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Experimental investigations of solid state steel energy absorbers for earthquake resistant structures Chow, Foo-Lin 1983

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EXPERIMENTAL INVESTIGATIONS OF SOLID STATE STEEL ENERGY ABSORBERS FOR EARTHQUAKE RESISTANT STRUCTURES by FOO-LIN CHOW A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (The 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 ©Poo-Lin Chow, 1983 In presenting this thesis i n 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 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 2324 Main Mall Vancouver, B.C. V6T 1W5 Canada Date: ABSTRACT This thesis suggests the use of curved plates and bars of hot rolled mild steel as energy dissipating devices for the design of earthquake-resistant structures. The proposed devices would be used in parallel with isolating systems in buildings or other structures. They are designed to deflect ela s t i c a l l y under minor loads such as wind and to deform plastically when subjected to major earthquake loadings. The devices have a large energy absorbing capacity at a high number of cycles; they are economical and, once installed, can be easily inspected and replaced. An engineering method i s presented for predicting the number of cycles to failure of the devices. The practical application and f e a s i b i l i t y of a base-isolated steel structure with discrete yield rings is demonstrated in a model test on a shaking table. A design method for the yield rings i s proposed. - i -TABLE OF CONTENTS Page ABSTRACT - i -LIST OF TABLES - i i i -LIST OF FIGURES - i v -ACKNOWLEDGEMENTS - v i -1. INTRODUCTION 1 2. X-SHAPED ENERGY ABSORBER 3 2.1. Description of Function 3 2.2. Experimental Investigations and Results 4 2.3. Analysis and Design 7 3. YIELD RING 9 3.1. Description of Function 9 3.2. Experimental Investigations and Results 9 3.3. Analysis and Design 11 4. IMPLEMENTATION OF YIELD RINGS 15 4.1. Description and Experimental Set-Up 15 4.2. Analytical Modeling 16 4.3. Test Results and Proposal for Yield Ring Design . . . 21 5. CONCLUSIONS 27 6. REFERENCES 29 7. TABLES 32 8. FIGURES 41 - i i -LIST OF TABLES Page Table 1: Dimensions of X-Shaped Energy Absorber 32 Table 2: Low Cycle Fatigue Test Results 33 Table 3: Theoretical and Experimental Values of Strain for X-Shaped Energy Absorber 34 Table 4: Theoretical and Experimental Values of Strain for Yield Ring 34 Table 5: Dimension of Yield Rings Used in Low Cycle Fatigue Tests 35 Table 6: Stiffness, Yield Force and Natural Frequencies for Different Yield Ring Combinations 35 Table 7: Peak Values for Accelerations and Displacement of Sinusoidal Table Excitation Used for Tests 36 Table 8: Peak Values for Accelerations and Displacements of Earthquake Table Excitation Used for Tests 36 Table 9: Displacement Ratios for Different Frequencies of Sinusoidal Excitation and Different Yield Rings. . . . 37 Table 10: Acceleration Response Attenuation Ratios for Different Sinusoidal Excitations 38 Table 11: Acceleration Response Attenuation Ratios for Different Earthquake Excitations 39 Table 12: Modified Mercally Intensity Scale 40 Table 13: Predominant Frequencies for Different Soil Conditions. 40 - i i i -LIST OF FIGURES Page Fig. 1: X-Shaped Energy Absorber 41 Fig. 2: Load-Displacement Hysteresis Loops for X-Shaped Energy Absorber and Yield Ring 41 Fig. 3: Test Set-Up Low Cycle Fatigue Tests 42 Fig. 4: X-Shaped Energy Absorbers 42 Fig. 5: Strain Gauges Applied to Energy Absorber 43 Fig. 6: Locations of Strain Gauges 43 Fig. 7: Test Results of Relation of Strain and Cycle to Failure 44 Fig. 8: Characteristic Values and Hysteresis Loop of Energy Absorber 45 Fig. 9: Microcrack Development in Low Cycle Fatigue Test . . . 45 Fig. 10: Hysteresis Loop for Biased Energy Absorber 46 Fig. 11: Anticlastic Bending of Energy Absorber 47 Fig. 12: Strain-Displacement Relation for Energy Absorber . . . 48 Fig. 13: Quarter Component of Double Yield Ring 49 Fig. 14: Geometric Deformation of Yield Ring 49 Fig. 15: Fractured Yield Ring 50 Fig. 16: Displaced Yield Ring 50 Fig. 17: Twisted Yield Ring 51 Fig. 18: Yield Ring with Applied Strain Gauges 51 Fig. 19: Locations of Strain Gauges on Yield Ring 52 Fig. 20: Displacement of Yield Ring in Y-Direction 52 Fig. 21: Displacement of Yield Ring in Z-Direction 53 - iv -F i g . 22: Strain-Displacement Relation of Y i e l d Ring 53 F i g . 23: Components of Base I s o l a t i o n Model llI 54 F i g . 24: R o l l e r Element /18/ 54 F i g . 25: Base-Isolation System With Two Quarter Y i e l d Rings . . 55 F i g . 26: Base-Isolation System With One Quarter Y i e l d Ring. . . 55 F i g . 27: Structure and Model With Base-Isolation and Y i e l d Ring 56 F i g . 28: Load Displacement Hysteresis Loop f o r Y i e l d Ring . . . 56 F i g . 29: Displacement M a g n i f i c i a t i o n Factor for D i f f e r e n t Attenuation Ratios 57 F i g . 30: Relation of Damping and D u c t i l i t y Factor 58 F i g . 31: Attenuation Ratio Over Frequency Ratio f o r Sinusoidal E x c i t a t i o n 59 F i g . 32: Attenuation Ratio Over Frequency Ratio for Earthquake E x c i t a t i o n 59 F i g . 33: X-Shaped Energy Absorber Implemented i n F l e x i b l e Spatial Piping System, Schematic from /4/ 60 F i g . 34: Y i e l d Rings Implemented i n Base I s o l a t i o n System, From III, Insert: Proposal for B i - D i r e c t i o n a l Use /18/. 60 - v -ACKNOWLEDGEMENTS The author wishes to thank the staff of the C i v i l Engineering Department who have contributed to the success of this project. In particular, I thank Dr. J.P. Duncan, who provided most of the test specimens from his numerically controlled m i l l , and Bernard Merkle and Max Nazar, who supported me in the experimental set-ups and conduction of tests. I would like to thank the technical staff in the workshop of the Department of C i v i l Engineering with Richard Postgate as i t s super-visory technician and Wolfram Schmitt from the Electronic Laboratory. Very helpful in discussions was my colleague student B i l l Lipsett and during conducting the shaking table tests B i l l Barwig, who repeat-edly stressed our supervisor's patience by his frequent presence in the laboratory, and the table operator Chris Dumont. I am i n f i n i t e l y grateful to my parents, who supported me here in Vancouver and to my wife, who is s t i l l waiting for my return in my mother country. Great acknowledgements I would like to express to the People's Republic of China for giving me the opportunity for further education i n Canada. I also would like to thank a l l my Canadian friends, whose