the operator established during the first step of the characterization. The results of this convolution are corrected for the errors created by the truncation of the signal 94 Chapter 6 General Control Scheme Figure 6-10: Structure of multivariable impedance file and transferred back into the time domain where they are superimposed. This technique lends itself well to the compensation of non-linear time signals, since correction is applied to each segment individually. The drive signal therefore does not lose its time-dependent frequency characteristics. Experience has shown that 2 or 3 runs at 10% of the final test amplitude are needed to adequately correct the signal. 95 CHAPTER 7 Rigid Mass Testing 7.1 B a c k g r o u n d The operational limits of a seismic simulator dictate the size and type of tests that can be conducted on it. A simple simulation technique was developed in Chapter 4, "Shake Table Performance" to predict the operational limits of hydraulic shake tables. A series of tests was conducted during the month of May 1997 to verify the accuracy of the simulation algorithm. The tests consisted of shaking a stack of steel plates that were attached to the table top. Three different loading cases were used to determine the influence of load on the simulator. Since the masses were almost rigidly attached to the table top, the influence of specimen flexibility could be neglected. This simplified the analysis of the results and provided data to calibrate the simulation model of the table. 7.2 Tes t O b j e c t i v e s The primary objective of this investigation was to measure the supply pressure drop, if any, that the system underwent during the replication of a time history. As mentioned in the chapter on performance, this pressure drop should only be related to the velocity demands of the particular test sequence and not to the mass on the platform. The added mass was provided in order to test this assumption and also to verify what would happen if the force limits of the 96 Chapter 7 Description of the Specimen actuators were surpassed. This testing did not include any vertical shaking or testing with offset mass. Although this type of testing would have been interesting, tight scheduling of the shake table made it impossible to extend the testing program any further. 7.3 D e s c r i p t i o n o f t h e S p e c i m e n The added mass was a series of solid steel plates stacked on top of each other. This arrangement was achieved by first attaching a large 530 kg steel base plate to the centre of the platform using six anchor bolts. A smaller 450 kg plate was welded to this base in order to provide a very stiff connection between the two. The remaining plates were stacked, then connected together with the use of four 25 mm rods fitted through a series of holes at each of their corners. A number of other alternatives had been tried before, but this setup was the only one that seemed to provide enough rigidity. The specimen could accept high excitation forces without any relative movement between the top and base of the stack. This was very important, since inconclusive results would be recorded if slips between the plates or the table occurred. A photo of the masses on the table (Figure 7-1) depicts the test series that used the largest amount of mass: eight 450 kg plates on top of the base plate. All three cases are summarized in Table 7-1. Setup # Description Mass 1 Table only 2000 kg 2 Table, base plate and 4 plates 4300 kg 3 Table, base plate and 8 plates 6100 kg Table 7-1: Table payload during testing 97 Chapter 7 Instrumentation Figure 7-1: Rigid mass specimen on shake table 7.4 I n s t r u m e n t a t i o n The tests were recorded using several types of transducers. The table is permanently instrumented with accelerometers and linear variable differential transformers (LVDTs) on each of the actuators. The data collected by these instruments are used by the feedback calculation algorithm to correct the drive signal. To measure the variation of the supply pressure, a pressure transducer was temporarily installed on the output of the hydraulic power supply. The value of the differential pressure between the two compartments of the main stage in each of the active actuators was also collected. This signal gave a measure of the force output in each of the cylinders. A description of the purpose of each type of instrument is included in Table 7-2. The generated signals were collected by one of the data acquisition 98 Cha pter 7 Description of Tests computers. Instrument Type Measurement Delta Pressure Transducer Pressure differential between main stage chambers Pressure Transducer Supply pressure Linear Variable Differential Transformer Absolute table displacement Kistler 8304 K-Beam Accelerometer Absolute table acceleration Table 7-2: Purpose of rigid mass testing instrumentation 7.5 Description of Tests 7.5.1 Preparation of the Input Time Histories The rigid mass tests employed two types of excitation. The first was a steady-state sinusoidal excitation, which was chosen since it provided a simple signal to simulate. The second was a transient time history replication which illustrated a more typical test case. The earthquake time histories were played back with different amplitudes to gauge the influence of different demand levels on the system. The sinusoidal motions were single frequency with a steady maximal amplitude. Figure 7-2 and Figure 7-3 show a 3 Hz recorded acceleration and displacement time history. They represent the recorded values in one of the orthogonal directions of the table. In most cases the table was actuated in both perpendicular horizontal directions to furnish the maximum demand on the hydraulic power supply. As can be seen, the first cycles of the signal are tapered in order to minimize the impact of these often brutal tests. 99 Chapter 7 Description of Tests 95 2 0 2 4 6 8 10 12 14 16 18 20 Time (s) Figure 7-2: Measured longitudinal acceleration of shake table during sine test (number 21) w -3 I _ . Q 0 2 4 6 8 10 12 14 16 18 20 Time (s) Figure 7-3: Measured longitudinal displacement of shake table during sine test (number 21) The earthquake replication tests utilized two distinct wave forms. One of the test's objectives being the calibration of the model, earthquakes simulation with different maximal amplitudes and frequency content were chosen. The first drive signal was derived from the Joshua Tree Fire Station recording, E-W component, of the 1992 Landers earthquake in southern California. Recorded shake table acceleration and displacement time histories of this earthquake are denoted here as Joshua Test and shown in Figures 7-4 and 7-5. The numbers in the parentheses indicates the test number for which the records shown corresponds to. The 100 Chapter 7 Description of teste second was obtained from the Network Equipment-Building System (NEBS) Requirements: Physical Protection ^ document. The test protocol described in this document is used to evaluate the seismic performance of network and telecommunication equipment. As part of the testing procedure, the test article must survive the shaking caused by an artificially generated shock-time history, namely the VERTEQII waveform. Its severity and wide frequency band content made it a natural choice for pushing the simulator to its operational limits. Figures 7-6 and 7-7 show a recorded acceleration and displacement caused by this excitation. 0 ) 0 . 5 < - 0 . 5 1 0 10 20 30 40 SO 60 70 Time (s) Figure 7-4: Measured longitudinal acceleration of shake table during Joshua test (number 24) 7.5.2 Test Schedule The table was shaken with a number of excitation histories. It was set up with three horizontal actuators, which permitted it to move in the longitudinal and transverse directions. The first tests were conducted with the VERTEQII and the Joshua Tree earthquake records. The set frequency sine signals were used to drive the table. Different frequency signals were used to determine the operational limits of the seismic simulator. A summary of all the tests is 1 0 1 Chapter 7 Description of Tests .2-10 I Q 0 10 20 30 40 50 60 70 Time (s) Figure 7-5: Measured longitudinal displacement of shake table during Joshua test (number 24) 31.5 Time (s) Figure 7-6: Measured longitudinal acceleration of shake table during VERTEQII test (number 25) 102 Chapter 7 Description of Tests T i m e (s) Figure 7-7: Measured longitudinal displacement of shake table during VERTEQII test (number 25) included in Table 7-3. Run Number Input Direction(s) Setup # 1 Joshua Tree Longitudinal/Lateral 1 2 VERTEQII Longitudinal 1 3 Sine 0.5 Hz Lateral 1 4 Sine 1.0 Hz Longitudinal/Lateral 1 5 Sine 1.0 Hz Longitudinal/Lateral 1 6 Sine 1.0 Hz Longitudinal/Lateral 1 7 Sine 2.0 Hz Longitudinal/Lateral 1 8 Sine 4.0 Hz Longitudinal/Lateral 1 9 Sine 3.0 Hz Longitudinal/Lateral 1 10 Sine 3.5 Hz Longitudinal/Lateral 1 11 Sine 4.5 Hz Longitudinal/Lateral 1 12 Sine 0.5 Hz Longitudinal/Lateral 2 13 Sine 1.0 Hz Longitudinal/Lateral 2 14 Sine 2.0 Hz Longitudinal/Lateral 2 Table 7-3: Summary of rigid mass tests 103 Chapter 7 Results f rom Tests Run Number Input Direction(s) Setup # 15 Sine 3.0 Hz Longitudinal/Lateral 2 16 Sine 3.5 Hz Longitudinal/Lateral 2 17 Sine 4.0 Hz Longitudinal/Lateral 2 18 Sine 0.5 Hz Longitudinal/Lateral 3 19 Sine 1.0 Hz Longitudinal/Lateral 3 20 Sine 2.0 Hz Longitudinal/Lateral 3 21 Sine 3.0 Hz Longitudinal/Lateral 3 22 Sine 3.5 Hz Longitudinal/Lateral 3 23 Sine 4.0 Hz Longitudinal/Lateral 3 24 Joshua Tree Longitudinal/Lateral 3 25 VERTEQII Longitudinal/Lateral 3 26 1 VERTEQII Longitudinal/Lateral 3 27 VERTEQII Longitudinal/Lateral 3 28 VERTEQII (3 times) Longitudinal/Lateral 3 29 VERTEQII Longitudinal/Lateral 2 30 Joshua Tree Longitudinal/Lateral 2 31 VERTEQII (3 times) Longitudinal/Lateral 2 Table 7-3: Summary of rigid mass tests 7.6 Results from Tests Some of the results of interest for this study are the table acceleration for both orthogonal directions of excitation and the hydraulic supply pressure. Several of the test runs were used to calculate theoretical system pressure drops. The results used in this chapter include the measured acceleration for both directions of the sine test number 21, and VERTEQII test number 25. The recorded acceleration signals for the longitudinal component of motion are 104 Chapter 7 D i s c u s s i o n o f R e s u l t s shown in Figures 7-2 and 7-6. The recorded supply-pressure oscillations are shown in Figures 7-8 and 7-11. The calculated force demands of test runs 21 and 25 were also compared to the measured values obtained from the longitudinal actuator force sensor. These recorded values are shown in Figures 7-13 and 7-14. 7.7 Discussion of Results The theoretical model was adjusted by comparing the supply pressure time history generated by the simulation algorithm with the recorded test history. A typical supply pressure time history recorded during a experiment using the VERTEQII waveform is shown in Figure 7-8. As can be seen, the pressure oscillates around the operational value of about 2000 N/mm2. During periods of high demand this value drops significantly, as does consequently the potential force that can be developed by the actuators. As the velocity demands drop the pump will try to stabilize the pressure to the operational value. The oscillation of the pressure is attributable to the demand from the actuators and the considerable dead band in the pump control loop. In this particular example all the three actuators in the system were commanded with the same input signal to maximize the flow demands on the hydraulic power supply. 