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Experimental investigation of the base storey design of base isolated steel buildings Barwig, Bill Barron 1983

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C I EXPERIMENTAL INVESTIGATION OF THE BASE STOREY DESIGN OF BASE ISOLATED STEEL BUILDINGS by BILL BARRON BARWIG B.Ap.Sc.,University Of British Columbia,1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department Of C i v i l Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1983 © B i l l Barron Barwig, 1983 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 i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C i v i l Engineering The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: November 4, 1983 i i Abstract Recent research indicates that base isolation of buildings eliminates or reduces seismic loading to an acceptable level. This paper presents the results of the experimental investigations of various base storey schemes for steel buildings with base isolation. A steel frame was designed and built for the shaking table tests, which were conducted in the Earthquake Simulator Laboratory at the University of British Columbia. The dynamic response of the frame was recorded for each base storey design, fixed base or base isolated. The base isolation system consisted of steel roller bearings with parallel, ductile steel energy absorbers(yield rings). These absorbers limit exessive displacement and absorb energy during severe earthquake excitation. They also provide restraint against wind loads and mild earthquake excitation. The new design of the base storey is aimed at eliminating the blind base storey or double foundation. The experimental tests show ways of better design methods and analytical studies are following to optimize them. Uncoupling of buildings from earthquake ground motion is relatively simple to achieve. However a base isolation system requires a certain restraint against minor horizontal loads such as wind loads which can be accomplished by energy absorbers. A new type of solid state energy absorber was used in the described tests. The newly proposed base storey is substantially different from conventional solutions used by other base isolation systems and results in a less expensive but safe design. Table of Contents Abstract i i List of Tables vi List of Figures v i i Acknowledgements x I. INTRODUCTION 1 II. SCOPE AND PROCEDURE OF EXPERIMENTS 4 III. TEST MODEL 5 1 . FRAME 5 2. BASE ISOLATION 10 IV. TEST EQUIPMENT 16 1 . SHAKING TABLE 16 2. INSTRUMENTATION 16 3. DATA ACQUISTION AND REDUCTION 17 V. REFERENCE BASE STOREY-FIXED BASE 18 1. NATURAL FREQUENCIES OF THE SHAKING TABLE 18 2. NATURAL FREQUENCIES OF THE FRAME 19 i . Computer Analysis 19 i i . Simplified Mathematical Model 21 i i i . Measured Frequencies(Fourier Spectrum) ...24 iv. SUMMARY OF RESULTS 25 3. DAMPING 26 VI. REFERENCE BASE STOREY - BASE ISOLATED 27 1. NATURAL FREQUENCY OF THE BASE ISOLATED FRAME 27 v. Computer Analysis 27 v i . Simplified Mathematical Model 28 v i i . Measured Frequencies 29 v i i i . Summary Of Results 32 2. DAMPING 33 VII. COMPARISON OF RESPONSES (REFERENCE BASE STOREY) 34 1. EXTREME VALUES 34 2. RESPONSES OF FIXED BASE AND BASE ISOLATED 34 3. COMPARISON OF RESPONSE RATIO FOR DIFFERENT EXCITATIONS 38 VIII. BASE STOREY DESIGN 41 1. CALCULATION OF THE BASE SHEAR AND BASE MOMENTS,REFERENCE BASE STOREY, FIXED AND ISOLATED BASE 41 2. DESIGN OF THE PROTOTYPE BASE STOREY 43 IX. PROTOTYPE BASE STOREY - FIXED BASE 44 1. NATURAL FREQUENCIES OF THE SHAKING TABLE 44 2. NATURAL FREQUENCIES OF THE FRAME 44 ix. Computer Analysis 45 x. Simplified Mathematical Model 45 x i . Measured Frequencies (Fourier Spectrum) ..47 x i i . Summary Of Results 48 3. DAMPING 49 X. PROTOTYPE BASE STOREY - BASE ISOLATED 50 1. NATURAL FREQUENCIES OF THE BASE ISOLATED FRAME ..50 x i i i . Computer Analysis 50 xiv. Simplified Mathematical Model 51 xv. Measured Frequency 52 V xvi. Summary Of Results 54 2. DAMPING 54 XI. COMPARISON OF RESPONSE, REFERENCE AND PROTOTYPE BASE STOREY 55 1. EXTREME VALUES 55 2. COMPARISON OF RESPONSE, FIXED BASE 55 3. COMPARISON OF RESPONSE, BASE ISOLATED 57 4. COMPARISON OF RESPONSE RATIOS 59 5. COMPARISON OF ENERGY LEVELS DUE TO EARTHQUAKE RESPONSE 59 XII. OBSERVED TORSIONAL FREQUENCY 63 1. REFERENCE BASE STOREY 63 2. PROTOTYPE BASE STOREY 63 XIII. CONCLUSION 64 XIV. APPENDIX A-SIMPLIFIED MATHEMATICAL MODEL, REFERENCE AND PROTOTYPE BASE STOREY 67 XV. APPENDIX B-FOURIER SPECTRUM 7 4 XVI. APPENDIX C-DAMPING VALUES 80 XVII. APPENDIX D-TIME HISTORIES, REFERENCE BASE STOREY ...95 XVI11. APPENDIX E-TIME HISTORIES, ACCELERATIONS, REFERENCE AND PROTOTYPE BASE STOREY 101 XIX. APPENDIX F-ENERGY LEVELS DUE TO EARTHQUAKE RESPONSE 107 BIBLIOGRAPHY 117 vi List of Tables I. Summary of Results, Fixed Base 25 II. Summary of Results, Base Isolated 32 III. Summary of Results, Base Shear and Base Moments. ..42 IV. Summary of Results, Fixed Base 48 V. Summary of Results, Base Isolated 54 VI. Percent of C r i t i c a l Damping in %, Reference Base Storey, Fixed Base 82 VII. Percent of C r i t i c a l Damping in %, Prototype Base Storey, Fixed Base 83 v i i List of Figures 1. Steel Frame, Reference Base Storey, Fixed Base, Concrete Blocks not shown 7 2. Steel Frame, Prototype Base Storey, Base Isolated, Concrete Blocks not shown 8 3. Testing Sequence of Base Storey Design 9 4. Base Isolation System Components 12 5. Design Proposal, Two Dimensional Isolation Pad with Yield Rings 13 6. Typical Load Displacement Behaviour of a Yield Ring. .15 7. Deflection of Frame with Fixed Base, Computer Model. Ii" i 8. StiffnessfK] and Mass Matrix[M], Fixed Base, Simplified Mathematical Model 22 9. Deflection of Frame with Fixed Base,Simplified Mathematical Model 23 10. Fourier Spectrum, Natural Frequencies 24 11. Deflected Frame, Base Isolated, Computer Model 27 12. Deflected Frame, Base Isolated, Simplified Mathematical Model 29 1.3. Fourier Spectrum of Acceleration Time History Decay. !30 14. Experimentally Determined Displacement Response from Frequency Sweep 31 15. Time Histories of Acceleration at the 4th Level 36 16. Time Histories of Relative Displacements 37 17. Response of the Frame subjected to Sinusoidal Excitation 39 18. Response of the Frame subjected to Earthquake Excitation 40 19. Deflection of Frame with Fixed Base, Computer Model. '.45 20. StiffnessfK] and Mass Matrix[M], Fixed Base, Simplified Mathematical Model 46 21. Deflected Frame, Fixed Base, Simplified Mathematical Model 46 22. Fourier Spectrum of the Acceleration Time History, Hammer Hit 47 23. Deflected Frame, Base Isolated, Computer Model 50 24. Deflected Frame, Base Isolated, Simplified Mathematical Model 51 25. Fourier Spectrum of Acceleration Time History Decay. .52 26. Experimentally Determined Displacement Response from Frequency Sweep 53 vi i i 27. Comparison of Acceleration Time History, Fixed Base. 28. Comparison of Acceleration Time Histories, Base I solated 58 29. Response of Frame to Sinusoidal Excitation 60 30. Response of Frame to Earthquake Excitation 61 31. Energy Levels due to El Centro Earthquake 62 32. Equivalent Model 67 33. Stiffness Matrix 68 34. Mass Matrix 68 35. Stiffness Matrix, Reference Base Storey, Simplified Mathematical Model 71 36. Mass Matrix, Reference Base Storey, Simplified Mathematical Model 71 37. Stiffness Matrix, Prototype Base Storey, Simplified Mathematical Model 73 38. Mass Matrix, Prototype Base Storey, Simplified Mathematical Model 73 39. Reference Base Storey, Hammer Hit 76 40. Reference Base Storey, Excitation Frequency: 20 Hz. .76 41. Reference Base Storey, Excitation Frequency: 11 Hz. .77 42. Reference Base Storey, Excitation Frequency: 9.7 Hz. .77 43. Prototype Base Storey, Hammer Hit 78 44. Prototype Base Storey, Excitation Frequency: 11 Hz. .78 45. Prototype Base Storey, Excitation Frequency: 5 Hz. ..79 46. Prototype Base Storey, Excitation Frequency: 2 Hz. ..79 47. Time History of Acceleration Decay,Reference Base Storey, Hammer Hit 84 48. Time History of Acceleration Decay, Reference Base Storey, 20 Hz Excitation 85 49. Time History of Acceleration Decay, Reference Base Storey, 11 Hz Excitation 86 50. Time History of Acceleration Decay, Reference Base Storey, 9.7 Hz Excitation 87 51. Time History of Acceleration Decay, Prototype Base Storey, Hammer Hit 88 52. Time History of Acceleration Decay, Prototype Base Storey, 11 Hz Excitation 89 53. Time History of Acceleration Decay, Prototype Base Storey, 5 Hz Excitation 90 54. Time History of Acceleration Decay, Prototype Base Storey, 2 Hz Excitation 91 55. Time History of Acceleration Decay, Base Isolated. ..93 56. Frequency-Response Plot, Base Isolated 94 57. Time History of the Acceleration at the 4th Level, San Fernando, Reference Base Storey 95 58. Time History of the Acceleration at the 4th Level, Parkfield, Reference Base Storey 96 59. Time History of the Acceleration at the 4th Level, Earthquake, Reference Base Storey 97 60. Time History of Displacement, San Fernando, ix Reference Base Storey 98 61. Time History of Displacement, Parkfield, Reference Base Storey 99 62. Time History of Displacement, Earthquake, Reference Base Storey 1 00 63. Time History of the Acceleration at the 4th Level, Fixed Base, San Fernando 101 64. Time History of the Acceleration at the 4th Level, Fixed Base, Parkfield 102 65. Time History of the Acceleration at the 4th Level, Fixed Base, Earthquake 103 66. Time History of the Acceleration at the 4th Level, Base Isolated, San Fernando 104 67. Time History of the Acceleration at the 4th Level, Base Isolated, Parkfield 105 68. Time History of the Acceleration at the 4th Level, Base Isolated, Earthquake 106 69. Energy Levels due to Parkfield Earthquake 107 70. Energy Levels due to San Fernando Earthquake 108 71. Energy Levels due to A r t i f i c a l Earthquake; Earthquake 109 72. Control Room of the Earthquake Simulator Laboratory. 