friendship I have enjoyed very much during my stay in Canada. I thank my supervisor Dr. S.F. Stiemer for his help and guidance during my graduate studies and these investigations, which were made possible by the funding provided by the Natural Sciences and Engineering Research Council of Canada, Grant No. A 1840. - v i -1. CHAPTER 1 INTRODUCTION Earthquake resistant design in structural engineering is achieved by several methods of which the following have recently received the highest interest: 1) sufficiently stiffening the buildings and intern-a l l y absorbing the earthquake forces by inelastic action i n beams or columns or, 2), designing a very flexible elastic structure and extern-a l l y absorbing the energy by additional discrete elements or, 3), uncoupling the building or structure from the exciting ground motion and restricting i t from excessive displacements by dampers. The latter approach has been readily accepted in theory but i t has been viewed as impractical for large c i v i l engineering structures. The lack of acceptance of this method has been caused in part by i t s complete contrast to the current approach to aseismic design described under 1). This method requires that the structure has to be analysed non-linear elas t i c a l l y , which usually i s not only d i f f i c u l t but costly. During an earthquake large yielding deformations and cracking occur, and although without total distruction the structure w i l l become either useless or wil l require expensive repair. Many different design proposals were introduced and implemented in prototypes, while the most recent ones (asymetric bracing, s a c r i f i c i a l shear walls, etc.) were trying to pre-determine the location of yielding and fracture and thus simplifying analysis, design and repair. Structures designed using methods 2) or 3) do not withstand earthquake loadings by the structure's strength or by sacrificing parts of the structure but limit the forces in the 2. structure by e l a s t i c i t y or by uncoupling i t from the ground. However, i f a structure designed by the elastic system, 2), does not include damping devices, there i s the obvious danger of i t developing resonan-ces during excitation which would cause failure. With a proper design which includes discrete damping devices this problem can be prevented. When a building is isolated from the ground motion, which is a rela-tively old but seldom used system, measures must be undertaken to prevent the relative displacements versus the ground during a severe earthquake from becoming so large and that minor loads could permanently displace the building. 3. CHAPTER 2 X-SHAPED ENERGY ABSORBER 2.1. Description of Function The investigations were aimed at the design of reliable, inexpen-sive solid-state energy absorbers for a) a mono-axial action and b) a multi-directional action. After considering a large variety of shapes and using results from previous research [1] - [5] a bending element was chosen for further development. Based on successful experiments in [3] and [4] bending action promised a yield element which i s easier to manufacture but possesses similar reserve capacity like a torsion element. A l l shear, compression, tension, and extrusion action apparently inherited major disadvantages. They were excluded from further design considerations. Simple hot rolled steel plates were used for the yield elements. Complicated machining or welding were avoided. No hinged bearings were required, the devices were rigidly clamped (ronationally fixed) at both ends. For the one-directional type a shape was chosen, which was composed from double tapers forming an X. To avoid stress concentra-tions at the clamped boundaries or in the middle, rounded transitions were chosen (Fig. 1). When this flat plate of mild steel was loaded in the weak direction, the fixed bending stresses at the apex of the tapers became uniform along the length, thus allowing yielding to develop over the f u l l length of both tapered sections. The plate deformed in a continuous S-shape. This assured an optimum use of the 4. existing material without stress concentrations at any location of the device and resulted in a high number of cycles far into the ductile range of the material. Because there was always a residual elastic core inside the yielding plate, the energy absorber achieved self-centering after being subjected to random load time-histories with decaying ends, which is a very beneficial behaviour in the case of earthquake loads. Although the fatigue l i f e , work hardening character-i s t i c s , and amount of energy absorption varied from steel to steel quality, even from batch to batch, the St 10-20 hot rolled mild steel showed a rather uniform behaviour (Fig. 2). 2.2. Experimental Investigations and Results A large number of specimens (see Table 1) were tested in order to get reliable results for the yielding region and the fatigue l i f e of the devices. Any length, thickness or width effects due to grain sizes or shape effects were tried to be covered. Investigations [9] and [10] on low cycle fatigue for mild steel indicated, that the number of cycles depended mainly on the absolute maximum strain under cyclic loading. A l l test specimens were machined by a numerically controlled m i l l , thus achieving highest accuracy of the geometric shape. The steel plates were made from St 10-20 hot-rolled mild steel, which i s commer-c i a l l y available in many different widths and thicknesses. One end of the plates was ri g i d l y clamped to the base beam of the test r i g , while the other was connected to a rod and a hydraulically actuated piston (see Fig. 3 and Fig. 4). The hydraulic system could be force- or displacement-controlled by an MTS-system Model 904.5 S. During most of 5. the tests, the displacement control was used. The cycle frequency was kept so low, that the plates did not heat up considerably (not more than 100°C). If the temperature i s not increased too much, the frequency has no significant effects on the final number of cycles to failure. I mostly used for one period one second. Tests were conduc-ted using strain gauges to measure the strain distribution on the surface of the specimen (see Figs. 5 and 6). The strain gauges were placed on each side of the plate. A high precision, computer-controlled strain and voltage data acquisition and analysis system (OPTILOG and Apple II) monitored displacements, forces, and deforma-tions during the tests. It was possible to store a l l data on magnetic disks for future display and discussion. The locations #3 and #4 (see Fig. 6) showed slightly higher strain