7.7.1 R e p r o d u c i b i l i t y o f Resu l t s The mathematical simulation of a system becomes very difficult if its behaviour changes from one test sequence to the next. The simulation algorithm developed in Chapter 4 outputs the 105 Chapter 7 Discussion of Results ST 2500 J 2000 1500 £ 1000 I 500 " • 0 10 _ . , . • 20 30 Time (s) Figure 7-8: Measured supply pressure time history for VERTEQII test 25 supply pressure oscillation for a given input acceleration. This pressure oscillation should be the same if the identical input signal is used. To verify this, a simple experiment was devised. A test sequence made up of three consecutive VERTEQII time histories was replicated, test run number 28. The recorded supply pressure time histories for each of the VERTEQII inputs were then overlapped to enable comparison. The result of this comparison is shown in Figure 7-9. Only the period of high demand, from 30 to 40 sec of the record, is illustrated. The supply pressure oscillations are almost identical since the three traces included in the figure overlap almost perfectly. | 2000 z oT 1500 3 W 0) 1000 1 CL 30 31 32 33 34 35 36 37 38 39 40 Time ( s e c . ) Figure 7-9: Measured supply pressure drop for three consecutive tests (run number 28) 106 Chapter 7 7.7.2 Influence of Load Discussion of Results One of the observations that can be derived by looking at the schematic representation of the flow model illustrated on Figure 4-9 on page 56 is that the supply pressure drop should not be related to the actuated load. The demand that the hydraulic actuators put on the pump and accumulators should only be related to their instantaneous velocity. The validity of this declaration could be easily tested for. As the test schedule shows, Table 7-3, the same amplitude and frequency sine signals were fed to the actuators with each of the three load cases. If the recorded pressure time histories of the equivalent frequency cases were the same, then it could be experimentally concluded that the actuated load did not affect the pressure oscillation. Figure 7-10 shows the recorded supply pressure value for each of the 3 Hz tests, run number 9, 15 and 21. The results of these test sequences are quite similar. The pressure drops slightly after the signal was turned on and stabilizes at a value of around 1900 N/cm2. This indicates that the pump could barely supply the actuator with enough flow and that it was working at almost full capacity. The other interesting point is that, as predicted, the load that the simulator actuates does not affect the supply pressure drop. The load on the platform almost triples between load case number 1, test run 9, and load case number 3, test run 21. This does not affect the demand on the pump and accumulators, since the pressure time histories for the three cases shown are almost identical. This finding has interesting implications for a motion simulator. The flow requirements of the 107 Chapter 7 Discussion of Results N 2300 £ 2200 ^ 2100 3 , 2000 1900 3 1800 W 1700 (1) 1600 Q. 0 2 4 6 8 10 12 14 16 18 20 Time (sec.) Figure 7-10: Three 3 Hz test sequences with different loads (tests number 9, 15, 21) input time history can be calculated without taking into account the actuated load. A theoretical supply pressure time history can be produced, based on the flow demands of the input history and the power of the hydraulic power supply. This supply pressure history can then be used to calculate the ultimate force capacity of the system at any given time during a test sequence. This capacity history is independent of the specimen placed on the table. A test article can therefore be designed based on this capacity history, without concern over its effect on the performance of the simulator. 7.7.3 Comparison of Simulated and Measured Values The accurate control of large specimens that generate great forces on the table becomes one of the typical concerns in shake table testing. The forces needed to actuate a model need to be known before the experiment is conducted. If they exceed the force capacity of the cylinders, high errors in the replication can be expected. A hydraulic actuator will probably not shut down completely if it is commanded to generate too much force or move too quickly. However, the difference between the command signal and the measured response signal will 106 Chapter 7 Discussion of Results increase drastically. If this situation occurred, the expected test inputs and recorded time histories would be very different, and the experimenters would probably not get the results they wanted. Another reason to calculate force demands before the execution of a test is that, unlike the performance test described in this chapter, most civil engineering tests are destructive in nature. The experimenters usually want to study the behaviour of a specimen once it has attained a state of non-linear behaviour. If the base shear requirements for a specimen to attain non-linear behaviour are too high, the simulator will not be able to push the structure into this state. The test would therefore not attain its objectives. The results of the computer simulation can be used to compare the demands to the capacity of the system. The actuator in the longitudinal direction of movement (see Figure 6-1 on page 78) was used to study the exactness of the approach. The maximum force capacity of the table is calculated using the right side of Equation 4-11 on page 50, and the force demand by Equation 4-9 on page 49. These two equations are presented below for convenience. These equations must be modified in order to make them useful for this survey. The second can be simplified substantially since the specimen is almost rigid. Also, the seal forces were assumed to be negligible and the weight of the table was included. Equation 7-2 could therefore be rewritten as: F = (Pl-P2)xAx§ Eq. 7-1 F = Mtxxt+Ve + Fs Eq. 7-2 109 Chapter 7 Discussion of Results Demand = (2043 + Ms) x xt Eq. 7-3 where: Ms: Mass of specimen The values for the area of the main stage of the longitudinal actuator, and the supply pressure are used to transform Equation 7-1. For more information, see "Hardware" on page 79. Ninety percent of the pressure differential was assumed to be usable to the actuator stage. This reduction is to account for the pressure drop through the servovalve. As a final simplification, the value of the return pressure was assumed to be negligible compared to that of the supply pressure. With these equations and the simulation algorithm, the value of the calculated and measured pressure loss, as well as the calculated and measured force, could be compared for the two basic excitation types. The measured force demands were calculated from the delta pressure transducer signal. Figures 7-11 and 7-12 show the measured and calculated supply pressure value for the typical sine and VERTEQII test sequences. Figures 7-13 and 7-14 show the measured and calculated force demands for the same test sequences. The measured and calculated pressure loss for the sine signal test compare very well. Both signals drop at approximately the same time and oscillate around the same value. As for the VERTEQII test some discrepancies are noticeable, but the general trends of the measured Capacity = P^x 80.9x0.9 Eq. 7-4 110 Chapter 7 Discussion of Results ?T 2500 I 2000 i-i 3 (A (A 0) 1500 1000 500 0 10 Time (s) Calculated Recorded 15 20 Figure 7-11: Pressure loss of a 3 Hz test sequence (test number 21) Q_ 15 20 Time (s) 25 30 35 Figure 7-12: Pressure loss of a VERTEQII test sequence (test number 25) signal are well represented by the calculated one. Considerable time was spent varying individual hardware properties in the simulation, in order to try to emulate the process more accurately. This exercise confirmed that the real physical value for the pump flow capacity, accumulator volume and piston area, reported in the previous chapter, gave the best results. Some effort was put into refining the simulation of the pump operation, since the original model could not reflect the oscillatory behaviour of the supply pressure around its operating m Chapter 7 Discussion of Results 100 £ -50 -100 10 Time (s) F=MA F=Force Sensor 15 20 Figure 7-13: Force demands of a 3 Hz test sequence (test number 21) F=MA F=Force Sensor 15 20 Time (s) 25 30 35 Figure 7-14: Force demands of a VERTEQII test sequence (test number 25) value. This included the addition of a variable flow equation in the part of the algorithm that represents the hydraulic power supply. The virtual pump therefore could not pass from a full flow condition to a null flow condition instantly. The comparison of the measured and calculated force demand shows very good agreement between the two quantities, see Figures 7-13 and 7-14. The signals are almost identical for the sine test, run number 21, and have only slightly different peak values for the VERTEQII test, 112 Chapter 7 Discussion of Results run number 25. The two sequences were performed with the biggest of the test loads. The study of these two figures proves a couple of things: first, the assumption that the masses are rigidly attached to the table is true, and second, using the acceleration trace to calculate the force requirements of this test is valid. The findings can be used to construct the calculated capacity and required force graph. Figures 7-15 and 7-16 show this type of construction for both the sine (run number 21) and VERTEQII tests (run number 25). For both cases, the capacity of the table is far more than the force requirements of the test. This is illustrated by the fact that the demand curve is always lower than the capacity curve. This sort of graph can be plotted before a test is actually executed, in order to foresee any problem. To perform this investigation, only the base acceleration trace, the weight of the specimen and the calculated base shear produced by its motions are needed. If the errors associated with the simulation method are small enough, then a very good idea of the test requirements are gained from the calculation algorithm. The relative exactness of the method, combined with its simplicity of implementation, make it a very useful tool in shake table test preparation. Another case was analysed in order to confirm than the system could not generate forces that are larger than the calculated capacity. The system was forced into a large pressure drop situation by feeding in a sine signal of high enough frequency and large enough amplitude. The test was conducted with the largest load case, test run number 23. Figure 7-17 illustrates the comparison of the calculated and measured supply pressure values. The match between the two is good initially, both dropping rapidly once the excitation signal is turned on. 113 Chapter 7 Discussion of Results Ci O 180 150 120 90 60 30 Demand Capacity 10 Time (s) 15 20 Figure 7-15: Capacity and demand for typical Sine test (test number 21) 180 150 120 o 90 o 60 30 0 Demand Capacity 10 15 20 Time (s) 25 30 35 Figure 7-16: Capacity and demand for typical VERTEQII test (test number 25) However, after a few seconds the measured signal stabilizes to a value of 1000 N/cm2 while the calculated drops down to almost zero. The measured force capacity and demand for the longitudinal direction are plotted in Figure 7-18. This graph shows that the stabilizing of the signal occurs once the capacity and demand are equal. By examining the demand curve, one determines that the system attempts to reach a higher steady state value, but once the pressure drop is large enough the signal drops in amplitude. The system could not generate a force that was larger than the value predicted by Equation 7-4. It did not shut down in a violent way 114 Chapter 7 Summary and Conclusions when this limit was attained, but the force output did not surpass the capacity of the system. CL 0 5 10 15 20 Time (s) Figure 7-17: Recorded and measured pressure drop for limit test (test #23) Demand Capacity 0 5 10 15 20 Time (s) Figure 7-18: Comparison of recorded demand and capacity for limit test (test #23) 7.8 Summary and Conclusions The rigid mass tests were conducted at the Structural Dynamics Laboratory of the University of British Columbia during the month of May 1997. They were used to evaluate the effectiveness of the simulation algorithm developed in Chapter 4 of this thesis. The testing used both sine and transient excitation to assess the behaviour of the shake table. A transducer 115 Chapter 7 5ummary and Conclusions was placed on the hydraulic supply line of the pump. This sensor recorded the oscillation of the supply pressure during a total of 31 test runs. Most of these tests used all of the three horizontal actuators to maximize the flow demands of the simulator. The test inputs consisted of two types of signals: constant amplitude single frequency sines, and transient earthquake test histories. The recorded values for the supply pressure time history are reproducible. If the same input time history was used, the same supply pressure time history was recorded. Three load cases were used in order to test the effects of the actuated load on the behaviour of the system. The load on the system did not affect the demands on the hydraulic power supply. The tripling of the mass did not cause the supply pressure to vary significantly. The flow requirements of the input time history can be calculated without taking into account the actuated load. The simulation algorithm was used to calculate theoretical supply pressure time histories for certain of the test runs. These theoretical curves were quite close to the recorded ones. The calibration effort put into the simulation program showed that the real hardware properties (pump flow, accumulator volume and actuator piston area) produced the best match between the recorded and calculated time histories. The addition of a response lag time for the pump flow helped reproduce the oscillatory behaviour of this piece of hardware. The input acceleration time history, along with the simulation algorithm, can be used to create 116 Chapter 7 Summary and Conclusions a capacity curve for the simulator. This time history can then be compared to the base shear demand curve of a specimen in order to determine if a test sequence can be executed. An actuator cannot produce a force larger than the value of the supply pressure times the area of its main stage piston. 