110 73. Earthquake Simulator F a c i l i t y , Loaded Steel Frame on Shaking Table 110 74. Base I solated,. Loaded Steel Frame with Prototype Base Storey Columns 111 75. Base Isolated, Loaded Steel Frame with Prototype Base Storey Columns 112 76. Base Isolation Pad Components, Lower Bearing Plate with Linear Bearings, Upper Bearing Plate and Rubber Pad 113 77. Assembled Base Isolation Pad 113 78. Base Isolation System 114 79. Base Isolation System showing Bearing Pad 114 80. Base Isolation Pad with Return Spring 115 81. Prototype Base Storey, Base Isolated 115 82. Base Isolation System, Reference Base Storey with Accelerometer and Displacement Meter 116 83. Base Isolation System, Prototype Base Storey with Displacement Meter 116 X Acknowledgement The research project was made possible through funding by the Canadian Institute of Steel Construction(CISC) and the University of British Columbia. The local office of the CISC with Mr. B. Garrick and i t s members supported actively this project. I would like to thank project coordinator of the CISC, Mr. D. Halliday for his support and Brittain Steel Ltd. for its donation and some of the construction of the structural material for the test set up. The professional work of a l l members of the technical staff of the department of C i v i l Engineering particularly Guy Kirsch, Max Nazar and Chris Dumont shall be greatly acknowledged. Without a l l this friendly help from the staff and fellow graduate students, the experimental studies could not show the results obtained. The author wishes to express sincere thanks to his parents for their endless support and patience. Also his advisor, Dr. S.F. Stiemer for his confidence and guidance . 1 I. INTRODUCTION The concept of reducing seismic loading on buildings and structures by isolation or reducing seismic response is not new. The earliest proposal was to decouple the structures from the ground by a sliding system[i]. Continuous research projects pursue various systems designed to reduce seismic loading on structures. Some techniques presently used or being investigated are base isolation, flexible f i r s t storey and integrated damping devices. Other methods being studied are frequency separation and energy absorption. In the case of frequency separation devices, moveable masses[2] and disengaging joints[3] allow the structure to change i t s fundamental mode shape during severe earthquakes and thus prevent dangerous resonances. Increasing the overall damping of a structure can also reduce the effects of earthquake excitations. It has been suggested to improve the overall damping by the introduction of fri c t i o n devices at the joints[4] or elasto-plastic elements[5] in the support members. Integrated damping devices like asymmetric bracing allow localized yielding in the bracing. This yielding of the bracing improves the overall damping of the structure. The flexible f i r s t storey concept is when the whole f i r s t storey behaves as an elasto-plastic system and allows large deflections. The earthquake energy is dissipated by these 2 large deflections and is not transmitted into the higher stories. This system produces sta b i l i t y problems due to the interaction of the vertical loads and the large lateral displacements and thus has been shown to be impractical. Finally, base isolation uncouples the structure from the earthquake excitation and reduces the structures lateral stiffness,so that,its f i r s t natural frequency is well below that of most typical earthquake frequencies. However, none of the techniques are without drawbacks. The additional devices which alter frequency response or damping characteristics are expensive, make the design and construction more complex and need maintenance. The main problems of conventional base isolation systems is the extra costs of a blind base-storey or double foundation to separate the base of the structure from the foundation. Also there is the possibility of excessive displacements occurring between the structure and the ground. Some base isolation systems cannot be used for structures located on very deep s i l t y soils where there is the possibility of dominant long period motion[6]. The most recent experimental investigations on base isolation!7] has shown that with a combination of rubber bearings and lead energy dissipators, the displacements at the base level can be controlled to an acceptable level without a significant increase in acceleration of the building. Steel buildings seem to be better suited for base isolation concept because (1) steel with its high strength-to-3 isolation concept because (1) steel with i t s high strength-to-weight ratio keeps the dead loads to a minimum, and (2) the forces resulting from the building weight or external loads are concentrated in the main columns at the base level, which is necessary for an easy application of the isolation elements. The base isolation system proposed by the author consists of steel roller bearings with newly developed ductile energy absorbers, yield rings, in parallel to limit excessive displacements and to absorb energy during earthquake excitation. These absorbers also provide restraint against wind and mild earthquake excitation. The design c r i t e r i a for the energy absorbers is the optimization between seismic acceleration and displacement. The steel roller bearings allow stable lateral displacements with nearly unlimited durability without maintenance or function control. One of the main goals in the reported research project was to redesign the base storey , eliminating the additional blind storey. This and the redesign of the main columns due to a reduced base shear and different moment distribution over the main columns provides additional savings of structural steel. Recent research studies[8] have shown that i t is economically feasible to rehabilitate an existing structure using a retrofitted base isolation system. 4 II. SCOPE AND PROCEDURE OF EXPERIMENTS A frame was constructed for these tests which would allow easy implementation of a base isolation system and subsequent substitution of the base storey. Easy installation of the base storey columns was another requirement. The frame was to be built of structural sections and of adequate size so that the base isolation system components could be purchased or manufactured locally. Size allowance for transportation into the Earthquake Simulator Room and the shaking tables capacity finalized the overall dimensions of the frame. The i n i t i a l tests of the loaded frame were performed with heavy reference base storey columns(W200X100) without base isolation, to monitor the response due to sinusoidal and earthquake excitation. The base isolation system was installed under the base storey columns without the introduction of a blind or second foundation. The response was again monitored using the same types of excitations. With the reduced base shear and bending moments due to the implementation of the base isolation system, the prototype base storey columns(Ml 00X19) were designed, manufactured and installed. The response of the loaded frame with the new base storey was recorded, using the same excitation as in the previous tests. The response of the isolated loaded frame with the reference and prototype base storey columns were compared. 5 III. TEST MODEL 1. FRAME The overall dimensions of the frame is 3.0x1.4m in plan and 3.9m in height, figure 1, page 7. There are several separate pieces to the frame which are bolted together for the ease of handling: the two side frames and their interconnecting crossbeams, the base storey columns and the base beams which are attached to the shaking table. In the i n i t i a l reference test series the columns are bolted to the base beams(unisolated) while in subsequent tests the base isolation system with yield rings is assembled between the column bases and the base beams. The side frames, which are oriented parallel to the direction of the excitation, represent a moment resisting construction(welded connections). In the opposite direction , perpendicular to the excitation, the frame is bolted. Three of the four floors are loaded with four concrete blocks, 300kg each. The total weight of the frame with the base beams and the reference base storey including the concrete blocks is 7300 kg. The new version of the base storey of the frame, which were prepared for the experimental tests (figure 2, page 8) results directly from the change of the bending moments and reduced base shear in the base storey columns after the base isolation is implemented. The column sizes can be reduced for building in regions where earthquake loads are governing. Tapered columns could also be considered. Bracing of the pin-6 ended columns may be necessary only where yield rings or centering springs are attached. These design optimizations w i l l be the subject of continuing tests and analyses. The total weight of the frame with the prototype base storey including the concrete blocks is 6540 kg. The testing sequence of the base storey design is shown in figure 3, page 9. The prototype base storey without bracing gave similar results as the prototype base storey with bracing , therefore no results w i l l be given for the braced system. The yield rings were not strong enough to require bracing of the prototype columns. For a l l the tests performed on the frame, fixed base, base isolated, prototype or reference base storey, three of the four floors were always loaded with the concrete blocks. 7 W150X24 3560mm W250X89 y y y y y y 1400mm H W150X2A r W100X19 W200X100 Figure 1 - Steel Frame, Reference Base Storey, Fixed Base, Concrete Blocks not shown Figure 2 - Steel Frame, Prototype Base Storey, Base Isolated, Concrete Blocks not shown. 