seismic analysis of a low-rise base-isolated structural...

Seismic Analysis of a Low-Rise Base-IsolatedStructural System

by

Halit Kaplan and Ahmet H. Aydilek

reprinted from

Journal ofLOW FREQUENCY

NOISE, VIBRATION AND ACTIVE CONTROL

VOLUME 25 NUMBER 2 2006

MULTI-SCIENCE PUBLISHING COMPANY LTD.

Seismic Analysis of a Low-Rise Base-IsolatedStructural System

Halit Kaplan1 and Ahmet H. Aydilek2

1The Sciemtitic and Technological Research Council of Turkey (TUBITAK)06100, Kavakliders, Ankara, Turkey.2Department of Civil and Environmental Engineering 1163 Glenn Martin HallUniversity of MarylandCollege Park, MD 20742, U.S.A.E-mail: [email protected]

received 30th March 2006Key Words: Earthquake, base isolation, mechanical springs, low-rise structure.

ABSTRACT: A base-isolation system was developed for earthquake protection of low-risestructures. The system incorporates spherical supports for the base, a speciallydesigned spring-cam system to keep the base supported under normalconditions, and moves for the duration of the earthquake under the constraint ofa spring with optimized stiffness characteristics. The dynamic behaviour of athree-story concrete structure with and without the base isolation subjected tothe Taft and El Centro earthquake loads was investigated. The results indicatedthat the absolute peak acceleration and displacement as well as shear forcesdecreased significantly with the application of a base isolation system, and it ispossible to achieve 87 to 94% reduction in the maximum accelerations andtransmitted forces. The movement of the base relative to the ground was lessthan 0.15 m in the optimized system, and the springs were not fully compressedat any time during application of the earthquake loads. The maximum inducedvertical forces as a result of the spherical base support were found to be less than1.5 % of the weight of the structure. Since the system performance is highlydependent on the rapid unlocking of the cams in the event of a seismicdisturbance, careful consideration should be given to the optimal design of thespring-cam system.

1. INTRODUCTIONIn seismically critical regions, the use of base isolation systems is considered as ameans of minimizing the earthquake effects. Several active and passive isolationsystems are currently being used for this purpose, including rubber-steel compositeisolators, frictional pendulum systems, active tendon mechanisms, rolling andsliding systems, tuned mass, liquid absorbers, and suspension mechanisms (Wangand Reinhjorn 1989, Kuroda and Saruta 1989, Mayes et al. 1990, Kareem 1994,Koike and Murata 1994, Mostaghel and Davis 1997, Jahilal and Utku 1998,Almazan et al. 1998, Zhou and Lu 1998, Kaplan and Seireg 2001).

The base isolation systems have been traditionally applied to various structuresunder earthquake loads (Fujita et al. 1994, Wang and Liu 1994, Youssef et al. 1994,Kaplan and Seireg 2000, Kaplan and Seireg 2002). Research has also been extendedto investigate the applicability of these systems in designing low-rise structures(Shing et al. 1996, Matheu et al. 1998), and wood structures (Symans 2002). Maranoand Greco (2003) isolated the base of a low-rise building by using high dampingrubber bearings. A stochastic approach was used to model the seismic accelerationacting at the base. The displacements and dissipation of energy decreased as a result

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of base isolators. Shake table tests on a five-storey benchmark model with baseisolation were conducted by Samali et al. (2003). Both translational and torsionalresponses of the structure were reduced by isolating the base with either laminatedrubber or lead-core bearings. Isolation system damping for which acceleration of thestructure attains a minimum value was used by Jangid and Kelly (2001). Hybridbase-isolation systems were also used for protection of an eight-storey structureunder earthquake loads (Tzan and Panadalidas 1994), and a power rate reaching lawhybrid control method developed by Zhao et al. (2000) provided comparable resultswith a model traditionally being used. Yang and Huang (1998) showed that theresponse of a structure to earthquake excitations can be effectively reduced using abase-isolation system formed of elastic bearings. In their study, each storey wasmodeled with translation and torsion, and the optimal point for mounting theconstruction equipment was shown to be the one where the equipment remainsundisplaced during vibration.