117 CHAPTER 8 Steel Shear Wall Testing 8.1 B a c k g r o u n d During the last three years, a considerable research effort into the performance of steel shear wall was conducted at the University of British Columbia and the University of Alberta. This study was initiated in order to investigate the performance of this building system as the primary lateral load resisting element for medium to high rise buildings located in regions of high seismic risk. A quasi-static test was performed at the Structural Laboratory of the University of British Columbia to test the basic performance of a prototype steel shear wall. This test study used vibration testing techniques to characterize the dynamic properties of the specimen. The force deformation characteristics were also measured to determine the stiffness degradation of the structure as the testing progressed. This study resulted in a M.A.Sc. thesis[80]. As part of the study program, a dynamic test of another identical scale model was included. This created the opportunity to compare the behaviour of two identical specimens tested with different methods. The scale model, because of its size, weight and proportion, would require the full force capacity of the seismic simulator. The test was conducted during the month of March 1997 at the Structural Dynamic Laboratory of the University of British Columbia and Chapter & resulted in a Ph.D. thesis^ 81 .^ Test Objectives 8.2 Test Objectives The overall research objectives of this project were: • To increase the body of knowledge on the differences between dynamic and static tests. • To understand the dynamic behaviour of a thin plate steel shear wall. • To extend the experience in scaled shake table tests using heavy and tall specimens in the Structural Dynamics Research Laboratory at UBC. The main operational objective of this test was to investigate the table behaviour when driven to its limit capacity. The general philosophy of model testing encourages the experimenters to build specimens that are as close to life-size as possible. The researchers also wanted to develop large non-linear action in the shear wall during the dynamic test. At the time of the planning of this test, the simulation method described in Chapter 4, "Shake Table Performance" had not been developed. It was therefore hard to predict if the chosen size of specimen could be plastified, since the force required to push it beyond the elastic behaviour range was very close to the limit of the table. In this chapter, the force capacity and requirement of this particular test will be investigated in order to show if the simulation method would provide more insight on test limits. 119 Chapter & 8.3 D e s c r i p t i o n o f t h e S p e c i m e n Description of the Specimen The specimen was a reduced scale model of a 4-storey steel frame building. The typical storey height of the four storey frame was 900 mm. A one bay steel plate shear wall was installed of the primary lateral load resisting element in the direction of motion of the three-dimensional testing frame. It was constructed with continuous S75 x 8 columns placed 900 mm centre-to-centre, and S75 x 8 beams for the bottom three storeys. A deep stiff beam, S200 x 34, was installed at the top floor to anchor the tension field forces generated in the upper storey plate. Full moment connections at all beam-to-column connections were provided by a continuous fillet weld of the entire beam section to the column flanges. The infill panels were constructed from 16 gauge (1.5 mm) hot rolled steel plate using a fish plate detail A picture of the test article is shown in Figure 8-1. The rest of the test article was constructed with pieces of a modular steel testing frame f83^84!. The columns were B 100x9, a special type of light section, and positioned at the four corners of the specimen. The beams, S75xll sections, linked the shearwall and the columns, providing the primary support for the test masses. Additional beams connected the columns in the longitudinal direction. The specimen was stiffened with circular steel rods placed in a cross pattern in each of the transverse panels. These 12 mm treaded braces were pretensioned to lessen the effect of unwanted vibrations. This arrangement formed the second primary lateral load carrying system. In the direction of motion the support frame was pin-connected, to insure that most of the lateral load created by the dynamic motions was resisted by the shear wall. 120 Chapter & Instrumentat ion Figure 8-1: Steel plate shear wall system viewed in the longitudinal direction 8.4 I n s t r u m e n t a t i o n The specimen was instrumented with a total of 44 channels of instrumentation. Accelerometers were placed, along with displacement transducers, at each of the stories of the specimen in order to measure its motions in three dimensions. Simple and rosette strain gauges measured the strains of various areas on and around the first storey steel panel. The transducers of interest for the study presented in this chapter include the table instrumentation (accelerometers, LVDTs and force transducer) and four accelerometers placed at each storey of the frame. A description of the purpose of each type of instrument is included in Table 8-1. 121 Chapter & Description of Tests The specimen instrumentation will provide the results for the calculations of the Specimen Base Shear: Vg. This value is used to determine the force demands of an experiment. This issue will be addressed in the following sections. Instrument Type Measurement Delta Pressure Transducer Pressure differential between main stage chambers IC Sensor 3110 Accelerometer Absolute acceleration of speci-men at each floor Linear Variable Differential Transformer Absolute table displacement Kistler 8304 K-Beam Accelerometer Absolute table acceleration Table 8-1: Purpose of steel shear wall testing instrumentation 8.5 D e s c r i p t i o n o f T e s t s 8.5.1 Preparation of the Input Time Histories This experiment used a number of excitation waveforms to test the specimen behaviour. Historical earthquake recordings, as well as artificial ones, provided a number of choices as to the amplitude and frequency content of the test history. As mentioned previously, the force requirements to push the specimen into non-linear behaviour were known to be very close to the force capacity of the table. One of the operational objectives of this test was then to shake the structure with the maximum possible number of cycles of near-limit force. The initial choice of waveform therefore included quakes with either large acceleration peaks or long duration. These could be then scaled in amplitude (to maximize force output) and frequency (to meet the model scaling law requirements) to meet the final needs of the experiment. Table 8-2 list all the waveforms utilized in the test. Throughout this chapter, these earthquakes are 122 Chapter & referred to as Petrolia, Tarzana, Joshua and VERTEQII respectively. Description of Tests Event Date Station Location Magnitude Unscaled Peak Acceleration (g) Cape Men-docino April 25/92 Petrolia CA 7.0 0.685 Northridge January 17/94 Tarzana, CA 6.6 1.927 Landers June 28/92 Joshua Tree, CA 7.3 0.29 VERTEQII ~ 1.64 Table 8-2: Characteristics of time histories considered for study of steel plate shear wall The time increments of the original recordings of the waveforms were all modified to reflect the scale of the model. The model was not an exact duplicate or reduced scale model of an existing structure. This meant that the scaling factor for the time variable could be chosen and not calculated rigorously, since it was still an independent variable. The time scale factor was therefore selected to be 0.5. This assumption reflected the general size and proportion of the test article. This scaling process is discussed extensively in the chapter on the concrete bent test. For more information, see "Description of Tests" on page 139. A number of low-amplitude preliminary tests were done, utilizing all the excitation traces. It became apparent that only the Tarzana and VERTEQII records, because of their frequency content and amplitude, could possibly damage the structure. 8.5.2 Test Schedule The specimen was tested with all four time histories described in the previous section. A 123 Chapter 8> Description of Tests number of low-level test runs were executed to verify that all the instruments were working properly and to calibrate the table. A summary of all test runs is included in Table 8-3. The last 4 runs were executed with a set frequency sine excitation. The frequency of these sine signals was chosen to be close to the measured first natural frequency of vibration of the specimen. Run Number Input %PGA of Historical recording or amplitude in g's 1 Joshua Tree 10 2 Joshua Tree 10 3 Joshua Tree 10 4 Joshua Tree 10 5 Joshua Tree 20 6 Joshua Tree 40 7 Tarzana Hill 10 8 Tarzana Hill 20 9 Tarzana Hill 20 10 Tarzana Hill 40 11 Tarzana Hill 40 12 Petrolia 10 13 Petrolia 20 14 Petrolia 40 15 Petrolia 80 16 Joshua Tree 80 17 Tarzana Hill 80 18 Tarzana Hill 80 19 VERTEQII 10 Table 8-3: Summary of steel plate shear wall tests 124 Chapter 8> Results from Tests Run Number Input %PGA of Historical recording or amplitude in g's 20 VERTEQII 20 21 VERTEQII 40 22 Tarzana Hill 120 23 VERTEQII 80 24 VERTEQII 60 25 Tarzana Hill 140 26 VERTEQII 50 27 VERTEQII 60 28 VERTEQII 70 29 VERTEQII 80 30 Tarzana Hill 150 31 VERTEQII 50 (5 times) 32 Tarzana Hill 120 (6 times) 33 Sine (5.5 Hz) #1 5%g 34 Sine (5.5 Hz) #2 10%g 35 Sine (5.5 Hz) #3 15% g 36 Sine (5.5 Hz) #4 20% g Table 8-3: Summary of steel plate shear wall tests 8.6 R e s u l t s f r o m T e s t s The results of interest for this study are the acceleration signals and force output in the main direction of excitation. More specifically, the results of test run 25 and 30 are used in the following section to illustrate recorded signals with significant noise pollution. These traces are shown in Figures 8-4 and 8-7. The recorded accelerations of the table and of the four 125 Chapter & Resu\l5 from tests storeys of the specimen for test runs 28 and 29 are used to calculate the demand and capacity of the table. The recorded accelerations of the table and of one of the storeys of the model are shown in Figures 8-2 and 8-3. In the next section, the calculated force output values are compared to the recorded force transducer signal. A typical recording of this transducer is shown on Figure 8-11. 