9 Fixed Base Reference Base Storey Base Isolated Reference Base Storey Base Isolated Prototype Base Storey with Bracing , J li O =3. 1 ft i 4 Base Isolated Prototype Base Storey without Bracing 1 J 1! 1 ft 9 E i Fixed Base Prototype Base Storey Testing Sequence of Base Storey Design. 10 2. BASE ISOLATION The base isolation pads are installed under each of the base storey columns. Yield rings (energy absorbers) are incorporated in the four outer columns only. This was considered adequate for the size of absorbers used. The base isolation pads consist of lower bearing plate, linear roller bearings, upper bearing plate and a thin layer of rubber. Presently the table only moves in one horizontal direction so one layer of roller bearings was used for the experiments (figure 4, page 12). For two dimensional excitation, two sets of bearings would be used. One set would be perpendicular to the other, providing two dimensional isolation (figure 5, page 13). Vertical isolation was not considered important because although i t s intensity is only one third of the horizontal acceleration, i t usually consists of higher frequencies which attenuate more rapidly. Also most structures have considerable excess of strength and stiffness in the vertical direction. The design of the base plates of the f i r s t storey columns are usually governed by the concrete bearing resistance. The roller bearing load is approximately of the same magnitude so the bearing pads would not have to be increased in size when compared to convential design. Previous research[9] has shown that the optimum design would have to allow for large displacements. The linear rolling bearings allow large displacements without danger of 11 in s t a b i l i t i e s like in the case of rubber bearings. The maximum peak to peak displacement of this base isolation system was 140 mm. A previous base isolation system was designed and built using a maximum peak to peak displacement of 150 mm [10]. Therefore the linear roller bearing base isolation system used in this report should have adequate travel for a l l known earthquakes. The thin rubber layer used in the tests are only incorporated to enhance the quality of measurements and will be omitted in the final design. 12 Components of the Base Isolation System; 1. base storey column 2. rubber pad 3. upper bearing plate 4. r o l l e r bearings 5. lower bearing plate 6. y i e l d ring base, building side 7. foundation or base beam (W250X89) 8. y i e l d rings 9. safety pad Figure 4 - Base Isolation System Components. Figure 5 - Design Proposal, Two Dimensional Isolation Pad with Yield Rings. 14 The new energy absorbers, yield rings, are mild steel strips(30x3mm) bent into a special shape, close to a semi-c i r c l e . These are attached to the floor beams and to the column bases parallel to the isolation pads. The yield rings are designed to withstand wind loads and mild earthquakes ela s t i c a l l y . During severe earthquakes the rings yield to limit excessive displacements and absorb energy. For the two dimensional movement the rings would be arranged pependicular to each other. This would ensure that the yield rings are always being deformed in the horizontal plane. These yield rings are easily manufactured and installed into the base isolation system. If they have to replaced after having survived a severe earthquake, their replacement would not be d i f f i c u l t . The rings show a hysteretic load-displacement behaviour (figure 6, page 15) and were designed to an ultimate percent of c r i t i c a l damping of approximately 10% and an elastic stiffness of 13.1 N/mm. In order to ensure that the frame returns to the original position after the yield rings have yielded, there were small centering springs(spring constant of 15.7 N/mm) installed. These springs were attached to the interior columns. Earlier tests have shown that very small forces were needed to return to the center position after an earthquake. 15 Displacement ' * j i n J T* TP Figure 6 - Typical Load Displacement Behaviour of a Yield Ring. 16 IV. TEST EQUIPMENT 1. SHAKING TABLE The experiments reported in this paper were carried out on the Earthquake Simulator Table at the University of British Columbia in the C i v i l Engineering Department. The table has the floor dimensions of 3.0x3.0m and the capacity to apply seismic ground excitation to structures up to 16.0 tonnes with a maximum acceleration of 2.5g(24m/sec,sec) horizontally and a displacement of 130mm peak to peak. The table alone weighs 2090 kg. The table is of welded aluminum construction with a grid of threaded steel inserts for attaching test specimens onto the table. The table and test specimen are supported by four vertical legs with universal joints at each end to ensure quasi-linear horizontal motion. Horizontal rotation is prevented by three hydrostatic bearings on the sides of the table. The hydraulic system(MTS) can be controlled by an oscillator(K&H) or directly by a computer(PDP-11/04) with digitized earthquake records . A wide choice of 144 different earthquake records are currently available. 2. INSTRUMENTATION There were five accelerometers monitoring the acceleration of the frame and shaking table. Four were attached to the cross beams, monitoring the accelerations at each storey level. One accelerometer was attached to the 17 table. The range of the accelerometers were, crossbeam: +20g, table accelerometer: +50g. A l l the accelerometers except the table accelerometer were strain-gauge types. The accelerometer on the table was a Kistler servo accelerometer. There were two LVDTs attached to the base storey columns to measure the relative displacements between the table and the frame. The LVDTs were installed only when the base isolation system was implemented. 3. DATA ACQUISTION AND REDUCTION The data acquistion and processing system is based on a Digital PDP11/04 mini-computer with 56K bytes of memory with RT11 operating software system and two RX01 disc drives. The analog signals of the accelerometers and LVDTs are fed to amplifiers and to a 16 channel multi-plexed A/D converter. Data is stored directly on magnetic discs for further reduction and manipulation. A HDLC data link to the main campus computer (Amdahl) enables the users to conduct extensive computations with a wide variety of programs at the convenience of a main frame system. 18 V. REFERENCE BASE STOREY-FIXED BASE 1. NATURAL FREQUENCIES OF THE SHAKING TABLE There are two natural frequencies associated with the shaking table. When the table is unloaded, i t has a weight of 2090 kg with a natural frequency of the system of 16 Hz. The hydraulic system which controls and activates the table has an unloaded natural frequency of 33 Hz. The reduction of these natural frequencies due to any load on the table i s ; f... = / Table Wt. ' f (5.1) NL Table Wt. Table Wt.+Load on Table NU Where f N L=natural frequency, table loaded f N U=natural frequency, table unloaded Table Wt. =2090kg Load on Table=6900kg (Frame with reference base storey columns and base beams) therefore f N L =.|2090kg 2090kg+6900kg 'NU f N L = ° ' 5 0 f N U (5.2) The natural frequencies become Hydraulic, (33)(0.50)=16.5 Hz, Table, (16)(0.50)=8.0 Hz when the table is loaded with the frame and reference base storey columns. 19 2. NATURAL FREQUENCIES OF THE FRAME Three techniques were used to determine and check the natural frequencies of the frame with the reference base storey and fixed base: computer analysis, simplified mathematical modelling and frequency analysis, Fourier Spectrum, of the experimental results. It is assumed that the percent of c r i t i c a l damping of the frame was less than 20%. i . Computer Analysis The computer program used was called DYNA.S which was written by David Law for the C i v i l Engineering Program Library. It is an interactive graphics program to perform linear elastic small deflection dynamic analysis of plane frame problems. The structure may be composed of pin-pin, f i x - f i x , pin-fix and fix-pin members. There are three major parts to the program: STRYDN, FREQ and DYNAM. STRYDN reads the structural data and assembles the global stiffness and mass matrices. The undeformed structure is also graphically displayed. The master stiffness matrix is constructed from standard plane frame beam stiffness matrices as described in any introductory structural analysis reference. Half the weight of each beam member was 20 concentrated at each end of the member, and point masses may be superimposed at any node. The resulting mass matrix is diagonal. The concrete blocks were applied as external loads at the appropriate nodes. FREQ finds the natural frequencies and mode shapes for the structure. The natural frequencies and mode shapes are found by solving the standard eigenvalue problem [A- B]=0. A modified iterative(power) method was used, as described in UBC:PRITZ. The solution is performed in double precision. DYNAM finds the response to, spectral response of natural modes, pure sinusoidal base acceleration time history and an earthquake acceleration time history. The response to excitation is found by integrating the uncoupled equations of motion, where each mode is treated as a damped single degree of freedom system. The various modes are added together, at selected times, and the resulting nodal displacement and member forces are displayed. The f i r s t two natural frequencies and mode shapes are shown in figure 7, page 21. 