levels than //2. For location #1 very small strains were measured, which was close to the theoretically expected value (no strain for an ideally centered strain gauge at midspan). Failure occurred i n a l l cases close to the clamped boundaries, approximately at locations #3 and #4. The dimensions of the test specimens and the number of cycles to failure are l i s t e d in Table 2 and plotted in Fig. 7. A simulated thermal bias, which resulted in a shift of the zero position i n the unloaded situation, reduced the maxi-mum number of cycles, when compared with an unbiased energy absorber. The idealized deflected shape of the energy absorber i s shown in Fig. 8. During one f u l l displacement cycle of +/-d the load-displacement curve describes a hysteretic loop. The area inside this loop represents the absorbed energy per cycle. This hysteretic loop was stable from approx. cycle number 3 to failure minus 10-20%. During the f i r s t three cycles, the loop gradually grew to the stable shape, which then remained i t s shape unt i l shortly before failure. Failure did not occur without warning. Microcracks in the expected area of fracture could be observed at the same instant when the hysteresis loo lowered i t s yield level. Although ordinary steel flats were used without special selection, the microcrack pattern was always nicely symetrical and very regular (see Fig. 9). When the simulated thermal bias was applied after the stable hysteresis loop had developed (after 50, 100, 150 cycles), a new stable loop shape formed subsequently in three cycles. This new stable shape was slightly unsymmetrical due to geometrical effects in the deflected S-shape. When the energy absorbe was bent i n the direction of the applied bias, some force was already applied in tension in the element, which showed up in the diagram as a deformation of the yield plateau (see Fig. 10). Another interesting effect could be observed: when the X-shaped plate was deflected with the maximum amplitude, a bending about i t s axis of symmetry could be seen (Fig. 11). This anticlasticly bent part stiffened this plate region. It performed like a shell, and the fracture line was forced outwards toward the clamped boundaries. The flared ends and the slightly rounded clamping blocks reduced the stresses directly at the boundaries, so that no fracture could occur at those locations. From a l l these effects, i t was expected that i t would not be simple to describe the behaviour mathematically exact i f no empirical factors should be used. 7. 2.3. Analysis and Design In the e l a s t i c region, the load-displacement r e l a t i o n f o r the X-shaped device i s l i n e a r up to the y i e l d point of (symbols see F i g . 8). In the i n e l a s t i c region, the pr o p o r t i o n a l i t y between load and displacement no longer holds. However, before s t r a i n hardening s t a r t s , the y i e l d plateau i s f a i r l y fat with an upper l i m i t of an ultimate load of 1.5 times the y i e l d load. This load was reached a f t e r approx. 0.1 to 2.5 times the y i e l d displacement, depending on the thickness/length r a t i o . But t h i s described only the behaviour of the energy absorber i n an undamaged, f u l l y operational state. In order to e s t a b l i s h a r e l a t i o n between the maximum number of cycles to f a i l u r e N and the maximum s t r a i n i n the outer f i b r e s of the device during each cycle a lower bound was found e m p i r i c a l l y ( F i g . 7): This formula i s of highest importance for the designer and represents one of the major r e s u l t s of t h i s t h e s i s . The actual s t r a i n of the outer f i b r e s of the device i s a function of the maximum end-displacements d. Sta r t i n g with the geometric r e l a t i o n of bending radius p and d : E b t 3 from (5) (2.1) _ 0.22 MAX. J77 (2.2) 8. (2.3) 4d The curvature of one section i s given by: XVz) (2.4) and then the strain as 2dt d*+t 2 (2.5) This would be true for a double circular deflected shape and ideal boundary conditions. Both could only approximately be achieved in the experimental tests and do not apply for practical use. An empirical correction factor i s suggested, which gives good correlation (see Table 3 and Fig. 12) with experimental measurements: It can be seen that for most earthquakes a design of an energy absorber with maximum strain of 2% i s quite sufficient because we s t i l l cover 100 excitations to the maximum amplitude. For structures of extremely high importance, i t i s suggested that the maximum strain in the energy absorber to be reduced to 1.4 - 1.6% in order to achieve a higher factor of safety. (2.6) 9. CHAPTER 3 YIELD RING 3.1. Description of Function The second type of energy absorbing device consisted of two curved plate in pairs like rings with planes perpendicular to each other (Fig. 13). This enabled energy absorption in any horizontal and even vertical direction, which was the logical evolution of the one-directional device described above. The main goal was to design an element, which shows a stable behaviour, that i s , after having experienced elastic and plastic deformation and being brought back to the i n i t i a l position, the geometric shape of the device should not have changed. The anticipated bending moment distribution was approximately matched by the moment resistances of the deformed plates. This type of energy absorber was aimed at the application in base isolated structures, where bearing pads like roller bearings undergo lateral parallel displacements or rubber pads where even three-directional displacements had to be accommodated. The following requirements for the design, being the same as those for the one-directional device, were governing: the material should be steel with a high ductility, i t should have an adequate fatigue l i f e , temperature independance, and i t should be possible not only to predict the yield behaviour but the l i f e span, too. 3.2. Experimental Investigations and Results The second focal point of my investigations was the curved plate 10. energy absorbers, i n the following referred to yield rings. Their action was a combined bending-torsion action. The torsion was kept small by devising high length/thickness ratios. Experimental tests for the case of fixed boundaries (see Fig. 13) have been conducted by [1] and lead to a simple analytical approach and result. My studies were mainly concerned about the case, when vertical and two-directional horizontal displacements would occur simultaneously. In this case, no fixed boundaries and no fixed curvature p were given. To simplify the interpretation