2.50 Time (s) Figure 8-2: Recorded table acceleration for run number 28 2.50 Time (s) Figure 8-3: Typical recording of storey acceleration for run number 28 126 Chapter & 8.7 D i s c u s s i o n o f R e s u l t s Discussion of Results A considerable problem arose during the early testing runs. The thin steel plates that form the panel of the steel shear wall vibrated out-of-plane causing very high acceleration vibrations. These were recorded by the sensitive control accelerometers of the table and caused them to saturate, which in turn shut the table down. An example of an acceleration recording from a Tarzana replication, run 25, is shown in Figure 8-4. The calculated normalized Fourier spectrum for this signal is shown in Figure 8-5. The large peak that appears at around 35 Hz is the result of this plate vibration. This high-level vibration caused the test article protection hardware to command the stoppage of the test sequence, since this type of acceleration is usually associated with extreme motions. This situation prevented the execution of higher level runs. It was necessary to dampen the out-of-plane motions of the plates before the experiment could continue. The specimen was therefore fitted with wooden beams fixed across its second and third storey panels. Figure 8-6 shows a picture of one of these beams and dampers. The gap that remained between the beam and the panel was filled with foam material which acted as a damper. This arrangement served to limit the high frequency motions of the panel without preventing the structural action. This was necessary since the Test Article Protection Hardware uses the unfiltered signals from the test run. The high acceleration peaks in these signals made the hardware controller shut down the test since peaks of this nature are usually associated with extreme and potentially dangerous simulator motion. 127 Chapter & Discussion of Results It was also necessary to change certain control parameters. The low-pass filters used as part of the signal conditioning system were set at a 10 Hz cut-off frequency instead of the usual 30 Hz. The acceleration control frequency band of the control software was also lowered from 30 Hz to a 10 Hz upper bound. These changes restricted the control of the specimen to a narrower frequency band, but permitted the system to function adequately. Figure 8-7 shows the recorded acceleration from another Tarzana test sequence (run 30) that was performed at a higher amplitude. The trace still contains some noise, indicated by the high frequency peaks, but it is not as prevalent in the Fourier spectrum. This change is quite noticeable in the calculated Fourier spectrum of this time series shown in Figure 8-8. The high frequency vibrations do not dominate the signal, and only the peaks generated by the structural vibrations are present. This type of test illustrates that the limitation of unwanted noise generation from the specimen or its support frame is crucial to the execution of a fully dynamic test. 2 1 6 o o < -1 -2 0 5 10 15 20 25 Time (s) Figure 8-4: Recorded acceleration of the table with significant frequency noise 126 Chapter & Discussion of Results Lateral Vibration a E < £ o Earthquake Response J L 10 20 30 Frequency (Hz) 40 50 Figure 8-5: Normalized fourier spectrum of signal with noise Figure 8-6: Dampers added on second story panel The strength of the specimen proved to be too high to push it fully into non-linear action. The final test sequence performed caused a shutdown of the system, since the capacity of the main 129 Chapter & Discussion of Results 5.0 ^ 2.5 ^ o.o i mittmiNimmm-^~ < -2 .5 -5.0 0 5 10 15 2 0 25 Time (s) Figure 8-7: Recorded table acceleration of Tarzana replication test (run #30) D. E < E o 10 2 0 30 Frequency (Hz) 40 50 Figure 8-8: Normalized fourier spectra of Tarzana replication test longitudinal actuator was surpassed. Figure 8-9 and 8-10 illustrates this situation. The first of the two figures represents the force output of the actuator during test run 28, the second the same type of graph for test run 29 when shutdown occurred. The requirements are calculated with the method outlined in a previous chapter. For more information, see "General System Performance" on page 42. The accelerations recorded at each of the storeys of the specimen were multiplied by the calculated lumped floor mass, which includes the steel plate and framing mass. The results of this calculation are the individual storey inertia forces. These 130 Chapter 8> Discussion of Results individual force traces were then added to compute the Specimen Base Shear: Ve. This trace, added to the force needed to move the table, resulted in the total force requirement for the experiment, represented by the solid curve shown on both figures. The other curve represents the same value, calculated from the signal of the force transducer placed inside the main actuator. The absolute force limit of the actuator is also illustrated by the solid horizontal lines. Z O o 200 -200 F = MA F = Force Sensor 10 15 Time (s) 20 25 Figure 8-9: Comparison of force requirements for test run 28 Z o 200 -200 F = MA F = Force Sensor 10 15 Time (s) 20 25 Figure 8-10: Comparison of force requirement for test run 29 The force demands, represented in Figure 8-9, show that the actuator limits are very close to 131 Chapters' Summary and Conclusions being reached. In fact, the force sensor signal, which seems to exhibit larger peak values than the signal calculated for the acceleration traces, indicates that the limits were surpassed at certain times. This discrepancy could be explained by the fact that the relatively old sensor and its mechanical parts do not generate linear signals when pushed to their operational limit. The test nonetheless could be executed without a shutdown of the system. Figure 8-10 shows that raising the excitation level from 140% to 150% of the historical intensity of the earthquake causes a major problem. The force levels, as displayed by the two curves, are much too large and surpass the limits of the cylinder. The system underwent a severe enough jolt to cause the TAPS unit to take over and perform a controlled stoppage of the test. This accounts for the tapering of the input signal at the end of the trace. The next set of figures shows the results of the same test sequence presented in a different fashion. Figures 8-11 and 8-12 illustrate the measured force requirement versus the calculated capacity of the table. The single axis tests only required one of the actuators to move; therefore, the flow demands of these tests were much lower than multi-axis tests. Accordingly, the supply pressure drops only for a instant because of the pump-flow lag, and the force capacity of the actuator is maintained during the whole of the test sequence. For the lower amplitude test, the capacity is again shown to be larger than the demand. 8.8 S u m m a r y a n d C o n c l u s i o n s Shake table testing of a steel shear wall specimen was conducted on the seismic simulator of the University of British Columbia during the month of March 1997. The main operational 132 Chapter & Summary and Conclusions £ 50 10 15 Time (s) 20 25 Figure 8-11: Demand and capacity of table during the test run 28 z u 200 Demand Capacity 10 15 Time (s) 20 25 Figure 8-12: Demand and capacity of the table during test run 29 objective of this test was to investigate the simulator behaviour when driven to its operational limits. The large and heavy specimen was too strong to be pushed into non-linear behaviour. The thin steel plates that form the panels of the shear wall vibrated out-of-plane causing very high acceleration vibrations. These were recorded by the sensitive control instruments and caused shutdowns of the simulator before the maximum actuator force could be developed. Dampers had to be installed to limit this noise pollution. The limitation of unwanted 133 ChapterS" Summary and Conclusions vibrations from a specimen or its support frame was crucial to the execution of this test. The simulation method developed in Chapter 4 was used to calculate the force requirements of the test. The algorithm was found to predict accurately the operational limits of the shake table. The demand was shown to exceed the capacity of the simulator during test run number 29 when a shut-down occurred. This simulation method would be useful to researchers in the planning phase of a test, since it would give them an estimate of the capacity of the table for any given input acceleration time history. 134 CHAPTER 9 Bridge Bent Testing 9.1 B a c k g r o u n d One of the continuing research efforts at the University of British Columbia over the last few years has been the evaluation of the seismic behaviour of concrete bridges. Specifically, the rehabilitation of the Oak Street bridge, situated in Vancouver B.C., has been the subject of an entire testing program. The project started when a number of retrofit schemes were evaluated using slow cyclic testing at the Structural Testing Laboratory on 45% scale models of a particular bent of this structure^85!. This testing instigated another study: the investigation of the behaviour of a 0.27 scale model of an asdouilt bridge bent under dynamic excitation. These tests were performed during the months of May and June 1996 and resulted in a M.A.Sc. thesis[86]. 9.2 O b j e c t i v e s o f T e s t s The overall research objectives of this project were: • To increase the body of knowledge on the differences between dynamic and static tests. • To understand the dynamic behaviour of an Oak Street Bridge bent. 135 Chapter 9 Description of the Specimen To extend the experience in scaled shake table tests of heavy specimens in the Structural Dynamics Research Laboratory at UBC. The latter of these was the main operational objective for this particular test. It is the principle subject of this chapter. At the time of project execution, most of the dynamic investigations done at the UBC Structural Dynamics Laboratory used unmodified recordings of historical earthquakes. The test sequences were executed with different input amplitudes, but the time increment of the test histories was never changed. Although this approach yields realistic results for specimens that are life size, it loses some validity when small-scale models are used'87-'. The relation between the behaviour of a "real" structure and its prototype is described by modelling theory. By using the similitude rules developed by this theory, the recordings of small-scale model testing can be modified to generate results applicable to the full-size structure. The theory behind this method will not be reviewed in this chapter, only the effects of its implementation on the scaling of the input time history. Several other sources describe the mathematical details in great depth [ 8 8 ] [ 8 9 ] [ 9 0 ] [ 9 1 ] . 9.3 D e s c r i p t i o n o f t h e S p e c i m e n The concrete specimen was a 0.27 scale replica of one of the bents of the Oak Street bridge in Vancouver, British Columbia. It had a height of 1.57 m and a length of 4.3 m. The square columns had an area of 327mm2 and were spaced 2.2m apart. A cap beam placed on the bent structure was used to transfer the load created by the inertia forces. It cantilevered over the 136 Chapter 9 Description of the Specimen columns by 703mm. The weight of this beam and the steel mass attached to it totalled 89kN. This arrangement of beam and masses was sized to replicate the high centre of gravity created by the deck in the modelled structure. Figure 9-1 shows the bent specimen ready to be tested. Steel cable Steel masses Transfer beam Figure 9-1: View of concrete bent specimen The specimen was tied down laterally with four steel wire ropes and supported with four hinged connections, two at the base of each of the columns. This permitted the test article to move freely in its intended uni-directional motion and restrain it from any out-of-plane movement. The ropes were pretensioned to prevent the slack from jolting the system. By adjusting this pretension force, the natural frequency of vibration of the wires could be controlled. The original loading force was increased at one point of the test in order to augment the natural frequency of the motion of the tie-downs. This procedure will be described in one of the following sections. 