21 Mode#1, Frequency = 20.0 Hz Mode#2, Frequency = 59.1 Hz Figure 7 - Deflection of Frame with Fixed Base, Computer Model. i i . Simplified Mathematical Model A four degree of freedom system was used to model the frame with concentrated masses and cantilevers joining the masses. The stiffness[K] and mass[M] matrix of the system (see Appendix A) is given in figure 8, page 22. 22 126139.6 -20470.2 0.0 0.0 -20470.2 40940.4 -20470.2 0.0 0.0 -20470.0 40940.4 -20470.2 1030.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 -20470.2 20470.2 0.0 0.0 0.0 178.0 N/mm Kg 4 { M4 ) X4 K4 3 -( H3 ) X3-K3 2 { M2 ) X2• K2 1 { Ml ) XI K l Figure 8 - Stiffness[K] and Mass Matrix[M], Fixed Base, Simplified Mathematical Model. The natural frequencies and mode shapes were found by solving the standard eigenvalue problem [A-?tB] = 0. [A] is the stiffness matrix and [B] the mass matrix. A modified iterative method was used, as described in UBC:DQZ. The f i r s t two natural frequencies and mode shapes are given in figure 9, page 23. The solution was performed in double precision. 23 Figure 9 - Deflection of Frame with Fixed Base,Simplified Mathematical Model. 24 i i i . Measured Frequencies(Fourier Spectrum) Experimental tests were conducted to determine the natural frequencies of the frame. The frame was exposed to an excitation and the results(acceleration decay) was analysed by using a Fourier Spectrum Analysis (see Appendix B). One of the excitations was striking the frame with a hammer. The other excitation was to have the frame exposed to a sinusoidal base motion(shaking table) and then stopping the sinusoidal motion. Some of the frequencies used for the sinusodial motion were the calculated natural frequencies of the loaded table and frame. A typical Fourier Spectrum plot is shown in figure 10. The major peaks represent the natural frequencies of the loaded table and frame. x E OJ C w CM FOURIER SPECTRUM 4TH LEVEL ACCELERATION REFERENCE BASE STOREY IFIXED BASE) IN I T I A L EXCITATION. HAMMER HIT o.o 7.5 I 1 1 1 1 5 . 0 2 2 . 5 3 0 . 0 3 7 . 5 FREQUENCY (Hz) 4 5 . 0 5 2 . 5 6 0 . 0 Figure 10 - Fourier Spectrum, Natural Frequencies. 6 7 . 5 25 The Fourier Spectrum plots in Appendix B are consistent and correlate well with the calculated natural frequencies. The f i r s t peak represents the natural frequency of the loaded table (8Hz). The next peak represents the natural frequency of the frame(20Hz) and the loaded table hydraulics(16.5Hz). They are so closely spaced that only one large spike shows. The last large peak is the second natural frequency of the frame(59Hz). The smaller peaks between the major peaks represent table noise due to hydraulic and electrical feedbacks. iv. SUMMARY OF RESULTS A summary of results is given in Table 1. The best correlation was between the computer analysis and the measured frequencies. The simplified mathematical model simplified the frame too much therefore the frame was represented too s t i f f . The measured frequencies also confirmed the natural frequencies of the loaded table, 8 Hz and 16.5 Hz. Method 1st Natural Frequency(Hz) 2nd Natural Frequency(Hz) Computer Analysis 20.0 59.1 Mathematical Model 26.8 74.5 Measured Frequency (Fourier Spectrum) 20.0 60.0 Table I - Summary of Results, Fixed Base. 26 3. DAMPING A direct value of the percent of c r i t i c a l damping,D, for the natural frequencies of the loaded frame can be determined using an acceleration time history decay (see Appendix C). 1 21? (5.3) logarithmic decrement acceleration percent of c r i t i c a l damping <20% where o = x = D = Two methods were used to create an acceleration time history decay record: sine wave excitation and hammer hit. These are the same procedures used for the Fourier Spectrum Analysis, page 24. The value for the percent of c r i t i c a l damping,D, was 4%-6%, which are typical values for steel buildings(see Appendix C) . 27 VI. REFERENCE BASE STOREY - BASE ISOLATED 1. NATURAL FREQUENCY OF THE BASE ISOLATED FRAME The same techniques to determine the natural frequencies of the fixed base, page 19, were used for the base isolated frame. Since the f i r s t natural frequency of the base isolated frame was important, only that frequency was investigated. The percent of c r i t i c a l damping value of the system was assumed to be less than 20%. i . Computer Analysis Using the program, DYNA.S and placing springs at the base of the columns to represent the elastic stiffness of the yield rings and return springs. The base of the columns were allowed to move horizontally. The frame ro l l s on the base isolation system as a rigid body deforming the yield rings and return springs only. The greatly reduced f i r s t natural frequency and mode shape is shown in figure 11. Mode#1, Frequency = 0.74 Hz Figure 11 - Deflected Frame, Base Isolated, Computer Model. 28 i i . Simplified Mathematical Model With the introduction of the base isolation system, the frame acts as a rigid body therefore the system is equivalent to a single degree of freedom spring-mass system. The natural frequency for a single degree spring-mass system i s ; W W -2TT V B *=-U/ j L (6.1) where f= frequency (Hz) k= stiffness (N/mm) m= mass of the frame=6220 kg The stiffness k of the base isolation system is the sum of the spring constants for the yield rings and the return springs. The elastic spring constant for the yield rings is 13.1N/mm. The spring constant for the return springs is 15.7 N/mm. The stiffness k is (8j(13.1)+(2)(15.7)=136.2 N/mm. ( l 3 f e - 2 ) ( 1 ° ° 0 ) . 0.74 H 2 6220 29 The mode shape would be a rigid body displacement since the model used was a single degree of freedom system. The mode shape is shown in figure 12. 'n-rr'o o t\ n n Mode#1, Frequency = 0.74 Hz Figure 12 - Deflected Frame, Base Isolated, Simplified Mathematical Model. i i i . Measured Frequencies The natural frequency of the base isolated frame was determined experimentally by two different methods. In the f i r s t method the table was operating in a sinusoidal motion and then the hydraulic system was turned off. The resulting decay was recorded and then analysed by a Fourier Spectrum Analysis (see Appendix B). The other method was to measure the absolute displacement of the frame when exposed to a frequency sweep. The maximum displacement occur at the natural frequency. As shown in figure 13, page 30, and figure 14, page 31, the experimental value for the f i r s t natural 30 frequency is 0.70 Hz. FOURIER SPECTRUM 4 T H LEVEL ACCELERATION REFERENCE BASE STOREY (BASE ISOLATED) INI T I A L EXCITATION FREQUENCY' < 1 HZ FREQUENCY (Hz) Figure 13 - Fourier Spectrum of Acceleration Time History Decay. 31 Displacement v s . Frequency Reference Base Storey Base Isolated Frequency (Hz) Figure 14 - Experimentally Determined Displacement Response from Frequency Sweep. 32 iv. Summary Of Results A summary of the results is shown in Table 2. There is good correlation between a l l four methods therefore the f i r s t natural frequency of a base isolated system can be calculated accurately enough by simple modelling. The only possibility to determine the second mode is by using the computer analysis. With the experimental procedure, this second natural frequency could not be established. However for base isolated systems the f i r s t natural frequency is of main importance and the inability to determine the second natural frequency using simple models is not a great loss. Method Natural Frequency(Hz) Computer Analysis 0.74 Mathematical Model 0.7-4 Measured Frequency (Fourier Spectrum) 0.70 Measured Frequency (Max. Displ.) 0.70 Table II - Summary of Results, Base Isolated. 33 2. DAMPING There were two techniques used in determining the percent of c r i t i c a l damping of the base isolated frame. One technique was using a decaying acceleration record from a sine wave excitation and equation 5.3, page 26. The percent of c r i t i c a l damping,D, determined with this technique was approximately 13% (Appendix C). The other method , Half Power Bandwidth [11] determined D to be approximately 18% (Appendix C). Assuming that the return springs introduce no damping, the percent of c r i t i c a l damping comes from the following sources. There is a constant rolling resistance associated with the linear roller bearing base isolation pad. This rolling resistance is coulomb damping which can be expressed as an equivalent viscous damping value. It contributes approximately 3%-7% to the total percent of c r i t i c a l damping. The remaining 11% must come from the yield rings. The estimated ultimate percent of c r i t i c a l damping of the yield rings was approximately 10% (page 14). This confirms that the yield rings were yielding and gives good agreement with the ultimate percent of c r i t i c a l damping. The assumption that the percent of c r i t i c a l damping was less than 20% was correct. 34 VII. COMPARISON OF RESPONSES (REFERENCE BASE STOREY) 1. EXTREME VALUES The frame was exposed to two different types of excitation and i t s response, acceleration and relative displacement (base isolated only) were recorded. The excitations were random signals (earthquakes) and sinusoidal. There were four earthquake records used, El Centro(SOOE), San Fernando(N21E), Parkfield(N65E) and an a r t i f i c i a l earthquake, called Earthquake, which consisted mainly of high frequency acceleration. The time scale of these earthquakes were not modified. The magnitude of El Centro and Parkfield were not modified, but the San Fernando earthquake used has twice i t s original magnitude. A sinusoidal excitation was used with a range of 1 Hz to a maximum of 20 Hz with a constant peak to peak displacement. When the base isolation system was installed, the diplacement of the frame became zero at 3 Hz, see figure 14,page 31, and any higher frequencies did not increase the response. 