Existing studies indicated that the base-isolation systems can significantlydecrease the peak acceleration, displacement, and shear loads in a fixed-basestructure (Lin and Hone 1993, Lin et al. 1995). Use of the base-isolation systems canbe quite helpful in decreasing the displacement and shear loads in residentialbuildings typically constructed in seismically sensitive regions. The objective of thisstudy was to investigate the performance of a low-rise base-isolated residentialbuilding under different earthquake excitations using a newly developed base-isolation system. To meet this objective, a fixed-base three-storey concrete structurewas subjected to the 1940 El Centro and the 1952 Tafts earthquake loads and theresponse to these loads was analyzed. Comparisons were made between theobserved performance of the rigidly supported (fixed-base) and base-isolatedstructures.

2. SYSTEM MODEL FOR THE CONVENTIONALLY DESIGNED FIXED-BASE STRUCTUREThe design analysis undertaken in this study suggests that a relatively simple, robustactive control can be implemented to protect a structure. A system similar to the onedeveloped for a 40-storey structure (Fujita et al. 1994, Kaplan and Seireg 2001) andspecifically the one developed for low-rise buildings (Kurota and Saruta 1989) wasused herein for a three-storey concrete residential building. The fixed-base systemwas modeled with three lumped masses and three stiffness coefficients (Figure 1).Structural damping was neglected for safety. The mass distributions for the first,second, and third floors were 79,000 kg, 58,000 kg, and 60,000 kg, respectively. Thecoefficients of stiffness were selected as 27, 900 ton/m, 16, 100 ton/m and 15, 100ton/m, respectively, based on a trapezoidal stiffness distribution for the floors. Thebuilding is 10 m-wide and 10 m-high. A depth of 6.5 m was considered for thestructure. The first, second, and third natural frequencies of the structure werecalculated as wn1= 1.318, wn2 = 3.334, and wn3 = 4.634 Hz, respectively.

Figure 1: Lumped mass model of fixed-base three floor concrete structure

Seismic Analysis of a Low-Rise Base-Isolated Structural System

JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL94

Dynamic equations of the system model can be written as follows (Kaplan andSeireg 2000):

(1)

(2)

(3)

where �(t) is the ground displacement, M1, M2, and M3 are mass, C1, C2, and C3 aredamping, K1, K2, and K3 are stiffness, and x1, x2, and x3 displacement values for eachfloor, respectively.

3. SEISMIC RESPONSE OF THE FIXED-BASE STRUCTUREThe fixed-base structure was separately subjected to the 1940 El Centro (M=6.7)and the 1952 Tafts (M=7.7) earthquake loads and its response to these loads wasanalyzed using the fourth-order Runge-Kutta numerical integration technique withvariable step size (Matlab 2001). The numerical integration was performed for theduration of the simulated earthquake, such as 53 seconds in this case. Figure 2provides the data for the two earthquakes.

Figure 2 Temporal characteristics of acceleration and displacement for the (a) El Centro earthquake, andthe (b) Taft earthquake

Figure 3 summarizes the results of simulations for the El Centro earthquakeloads. All acceleration and displacement values are “absolute” values and they willsimply be called acceleration and displacement in the rest of the paper. Comparisonof Figures 2a and 3 suggests that peak acceleration at the top of the building (thethird floor) is approximately 3.5 times higher than the peak ground acceleration. Thepeak displacement on the third floor is 1.8 times of the ground displacement. Asexpected, the peak acceleration and displacement generally increased for the higherfloors, and the maximum shear force occurred at the lower portion of the building.