137 Chapter 9 9.4 I n s t r u m e n t a t i o n Instrumentat ion This experiment was instrumented with a total of 32 channels of transducers. These instruments provided both internal and external measurements. A number of strain gauges were placed on the longitudinal reinforcement bars of the bent and two stirrups were placed near the beam-column connection. The remaining channels of instrumentation were dedicated to the measurement of the acceleration and absolute displacement of the table and specimen. The transducers of interest for the study done in this chapter include the table instrumentation (accelerometers, LVDTs and Force Transducer) and the accelerometer placed on top of the test article. A description of the purpose of each type of instrument is included in Table 9-1. Instrument Type Measurement IC Sensor 3110 Accelerometer Absolute acceleration of top of specimen Linear Variable Differential Transformer Absolute table displacement Kistler 8304 K-Beam Accelerometer Absolute table acceleration Table 9-1: Purpose of bridge bent testing instrumentation The motions of the bent were also recorded using a high speed video camera. This system was used to determine the crack development pattern, and also to what extent these opened and closed during the test sequences. 130 Chapter 9 9.5 D e s c r i p t i o n o f T e s t s Description of Tests 9.5.1 Preparation of the Input Time History The concrete specimen was tested with only one excitation history. The nature of the specimen dictated this choice. Since the specimen could not undergo large motions without being significantly damaged, this limited the number of test sequences that could be executed without drastic changes in its behaviour. The test history was therefore chosen by testing its potential for damage on a finite element model of the specimen. An initial list of possible earthquakes was chosen from the lists provided in a NEHRP report^. A finite element model of the reduced scale bent was constructed. Linear and non-linear analysis were executed to gauge the damage potential of these records on the model^. The calculated response spectrum associated with each of the time histories was also compared to the Canadian Building Code design spectrum for similitudes. The final choice of excitation history rested on the E-W component of the 1992 Landers earthquake recorded at the Joshua Tree fire station. This record, because of its long duration, amplitude, and similitude of its calculated response spectrum to the Canadian Building Code design spectrum was the best possible choice as a test history. To follow the scaling laws, the test history needed to be modified. By selecting a number of arbitrary values for scale factor, pertaining to the length, stress and mass of the prototype, the final scaling value for the time variable was calculated to be 0.279. The time increment of the original recording was 0.02 seconds; therefore, the time increment of the modified history was 139 Chapter 9 Description of Tests 0.006 seconds. This compression of the earthquake record had two immediate effects: the frequency band of the signal changed, and the displacement needed to replicate the acceleration record dropped significantly. This procedure was also used in the Steel Shear Wall testing described in Chapter 8. A better understanding of the effects of the scaling process on the input time history can be gained by comparing the original, concrete bent with steel shear wall reference time histories. The shear wall was not constructed to model a specific structure. This meant that the scaling factor for the time variable could be chosen and not calculated rigorously since it was still an independent variable. The time scale factor was therefore selected to be 0.5. The time increment of the original recording was 0.02 seconds; therefore, the time increment of the modified history was 0.01 seconds. A comparison of the effects of the preparation process on the Joshua quake for both the concrete bent and the shear wall experiment is included in Figures 9-2,9-3 and 9-4. 140 Chapter 9 Description of Acceleration 0.50 -0.50 | o.oo 20 10 "5. 0 </> 5 -10 -20 10 20 30 40 50 60 70 80 Time (s) Displacement 10 20 30 40 50 Time (s) 60 Zoom of acceleration post-pulse 70 80 0.025 U 0.000 o < -0.025 75.0 78.5 Time (s) Normalized Fourier Spectrum 82.0 10 Frequency (Hz) 15 Figure 9-2: Joshua earthquake record with time increment of 0.02 sec (original) Chapter 9 Description of Tests Acceleration 0.50 0.25 0.00 u u < -0.25 -0.50 10 20 30 40 50 Time (s) Displacement 60 70 80 E 10 5 0 CO 5 -5 -10 10 20 Time (s) 30 Zoom of acceleration post-pulse 40 0.025 3 o 0.000 o < -0.025 35 Time (s) Normalized Fourier Spectrum 40 Q. E < o z 10 Frequency (Hz) 15 Figure 9-3: Joshua earthquake record with time increment of 0.01 sec (compressed) 142 Chapter 9 Description of Tests Acceleration 0.50 _ 0.25 U) *T 0.00 o o < -0.25 -0.50 10 20 30 40 Time (s) Displacement 50 60 70 80 E (A 5 10 15 Time (s) Zoom of acceleration post-pulse 20 25 3 6 u < 0.025 0.000 -0.025 22 23 24 Time (s) Fourier Spectrum 25 Q. E < o z 5 Frequency (Hz) 1 0 15 Figure 9-4: Joshua earthquake record with time increment of 0.006 sec (compressed) 143 Chapter 9 Description of Tests The first page illustrates the earthquake record as it was recorded. The second page shows the scaled history used for the steel shear wall project, described in the previous chapter. The third pictures the time history used for the concrete bent test. The top part of each of these figures shows the acceleration time history of the Joshua earthquake, plotted to the same scale but with modifications to the time increment. In all cases, the amplitude associated with each of the time steps of the acceleration trace is identical, but as the value of the increment reduces between these steps, the resulting amplitude of the calculated displacement also decreases. The second graph of each figure illustrates this. This result can be beneficial in certain circumstances. Historical earthquakes often have peak displacement demands greater that the stroke of the actuators on a simulator. This makes them useless in their unmodified form. If a reduced scaled test is conducted on a shake table, the input records need to be compressed. This would lower the displacement demands of any input record. Therefore a greater number of large displacement records become available to researchers for their tests. As mentioned in Chapter 5, two half sine pulses are added at the end of the acceleration time history used at the UBC shake table, in order to insure that any displacement and velocity drift, that naturally occur in a historical earthquake, is limited. This makes the input time history usable in three-variable control. As reported in the previous paragraph, the displacement associated with a particular acceleration trace drops considerably as its time increment is scaled down. This reduces the time span the corrective post pulses have to be applied, since the drift also diminishes. An enlarged view showing these pulses at the end of 144 Chapter 9 Description of Tests the acceleration frame is provided in the third graph of each of the figures. The corrective effects of these pulses are noticeable at the very end of each of the displacement traces. The final value of the displacement time history is brought by the applied acceleration pulses to near zero. For more information, see "Post-pulse Compensation of Strong Motion Records" on page 71. The frequency content of each of the acceleration traces pictured by the normalized Fourier spectrum, the fourth plot of each of the previously mentioned figures, also changes drastically because of the scaling process. As the time increment shrinks, the frequency content of the signal goes up. This characteristic of the input trace is crucial in any dynamic test. If the natural frequencies of vibration of the test article are far from that of the excitation, the specimen probably will not undergo large relative motions, which are critical to any destructive test. The frequency content of the scaled time history should be compared with the predicted, or better yet, the measured natural frequencies of the test specimen. If a destructive test is required, and the scaling process forces the frequency content of the excitation far above the first natural frequency of vibration of the specimen, an alternate input history should be considered. 9.5.2 Test Schedule This test was conducted using only one input time history. The main difference between the different runs in the test sequence was the amplitude. The same record was replicated with different levels. Table 9-2 describes the sequence of input records. The first three runs were 145 Chapter 9 Results f rom Test used to calibrate the table, this subject will be addressed in the discussion of results. Run Number Input %PGA of Historical recording Calibration 1 Joshua Tree 5 Calibration 2 Joshua Tree 10 Calibration 3 Joshua Tree 10 1 Joshua Tree 20 2 Joshua Tree 40 3 Joshua Tree 80 4 Joshua Tree 120 5 Joshua Tree 160 6 Joshua Tree 240 7 Joshua Tree 300 Table 9-2: Summary of bridge bent tests 9.6 R e s u l t s f r o m Tes t The results of interest for this study are the table acceleration and displacement in the main direction of excitation for the highest level of excitation run, test number 7. These two traces are pictured in Figures 9-5 and 9-6. The top of specimen acceleration of this test run is also used in the demand calculations of the next section and is shown in Figure 9-7. 9.7 D i s c u s s i o n o f R e s u l t s As in the steel shear wall test, the restraining apparatus used to insure uni-directional movement in the bent experiment initially caused control problems. The tie-down wires rope originally were pre-tensioned with an arbitrary force. The resulting frequency of their first 146 Chapter 9 Discussion of Results 1.5 Time (s) Figure 9-5: Recorded table acceleration from test number 7 5 10 15 20 25 30 Time (s) Figure 9-6: Recorded table displacement from test 7 natural mode of vibration was about 4.4 Hz. This frequency was close to the excitation input and to that of the first natural frequency of vibration of the specimen, which was measured at about 7.6 Hz. This caused a problem since the cable were excited by the test sequence. This swinging motion was predominantly associated with the first natural mode of vibration. The motions of the tie-downs polluted the feedback signal recorded by the table instrumentation. This caused the off-line compensation algorithm to diverge and the replication errors to increase dramatically, instead of reducing from test sequence to test sequence, as shown by 147 Chapter 9 Discussion of Results 1.5 1.0 U) 0.5 0.0 O -0.5 < -1.0 -1.5 0 5 10 15 20 25 30 Time (s) Figure 9-7: Recorded top of specimen acceleration from test 7 Figure 9-8. The first test of this series was performed at 1.7% of the final test amplitude, the second and third at 3.3%. Two corrective measures were therefore taken to solve this divergence problem. Firstly, the tension force in the tie-downs was increased to boost their first natural frequency of vibration to about 12 Hz. Secondly, the control bandwidth used in the test was limited to an upper value of 15 Hz. This prevented the high acceleration vibrations, caused by the second and third harmonics of the cables, from polluting the feedback signal, while providing adequate control. For more information, see "General Control Scheme" on page 91. J | ^ i j | ^ w o i _ LU ns v 0. 