of the experimental results, my tests were designed to be conducted without fixed boundaries, thus simulating the case for d vert = 0. However, the deflected shape (see Fig. 14) and the location of fracture (see Fig. 15) seems not be favourable, i f a maximum use of the material i s desired. For practical applications, I would like to suggest a double tapered curved yield ring, which promises a much better long cycle behaviour, because yielding would occur over the f u l l length of the ring. Due to the limited time available to conduct this thesis, the tests with this type of yield ring could not be finished, but i t is strongly recommended to pursue this type in future investigations. The efficiency (absorbed energy per volume material) w i l l be much greater, i f not only two plastic hinges develop but the f u l l length of the device Is u t i l i z e d . The same test r i g and measurement equipment like for the X-shaped energy absorber were used. The set-up is shown in Fig. 16 - Fig. 19. Only one quarter of a double yield ring was tested at a time. The ends of the half rings were displaced parallel (not on an arc like the X-shaped energy absorbers). Low cycle fatigue tests and strain 11. measurements were conducted. Fracture occurred at the locations of the plastic hinges (see Fig. 15) after a number of cycles, which can be predetermined (see Chapter 3.3). For excitation in two directions (Fig. 20) the tests showed, that only very small reductions for the maximum number of cycles have to be taken into account. For the example of a bias of 3 in and 2.5 in cyclic displacement, the number of cycles to failure were reduced only about 6%. Although this agrees with the theoretically expected value, more tests w i l l be required to establish a more exact design formula. For the being, i t i s suggested to use Eq. 2.2 even at 100% bias for the design. The results are s t i l l conservative enough. 3.3. Analysis and Design The bending action of the yield rings resulted in the formation of plastic hinges at the boundaries (see Fig. 13). This location is fixed for any magnitude of stroke, that means the plastic hinge shifted from A to B. As i t was shown in [1] that for high length/thickness ratios the axial force can be neglected, we were dealing with the simple situation of an ideal plastic hinge for which the amount of rotation was limited. So the maximum strain £ = - ^ - R = p (3-D was Independent from the stroke d. However, when the vertical stroke was allowed simultaneously, then the radius R was no longer constant and the rings developed plastic hinges at their clamped attachments (see Fig. 21) . 12. In the case of omitted boundaries (Fig. 14) and Inelastic deforma-tion of the yield ring the following geometrical relations can be found: If the displacement d i s larger than the yield displacement dy, then the straight segment AB = L of the plate can be approximated as a circular arc AB. This assumption i s reasonable, because the cross section is uniform. For a certain displacement d at one end of the ring, the centre of the ring C w i l l displace from location C to C . The secant AC moves to AC rotating about A with the angle a as the plastic hinge forms at A. So C*= 0(1—0(2 (3-2) with (3.3) while point B moves to B' rotating about B (3.4) The radius of the arc AB' is found by 4e 2-r(gL) 2 = L («'+/) 8e 2<x (3.5) and the curvature of the shape is given by (3.6) with t = thickness of the yield ring. Therefore, the strain i s given by c_ i t _ <xt L(ot 2+/; ( 3 , 7 ) If the error caused by assuming a circular shape for segment AB is considered, this has to be corrected by a factor found empirically as Pit 3l d L (<*'+<) J 15 (3.8) This formula is not very convenient for practical design and a simplification i n case of L = R/2 i s proposed * c - ' L+R „. -i (L+R) ~  d/z 0C= Sin =========== - Si n , , • (3-9) « — c ~l—±UL- r - I S R - d / Z (3.10) with m = d/R (3.11) and f i n a l l y <*= 0.983-s.-.-' ' - 5 - ^ J — or V l + [ l-5 - f % ) ) f ( 3 - 1 2 ) 0 ( = f ( W ) (3.13) This theoretical relation i s in good correlation with the measured values (see Fig. 22 and Table 4). In summary, knowing the displacement d the value of a can b obtained by eq. 3.12 and the strain e by eq. 3.8. The same formula Eq. (2.2) for establishing the maximum number cycles to failure i s valid for the yield rings and shows a very good correlation to the experimental results for this type of solid state steel energy absorber (Fig. 7). It represents a lower bound, thus giving conservative design values. 15. CHAPTER 4 IMPLEMENTATION OF YIELD RINGS 4.1 Description of Experimental Set-Up In the preceding chapters the characteristics and analysis of the x-shaped energy absorber and the yield rings were described, separated from the practical application. While the application in a structure was investigated in [4] for the x-shaped energy absorber, this chapter now i s going to set the yield rings i n context with a practical use. Both devices can be used in a multitude of applications. The implemen-tation as a wind restraint and displacement limitation i n a building or structure subjected to seismic loads is only one practical example. The purpose of the test described in the following was to serve as a basis for a correlation study with an analytical method for the design of the yield rings depending on the magnitudes of the expected earthquakes and the size of the buildings. A model of a steel building with a moment resisting frame was used, which was the main subject of other investigations and is described in detail in [7]. The overall dimensions of the frame were 10 ft x 4.6 ft in plan and 12.8 ft in height. Three of the four floors were loaded with concrete blocks, resulting in a total mass of the structure of 16 kips. A base-isolating system was implemented in this building, which the main component consisted of steel r o l l e r bearings (see Figs. 23 and 24). These elements had a static f r i c t i o n c o e f f i -cient of us = .2/16 = .012 and a kinetic f r i c t i o n coefficient of us = .1/16 = .006. Two return springs were installed, each with a 16. stiffness of 90 lbs/in. This structure was placed on the earthquake simulator f a c i l i t y of the Department of C i v i l Engineering, University of British Columbia. The shaking table has the floor dimensions of 10 f t x 10 f t and a maxi-mum capacity of 30.5 kips for test models. Up to this mass a maximum acceleration of 2.5 g with peak-to-peak displacements of 2.5 i n can be achieved. An MTS hydraulic system drives the table which can be controlled either by a function generator for regular waveforms or by a minicomputer (PDP 11/04) for time histories of real or a r t i f i c i a l earthquake. Currently approximately 150 different earthquake records are readily accessible in digital form. During a sequence of tests five different yield ring sets were tested. The yield rings were placed in parallel with the base isola-tion system (see Figs. 25 and 26). The dimensions and characteristic values are shown in Tables 5 and 6. 