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(a)

(b)

Figure 3 Seismic response of the fixed-base structure subjected to the El Centro earthquake loads

Figure 3 (cond’d) Seismic response of the fixed-base structure subjected to the E1 Centro earthquake loads



4. SYSTEM MODIFICATION USING A CONCAVE-BALL SUPPORT BASEA physical model comprising a spring-cam system previously developed by Kaplanand Seireg (2000) was used herein to isolate the base of the structure. The systemimproves the performance of the building against earthquake loads by controllingthe displacement of the base and transfer of shear forces between the floors. Thecams compress fully the springs under normal conditions and are released when anearthquake is sensed. A side view of the system with steel balls and concave basesupports is shown in Figure 4. A diagrammatic representation of the spring-camsystem along with the force-displacement curve of the spring is shown in Figure 5.Both the steel balls and the base support were assumed to be polymer-coated.Preliminary analysis by Kaplan (2002) indicated that a choice of twenty-five for thenumber of balls during the design was sufficient for the sensitivity of the analysis.In this case, each ball was placed between concave surfaces that tend toautomatically restore balls and the base to their original position even if the systemundergoes some rotational response. Another advantage of the use of concavesurfaces is a reduction of the contact stresses as a result of their curvatures. Detaileddescription of the design can be found in Kaplan and Seireg (2000).

Figure 4 (a) Side and (b) top view of the three-storey concrete base isolated structure with steel balls andconcave base supports

Figure 5 (a) The force displacement characteristics of the spring, and (b) diagrammatic representation ofthe spring cam system

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The spring function Kb used as part of the base isolation system herein representsthe equivalent restoring stiffness on the base as it contacts the springs which areplaced radially (Figure 4). The spring function Kb is not sensitive to the traveldirection of the shock wave in this type of spring arrangement. A restoring functionwith an eight-spring arrangement for different directions of wave propagationindicated that Kb can be defined by the following formula:

(4)

where K is the stiffness of each individual spring, and l is the directional cosine foreach spring relative to the direction of displacement. Accordingly, Kb = 2K is validfor the considered system. A detailed diagrammatic representation of the spring camsystem is given in Figure 5b.

5. DYNAMIC EQUATIONS OF THE ISOLATED SYSTEMThe dynamic equations of the base-isolated system can be written for two separatecases. The first case is the one in which the absolute relative displacement of thebase (xb) with respect to displacement of the ground (�(t)) is greater than thedistance of the free movement between the spring and the base (b) that is, max|xb -�(t)|≥ b. The corresponding equation is:

(5)

where Mb is the mass of the base, Ms is the mass of the structure, and g is thegravitational acceleration. Note that Equation-5 is valid when the spring is beingcompressed. The vertical acceleration at the base, ÿb, and the total horizontal forceacting on the base. H, are defined with the following equations (see Appendix fordetails):

(6)

(7)

where R is the radius of the concave support, and r is the radius of the hollowspherical balls. The effective coefficient of friction at the base, µeff, was defined byKaplan (2002) as follows:

(8)

where µ0 is the coefficient of rolling friction.

The second case is in which max|xb - �(t)| < b and the differential equation of thissystem becomes:



(9)

(10)

(11)

(12)

The damping effects are neglected (i.e., C1 = C2 = C3 = 0 ) for simplicity, and themass of isolated structure is defined by:

(13)

and Mb is set to a practical value

(14)

And finally, the total vertical force acting on the base, V, can be defined as follows:

(15)

6. DESIGN OPTIMIZATIONThe main goal of the design problem was to minimize the peak shear force in theisolated structure by constraining the relative displacement of the structure to theground. An optimization scheme was developed for this purpose and is presentedbelow. Since, well-stablished codes and standards are available for designing thestructural component of the low-rise buildings in seismic sensitive regions, theoptimization model was applied only to the base isolation system. The decisionparameters of the system are the parts of the base isolated mechanism whereconcave seats are supported by the hollow spherical balls and the system iscontrolled by a spring-cam system. Therefore, the parameters considered duringdesigning the base isolation system were R, r, Kb, b, Mb, Meff, and d. All theparameters were defined above, except the parameter d is the distance between thebase and the fully compressed spring. Figure 6a provides a schematic of the basesystem.