700 600 500 400 300 200 100 0 3 Displacement Acceleration Run Number Figure 9-8: Peak displacement and acceleration errors for initial test sequences 146 Chapter 9 Discussion of Results These changes permitted the correction algorithm to compensate the original drive signal in a correct way and limit the replication errors to an acceptable level. The peak errors calculated between the reference and recorded signal are shown in Figure 9-9. The first run of this sequence was performed at 6.7% of final test amplitude, the second at 13.3%, the third at 26.7% and the fourth at 40%. Other tests were conducted after these but the error values are not shown. The errors for these last few tests stabilized at the level shown for the fourth run. The acceleration peak error is still higher than in most tests, for which a value of 15% or less was typically attained, but considering the situation, this was deemed acceptable. W O i _ i _ LU ca a> o_ 60 50 40 30 20 — 10 — 0 2 3 Run Number 3 Displacement Acceleration Figure 9-9: Peak displacement and acceleration errors for second set of test sequences The scaling of the Joshua quake decreased the velocity demands of the experiment, which in turn limited the oil flow needed to generate the motions. Therefore, the replication of the time histories did not cause the supply pressure to drop any considerable amount, and the bent could be shaken with high base acceleration. Figure 9-10 shows the calculated capacity of the main actuator with the calculated demand. The capacity was calculated with the simulation algorithm already mentioned in a previous chapter. The demand was calculated by 149 Chapter 9 5ummary and Conclusions multiplying the recorded base acceleration with the mass of the table, and adding the product of the acceleration recorded at the top of the specimen with the mass of the test article. For more information, see "General System Performance" on page 42. The recorded values from the highest amplitude run, test number 7, were used to generate this figure. The demand, although close to the capacity, never exceeded it. 200 1 150 8 100 £ 50 10 15 Time (s) 20 25 Figure 9-10: Calculated demand and capacity for highest amplitude bent test 9.8 S u m m a r y a n d C o n c l u s i o n s Dynamic testing of a 0.27 scale specimen of an Oak Street Bridge bent was conducted on the seismic simulator of the University of British Columbia during the months of May and June 1996. The main operational objective of this test was to extend the experience in scale shake table testing of heavy specimens. Researchers used model scaling laws to relate the behaviour of a scale test article to the real structure. When scale testing is executed with an historical earthquake, its duration has to be reduced. This shifts the frequency content of the input history. This shift has to be considered, 150 Chapter 9 Summary and Conclusions because it affects the damage potential of the time history. The shrinking of the time increment lowers the displacement demands of a particular trace. The two half sine post pulse compensation technique of acceleration time history limits the naturally occurring velocity and displacement drift in historical earthquakes. The limitation of this drift is crucial when multi-variable control is used. This technique normally requires that a near zero displacement be achieved at the end of a test sequence. The swinging of the tie downs used in the experiment created vibrations that polluted the feedback signal to the controller. The pre-stress force used to tension the tie downs had to be increased. This augmented the first natural frequency of vibration of the cable, and moved it out of the range of interest of the test. The limitation of unwanted vibrations from the specimen or its support frame was crucial to the execution of this test. 151 CHAPTER 10 Seismic Rated Relay Rack Testing 10.1 B a c k g r o u n d Relay racks are used to mount equipment which is crucial for communication networks and are therefore a critical component in the event of an earthquake. BC TEL, the main provider of communication services in British Columbia, developed its own design for relay racks. Static and dynamic tests were conducted on prototype racks in order to confirm the behaviour expected by design engineers. These tests were conducted by Civil Engineering personnel in June and July 1996 at the University of British Columbia. 10.2 O b j e c t i v e s o f T e s t s The objective of these tests was to determine whether the relay racks conform with the earthquake environmental criteria of the NEBS requirements for seismic zone IV'-76-'. Compliance with NEBS requirements ensures that the relay racks are suitable for use in telecommunication networks in seismically active zones. This document recommends that the racks be tested both with monotonic static loading and fully dynamic excitation^93-'. In this chapter, only the dynamic tests will be discussed. These tests differ from most civil engineering experiments, since the racks had to undergo 152 Chapter 10 Specimen description very specific base excitation, namely a sinusoidal sweep and an artificial earthquake time history. Usually, a perfect replication of the desired waveform is not needed, since researchers use the recorded signals for their analysis. For this series, however, the specimens had to meet requirements based on specific excitation demands explicitly included in the NBES document. The replication of the waveforms was therefore a necessary condition for the success of the testing sequence. The operational objectives for the dynamic tests were: • replication of the frequency sweep from 1 to 50 Hz • replication of the VERTEQII shock time history The second objective posed a problem. The VERTEQII Zone IV waveform was developed to generate shake table motions up to 25.4 cm peak-to-peak displacement. The UBC shake table has only a 15.2 cm peak-to-peak stroke; therefore, a control solution had to be devised to provide an acceptable alternative to the replication of the actual waveform. This solution will be discussed in the following sections: 10.3 S p e c i m e n d e s c r i p t i o n The relay racks are manufactured with 100 X 50 X 4 Hollow Structural Sections (HSS) as the main vertical load-carrying members and top cross piece. The base of each HSS column is welded to two 150 X 100 X 10 angle (L) sections to provide a mounting base. Additional 12 mm-thick steel gusset plates connecting the two columns are used as stiffeners in order to 153 Chapter 10 Instrumentat ion insure proper load transfer from the columns to the base plate. Two types of units were tested, both 2.1 m tall, but with different widths: 48 cm and 58 cm. Both of these models could be fitted with additional lateral steel plate stiffeners. The racks were attached to concrete slabs using Ml2/25 HSL heavy-duty expansion anchors to simulate field installation conditions. Steel plates (weights), which were used to simulate equipment payload loads, were placed on rack shelves designed specifically to support them. Photos showing details of the rack element are presented in Figure 10-1 and Figure 10-2. 10.4 I n s t r u m e n t a t i o n This experiment was instrumented with a total of 12 channels of transducers. These instruments provided both the measurement of the table motions and that of the specimens. 154 Chapter 10 Instrumentat ion Figure 10-2:48 cm and 58 cm racks with obsolete equipment load Four of the channels measured the acceleration and displacement of the table. The remaining channels of instrumentation were dedicated to the measurement of the acceleration and absolute displacement of the top of the specimen. The transducers of interest for the study done in this chapter are the table instrumentation (accelerometers, LVDTs). A description of the purpose of each type of instrument is included in Table 10-1. Instrument Type Measurement Linear Variable Differential Transformer Absolute table displacement Kistler 8304 K-Beam Accelerometer Absolute table acceleration Table 10-1: Purpose of BC Tel testing instrumentation 155 Chapter 10 10.5 D e s c r i p t i o n o f T e s t s Description of Tests 10.5.1 Preparation of the Input Time History The UBC shake table did not meet all the test equipment requirements of the NEBS document. It can only achieve 60% of the required peak-to-peak stroke of 25.4 cm. This posed the problem of how to partially replicate the "true" waveform without affecting the underlying aim of testing the specimen to a fixed requirement. One option was to scale down the amplitude of the entire acceleration record, so that the displacement demands were lower than the limits of the simulator. Another option was to filter out the low frequencies in the test history, so that the maximum stroke of the table was not surpassed. This would preserve the contribution of the higher frequencies to the excitation of the test articles. The second option proved to be the best method, since the relay racks had a fairly high first natural vibration frequency. The low frequency components of test history do not affect the response of a stiff specimen, since they do not excite the fundamental mode of vibration. It was concluded that a test history with a resulting Fourier spectrum that would match the required Fourier spectrum from one half to twice the first natural frequency of the test article should provide adequate excitation. The VERTEQII acceleration time history was therefore filtered using a digital high-pass filter. The lower frequencies of the excitation were removed until the maximum displacement, calculated with a digital integration routine, was lower than the maximum stroke limit of the actuator. The resulting modified VERTEQII waveform was then used to test Chapter 10 the racks. Description of Tests A comparison of the two acceleration traces is shown in Figure 10-3. It is evident that the general features of the two signals are alike, including the level of the peak acceleration. The effects of the filtering process can be viewed in Figure 10-4. The Fourier spectra of the experimental and original VERTEXII waveform were computed. The spectrum of the recorded signal matches adequately the spectrum of the original waveform for frequencies above 3 Hz. The first natural frequency of vibration of the specimens were determined to be 6.2 Hz for the 48 cm rack and 6.9 Hz for the 58 cm rack along their weak axis by impact hammer testing^77^78^ and ambient vibration testing^. This feature is represented by a thick line in Figure 10-4. The modified signal therefore matches the required spectra in the frequency band that spans roughly half to twice the first natural frequency of vibration of the specimens. The calculated response spectra are also compared in Figure 10-5. The same amplitude variation between the two signals can be viewed in this figure as in the previously mentioned figure. The spectrum of the recorded signal has less amplitude than the spectrum of the original waveform at frequencies below 3 Hz and a bit more amplitude at frequencies above that value. The two prototype racks were therefore adequately excited by the test history, since enough energy was provided in this critical frequency band. Another way of reducing the displacement requirements of the test would have been an overall scaling of the acceleration trace. This process would reduce the low and high frequency content of the signal. The original and modified VERTEQII waveforms would have been identical except for their amplitudes. The higher frequency acceleration peaks would 157 Chapter 10 Description of Tests Original waveform u> 6 o < 15 20 Time (s) 25 30 35 Recorded waveform 5 d u < 10 15 20 Time (s) 25 30 35 Figure 10-3: Comparison of original and recorded acceleration waveforms First natural of specimen Recorded Verteqll 4 6 Frequency (Hz) 10 Figure 10-4: Comparison of Fourier spectrum of the recorded and original waveform 153 Chapter 10 Description of Tests 10 First natural of specimen Recorded Verteqll </> E < 10 0 2 4 6 8 Frequency (Hz) Figure 10-5: Comparison of calculated response spectrum have been lower and would not have provided enough excitation around the first natural frequency of vibration of the specimens. This shortfall prompted the use of the filtering method over the overall scaling method. A comparison of the recorded displacement waveform with the displacement trace calculated from the original VERTEQII acceleration signal is included in Figure 10-6. As predicted, the displacement demands of the modified waveform were under the limits of the actuators. These limits are shown as dotted lines on the graphs. Because of the modification of the source acceleration trace the two signals were distinct. The recorded displacement still contained the same trends, but the large excursions were diminished by the digital filtering process. The displacement trace, since it contained the low frequency information of the prescribed motions of the table, was the most affected quantity in the replication process. The replication of the sine sweep did not pose such problems. The table actuators could easily accommodate the displacement demands of this particular waveform. Figures 10-7 and 10-8 159 Chapter 10 Description of Tests Original waveform 10 15 Time (s) 25 30 20 10 Q. 0 to Q -10 -20 Recorded waveform v 10 15 20 Time (s) 25 30 35 Figure 10-6: Comparison of original and replicated displacement traces show a typical acceleration and displacement recording from such a test. The requirements prescribe a constant 0.2 g acceleration frequency sweep from 1 to 50 Hz. The acceleration trace shows that this was attained. The displacement was high in the first few seconds of the test sequence but diminished as it continued. The required displacement to produce a 0.2 g signal is smaller as the frequency of the sweep increases. 