2. RESPONSES OF FIXED BASE AND BASE ISOLATED The maximum values of the accelerations and relative displacements(base isolated only) were compared, see Appendix D. The maximum accelerations of the fourth level for each earthquake were compared. A typical comparison is shown for 35 El Centro, figure 15, page 36. The average reduction in the fourth level peak acceleration between fixed base and base isolated was 80%. For earthquakes with high frequencies such as San Fernando, the reduction was greater. The maximum relative displacements was also compared and a typical comparison is El Centro figure 16, page 37. The results show that the yield rings do limit the displacement of the frame during earthquake excitation. Without the yield rings the relative displacements would be much larger but no acceleration would be transmitted into the frame. When the relative displacement is controlled as in this case, some acceleration is transmitted into the frame, figure 15, page 36. EL CENTRO EARTHOUAKE TABLE R C C E L E R R T I O N F I X E D B A S E EL CENTRO EARTHQUAKE 4TH LEVEL ACCELERAT J ON REFERENCE BASE STOREY (FIXED BASE) EL CENTRO EARTHQUAKE 4 T H LEVEL ACCELERATION REFERENCE BASE STOREY (BASE ISOLATED) Time Histories of Level. Accelerat ion at the 4 37 T A B L E D I S P L A C E M E N T E L C E N T R O E A R T H O U A K E B A S E I S O L A T E D . R E F E R E N C E B A S E S T O R E Y FRAHE DISPLACEMENT EL CENTRE EARTHQUAKE BASE ISOLATED. REFERENCE BASE STOREY Figure 16 - Time Histories of Relative Displacements. 38 3. COMPARISON OF RESPONSE RATIO FOR DIFFERENT EXCITATIONS The response over excitation ratio for the fourth level was calculated for the frame with the reference base storey for rigid base and base isolated. The excitations used were sinusoidal and earthquakes. Figure 17, page 39 and figure 18, page 40 show the results. At higher frequencies, the difference between the fixed base ratio and base isolated ratio increases for both sinusoidal and earthquake excitation. San Fernando has a high frequency acceleration spike, so the difference in the response ratio between fixed base and base isolated is large. Earthquake, which is composed of high frequency acceleration, also has this large difference. Base isolation is most effective for high frequency, short period excitation. 39 Figure 17 - Response of the Frame subjected to Sinusoidal Excitation. 40 Ratio of Response oyer Excitation vs. Earthquakes 2D Earthquakes Figure 1 8 - Response of the Frame subjected to Earthquake Excitation. 41 VIII. BASE STOREY DESIGN 1. CALCULATION OF THE BASE SHEAR AND BASE MOMENTS,REFERENCE  BASE STOREY, FIXED AND ISOLATED BASE The base shear and base moment were calculated using the experimentally measured values of the acceleration for each level during the earthquake excitations. The frame with the reference base storey was modelled using a concentrated mass for each level. The same mass matrix as in figure 8, page 22, was used except the diagonal values are twice as large because the complete frame was modelled. The maximum fourth level acceleration for each earthquake occurred at a specific time. The maximum acceleration for the remaining levels also occurred at this time. These accelerations were used on the modelled frame to determine the base shear and base moments. The base isolated frame was done in the same manner. From figure 15, page 36, the maximum base isolated acceleration occurs at the same time the maximum fixed base acceleration occurs. Table 3, page 42, shows the results, the base shear and base moment were reduced by at least 90% using this size of yield rings. 42 BASE SHEAR Earthquake Fixed Base (kN) Base Isolated (kN) % Reduced KL Centro 36.00 0.70 98 San Fernando 89.60 5.10 94 Parkfield 21.00 0.17 99 Earthquake 10.^ 0 0.03 99 BASE MOMENT Earthquake Fixed Base (kNra) Base Isolated (kNm) % Reduced El Centro 74.70 3.05 96 San Fernando 189.80 8.50 96 Parkfield 38.30 2.32 94 Earthquake 17.50 0.78 96 T a b l e I I I - Summary o f R e s u l t s , B a s e S h e a r a n d Ba s e Moments. 43 2. DESIGN OF THE PROTOTYPE BASE STOREY With the great reduction in base shear and base moment shown in table 3, page 42, the base storey columns can be replaced with substantially weaker columns. In the case of our frame this would have led to very thin columns, which are not readily available as rolled sections. So the smallest commerical I section was used, Ml 00X19, for the prototype base storey columns. With the yield rings and the magnitudes of the earthquakes used, these columns were s t i l l too strong, but substantially weaker than the reference base columns, W200X100. 44 IX. PROTOTYPE BASE STOREY - FIXED BASE 1. NATURAL FREQUENCIES OF THE SHAKING TABLE With the new base storey columns, the weight of the frame is reduced therefore the natural frequencies of the loaded shaking table has to be recalculated. Using equation 5.1, page 18, with a load on the table of 6540 kg(frame with the prototype base storey columns and base beams.) f = /2080kg f N U ]J 2080kg+6540kg f N L = 0 ' 5 0 f N U This is the same expression as 5.2, page 18. The reduction in weight of the frame due to the prototype base storey was not enough to cause a significant change in the natural frequencies of the loaded table. These frequencies are 8 Hz and 16.5 Hz. 2. NATURAL FREQUENCIES OF THE FRAME The same methods and assumptions as in Chapter 5 were used to determine the f i r s t two natural frequencies. 45 i . Computer Analysis The modified frame was analyzed by the same program, DYNA.S. The f i r s t two natural frequencies and mode shapes are shown in figure 19. The simplified mathematical model of the frame was represented by a four degree of freedom system with concentrated masses and cantilevers joining the masses. The stiffness[K] and mass[M] matrix were similar to the one in Chapter 5 but, slightly modified because of the new base storey columns (Appendix A). The matrices are given in figure 20, page 46. 4 6 IKJ 25123.8 -20470.2 0.0 0.0 -20470.2 40940.4 -20470.2 0.0 0.0 -20470.0 40940.4 -20470.2 0.0 0.0 -20470.2 20470.2 N/mm X3-[M] 959.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 0.0 178.0 Kg Figure 20 - Stiffness[K] and Mass MatrixfM], Fixed Base, Simplified Mathematical Model. Solving for the eigenvalues determines the natural frequencies and mode shapes,figure 21. « T T4 Mode#1, Frequency = 11.6 Hz Mode#2, Frequency = 49.4. Hz Figure 21 - Deflected Frame, Fixed Base, Simplified Mathematical Model. 47 i i i . Measured Frequencies (Fourier Spectrum) Experimental tests using the same experimental methods as in Chapter 5 were done to determine the natural frequencies of the frame. A typical Fourier Spectrum plot is given in figure 22. The major peaks represent the natural frequencies of the loaded table and frame. FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION: HAMMER HIT • i i i i i 1 1 1 1 1 0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 FREQUENCY (Hz) Figure 22 - Fourier Spectrum of the Acceleration Time History, Hammer Hit. The diagrams of the Fourier Spectrum in Appendix B show good correlation with the analytically derived natural frequencies. The f i r s t major peak represents the natural frequency of the loaded table (8Hz ) and the f i r s t natural frequency of the frame(11.3Hz). Next peak is the natural 48 frequency of the table hydraulics(16.5Hz). The second natural frequency of the frame did not appear in figure 22, page 47. This is probably due to the hammer hit not being strong enough. iv. Summary Of Results A summary of the results is given below in table 4. There is very good correlation between a l l three techniques for the f i r s t natural frequency. For the second natural frequency, the computer analysis and experimental results agree. The simplified mathematical model appears to be too s t i f f and thus has a second natural frequency that is too high. The high second natural frequency has occurred before, Chapter 5, page 25, when using a simplified mathematical model. Method 1st Natural Frequency(Hz) 2nd Natural Frequency(Hz) Computer Analysis 11.3 AO. 7 Mathematical Model 11.6 49.4 Measured Frequency (Fourier Spectrum) 11.0 -Table IV - Summary of Results, Fixed Base. 49 3. DAMPING The methods used to determine the damping are described in chapter 5 (see Appendix C). Applying equation 5.3 to a decaying acceleration time history, the percent of c r i t i c a l damping,D, was established at l%-6% (Appendix C). These values are in agreement with results from page 26, as they represent typical values for steel buildings. 50 X. PROTOTYPE BASE STOREY - BASE ISOLATED 1. NATURAL FREQUENCIES OF THE BASE ISOLATED FRAME i . Computer Analysis With the implementation of the prototype base storey columns, the frame properties changed but the base isolation system remained the same. The same spring rates used for the yield rings and return springs in Chapter 6 were used again. As expected the frame behaves as a rigid body. The f i r s t natural frequency is shown in figure 23. Mode#1, Frequency = 0.77 Hz Figure 23 - Deflected Frame, Base Isolated, Computer Model. 51 i i . Simplified Mathematical Model In the simplified mathematical model a single degree of freedom spring-mass system was used. Following equation 6.1, with k=l36.2 N/mm and the new reduced mass of the frame, 5860 kg, the natural frequency i s , The mode shape is equivalent to a rigid body displacement and shown in figure 24. The f i r s t natural frequency of the frame with the prototype base storey is increased slightly because of i t s reduced weight. 0.77 Hz r i- rr'n o M o n Mode#1, Frequency = 0.77 Hz Figure 24 - Deflected Frame, Base Isolated, Simplified Mathematical Model. 