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(a)

Figure 6 (a) Illustration of the motion in the base system and the parameters considered duringoptimization scheme, and (b) change in shear forces for different relative base displacementvalues

The only design variables considered in the optimization scheme were R, Kb, andb, since the parameters Mb, r and µ0 were set to their practical values consideringthe geometry and material properties (Mostaghel and Davis 1997, Seireg 1998). Apositive value of d denotes that the springs are not fully compressed at any timeduring the action of the disturbance. A reasonable value of 0.3 m was assumed ford to limit the movement of the base during the search for the solution. The objectivefunction was selected to minimize the peak shear force at the critical storey in theisolated structure normalized by the maximum shear force in the fixed-base case andis given by:

(16)

or

(17)

where Fi and Fr are the peak shear forces transmitted to each floor for the isolatedand the fixed-base case, respectively.

The following constraints were considered for the optimization scheme:1. The maximum displacement of the base relative to the ground motion should

be set to a maximum allowable value at which the peak shear force (i.e.,transmitted force) in the structure is minimized. The shear forces weredetermined for different peak values of relative displacements and are plottedin Figure 6b. As seen from the figure, the numerical minimum stress can beachieved by allowing the base to be displaced 0.15 m, at which an acceptably



low transmitted force can be obtained. Therefore, a maximum value of b =0.15 m was chosen for the optimization scheme:

(18)

The main purpose herein was to control the maximum displacement of thestructure. Considering the fluctuations in the curve in Figure 6b, the springwas assumed to be fully compressed when max|xb - �(t)|≥ 0.30 m, and theboundary conditions became xb = �(t) and

.xb = –�(t)

2. Upper and lower limits were assigned to the radius of concave curvature (R),the spring stiffness (Kb), and the free movement distance between the springand the base (b) considering the practicality of the application:

(19)

(20)

(21)

Based on the given design parameters, differential equations of motion weresolved using the fourth-order Runge-Kutta numerical integration technique with avariable step-size. Similar to the fixed-base case, the numerical integration wasperformed for the duration of the simulated earthquake. Then, the relevant quantitiesin the objective function (maximum shear forces) were obtained indirectly utilizingthe numerical simulation data. The Quasi-Newton method provided in the Matlabprogramming language was used to optimize the design parameters. The followingoptimum design parameters were used for simulating the response of the base-isolated system to the earthquake loads: R= 4 m, Kb = (0.005) K1 N/m, and b= 0.05m.

Figure 7 Acceleration versus time response of the base-isolated structure with subjected to the El Centroearthquake loads

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Figure 8 Displacement versus time response of the base isolated structure with base isolation subjected tothe El Centro earthquake loads

7. SEISMIC RESPONSE OF THE BASE-ISOLATED SYSTEMIn order to define the change in structural performance due to base isolation,acceleration and displacement of the base and each floor were plotted versus timein Figures 7 and 8, respectively. The El Centro earthquake data were used incalculations. As expected, the peak acceleration and displacement generallyincreased for the higher floors. However, comparisons with the fixed-base structurein Figure 3 indicate that the base isolation decreased the peak acceleration of thestructure about 14 times. Similarly, the peak displacement of the base isolatedstructure was 0.13 m as compared to a peak value of 0.18 m determined for thefixed-base structure, which indicates a decrease of about 28%. Additionally, theacceleration or displacement value at any given time was lower for the isolated case.

Figure 9 provides the relative displacement and shear forces in each storey. Sincethe earthquake performance of a storey is affected from the floors above and belowit, relative displacements were necessary for defining the performance of thestoreys. Additionally, the shear force transmitted from one floor to another wasplotted versus time in Figure 10. The transmitted shear force was lower for the upperfloors, similar to the behaviour observed for the fixed-base structure. A comparisonof Figures 3 and 10 indicates that shear forces decreased significantly aftermodifying the system with a base isolation. For instance, examination of the plotsrevealed that the peak shear force transmitted into storey #l decreased from l500kNto about l30kN.