10.5.2 Test Schedule This test used two types of excitation: the modified VERTEQII waveform and a sine sweep. For the qualification testing of the racks a total of 16 test runs were executed. The racks were 160 Chapter \0 Description of Tests 0.40 - , 0 50 100 150 200 250 300 350 Time (s) Figure 10-7: Typical acceleration recording for sine sweep test 10.0 - , •H- iiliiiiiiniiiiii f °-° — £ -io-o -I 1 1 1 1 1 1 1 0 50 100 150 200 250 300 350 Time (s) Figure 10-8: Typical displacement recording for a sine sweep test excited in both the longitudinal and lateral directions of motion of the table. They were tested with different pay loads, specifically 160 and 227 Kg. Some runs were performed on racks fitted with lateral steel plate stiffeners. Additional tests, runs number 17 and 18, were conducted with equipment payloads to simulate actual field conditions. Run Number Test Type Direction(s) Payload (kg) Stiffeners 1 Earthquake, VERTEQII Lateral 160 Yes (4) 2 Sine Sweep Longitudinal 160 Yes (4) Table 10-2: Summary of BC Tel testing 161 Chapter 10 Results f rom Test Run Number Test Type Direction(s) Payload (kg) Stiffeners 3 Sine Sweep Lateral 160 Yes (4) 4 Earthquake, VERTEQII Longitudinal 160 Yes (4) 5 Earthquake, VERTEQII Lateral 160 No 6 Sine Sweep Lateral 160 No 7 Sine Sweep Longitudinal 160 No 8 Earthquake, VERTEQII Longitudinal 160 No 9 Earthquake, VERTEQII Lateral 227 No 10 Sine Sweep Lateral 227 No 11 Sine Sweep Longitudinal 227 No 12 Earthquake, VERTEQII Longitudinal 227 No 13 Earthquake, VERTEQII Lateral 227 Yes 14 Sine Sweep Lateral 227 Yes 15 Sine Sweep Longitudinal 227 Yes 16 Earthquake, VERTEQII Longitudinal 227 Yes 17 Earthquake, VERTEQII Longitudinal Equip-ment No 18 Earthquake, VERTEQII Lateral Equip-ment No Table 10-2: Summary of BC Tel testing 10.6 R e s u l t s f r o m T e s t The results of interest for this study are the table acceleration and displacement in both directions of excitation. Some calibration runs were performed before the qualification test was executed. These were not included in the summary of dynamic tests shown in Table 10-2. The calibration algorithm uses low amplitude runs in order to minimize the errors between the reference and recorded signals. The results from this procedure will be discussed in the next 162 Chapter 10 Discussion of Results section. For the demand calculations of this test, included in the discussion of results section of this chapter, the recorded and displacement traces from a longitudinal VERTEQII replication, namely run number 1, are used. Typical recorded values from such a run are shown in Figures 10-3 and 10-6. 10.7 D i s c u s s i o n o f R e s u l t s The dynamic testing of specimens to specific requirements sometimes poses problems. The physical limits of a shake table system are often a large contributor to these complications. The stroke limitation of the UBC simulator was the major stumbling block in this test. Although the actual VERTEQII waveform could not be exactly replicated, a suitable alternative waveform was developed using digital filtering and scaling methods.This waveform matched the desired excitation from half to twice the first fundamental frequency of the specimens. The control of a shake table involves a number of steps, taken prior to the actual test, that are crucial to the execution of a successful experiment. The replication errors obtained from the comparison of the modified shock waveform and the recorded values are low. Figures 10-9 shows the values of the RMS error between recorded and reference displacement and acceleration traces. The results from a number of increasing amplitude test runs are included. The first test was done at 12.5% of full amplitude, the second at 37.5%, the third at 62.5% and the fourth at 100%. An off-line compensation of the reference time history was done after the first three test sequences. The errors are all in the expected range. The acceleration errors are higher than the displacement errors. The racks produced 163 Chapter 10 Summary and Conclusions some pollution in the high frequency range, which was recorded by the accelerometers. This pollution increased the acceleration errors. The displacement errors, on the other hand, are quite low, which shows that the low frequency component of the prescribed motions were very well replicated. 20 CO 5 1 5 W 10 CO 2 5 CC -0 ] Displacement Acceleration 2 3 Run Number Figure 10-9: Calculated errors for VERTEQII replication The force requirements for this test were quite low since the only added weight was the attachment bases for the specimens. The flow demands were minimized by shaking the specimens in one of the table's orthogonal directions at a time. Figure 10-10 shows the force demand and capacity for a typical VERTEQII replication test sequence. As can be noted, the requirement trace never comes close to intersecting the capacity trace.This means that the simulator had no physical problems in replicating the waveform. 10.8 Summary and Conclusions The seismic relay rack testing for B.C. Tel. was conducted at the Structural Dynamics Laboratory of the University of British Columbia during the month June and July 1996. The 164 Chapter 10 Summary and Conclusions 200 Demand Capacity O o 150 100 50 0 0 25 30 35 Figure 10-10: Calculated demand and capacity for typical VERTEQII replication objective of these tests was to determine whether the relay racks conform with the earthquake environmental criteria of the NEBS requirements for seismic zone IV [ 7 6 ] . This testing included both dynamic and static testing, but only the dynamic testing was discussed in this chapter. This testing program was an example of true replication testing. A specified transient waveform had to be replicated in order to insure that the racks be subjected to a minimum amount of excitation. A sine sweep that ranged from 1 to 50 Hz was also reproduced. The control system was able to reproduce these specified waveforms to an acceptable level. The transient waveform was developed for a motion simulator that has 25.4 cm of peak to peak stroke. The University shake table has only 15.2 cm of peak to peak stroke. The transient waveform had to be digitally filtered to reduce its stroke requirements. This technique was chosen instead of strait amplitude scaling, since this permitted the specimen to be excited with the specified energy from half to twice its first natural frequency of vibration. 165 Chapter 10 Summary and Conclusions The algorithm developed in chapter 4 was used to calculate the hydraulic requirements of this test. The VERTEQII transient waveform produced some loss of pressure in the system, but the weight of the specimen was relatively low. The demand was therefore always lower than the capacity. 166 CHAPTER 11 Summary, Conclusions and Further Research The upgrade of the seismic simulator at the University of British Columbia in 1994-95 provided researchers with a state-of-the-art system for dynamic testing of civil engineering specimens. This upgrade included the addition of new actuators, which increased the number of degrees of freedom the table could reproduce, and a new controller, which permitted three-variable digital feedback control. With more capabilities also come new requirements in the planning and execution of tests. In this thesis, the physical and control demands of a large high-performance hydraulic simulator and a sample of the tests done were reviewed. A series of test were used as examples of dynamic testing. The conclusions that can be drawn for this body of research are: • A simplified simulation method, developed as part of this thesis, can be used to determine the physical demands of a test sequence on a hydraulic system. With some basic characteristics of the specimen and system an accurate pretest simulation can be executed to determine if the system capacity is adequate to perform as expected for the planned test sequence. • An algorithm that calculates the application of two half sine post-pulses of arbitrary amplitude proved to be a useful tool for the preparation of earth-quake histories for simulation by a three-variable controller. The drift that naturally occurs in a historical earthquakes needs to be limited so that the simulator is not left in non-zero position at the end of a test sequence, since this proves to be a problem for feedback correction calculations and normal operation of hydraulics. 167 The control that researchers have over an experiment and the shake table that drives it can determine the limits of any test. In many of the seismic simulators of today, digital hardware or computer software is used on a reg-ular basis. The point of the control sequence at which the digitalization process takes place therefore becomes an important characteristic of such a system. A simple classification method for seismic simulators was devel-oped as part of this thesis. It helps illustrate the differences in control tech-niques. The rigid mass tests were used to calibrate the simulation algorithm. The addition of a response lag time for the pump flow rendered the simulation accurate enough for the estimation of experimental demands from both sine sweep and shock test histories. The final physical properties of the simulated hydraulic system are very close to the actual system values. This shows that unless a very exact simu-lation is needed, the real system values can be used without a extensive cal-ibration test. The steel shear wall tests showed that the calculation technique, developed to gauge the force demands of a specimen and table system, can be used to predict the maximum attainable test amplitude. The concrete bent, as well as the shear wall test, demonstrated the impor-tance of controlling noise pollution emanating from the test article or its supporting frame. This pollution can easily confuse the feedback algorithm and also generate premature shutdowns of the system. The test waveform used in the concrete bent test exemplified scaling and post-compensation techniques. The shrinking of the time increment of his-torical earthquakes is used to make the testing results more compatible with physical laws. Post-compensation is used to limit natural drift in a wave-166 Chapter 11 form, making it more amenable to three-variable control. • The equipment rack testing was used as an example of true replication test-ing. In this test the specimens had to endure the force produced by a speci-fied waveforms. The control system was able to produce all desired sequences with acceptable errors. • The physical limitations of the simulator forced the modification of the earthquake waveform used in the equipment rack testing. Digital filtering methods instead of straight forward amplitude scaling was chosen, since this permitted the specimen to be excited with the specified energy from half to twice its first natural frequency of vibration. A few topics warrant further research. The simulation method discussed in this document was verified using many experiments, but only with one hydraulic system. To completely demonstrate the accuracy of this approach, it should be verified with results from the tests performed on other shake tables. Noise emanating from specimens during experiments proved to be a problem for the proper compensation of the input signal to the actuators. New methods of obtaining feedback signals for the digital compensation algorithms could be explored. Testing with the rigid mass arrangement could be expanded. For instance, vertical shaking tests could be done. Test to determine the effect of mass offset could be executed. This type of testing would explore the rotational limits of performance of the seismic simulator. 169 Chapter 11 Shake table testing generates a large amount of test data. The performance of automated methods that process the electrical signals generated by the instruments into data that can be used by researchers need to be investigated. Research into this aspect of shake table testing would be very practical. 