4.2 Analytical Modelling The model steel frame, which I used, responded to ground excita-tion primarily like a single degree of freedom system, due to i t s relatively r i g i d frame and base-isolating system with soft yield rings. If the damping provided by the yield rings is described in a form of equivalent viscous damping the system can be modelled like in Fig. 27. For very small stiffness K and damping this representation of the displacement dependent damping (see hysteresis loop i n Fig. 28) should be allowed. For this single degree of freedom system the description of i t s response due to a ground motion i s straight forward. The differential equation of the motion is given as M X f t - f C e ? X f t 4 KXa = C e g X j + K Xq (4.1) and then the equivalent damping ratio follows as *L 2MU)n with the natural frequency Eq. 4.1 can be reformulated as not x^e Then X a = H ( t O ) e ' W t and (4.6) Because this transfer function mainly represents the performance of the isolating system and the yield rings, i t i s called in the following "acceleration attenuation ratio" AR. It is possible to solve Eq. 4.7 for the equivalent damping (4.2) CO = (4.3) To determine the transfer function H(u>) for this system let (4.5) 18. < / ' - A R ' [ i - ( - & ) T The acceleration attenuation ratio AR = H(OJ) and the equivalent damp-ing can be used to develop a design procedure for the yield rings. Firs t l y , I have to find the relation between the relative displacement du between ground and structure and the equivalent damp-ing of .the yield rings. (4.9) Now the basic differential equation of motion can be written as M du+ C^&u + K du = - H X ^ (4.10) Dividing this by M du + 2$ej«0||du + ( J „ du = -X<i ( 4 . i i ) The transfer function is found by letting X ? = e (4.12) and iiot du = G(co)e" (4.13) 19. Substituting this into Eq. 4.11 du (4.14) The equivalent damping was given by Eq. 4.8. Solving for the maximum absolute value of displacement |du|: du U)2 (4.15) This can be expressed as du = • T (4.16) where the maximum absolute displacement of the exciting ground i s to1 (4.17) and the displacement factor is T = (4.18) which is plotted in Fig. 29 for different attenuation ratios. It can be seen, that for (4.19) 20. This can be looked upon as the limit state for our design. It shows that for a more effective acceleration attenuation a greater amount of energy has to be absorbed by the yield rings, however this i s nonlinear related. As i t w i l l be seen later, this theoretical value could be verified by experiments with a good accuracy. Several methods for deriving the equivalent damping from a load-displacement hysteresis loop have been tried. The damping i s directly related to the enclosed area of the hysteresis loop. This area is approximately (4.20) with du (4.21) which w i l l be called ductility factor of the yield ring. The equivalent viscous damping amounts to The equivalent damping ratio can be written as (4.23) note: Mto2= K (4.24) (4.25) K With th i s the equivalent damping r a t i o can be s i m p l i f i e d (4.26) with /3 = 2 0 - M ) 7f X- (4.27) The expression 3 w i l l be ca l l ed absorber damping f a c to r , which depends on the d u c t i l i t y f ac to r u of the y i e l d r i ng and represents the equivalent damping r a t i o of the system. When th i s i s d isp layed as a funct ion i n F i g . 30, i t can be seen, that the damping fac tor has i t s maximum value fo r u = 2, which i s the c r i t i c a l absorber damping f ac to r . For higher values of u the damping f ac to r decreases. It seems to be e f f e c t i v e i n design to aim at th i s va lue . If Eq. 4.26 i s combined with Eq . 4.7 the a cce l e r a t i on at tenuat ion factor AR i s 4.3 Test-Results and Proposal f o r Y i e l d Ring Design The tes t se r i es inc luded regular sine-wave exc i t a t i ons and (4.28) 22. earthquake time-histories (see Tables 7 and 8). The summary of the sine-wave excitation is shown in Table 9. The table shows the correlation values for relative displacements, and i t has to be noted, that the theoretical value are quite conservative. In Table 10 and Fig. 31 the measured values are compared with those theo-re t i c a l l y expected. The ratio of attenuation ratios shows, that for different yield ring systems and excitation frequencies a relatively good correlation could be achieved. Theoretical values are slightly higher. This error was traced to come from the choice of the represen-tative acceleration of the structure. If the average value for the whole structure would have been taken, instead of the f i r s t storey value, the correlation would have been even better. In the case of earthquake excitation the predominant frequency of the earthquake spectrum should be taken as the exciting frequency. In my test series this resulted in a slightly too smaller attenuation ratio for the theoretical value than the measured value, which can be explained by the fact, that the exact exciting frequency UJ i s lower than the predominant frequency (Op . To correct for this error the correction factor / - ^ f should be used, which yields better results for AR M _ ^_ , j+ 4/3* / <JP * r i I K - S O T J ^ (4.29) with (On - natural frequency of the system ( RAVS./$ ) lOp - predominant frequency of the earthquake excitation ($ - absorber damping factor from above. 