52 i i i . Measured Frequency The experimental results were similar to the previous results obtained in Chapter 6 with the reference base storey. Figure 25 and figure 26, page 53, show that the experimentally measured f i r s t natural frequency was 0.70 Hz. It was not possible to achieve a higher accuracy with the available experimental instrumentation. FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (BASE ISOLATED) „ INITIAL EXCITATION FREQUENCY: < 1 HZ i i I i i i i 1 — i = 1 0 . 0 2 . 0 4 . 0 6 . 0 8 . 0 1 0 . 0 1 2 . 0 M . O 1 6 . 0 1 8 . 0 FREQUENCY (Hz) Figure 25 - Fourier Spectrum of Acceleration Time History Decay. 53 Displacement vs. Frequency Prototype Base Storey Base Isolated Frequency (Hz) Figure 26 - Experimentally Determined Displacement Response from Frequency Sweep. 54 i v . Summary Of R e s u l t s A summary of the r e s u l t s i s g i v e n i n T a b l e 5. The v a l u e s f o r the f i r s t n a t u r a l f r e q u e n c y c o r r e l a t e d w e l l f o r a l l methods used and were s i m i l a r t o the agreement i n Chapter 6. The base i s o l a t e d frame c o u l d be m o d e l l e d a c c u r a t e l y by a s i n g l e degree of freedom m a s s - s p r i n g system w i t h s u f f i c i e n t a c c u r a c y . Method Natural Frequency(Hz) Computer Analysis 0.77 Mathematical Model 0.77 Measured Frequency (Fourier Spectrum) 0.70 Measured Frequency (Max. D i s p l . ) 0.70 T a b l e V - Summary of R e s u l t s , Base I s o l a t e d . 2. DAMPING The p e r c e n t of c r i t i c a l damping,D, was the same as b e f o r e , 13%—18%. A change i n the frame p r o p e r t i e s d i d not a f f e c t t h e damping c a p a c i t y . 55 XI. COMPARISON OF RESPONSE, REFERENCE AND PROTOTYPE BASE STOREY 1. EXTREME VALUES The frame with the prototype base storey was exposed to the same extreme values as described in Chapter 7, section 7.1, page 34. 2. COMPARISON OF RESPONSE, FIXED BASE The fourth level acceleration of the frame with the prototype base storey was greater than the fourth level acceleration of the frame with the reference base storey, see figure 27, page 56 and Appendix E. This was due to the reduction of the base storey stiffness. With the smaller columns and thus reduced natural frequency, more acceleration was transmitted into the upper levels. 56 E L C E N T R O E A R T H Q U A K E 4 T H L E V E L A C C E L E R A T I O N R E F E R E N C E B A S E S T O R E Y ( F I X E D B A S E ) Figure 27 - Comparison of Acceleration Time History, Fixed Base. 57 3. COMPARISON OF RESPONSE, BASE ISOLATED With the implementation of the base isolation system to the base of the prototype base columns, the maximum fourth level acceleration records were similar to the reference base storey, figure 28, page 58 or Appendix E. The prototype base storey is much weaker than the reference base storey as shown by i t s reduced natural frequency, but when base isolated, this reduction in strength does not alter the response of the frame. The fourth level acceleration is mainly dependant upon the strength of the yield rings. The behaviour and design of these yield rings are subject to current and future investigations. 58 E L C E N T R O E A R T H Q U A K E 4 T H L E V E L A C C E L E R A T I O N R E F E R E N C E B A S E S T O R E Y ( B A S E I S O L A T E D ) 8 d o EL CENTRO EARTHQUAKE &TH LEVEL ACCELERATION PROTOTYPE BASE STORE* COLUMNS BA5E ISOLATED O LxJ C J m, L J 2? CX m . O _ Figure 28 - Comparison of Acceleration Base Isolated. Time Histories, 59 4. COMPARISON OF RESPONSE RATIOS The response over the excitation ratio for the fourth level was calculated for the frame with the prototype base storey for rigid base and base isolated. The excitations were sinusoidal and earthquakes. The results are shown in figure 29, page 60, and figure 30, page 61. The results are similiar to the results in Chapter 7, section 7.3, pages 39-40. As the frequency increases, the difference between the fixed base ratio and base isolated ratio increases. 5. COMPARISON OF ENERGY LEVELS DUE TO EARTHQUAKE RESPONSE A Fourier Spectrum Analysis of the earthquake response for different locations on the frame can determine the amount of energy that is present at those locations. A typical example is El Centro, figure 31, page 62. The other earthquakes are shown in Appendix F. The base isolated frame, regardless of the base storey design, shows the lowest energy levels. Fixed base, especially the prototype base storey, shows the highest energy level. 60 Ratio of Response over Excitation vs. Frequency of Excitation Rigid Frame (Reference Columns) Rig i d Frame (Prototype Columns) Base Isolated (Reference Columns) Base Isolated (Prototype Columns) 2 -3 A Frequency of Table E x c i t a t i o n (Hz) Figure 29 - Response of Frame to Sinusoidal Excitation. 61 Ratio of Response over E x c i t a t i o n vs. Earthquakes ~ 6.0 n c a B O X J3 (0 7.0' 6.0-5.0' 4.0-3.0-2.0-1.0 0.0 2&n Rigid Frame (Reference Columns) Rigid Frame (Prototype Columns) Base Isolated (Reference Columns) Base Isolated (Prototype Columns) San Fernando Earthquake E l Centre P a r k f i e l d Earthquakes Figure 30 - Response of Frame to Earthquake Excitation. 62 Maximum Energy Levels due to Earthquake Response, E l Centro Earthquake Table ^ 4.th Level, Base Isolated 4th Level, Reference Base Storey (fixed base) 4th Level, Prototype Base Storey (fixed base) 0.1 0.0 F i g u r e 6 3 XII . OBSERVED TORSIONAL FREQUENCY 1. REFERENCE BASE STOREY There was an observed torsional natural frequency at 9.7 Hz. It does not appear in the Fourier Spectrums, figure 10, page 24 and in Appendix B because the acceleration time histories were monitored in one direction only. Once the frame became base isolated, this torsional natural frequency seemed to have disappeared. 2. PROTOTYPE BASE STOREY A torsional natural frequency of 7 Hz was observed. Although not appearing up in the Fourier Spectrums, figure 22, page 47 and in Appendix B, this torsional natural frequency was very apparent in the acceleration record for El Centro, fixed base, figure 27, page 56 and in some of the other earthquakes in Appendix E. The frame was resonating at this 7 Hz frequency during the earthquakes. Once the frame became base isolated, this torsional natural frequency disappeared, figure 28, page 58, confirming that base isolation can reduce the effect of any torsional response of the frame or building. 64 XIII. CONCLUSION With the implementation of the described base isolation system in the steel frame, the dynamic response, forces and base moments were reduced by 80-90%. Also torsional response was greatly reduced or eliminated. This is dependent upon the strength of the yield rings and magnitude of the earthquakes. The yield rings are designed to resist wind loads and minor earthquakes elas t i c a l l y . Their behavior in the post-yield region has to be carefully considered to balance maximum accelerations with excessive displacements. Further investigations are currently underway to develop design rules for this device and to determine the long cycle limits. The new design of the f i r s t storey due to the reduced base shear differs considerably from conventional design and has various consequences on the design of the remaining building. (1) The reduced base shear results in lighter columns throughout the whole building. (2) Eliminating the necessary double or blind foundation does not contribute to increased costs when compared to conventional design. (3) The structural design can be standardized because of the base isolation system. It no longer matters what region of earthquake risk the building is erected in, only wind load governs. (4) The building remains in the elastic region, only 65 the yield rings perform plast i c a l l y . Large interior systems and equipment do not need to be prevented from dynamic excitation. This is crucial for strategically important or potentially dangerous buildings such as hospitals, government buildings, bridges, nuclear power plants, research stations, emergency power supplies, etc. These structures might have their highest value by continued operation during or immediately after an earthquake. The base isolation system has not only proven i t s f e a s i b i l i t y in laboratory tests and implementing in prototype, but is now advanced enough in i t s design to be economically competitive for steel buildings. In some cases i t will be useful to retrofit base isolation systems into existing buildings, such as historically valuable buildings or monuments etc. which were not designed for earthquake loadings. A recent research study[8] has shown that with base isolation i t is economically feasible to rehabilitate an existing structure to meet or exceed present earthquake code requirements. The estimated costs to rehabiliate an existing structure with base isolation are comparable to or smaller than those for a conventional rehabilitation. The base isolation system used in the reported tests is stable, self centering, has limited displacements, introduces predetermined small accelerations and does not rock on i t s base during an earthquake. They are maintenance and control free with low relative costs. 67 XIV. APPENDIX A-SIMPLIFIED MATHEMATICAL MODEL, REFERENCE AND PROTOTYPE BASE STOREY  Equivalent Model The loaded frame was modelled using a four degree of freedom system with four concentrated masses joined together by cantilevered beams. The modelled system was equivalent to four individual masses on rollers with springs joining the masses (figure 32). I Kl | ^ X 1 | X2 ( — X 3 | — X 4 Ml rm K2 r - A / V - l H2 j - A / H M3 rrn K3 rm K4 K4 K3 K2 ® X4-X3-X2-XI K l Figure 32 - Equivalent Model. Stiffness Matrix The stiffness matrix, [K], for the equivalent model was determined by displacing each mass independantly. The resulting stiffness matrix is shown in figure 33, page 68. 