170 CHAPTER 12 List of References [1] Wood, R.M., "Robert Mallet and John Milne- Earthquakes Incorporated in Victorian Britain", Earthquake Engineering and Structural Dynamics, Vol. 17,188 pp.107-142, 1988. [2] "Assessment of Earthquake Engineering Reasearch and Testing Capabilities in the United States", Earthquake Engineering Research Institute Publication No. WP-01, Septem-ber 1995, 23 p. [3] Abrams, D.P., "Testimony of Dr. Daniel P. Abrams before the Subcommittee on Basic Research of the U.S. House of Representatives", EERI On Line Exclusive, Oakland, Califor-nia; source: http://www.eeri.org/Features/Abrams.html; material dated April 24, 1997, retrieved November 17, 1997. 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[93] Ventura, C.E., and Latendresse, V , "5C TEL Seismic Rated Relay Rack Testing", Department of Civil Engineering, Report Number 96-002, University of British Columbia, November 1996, 38 p. 176 Appendix A This appendix contains an example of the MATHCAD© calculation sheet used to determine the amplitude and duration of two half sine post pulses. These post pulses remove the undesir-able effects of terminal velocity and displacement of a simulated strong motion time history. There are a number of user inputs required to calculate the pressure loss: • the time increment of the input time histories, • the number of data points in the input time histories, • the scaling factor applied to the time histories, • the time at which the analysis should stop, • the names of the input file. The resulting pressure versus time function is plotted as a result of the calculations. Additional examples of the application of the post-pulse calculation sheet are shown at the end of the appendix. 179 Post-Compensation Pulses: 2 Half-Sines Define array sizes: Time Increment: A := 0.02 Scaling Factor: F := 1.0 Total number of points in record: N := 4000 ==> Duration, Td := A-(N - 1 )==> Td = 79.98 Select time at which motion stops and post-pulses are added: Ts := 79 so that Ns := Ts-A '==>Ns = 3950 Discrete times and counters: Te = Ts + 0 Ne := Te-A 0..Ne t Zeroe the acceleration array: A ( := 0 lag := Ne - Ns ==> lag =0 Read data (use "Associate Filename" option to relate "Accel" to data filename): ANFj := i f ( i < l a g , 0 , R E A D ( A c c e l ) - F ) with peak value: am := m a x \ | A N F | (Values of A are in cm/secA2) First we will try and filter the acceleration record to remouve any of the lower frequencies Setup our filter C := i irhigh(butter(2) ,.0001) x f := 0,0.001.. .5 j := 3..Ne ==> am = 278.377 |gain(C,xf)| A := response( A N F , C ,Ne +- 3) Compute Velocity and Displacement Time Histories by 3rd Order Extended Formula: Define coefficients of the recursive equation: Compute velocity and corresponding displacement terms: and b 160 Velocity First three terms are equal to zero because of band of zeroes added at the beginning of record V := 0 V = 0 V = 0 and D = 0 D := 0 D = 0 0 1 2 0 1 2 Remaining terms: V. Displacement A J - n j - b n j ^ - V V j - i nj = 0 D- V. -b . a D. j - nj nj 24 l J " 1 nj = 0 In graphical form: 1fi>1 t. 1 Terminal values of Acceleration, Velocity and Displacement at Te = 79 At this time ==> A . , =-0.485 , v := V M i.e., v = 0.072 and 8 = D M Ne Ne Ne Set amplitude of pulses (r) to be real and at least 1 % of the peak acceleration between 0 and Te, and set the polarity of the first pulse opposite to that of 8: Let lim := 0.0lam==> lim = 2.784 v -n v - J i \ o \ and fac := if > l i m , ,limthen r := - 1 -fac==> T =-2.784 \4 - |8 | 4-1SI / \ |s|/ Compute duration of each half-pulse, T1 and T2, ensuring that both are real, positive values: => T2 = 1.009 7t T2 := — 4 2-V 8-8 T l - 7 C V 2T r n-r T2==> T l = 1.049 or T l a := - 7 T V 2-r Duration of both pulses: TT := T l + T2 ==> TT =2.058 T2==> T l a =-0.968 then: T l := i f ( T l > 0 ,T1 ,T1 and Te l = Te + T l Extended duration of record: Tt := Te + TT ==> Tt = 81.058 182 Define extended arrays: m ; = floor H = = > m = 5 2 a n d N 2 ; = floor J 2 \ A / \ A N3 := N l + N2 i l := 0 . .N3 => N2 = 50 Build-up post-pulses: A l u := if| A-7T i l <N1 ,sin i l | , -s in T l A-7t T2 • ( i l - N l ) The post-pulses look like: Append pulses to record: v N e + i l A l : 1 2 3 Time (sec) The length of this array is: A 1 N 3 = 0.075 N := length( A)i.e., N = 4053 Then, i := 0.. N - 1 t. := i- A j:=Ne.. N - l Continue computing velocity and displacement time histories: Velocity Displacement 3 3 Y= £ V n / V i r v V i D J : = £ v i - n j V i 4 arD. > nj = 0 nj = 0 Check end-values: end := N - 1, Tend = (N - l)-A==> Tend = 81.04 A end = 0 0 7 5 V end = 3 - 2 1 3 * l 0 " 3 D end = 0 0 2 4 Write records to files: WRITEPRN(Cal_a) := A WRITEPRN(Cal_v) := V WRITEPRN (Cal_d) = D 163 Time History Plots: A . Acceleration TTel 1 " T V iff 10 20 30 40 50 60 70 80 90 t. 1 Velocity V. 0 TTel TTel 184 Time History Plots (zoom in at end of record): Acceleration 2 T Tel 78.8 79 79.2 79.4 79.6 79.8 80 80.2 80.4 80.6 80.8 81 t. 1 Velocity 5 Te Tel /8.8 79 79.2 79.4 79.6 79.8 80 80.2 80.4 80.6 80.8 81 Displacement D. o Te T e l 78.8 79 79.2 79.4 79.6 79.8 80 80.2 80.4 80.6 80.8 81 t. 1 185 Time History Plot for the Post compensated Northridge (Jan. 17 1994) Earthquake Channel 1 (90°) of the Tarzana - Cedar Hill Nursery recording station. Time History Plots: Acceleration (cm2/s) v. Velocity (cm/s) TTel Displacement (cm) / 1 AA /N TTe rN v y r 1 136 Time History Plot tor the Post compensated Northridge (Jan. 17 1994) Earthquake Channel 1 (90°) of the Tarzana - Cedar Hill Nursery recording station. This record has been cut off at 12 s to show the use of the post pulse on records with larger terminal velocity and displacement. Time History Plots: Acceleration (cm2/s) 6 8 t. 1 TTel 10 12 Velocity (cm/s) TfTel 6 8 Displacement (cm) TeTel Time History Plot for the Post compensated Santa Cruz Mountains (LOMA PRIETA) Earthquake Channel 1 (90°) of the Treasure Island recording station. Time History Plots: Acceleration (cm2/s) 200 -200 r\jA fr»A_A>JX.AM A. lift -—\s\ fe fel If 0 5 10 15 20 25 30 35 ' i Velocity (cm/s) 50 V. Te Te! r — y— " 0 5 10 15 20 25 30 t. 1 Displacement (cm) Te Te! 5 J 0 5 10 15 20 25 30 t. 188 Appendix B This appendix contains an example of the MATHCAD© calculation sheet used to determine the pressure loss in a hydraulic system. There are a number of user inputs required to calculate the pressure loss: • the time increment of the input time histories, • the number of data points in the input time histories, • the scaling factor applied to the time histories, • the time at which the analysis should stop, • the names of the input files (up to three). The resulting pressure versus time function is plotted as a result of the calculations. 139 Pressure determination of a theoretical shake table system Define array sizes: Time Increment: A := 0.005 Scaling Factor: F := 981 Total number of points in record: N = 4000 ==> Duration, Td = A-(N - 1 )==> Td = 34.5 Time at which analysis is stopped: Ts := 20 so that Ns := Ts-A ' ==> Ns = 4000 Discrete times and counters: Te := Ts Ne := Te-A 1 i := 0.. Ne t; = i-A j = 3..Ne Zeroe the acceleration array: A ; := 0 lag := 0 Read data (use "Associate Filename" option to relate "Accel" to data filename): AO; := if(i< Lag +- 5 ,0 ,READ( Accel)-F) A L := if(i<lag + 5,0,READ(Accel l )-F) A2 ; := if(i<lag+ 5 ,0 ,READ( Accel2)F) Compute Velocity Time Histories by 3rd Order Extended Formula: Define coefficients of the recursive equation: a := | j and b := Compute velocity and corresponding displacement terms: Velocity First three terms are equal to zero because of band of zeroes added at the beginning of record V0 := 0 V0 := 0 V0 := 0 0 1 2 VI := 0 V I := 0 VI := 0 0 1 2 V2 := 0 V2 := 0 V2 := 0 0 1 2 . 9 19 -5 1 190 Remaining terms: 3 VO; := ^ A O i ni-bni • — - a VO. J WLt ) - » ) "J 24 l J nj = 0 3 A VI. := ^ A l . .-b . a VI . nj = 0 3 A2. n i-b . a -V2. j - nj nj 24 ' J nj = 0 Calculation of the system pressure using simple model P r e s ( A , N p , V O , V l ,V2) := V o « - 2 9 0 0 Ql<- 100 Q p « - 4 4 1 5 AO*-45.16 Al*-45.16 A2«-80.88 Pmax<— 1990 Vold<-Vo Pold<— Pmax Pnew<—Pmax Plag<- 5 for I E 0.. Plag Perr,<-0 for k e 0.. Np - l V 0 a « - | V0 f c | -A0-A Vla<- | V l k | - A l - A V2a<- | V 2 k | - A 2 - A Vl<-AQl -3 for le 0.. Plag - l Perr,«—Perr, , P e r r p i a g « - 0 if (Pmax - Pnew)<-100 Pen-p, <-0 if ((Pmax - Pnew)<0)-((Pmax - Pnew)>-100) Perr, ((Pmax - Pnew) - 300)3 3003 + l if ((Pmax - Pnew)<300)-( Vp<-AQpPerr ii Vnew<-(V0a + V i a +• V2a -t- VI) - Vp +- Void Err.«— Perr k n 192 Pnew<- Pold \ Vnew / Pold*— Pnew Vold<— Vnew P k «— Pnew 193 P. := 0 i := O . .Ne - 1 P := P r e s ( A , N e , V O , V l ,V2) Pressure vs. Time Ifti 0 2 4 6 8 10 12 14 16 18 20 22 24 t. 1 Weight of specimen and Table: Area or the piston: Mass := 6200 Areal := 80.88 Available force Fj := Areal-R-0.90 Available acceleration A v a i l := too Mass 194 = Appendix C This appendix contains test check list. The first list covers test preparation. The second the preparation of time histories for testing. The third list covers the basic testing steps at the UBC structural dynamics laboratory. 195 Test Preparation Check List • Specify test objectives What is the purpose of the test? What are the critical variables to be measured? What type of test is this? Qualification or research and development. Is it a full scale or reduced-scale test? If the test specimen is reduced scale, determine a scale factor. • Design test set-up. Is the test is destructive? If so, is the specimen self supporting during all the test sequence? What motions are permitted during a test? Is it a two dimensional test or a three dimensional test? Unwanted vibrations emanating from the test set-up should be minimized. Always consult the laboratory technician several times during the design of the test set-up. • Instrumentation What type of measurements are desired? (displacement, acceleration, veloc-ity, pressure) What precision is required? What type of signal filtering is required? What type of signal amplification is required? Can the instruments be mounted on the specimen? Keep records of all instrumentation used on the project. Always consult to the instrument technician several times during the design of the test set-up. 196 Time History Preparation Check ilet • Chooee acceleration test time history (ies) Earthquake, sinusoidal, random, etc. • Scale amplitude and/or test history time step. Use the test article scale factor to calculate the scalling factor of the time history or time histories. Determine the amplitude scale factor of desired base input acceleration level. • Integrate the acceleration time history twice to obtain the desired displacement time history If the displacement demands are to high filter low frequencies out of accelera-tion time history. Verify the "quality" of the input time histories: given acceleration time history, computed velocity and displacement. Do the time histories drift, contain spikes, etc.? If so, correct anomalies or start with another input acceleration time history. • Calculate flow demands of the acceleration time history with the simplified simula-tion method. If the force limit of the simulator are surpassed scale amplitude of the desired input time history or start with a new time history. • Calculate the duration of acceleration post pulses with the Mathcad calculation sheet. 197 Test Check List • The input time history should be resampled so that its sampling rate matches the seismic simulator's control sampling rate (MEVCS sampling rate). • The input acceleration should be transferred to the control program (MEVCS) with the FTP program. • The MEVCS calculates the desired output time histories (acceleration, velocity and displacement). Verify the "quality" of the input time histories: given acceleration time history, computed velocity and displacement. Do the time histories drift, contain spikes, etc.? If so, correct anomalies or start with another input acceleration time history. • Characterise the test specimen using the MEVCS program (see page 91). • Using the calculated Impedance matrix, from the characterisation test the control software calculates the initial actuator drive histories. • Use low level testing to correct the actuator drive histories. • Raise amplitude of test sequence to desired level. • Verify "quality" of recorded results. 196 

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