23. The comparison i s l i s t e d in Table 11 and plotted in Fig. 32 for the following earthquake excitations: El Centro, San Fernando, Parkfield (each with different damping arrangements). The modified Eq. 4.28 yields conservative values for AR for the design. Theoretically for most modern flexible structures with low natural frequencies these earthquakes would be rather dangerous, but my experimental results indicate, that particularly i n the low frequency area a higher safety reserve is actually existing. In the following a summary of the design procedure i s described. For a given characteristical acceleration for a specific building site and the desired return period (e.g. 50 or 100 years) and the desired (or maximum allowable) acceleration of the structure the acceleration attenuation ratio i s calculated, representing the basic design parameter. Now an energy absorbing system has to be designed, thus determining the basic properties of the energy absorber with , , and K. The damping factor g can be computed and the design attenuation ratio AR. An acceptable design i s achieved when AR < [AR] and the number of cycles to failure N is large enough (100-300). A step-by-step procedure would have the following detailed sequence: 1) Determine the maximum ground acceleration and the predominant frequency of the expected design earthquake. The maximum ground acceleration depends on the expected earthquake magnitude M and the expected distance R from the epicentre of the building site. These values can be obtained from the design codes or approximately by computation ([13] and [14]) 24. or 0.8M » sboo e 3 ( 4-3D An alternative method is presented in [16] and [17], in case the area i s divided in zones, for which a Mercalli Intensity Scale i s determined (see Table 12). The predominant frequency 6Jp depends on local s o i l conditions. From the Table 13 values for the predominant period Tp can be taken, which related to the frequency by n -J2L P tT (4.32) or in case the depth of the soil layer H and average velocity of a shear wave i s known - r - _ 4H p v7 (from [12]) (4-33) 2) Determine the maximum allowable acceleration response of the structure. In the case of a base isolated building, like described i n this thesis, the building can be represented by a single degree of freedom system. The limiting acceleration can be taken as the maximum value from the National Building Codes for Structures not requiring special design considerations for earthquake loads. Typically this corresponds with the modified Mercalli Intensity Scale V with a maximum design acceleration of 0.021 g (see Table 31). For this "general case" and 25. for buildings of very high importance a safety factor ranging from 1.5 to 3.0 should be considered, i f not otherwise specified. 3) Design the isolating and energy absorbing system. Isolators: Any isolating system (rubber pads, sliding pads, r o l l e r bearings, etc.) can be used. Current research [7] indicates, that the roller bearings have a slight edge above the other systems what r e l i a b i l i t y , s t a b i l i t y , availability, and cost is concerned. Energy Absorbers: Start the design with a t r i a l value for the thickness t, width b, radius R and length L (recommendations see previous chapters) of the yield ring. A good value for the radius Is R > 10 t (from [18]). Now compute the yield force (4.34) The yield displacement is given by Py (4.35) K and the stiffness by (4.36) The Young's modulus should be taken as 28000 ksi and the yield strain as .002 for mild steel. Now the natural frequency 60M can be calculated, where M is the mass of the structure. A recommended value 26. for the yielding force i s 5% of the weight of the structure, i f not specified by the value for the wind restraint. 4) Determine the damping factor $ of the yield rings. After the maximum displacement du of the yield ring has been computed by using Eq. 4.15 or Eq. 4.16 or taken from Fig. 4.7, check the geometry for the maximum extended position of the yield ring. It should be just about to loose i t s curved shape, thus starting to act in tension rather than bending to act as a soft stop. With the ductility factor pi — , the damping factor i s found from Eq. 4.27 or taken from Fig. 4.8. 5) Check the acceleration attenuation ratio. The value of the acceleration attenuation ratio AR associated with the desired design can now be computed by Eq. 4.29 and the condition AR < [AR]. If this is not satisfied, choose new t r i a l values for yield ring. 6) Check the earthquake resistant performance of the yield rings. The maximum number of cycles to failure should generally be not smaller than 100 i f not exactly determined by site conditions and l i f e span of the building. Then Eqs. 2.2 and 3.8 can be used. The described procedure can be used without the ava i l a b i l i t y of computer analysis. However, the development of an interactive, computer aided design approach seems to be desirable and is hopefully subject of continuing research. 27. CHAPTER 5 CONCLUSIONS A comprehensive study of a l l available data of our own test results and from others leads to the following general conclusions: Solid state steel energy absorbing devices represent an efficient, inexpensive, reliable, and maintenance free means for providing damping in flexible or base-isolated buildings. Design formula are now available, which describe the yield load, the strain level, and the l i f e span simply and accurately enough to be used for engineering purposes. Both devices under investigation act in the same sequence: elastically up to the yield point, plastically with small amounts of el a s t i c i t y (slightly sloped yield plateau), and f i n a l l y due to strain hardening and geometrical deformation as a soft stop for excessive deflections. The one-directional X-shaped energy absorber, which has no hinged connection rods like previous designs, is insensitive to limited torsional action. The multi-directional double yield rings enable energy absorption in any horizontal and vertical direction. Earthquake excitation forces can be greatly reduced in buildings or structures when flexible systems with energy absorbers or base-isolated system with wind restraint and displacement limitations are used (Figs. 33 and 34). The energy absorbing devices can be designed for any type of 28. earthquake and rate of energy absorption. Possible damage is restricted to special replaceable devices. The main structure remains elastic during a l l types of excitations and requires only linear elastic analysis. The energy absorbing devices can be retrofitted into existing buildings and structures, to upgrade the earthquake resistance. Implementation into new structures results very l i k e l y i n considerable savings and higher safety. A case study would be an interesting topic for a future research project. 