68 [K] K1+K2 -K2 0.0 0.0 -K2 K2+K3 -K3 0.0 0.0 -K3 K3+K4 -U 0.0 0.0 -U mm Figure 33 - Stiffness Matrix. Mass Matrix The mass matrix, [M], for the equivalent model is as shown in figure 34. [M] M1 0.0 0.0 0.0 0.0 M2 0.0 0.0 0.0 0.0 M3 0.0 0.0 0.0 0.0 M4 Kg Figure 34 - Mass Matrix. To simplify the analysis only half the loaded frame was used. Concentrated masses represent the weight of the beams, columns, cross beams and concrete blocks. 69 Reference Base Storey, Stiffness Matrix Stiffness, Kl , was determined by using equation A.1, which represents the stiffness of a cantilevered beam with shear deformation. The length of the columns were small therefore shear deformation could not be neglected. K1 = 3EI (A.1) L 3 (1+g) where g = 3EI 2 AvGL Av = shear area (mm ) E = elastic modulus (MPa) G = shear modulus (MPa) 4 I = moment of inertia (mm ) L = length (mm) For the reference base storey columns, W200X100, the following values were used: g = 0.22 6 4 I = 113x10 mm E/G = 2.5 L = 1161 mm To simplify the analysis only half the frame was used, three columns. Substituting the above values into equation A.1, the total base storey stiffness became; 70 K1 = 105669.39 N/mm The interstorey stiffness, K2,K3 and K4 were determined by using equation A.1. For the interstorey members, W100X19, the following values were used: g = 0.09 6 4 I = 4.76x10 mm L = 800 mm Substituting these values into equation A.1 and using half the frame, four columns, the interstorey stiffness became; K2 = K3 = K4 = 20470.20 N/mm Substituting the values K1,K2,K3 and K4 into the stiffness matrix, figure 33, page 68, yielded the stiffness matrix, figure 35, page 71, which is the same stiffness matrix as in figure 8, page 22. 71 [K] 126139.6 -20470.2 0.0 0.0 -20470.2 40940.4 -20470.2 0.0 0.0 -20470.0 40940.4 -20470.2 0.0 0.0 -20470.2 20470.2 N/unn F i g u r e 35 - S t i f f n e s s M a t r i x , R e f e r e n c e B a s e S t o r e y , S i m p l i f i e d M a t h e m a t i c a l M o d e l . R e f e r e n c e Base S t o r e y , Mass M a t r i x U s i n g t h e mass m a t r i x , f i g u r e 34, page 68, and s u b s t i t u t i n g t h e c o r r e c t v a l u e s f o r M1,M2,M3 a n d M4, t h e r e s u l t i n g mass m a t r i x , f i g u r e 36, was f o r m e d . T h i s mass m a t r i x i s t h e same m a t r i x a s i n f i g u r e 8, page 2 2 . [M] 1030.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 0.0 892.0 0.0 Kg 0.0 0.0 0.0 178.0 F i g u r e 36 - Mass M a t r i x , R e f e r e n c e B a s e S t o r e y , S i m p l i f i e d M a t h e m a t i c a l M o d e l . 72 Prototype Base Storey, Stiffness Matrix With the new base storey the K1 value changed. For the prototype base storey columns, M100X19, the following values were used: g = 0.09 6 4 I = 4.41x10 mm L = 800 mm Substituting these values into equation A.1 and using half the frame, three columns, the total base storey stiffness became; K1 = 4653.6 N/mm The interstorey stiffnesses K2,K3 and K4 did not change and remained at 20470.20 N/mm. Again substituting the values K1,K2,K3 and K4 into the stiffness matrix figure 33 , page 68, created the stiffness matrix figure 37, page 73, which is the stiffness matrix figure 20, page 46. 73 [K] 25123.8 -20470.2 0.0 0.0 -20470.2 40940.4 -20470.2 0.0 0.0 -20470.0 40940.4 -20470.2 0.0 0.0 -20470.2 20470.2 N/mm F i g u r e 37 - S t i f f n e s s M a t r i x , P r o t o t y p e Base S t o r e y , S i m p l i f i e d M a t h e m a t i c a l M o d e l . P r o t o t y p e Base S t o r e y , Mass M a t r i x Only one v a l u e , M1, changed due to the change in the base s t o r e y . The masses M2, M3 and M4 remained the same. M1 became 959 kg and the mass m a t r i x became the mass m a t r i x , f i g u r e 38, which i s the mass m a t r i x , f i g u r e 20, page 46. 959.0 0.0 0.0 0.0 0.0 892.0 0.0 0.0 0.0 0.0 892.0 0.0 Kg 0.0 0.0 0.0 178.0 F i g u r e 38 - Mass M a t r i x , P r o t o t y p e Base S t o r e y , S i m p l i f i e d M a t h e m a t i c a l M o d e l . 74 XV. APPENDIX B-FOURIER SPECTRUM F o u r i e r S p e c t r u m A n a l y s i s A s t a n d a r d method o f e x h i b i t i n g t h e f r e q u e n c y c o n t e n t o f a f u n c t i o n , s u c h a s a a c c e l e r o g r a m , i s by means o f a F o u r i e r A m p l i t u d e S p e c t r u m . F o r any s i m p l e mass s p r i n g s y s t e m , p e r c e n t o f c r i t i c a l d a m p i n g l e s s t h a n 20%, t h e e q u a t i o n o f m o t i o n i s mx+kx = ma, where x was t h e r e l a t i v e d i s p l a c e m e n t a n d a t h e a c c e l e r a t i o n a c t i n g on t h e body. 3 - V W H The v i b r a t o r y r e s p o n s e f o r r e l a t i v e d i s p l a c e m e n t a t t i m e t i s , x(t,w) =J_ | i(T )sinw(t-r )dT (B . 1 ) W o where w = k/m = (2TT/T) , T = n a t u r a l p e r i o d o f v i b r a t i o n a n d V i s a dummy i n t e r g r a t i o n v a r i a b l e . F o r a s i m p l e mass s p r i n g s y s t e m , t h e t o t a l e n e r g y .2. 2. E=(1/2)mx + d / 2 ) k x , i s t h e sum o f t h e k i n e t i c a n d s t r a i n energies. U s i n g equation B.1 and some a l g e b r a i c manipulation, jasinw ' CdT l + I l a c o s w T d f t h e t o t a l e n e r g y ; E ( t , w ) = ( ! / 2)m 75 The square root of twice the energy per unit mass i s ; If the duration of a was from t=0 to t=t,, the square root of twice the energy per unit mass at time t, i s , The right hand side of the last equation is a function of w = 2TT/T = 2 Iff. When evaluated and plotted as a function of w or f, i t was called the Fourier Amplitude Spectrum, being a measure of the final energy in the mass spring system as a function of period. The peaks on the spectrum curve represented frequencies at which relatively large amounts of energy were put into the system. The maximum value of the energy E(t m,w) will likely occur at some time t m<t, . In this special case, the maximum energy can be thought of being a measure of maximum displacement and therefore natural frequency of the system. [12] 76 Fourier Spectrum Plots FOURIER SPECTRUM 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION: HAMMER HIT ~i r 30.0 37.5 FREQUENCY (Hz) 67. 5 Figure 39 - Reference Base Storey, Hammer Hit FOURIER SPECTRUM 4 T H LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 20.0 HZ O.o 7.S 15.0 "i r 22-5 30.0 37.5 45.0 52.5 60.0 FREQUENCY (Hz) Figure 40 - Reference Base Storey, Excitation Frequency: 67.5 20 Hz. 77 FOURIER SPECTRUM 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 1 1 . 0 HZ 22.5 30.0 37.5 FREQUENCY (Hz) 4 5 . 0 52. S 60.0 67.5 Figure 41 - Reference Base Storey, Excitation Frequency: 11 Hz. FOURIER SPECTRUM 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 9.7 HZ 6 d" 0.0 l — 7 . 5 I5.0 22.5 45.0 52.5 60.0 30.0 37.S FREQUENCY (Hz) Figure 42 - Reference Base Storey, Excitation Frequency 67.5 9.7 Hz. 78 FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION: HAMMER HIT 22.5 3D.0 37.5 FREQUENCY (Hz) 52.5 60.0 67.5 X r CQ 10 t>0 o' U 0) CM Figure 43 - Prototype Base Storey, Hammer Hit. FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 11.0 HZ - i — 7.5 0.0 Figure 44 15.0 15.0 52.5 60.0 22.5 30 0 37.5 FREQUENCY (Hz) Prototype Base Storey, Excitation Frequency: 67.5 11 Hz. 7 9 FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 5 HZ o. o 7.5 15.0 T_= r 22.5 30.0 37.5 FREQUENCY (Hz) 45. c 52.5 60.0 67. 5 Figure 45 - Prototype Base Storey, Excitation Frequency: 5 Hz. FOURIER SPECTRUM 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 2.0 HZ 45.0 52.5 60.0 67.5 FREQUENCY (Hz) Figure 46 - Prototype Base Storey, Excitation Frequency: 2 Hz. 80 XVI . APPENDIX C-DAMPING VALUES Logarithmic Decrement with Accelerations The usual logarithmic decrement,&, is calculated using equation C.1, 8 = I n / X, \= 2TTD 2. (C.1 ) where X j , X^ are displacements at natural period inter v a l s and D i s the percent of c r i t i c a l damping. During the experiment accelerations were recorded therefore equation C.1 has to be modified to accommodate accelerations. The displacement, X, can be expressed as, "DWnt X = Ae ( C 2 ) where A = maximum displacement wn= natural frequency (rad/sec) w^ = damped natural frequency (rad/sec) 0 = phase angle Taking the r a t i o of the accelerations, the second derivative of C . 2 , 81 -DWnt, "DWnt, X, = e cos(w^t, -0) + e sin(w^t,-,0) (C.3) X^ = e cos(w^t2-p)+ e sinfw^t^-p) But t^=t(+T and T= 2Tt/w^ where T is the natural period (sec). Therefore, cos(w^tz-^) = cosfw^t,-0) (C.4) sin(w^t2-0) = sin(w^t|-^T) (C.5) Substituting equations C.4 and C.5 into C.3, the ratio of the accelerations becomes, Dw n T _X, = e *2 £ = In/ X i V D w n T = 2TTD XW A/ 1-D Assuming the logarithmic decrement is small, and the percent of c r i t i c a l damping,D, less than 20% then, D = _£ = ln /_X, \ 1 (C.6) 21Y 2TT' 82 PERCENT OF CRITICAL DAMPING in %, FIXED BASE  Reference Base Storey Table 6 contains the results of analysing the decaying acceleration graphs, figure 47 to 50, page 84-87, using equation C.6. The percent of c r i t i c a l damping ,D, in % amounts to 4%-6%. I n i t i a l E x c i t a t i o n C r i t i c a l Damping i n % H a n a e r H i t 4.2 20Hz S i n u s o i d a l 5.4 11Hz S i n u s o i d a l 4.9 9.7Hz S i n u s o i d a l 4.8 Table VI - Percent of C r i t i c a l Damping in %, Reference Base Storey, Fixed Base 83 Prototype Base Storey Table 7 contains the results of analysing the decaying acceleration graphs, figure 51 to 54, page 88-91, using equation C.6. The percent of c r i t i c a l damping ,D, in % amounts to l%-6%. Initial Excitation C r i t i c a l Damping in % Hammer Hit 2.0 11Hz Sinusoidal 5.7 5Hz Sinusoidal 2.3 2Hz Sinusoidal 1.3 Table VII - Percent of C r i t i c a l Damping in %, Prototype Base Storey, Fixed Base 64 Figure 47 - Time History of Acceleration Decay,Reference Base Storey, Hammer Hit. 85 Figure 48 - Time History of Acceleration Decay, Reference Base Storey, 20 Hz Excitation 86 DAMPING TEST 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY. 11 HZ Figure 49 - Time History of Acceleration Decay, Reference Base Storey, 11 Hz Excitation 87 DAMPING TEST 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 9.7 HZ TIME SECONDS 0.75 1.0 1.25 1.5 1.75 2.0 2.25 F i g u r e 50 - T i m e H i s t o r y o f A c c e l e r a t i o n D e c a y , B a s e S t o r e y , 9.7 H z E x c i t a t i o n R e f e r e n c e 88 DRMPING TEST 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION: HAMMER HIT i n " o SFCONDS 3.75 » J . u 4.5 6 . 