29. CHAPTER 6 REFERENCES Kelly, J.M., Skinner, R.I., Heine, A.J.: Mechanisms of Energy Absorption i n Special Devices for Use in Earthquake Resistant Structures, in Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 5, No. 3, 63-88, Sept. 1972. Kelly, J.M., and Skinner, J.S.: The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power Plants for Enhanced Safety, Vol. 4, A Review of Current Uses of Energy-Absorbing Devices, Report No. UCB/EERC-79/10, Earthquake Engineering Research Center, University of California, Berkeley, Feb. 1979. Stiemer, S.F., and Godden, W.G.: The Design of Steel Energy Absorbing Restrainers and Their Incorporation into Nuclear Power Plants for Enhanced Safety, Shaking Table Tests of Piping Systems with Energy-Absorbing Restrainers, UCB/EERC-80/33, Earthquake Engineering Research Center, University of California, Berkeley, Sept. 1980. Stiemer, S.F., Godden, W.G., and Kelly, J.M.: Experimental Behaviour of a Spatial Piping System With Steel Energy Absorbers Subjected to a Simulated Differential Seismic Input, UCB/EERC-81/09, Earthquake Engineering Research Center, University of California, Berkeley, July 1981. Schneider, S., Lee, H.M., and Godden, W.G.: Behaviour of a Piping System Subjected to Seismic and Thermal Loading, i n Proceedings of 30. the Fourth Canadian Conference of Earthquake Engineering, p. 140-150, Vancouver, Canada, June 1983. [6] Zackay, V.F., Kelly, J.M., Penzien, J., Powell, G., Wilson, E.L., Bush, S.H., Finnie, I., and Stiemer, S.F.: The Design of Steel Energy Absorbing Re strainers and Their Incorporation into Nuclear Power Plants for Enhanced Safety, Prepared for the Department of Energy under Contract DE-AS03-76SF00035 PA DE-AT03-ER70296, College of Engineering, University of California, Berkeley, California Progress Report, March 1980, Section 2, 2-5 - 2-12. [7] Barwig, B.B., and Stiemer, S.F.: Base Isolation Design for Earthquake Resistant Steel Buildings, Proceedings of the Fourth Canadian Conference of Earthquake Engineering, p. 382-391, Vancouver, Canada, June 1983. [8] Kelly, J.M., Skinner, M.S., and Beucke, K.E.: Experimental Testing of an Energy-Absorbing Base Isolation System, Report No. UCB/EERC-80/35, Earthquake Engineering Research Center, University of California, Berkeley, Feb. 1979. [9] Tyler, R.G.: A Tenacious Base Isolation System Using Round Steel Bars, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 4, Dec. 1978. [10] Tyler, R.G.: Tapered Steel Energy Dissipators for Earthquake Resistant Structures, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 4, Dec. 1978. [11] Dowrick, D.J.: Earthquake Resistant Design, John Wiley & Sons Ltd., 1977, 374 p. [12] Bolotin, V.V.: Sta t i s t i c a l Theory of a Seismic Design of Structures, Proc. Second World Conference on Earthquake 31. Engineering, Tokyo, 2, 1365-1374, 1960. [13] Amin, M., and Ang, A.H.S.: A Nonstationary Stochastic Model for Strong-Motion Earthquakes, Structural Research Series No. 306, University of I l l i n o i s , Department of C i v i l Engineering, April 1966. [14] Seed, H.B., Ugas, C , and Lysmer, J. : Site Dependent Spectra for Earthquake Resistant Design, Report No. UCB/EERC-74/12, Earthquake Engineering Research Center, University of California, Berkeley, Nov. 1974. [15] Ambraseys, N.N.: Dynamics and Response of Foundation Materials in Epicentral Regions of Strong Earthquakes, Proc. 5th World Conference on Earthquake Engineering, Rome, 1, CXXVI-CXLVIII, 1973. [16] Okamoto, S.: Introduction to Earthquake Engineering, University of Tokyo Press, 1973. [17] Singer, F.L. and Pytel, A.: Strength of Materials, Third Edition, 1980. [18] Barwig, B.B.: Experimental Investigation of the Base Storey Design of Base Isolated Steel Buildings, Department of C i v i l Engineering, University of British Columbia, Canada, Nov. 1983. LENGTH WIDTH THICKNESS STROKE THERMAL CYCLES/ AT ROOT BIAS T.B. TEST L W T S TB CTB Ql 5 L/2 1/4 L/4 0 0 Q2 5 L/2 1/4 L/4 0 0 Q3 5 L/2 1/4 L/4 0 0 Q4 5 L/2 1/4 L/4 0 0 Q5 5 L/2 1/4 L/4 0 0 Tl 5 L/2 1/8 L/4 0 0 T2 5 L/2 3/16 L/4 0 0 T3 5 L/2 1/4 L/4 0 0 T4 5 L/2 5/16 L/4 0 0 SI 5 L/2 1/4 L/10 0 0 S2 5 L/2 1/4 L/5 0 0 S3 5 L/2 1/4 3L/10 0 0 S4 5 L/2 1/4 2L/5 0 0 S5 5 L/2 5/16 L/10 0 0 S6 5 L/2 5/16 L/5 0 0 S7 5 L/2 5/16 3L/10 0 0 S8 5 L/2 5/16 2L/5 0 0 LI 2 L/2 1/4 L/4 0 0 L2 3 L/2 1/4 L/4 0 0 L3 4 L/2 1/4 L/4 0 0 L4 5 L/2 1/4 L/4 0 0 L5 6 L/2 1/4 L/4 0 0 L6 7 L/2.6 1/4 L/4 0 0 L7 8 L/2.6 1/4 L/4 0 0 TBI 5 L/2 1/4 L/4 L/10 0 TB2 5 L/2 1/4 L/4 L/5 0 TB3 5 L/2 1/4 L/4 3L/10 0 TB4 5 L/2 1/4 L/4 2L/5 0 CTB 5 L/2 1/4 L/5 0 50 +L/5 50 0 50 -L/5 50 Rl 5 2L/5 1/4 L/4 0 0 R2 5 L/2 1/4 L/4 0 0 R3 5 2L/5 1/4 L/4 0 0 Table 1: Dimensions of X-Shaped Energy Absorber 33. SPECIMEN du t L e max N (in) (in) (in) (from 2-6) (from test) Q1~Q2 1.25 0.25 5 0.0176 177,178,230, 253,292 Tl 1.25 0.125 5 0.0088 126 T2 1.25 0.1875 5 0.0132 364 T3 1.25 0.25 5 0.0351 301 T4 1.25 0.3125 5 0.0468 182 SI 0.5 0.25 5 0.011 1710 S2 1.0 0.25 5 0.0266 466 S3 1.5 0.25 5 0.0436 179 S4 2.0 0.25 5 0.0602 114 S5 0.5 0.3125 5 0.0136 1173 S6 1.0 0.3125 5 0.0333 298 S7 1.5 0.3125 5 0.0546 144 S8 2.0 0.3125 5 0.0751 72 LI 0.5 0.25 2 0.0638 42 L2 0.75 0.25 3 0.0491 138 L3 1.0 0.25 4 0.0402 124 L4 1.25 0.25 5 0.0351 276 L5 1.50 0.25 6 0.0311 229 L6 1.75 0.25 7 0.0281 404 L7 2.0 0.25 8 0.0257 431 R1-R3 1.25 0.25 5 0.0351 134,263,173 TBI 1.75 0.25 5 0.0521 277 TB2 2.25 0.25 5 0.0672 229 TB3 2.75 0.25 5 0.0816 168 TB4 3.25 0.25 5 0.0939 142 CA1-CA5 0.5 0.125 2 0.0407 147,189,161, 185 *emax °^ Q1~Q2 is from measurement. Others from calculation using formula (2-6). Table 2: Low Cycle Fatigue Test Results 34. DISPLACEMENT (in) THEORETIC VALUES e FROM (2-6) (10~ 6) MEASURING VALUE [e] POINT 34 IN FIG. 6 (lO" 6) e/[e] 0.125 866 956 0.91 0.250 2178 2130 1.02 0.375 3729 3775 0.99 0.500 5448 5463 0.99 0.625 7298 7322 0.99 0.75 9242 9416 0.98 ** This plate is shown in Fig. 6. L=5", t=l/4". *** d i s shown i n Fig. 8. Table 3: Theoretical and Experimental Values of Strain for X-Shaped Energy Absorber DISPLACEMENT ANGLE VALUE a THEO. VALUE e MEASURING VALUE FROM (3.12) FROM (3-8) [e] POINT 1 IN (in) FIG. 19 1.0 0.0480 0.0021 0.002114 0.99 1.25 0.0518 0.0028 0.002878 0.47 1.65 0.0700 0.0042 0.003774 1.12 2.0 0.0867 0.0055 0.005808 0.95 2.5 0.1119 0.0076 0.007350 1.03 ** This plate is shown in Fig. 19. L=2", R=4", t=l/4" *** d i s shown i n Fig. 14. Table 4: Theoretical and Experimental Values of Strain for Yield Ring 35. pseudo static test NO. OF PLATES R (in) L (in) t (in) b (in) k (kips/in) p y (kips) El 3 1.5 1/8 1.25 0.067 0.0625 E2 3 1.5 3/16 1.25 0.133 0.125 E3 3 1.5 1/4 1.25 0.200 0.25 Table 5: Dimension of Yield Rings Used in Low Cycle Fatigue Tests COMBINE PLATES OF SYSTEM STIFFNESS OF SYSTEM K (kips/in) YIELDING FORCE OF SYSTEM P y (kips) NATURAL FREQUENCE OF SYSTEM** f (Hz) 8E1 0.72 0.62 0.61 4E2 0.71 0.60 0.76 6E2 0.98 0.85 0.83 2E3 0.78 0.80 0.90 4E3 0.98 1.10 1.16 * K, P , u>n consider the stiffness of springs and fri c t i o n of rollers besides curved plates. ** Natural frequencies have been checked with a "free vibration test" Table 6: Stiffness, Yield Force and Natural Frequencies for Different Yield Ring Combinations 36. FREQUENCY OJ (Hz) MAX. ACCELERATION OF TABLE X (g) MAX. DISPLACEMENT OF TABLE X g(in) 1.0 0.178 1.475 2.0 0.656 1.463 3.0 1.96 1.440 4.0 2.089 0.948 Table 7: Peak Values for Accelerations and Displacement of Sinusoidal Table Excitation Used for Tests NAME OF E/Q RECORDS PREDOMINANT FREQUENCY RANGE** to (Hz) MAX. ACCELERATION* OF TABLE X g(g) MAX. DISPLACEMENT OF TABLE X g(in) EL CENTR0 1.2 ~ 2.2 (1.5) 0.349 1.749 SAN FERNANDO 4.0 ~ 5.7 (4.0) 0.793 1.076 PARKFIELD 0.6 ~ 2.3 (1.5) 0.233 1.704 ** From the Fourier Spectra of acceleration record. * Only use the f i r s t 10 seconds of E/Q which included the peak value of acceleration. Table 8: Peak Values for Accelerations and Displacements of Earthquake Table Excitation Used for Tests Energy Frequency du (in) du Absorber of Sine-Wave a r theor, du measuring[du] un X [du] System Excitation (from test) (Hz) 0.6 2.106 3.0 1.33 0.45 1.399 1.19 8EI 2.0 2.64 0.08 1.18 1.89 1.581 1.48 0.9 3.95 0.03 1.07 2.28 1.538 1.0 1.21 0.42 1.871 4E2 2.0 2.64 0.09 1.18 1.88 1.526 1.23 3.0 3.95 0.03 1.07 2.28 1.531 1.49 1.0 1.21 0.56 1.946 6E2 2.0 2.41 0.13 1.23 1.97 1.604 1.23 3.0 3.62 0.05 1.09 2.31 1.502 1.54 1.0 1.11 0.52 1.901 2E3 2.0 2.22 0.12 1.29 2.07 1.579 1.31 3.0 3.34 0.04 1.10 2.34 1.492 1.57 4.0 4.45 1.305 1.0 0.86 0.87 2.114 4E3 2.0 1.73 0.20 1.70 2.72 1.668 1.63 3.0 2.59 0.07 1.19 2.53 1.515 1.67 4.0 3.45 0.05 1.10 0.94 0.957 0.98 Table 9: Displacement Ratios for Different Frequencies of Sinusoidal Excitation and Different Yield Rings Frequency Absorber Damping Factor B Measured [AR] Table System du dy Theoretic. Energy Id * (measured) (measured) u « i " . a . 2 (u-1) P -w- m X a AR - — [X g] [x a]** - y Absorber n (In) (In) dy M h (g) (g) [X-I Ratio System (Hz) (Hs) o AR/ [AR] 0.6 0.61 0.98 2.106 1.0 2.11 0.159 3.27 0.051 0.068 1.33 2.46 8E1 0.9 0.61 1.48 1.399 1.0 1.40 0.150 0.85 0.108 0.049 0.45 1.89 2.0 0.61 3.28 1.581 1.0 1.58 0.148 0.11 0.656 0.054 0.08 1.38 3.0 0.61 4.92 1.538 1.0 1.54 0.145 0.04 1.96 0.054 0.03 1.33 1.0 0.76 1.32 1.871 0.75 2.49 0.153 1.30 0.178 0.074 0.42 3.10 4E2 2.0 0.76 2.63 1.526 0.75 2.04 0.159 0.18 0.656 0.061 0.09 2.0 3.0 0.76 3.95 1.531 0.75 2.04 0.159 0.07 1.96 0.066 0.03 2.33 1.0 0.83 1.20 1.946 0.75 2.60 0.151 1.96 0.178 0.100 0.56 3.50 6E2 2.0 0.83 2.41 1.604 0.75 2.13 0.159 0.22 0.656 0.082 0.13 1.69 3.0 0.83 3.61 1.502 0.75 2.00 0.159 0.09 1.96 0.090 0.05 1.80 1.0 0.90 1.11 1.901 0.6 3.17 0.137 2.89 0.178 0.092 0.52 5.56 2E3 2.0 0.90 2.22 1.579 0.6 2.63 0.150 0.26 0.656 0.076 0.12 2.17 3.0 0.90 3.33 1.492 0.6 2.48 0.153 0.10 1.96 0.079 0.04 2.50 4.0 0.90 4.44 1.305 0.6 2.17 0.158 0.06 — 0.085 1.0 1.16 0.86 2.114 0.6 3.52 0.129 2.82 0.178 0.154 0.87 3.24 4E3 2.0 1.16 1.72 1.668 0.6 2.78 0.147 0.53 0.656 0.131 0.20 2.65 3.0 1.16 2.58 2.515 0.6 2.53 0.152 0.18 1.96 0.135 0.07 2.57 4.0 1.16 3.44 3.957 0.6 1.60 0.149' 0.10 1.39 0.113 0.08 1.25 * Natural frequencies have been checked with a "free vibration test". ** [Xg] is a measured value from accelerometer on firs t floor (A-^). Table 10: Acceleration Response Attenuation Ratios for Different Sinusoidal Excitations co Frequency Absorber Damping Factor B Measured [AR] Energy Absorber System Earthquake Predominant Frequency of E/Q "p System % du (In) dy (in) u - in dy Theoretic. AR - — *y [X gl (g) [X a]** (g) [AR] - ^ Ratio AR/ [AR] 8E1 El Centro San Fernando Parkfleld 1.5 4.0 1.3 0.61 0.61 0.61 2.46 6.56 2.13 2.84 1.592 2.34 1.0 1.0 1.0 2.84 1.592 2.34 0.323 0.064 0.431 0.349 0.793 0.233 0.091 0.054 0.091 0.26 0.068 0.391 1.24 0.94 1.10 4E2 El Centro San Fernando Parkfleld 1.5 4.0 1.3 0.76 0.76 0.76 1.97 5.26 1.71 2.49 1.504 1.979 0.75 0.75 0.75 3.134 2.159 2.150 0.502 0.090 0.701 0.349 0.793 0.233 0.114 0.059 0.114 0.327 0.074 0.489 1.54 1.22 1.43 6E2 El Centro San Fernando Parkfleld 1.5 4.0 1.3 0.83 0.83 0.83 1.81 4.82 1.57 1.774 1.491 2.083 0.75 0.75 0.75 2.155 1.159 2.147 0.613 0.104 0.874 0.349 0.793 0.233 0.101 0.077 0.161 0.289 0.097 0.691 2.12 1.07 1.27 2E3 El Centro San Fernando Parkfleld 1.5 4.0 1.3 0.90 0.90 0.90 1.67 4.44 1.44 1.954 1.547 2.20 0.60 0.60 0.60 3.135 2.151 3.126 0.740 0.118 0.122 0.349 0.793 0.233 0.106 0.070 0.189 0.304 0.088 0.811 2.43 1.34 1.38 4E3 El Centro San Fernando Parkfleld 1.5 4.0 1.3 1.16 1.16 1.16 1.29 3.45 1.12 1.939 1.292 1.607 0.60 0.60 0.60 3.136 2.158 2.149 0.640 0.179 0.818 0.349 0.793 0.233 0.155 0.131 0.139 0.444 0.165 0.597 3.69 1.09 4.72 Table 11: Acceleration Response Attenuation Ratios for Different Earthquake Excitations MM SCALE *xg (%g) V 1 ~ 2.1 VI 2.1 ~ 4.4 VII 4.4 ~ 9.4 VIII 9.4 ~ 20.2 IX 20.2- 43.2 X > 43.2 Table 12: Modified Mercally Intensity Scale SOIL CONDITION T p(s) Rock Stiff s o i l Deep cohesionless soils Soft to medium clay and sand 0.1 ~ 0.15 = 0.2 = 0.3 = 0.7 Table 13: Predominant Frequencies for Different Soil Conditi Fig. 1: X-Shaped Energy Absorber load-Displacement Hysteresis Loops for X-Shaped Energy Absorber and Yield Ring 43. Fig. 6: Locations of Strain Gauges 44. 2 U 6 8 10 12 H 16 NUMBER OF CYCLES TO FAILURE in 100's Fig. 7: Test Results of Relation of Strain and Cycle to Failure 45. Fig. 9: Microcrack Development i n Low Cycle Fatigue Test 46. TEST TB3 DATE 28.12.82 FREQ. O.1 Hz FAIL. 168 LOC. TOP -2 -30 •10 10 30 MEAS. DISPL. / THEOR. YIELD DISPL. Fig. 10: Hysteresis Loop for Biased Energy Absorber Fig. 11: Anticlastic Bending of Energy Absorber Fig. 12: Strain-Displacement Relation for Energy Absorber 49. Fig. 14: Geometric Deformation of Yield Ring 50. Fig. 16: Displaced Yield Ring Fig. 18: Yield Ring with Applied Strain Gauges Fig. 20: Displacement of Yield Ring in Y-Direction 53. Fig. 21: Displacement of Yield Ring in Z-Direction 1.00 DISPLACEMENT d in [INCH] Fig. 22: Strain-Displacement Relation of Yield Ring 54. 1. base column 2. rubber pad 3. upper bearing plate 4. r o l l e r bearings 5. lower bearing plate 6. absorber base, building side 7. foundation beam 8. steel ring energy absorber 9. safety pad Fig. 23: Components of Base Isolation Model [7] <> m ifMuiiH iiwitm mmiiu IMKIHtl ItilUllll HUllitll mkj&»., „xi,. * . ..... HII1IKII IIIHHIttHHItHI! IMU « JliUUHiltlitHiaaiHUIH H Fig. 24: Roller Element [18] Fig. 26: Base-Isolation System With One Quarter Yield Ring 56. Fig. 27: Structure and Model With Base-Isolation and Yield Ring P d Fig. 28: Load Displacement Hysteresis Loop for Yield Ring 57. Fig. 29: Displacement Magnificiation Factor for Different Attenuation Ratios 59. 1 2 3 4 S 6 7 Fig. 31: Attenuation Ratio Over Frequency Ratio for Sinusoidal Excitation CO < o w 53 H D O E l Centro / \ San Fernando • P a r k f l e l d o 0 DO * A 4 5 Fig. 32: Attenuation Ratio Over Frequency Ratio for Earthquake Excitation 60. Fig. 34: Yield Rings Implemented in Base Isolation System, From (7). Insert: Proposal for Bi-Directional Usej.[18] 

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