2 5 6 . 0 _ ! 6 . 7 5 _J Figure 51 - Time History of Acceleration Decay, Prototype Base Storey, Hammer Hit. 89 DRMPINC TEST 4TH LEVEL ACCELERATION FROTOTYFE BASE STOREY (FIXED BASE) S INITIAL EXCITATION FREQUENCY: 11 HZ CO Figure 52 - Time History of Acceleration Decay, Prototype Base Storey, 11 Hz Excitation 90 DAMPING TEST 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE) INITIAL EXCITATION FREQUENCY: 5 HZ Figure 53 - Time History of Acceleration Decay, Prototype Base Storey, 5 Hz Excitation 91 DAMPING TEST 4TH LEVEL ACCELERATION FROTOTYPE BASE STOREY (FIXED BASF I « INITIAL EXCITATION FREQUENCY: 2 HZ O o l Figure 5 4 - Time History of Acceleration Decay, Prototype Base Storey, 2 Hz Excitation 92 PERCENT OF CRITICAL DAMPING in %, BASE ISOLATED Both the reference and prototype base storey responded the same way when base isolated so they w i l l not be treated separately. Two techniques were used, the decaying acceleration record with equation C.6 and the One-half Power Bandwidth[11]. Using equation C.6 and figure 55, page 93, the percent of c r i t i c a l damping is 13%. To determine the percent of c r i t i c a l damping,D, using the One-Half Power Bandwidth method, equation C.7 is used. D = f 2 - f, (C.7) The sequence of steps to determine f | and f ^ using a frequency - response curve is as follows; (1) Determine peak response (2) Construct line at peak/^/T"1 (3) Determine the two frequencies at which the line cuts the response curve, f ^ and fj Using figure 56, page 94, peak response is 23.3mm , f j = 5.8 Hz and f^ = 8.4 Hz. Using equation C.7, the percent of c r i t i c a l damping,D, is 18%. 9 3 DAMPING TEST 4TH LEVEL ACCELERATION BASE ISOLATED INITIAL EXCITATION FREQUENCY: < 1 HZ 9 . 0 10.0 _J 11.0 Figure 55 - Time History of Acceleration Decay, Base Isolated. 94 Figure 56 - Frequency-Response Plot, Base Isolated 95 XVII. APPENDIX D-TIME HISTORIES, REFERENCE BASE STOREY SUN FfRNRNDO EPRTHOUOKE TABLE MXELFRfiTlON FIXED BASE SSN FFRNBNOB ERFTHOUBKE 4TH LEVEL RCCELERRUON REFERENCE BRSE STOREt IFJXED BRSE) 15.0 13.5 _i i SRN FERNANDO EORTHOUAKE 4TH LEVEL ACCELERATION REFERENCE BRSE STOREY (BRSE ISOLATED) Ui 3.0 «.5 6,0 1.5 TIME SECONDS 1.5 9.0 Figure 57 - Time History of the Acceleration at the 4th Level, San Fernando, Reference Base Storey 96 P B R K F I F I O EPRTMOUflKE TABLE RCCELFRRTION FIXED BASE PARKF !ELD EWHDUfWE 4TM LEVEL ACCELERATION REFERENCE BASE STORE* (FIXED BASE) PARKFIELD EARTHQUAKE 4TH LEVEL ACCELERATION REFERENCE BASE 5T0REY (BASE ISOLATED! Figure 58 - Time History of the Acceleration at the 4th Level, Parkfield, Reference Base Storey 97 EARTHQUAKE TABLE ACCELERATION FIXED BASE EARTHQUAKE <TH LEVEL ACCELERATION REFERENCE BASE STORE T (BASE ISOLATED) TIME SECONDS 12.0 IS.5 10.5 12.0 13.5 Figure 59 - Time History of the Acceleration at the 4th Level, Earthquake, Reference Base Storey Figure 60 - Time History of Displacement, Reference Base Storey San Fernando, 99 T A B L E D I S P L A C E M E N T P A R K F 1 E L D E A R T H Q U A K E B A S E I S O L A T E O . R E F E R E N C E B A S E S T O R E Y m sh F R A M E D I S P L A C E M E N T P A R K F 1 E L D E A R T H O U A K E B A S E I S O L A T E D . R E F E R E N C E B A S E S T O R E Y OO m Figure 61 - Time History of Displacement, Parkfield, Reference Base Storey 100 Figure 62 - Time History of Displacement, Reference Base Storey Earthquake, 101 XVIII. APPENDIX E-TIME HISTORIES, ACCELERATIONS, REFERENCE AND PROTOTYPE BASE STOREY SAN FERNANDO EARTHQUAKE 4 T H LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) 13.5 S A N F E R N A N D O E A R T H Q U A K E 4T H L E V E L A C C E L E R A T I O N P R O T O T Y P E B A S E S T O R E Y ( F I X E D B A S E ) Figure 63 - Time History of the Acceleration at the 4th Level, Fixed Base, San Fernando. 1 0 2 PARKF]ELD EARTHQUAKE 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) Figure 64 - Time History of the Acceleration at the 4th Level, Fixed Base, Parkfield. 103 EARTHQUAKE 4TH LEVEL ACCELERATION REFERENCE BASE STOREY (FIXED BASE) tc i n rC -m J EARTHQUAKE 4TH LEVEL ACCELERATION PROTOTYPE BASE STOREY (FIXED BASE > 13.S Figure 65 - Time H i s t o r y of the A c c e l e r a t i o n at the 4th L e v e l , F i x e d Base, Earthquake. 104 S A N F E R N A N D O E A R T H Q U A K E 4 T H L E V E L A C C E L E R A T I O N R E F E R E N C E B A S E S T O R E Y ( B A S E I S O L A T E D ) — LS 3.0 4.5 6.0 7.5 T I M E S E C O N D S "5 9.0 10.5 12.0 13.5 0 1 P-l S A N F E R N A N D O E A R T H Q U A K E 4 T H L E V E L A C C E L E R A T I O N P R 0 T 0 T Y F E B A S E ST O R E Y C O L U M N S B A S E I S O L A T E D T I M E S E C O N D S 4,. 5 6.0 1.5 9.0 10.5 12.0 13.S - i — . -I..,*-™-. 1 „ 1 1 1 Figure 66 - Time History of the Acceleration at the 4th Level, Base Isolated, San Fernando. 105 F R R K F I E I D ERRTHQURKE 4TH L E V E L A C C E L E R A T I O N REFERENCE BRSE STOREY IBRSE ISOLATED) P A R K F I E L D EARTHQUAKE 4TH L E V E L A C C E L E R A T I O N PROTOTYPE BASE STOREY COLUMNS BASE I S O L A T E D Figure 67 - Time History of the Acceleration at the 4th Level, Base Isolated, Parkfield. 106 EARTHQUAKE 4TH L E V E L A C C E L E R A T I O N REFERENCE BASE STOREY (BASE ISOLATED) T I M E S E C O N D S 10.5 12.0 E A R T H Q U A K E 4TH L E V E L A C C E L E R A T I O N P R O T O T Y P E B A S E S T O R V C O L U M N S B A S E I S O L A T E D Figure 68 - Time History of the Acceleration at the 4th Level, Base Isolated, Earthquake. 1 07 X I X . APPENDIX F-ENERGY LEVELS DUE TO EARTHQUAKE RESPONSE 0.3 to ta a) 5 E S3 s* iS 0.2 0.1 0.0 Maximum Energy Levels due to Earthquake Response, Par k f i e l d Earthquake Table ^ 4th Level, Base Isolated 4th Level, Reference Base Storey (fixed base) 4th Level, Prototype Base Storey (fixed base) 5.0 10.0 15.0 Frequency (Hz) F i g u r e 69 - E n e r g y L e v e l s due t o P a r k f i e l d E a r t h q u a k e . 1.0 108 Maximum Energy Levels due to Earthquake Response, San Fernando Earthquake 0.8 0.6 s 0.L 0.2 o . o L i a Table g | j 4th Level, Base Isolated 4th Level, Reference Base Storey (fixed base) ^ 4th Level, Prototype Base Storey (fi x e d base) PJH 5.0 10.0 15.0 Frequency (Hz) Figure 70 - Energy Levels due to San Fernando Earthquake. 109 Maximum Energy Levels due to Earthquake Response, A r t i f i c a l Earthquake; Earthquake Frequency (Hz) Figure 71 - Energy Levels due to A r t i f i c a l Earthquake; Earthquake. 110 Figure 73 - Earthquake Simulator Fa c i l i t y , Loaded Steel Frame on Shaking Table. 111 Figure 74 - Base Isolated, Loaded Steel Frame with Prototype Base Storey Columns. 1 12 F i g u r e 75 - B a s e I s o l a t e d , L o a d e d S t e e l Frame w i t h P r o t o t y p e B ase S t o r e y C o l u m n s . 1 13 nnutw m\mm usumti Figure 76 - Base I so la t ion Pad Components, Lower Bearing Plate with Linear Bearings, Upper Bearing Plate and Rubber Pad. Figure 77 - Assembled Base I so la t ion Pad. 1 1 4 Figure 78 - Base Isolation System. Figure 79 - Base Isolation System showing Bearing Pad. 1 15 Figure 81 - Prototype Base Storey, Base Isolated. 1 16 Figure 83 - Base Isolation System, Prototype Base Storey with Displacement Meter. 117 BIBLIOGRAPHY 1. Calantarients, J.A.: Improvements In and Connected with Building and Other Works and Appurtenances to Resist the Action of Earthquakes and the Like, Paper No. 325371, Engineering Library, Standford University, California, 1909. 2. Matsushita, K. and Izumi, M.: Application of Input Controlling Mechanisms to Structural Design of a T a l l Building, Fifth World Conference on Earthquake Engineering, No.8. 3. Aizenberg, Y.M. and Chachua, T.L.: Application of Disengaging Joints to Increase Earthquake Resistance of Tal l Building with Stiffening Diaphrams and Core, Seismostoike Stroitelsto, 3, 1977. 4. Pall , A.S.: Friction Devices for Aseismic Design of Buildings, Fourth Canadian Conference on Earthquake Engineering, June 15,1983. 5. Mallik,A.K. and Gosh, A.: Improvement of Damping Characteristics of Structural Members with High Damping Elastic Inserts, Journal of Sound and Vibration, 27, march 8, 1973. 6. Lee, D.M. and Medland, I.C.: Estimation of Base Isolated Structure Responses, Bulletin of the New Zealand National Society for Earthquake Engineering, No.4, December, 1978. 7. Kelly, J., Eidinger, J.M., Derham, D.J.: A Practical Soft Storey Earthquake Isolation System, UCB/EERC-Report No. 77/27, November, 1977. 8. Kelly, J.M.: The Economic Feasibility of Seismic Rehabilitation of Buildings by Base Isolation, UCB/EERC-Report No. 83/01, Earthquake Engineering Research Center, University of California, Berkeley, 1983. 9. Bhatti, M.A., Pister, K.S., Polak, E.: Optimal Design of an Earthquake Isolation System, UCB/EERC-Report No. 78/22, Earthquake Engineering Research Center, University of California, Berkeley, 1978. 10. Megget, L.M.: Analysis and Design of a Base-Isolated Reinforced Concrete Building, Bulletin of the New Zealand National Society for Earthquake Engineering, No. 4, December, 1978. 11. Clough, R.W. and Penzien, J.: Dynamics of Structures, McGraw-Hill Book Company, 1975. 118 12. Wiegel, R.L.: Earthquake Engineering, Prentice-Hall, Inc. 

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