In order to provide a direct comparison between the fixed-base and isolated casethe peak values of acceleration, displacement, and shear forces were plotted for theEl Centro and Taft earthquakes in Figures 11 and 12, respectively. The base isolationsystem caused a significant decrease in the acceleration, and displacement valueswhen the structure was subjected to the El Centro earthquake or the Taft earthquakeloads. The decreases in maximum acceleration, displacement, and shear force were93%, 47%, and 94%, respectively under the Taft earthquake loads.

The results indicated that the base isolation system increased the earthquakeresistance of the structure significantly. In addition, the effective coefficient of



friction of the base was small (Figure 13). Even though not presented herein, theobserved movement of the base relative to the ground did not exceed 0.15 m whensubjected to either of the earthquakes. Moreover, maximum induced vertical andhorizontal forces as a result of the base support were determined to be less than1.5% and 6%, respectively, of the weight of the structure.

Figure 9 Relative displacement versus time response of each storey subjected to the El Centro earthquakeloads

Figure 10 Transmitted force (shear force) versus time response in each storey subjected to the El Centroearthquake loads

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Figure 11 Seismic responses of fixed-base and the base-isolated structure subjected to the El Centroearthquake loads

Figure 12 Seismic responses of fixed-base and the base-isolated structure subjected to the Taft earthquakeloads.



Figure 13 Response of effective coefficient of rolling friction to the El Centro earthquake loads

CONCLUSIONSA base isolation system that incorporates a spring-cam system with a sphericalsupport was developed for earthquake protection of a low-rise building. Thedynamic behaviour of a three-storey concrete structure subjected to the Taft and ElCentro earthquakes was investigated. The results indicated that the measuredmaximum acceleration, displacement and shear forces decreased significantly withthe application of a base isolation system. The decreases were 93%, 24%, and 87%,respectively, for the El Centro earthquake and 93%, 43%, and 94%, respectively, forthe Taft earthquake. The movement of the base relative to the ground was less than0.15 m in the optimized system, and the springs were not fully compressed at anytime during disturbance. The maximum induced vertical forces as a result of theproposed spherical base support were found to be less than 1.5 % of the weight ofthe structure and, consequently, their effect on the structure can be neglected incomparison with the shear forces.

Since the system performance is highly dependent on the rapid unlocking of thecams in the event of a seismic disturbance, careful consideration should be given tothe design of a reliable cam release control. This can be achieved by spring loadingeach cam such that it would be normally unlocked. A hydraulic actuator may beused to force it rotate to the locking position under fluid pressure that would beconstantly maintained at the design level during normal conditions. The actuator canbe equipped with a quick response release valve for rapidly releasing the pressureand consequently unlocking the cam as soon as an earthquake is detected.

REFERENCESAlmazan, J. L., De la Llera, J. C., and Inaudi, J.C., 1998. “Modeling Aspects of

Structures Isolated With the Frictional Pendulum System”, EarthquakeEngineering and Structural Dynamics, Vol. 27, No. 8, pp. 845- 867.

Fujita S., Furuya, O., and Fujita, T., 1994. “Dynamic Tests on High DampingRubber Damper for Vibration Control of Tall Buildings”, FA2-3; First WorldConference on Structural Control, Los Angeles, California, USA.

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Jahilal, P. and Utku, S., 1998. “Active Control In Passively Base Isolated BuildingsSubjected to Lower Power Excitations”, Computers and Structures, Vol. 66,No. 2-3, pp. 211-224.

Jamgid, R.S. and Kelly, I.M., 2001. “Base Isolation for Near-Fault Motions”,Earthquake Engineering and Structural Dynamics Vol. 30, No. 5, pp. 691-707.

Kaplan, H. and Seireg, A., 2000. “A Computer Controlled System for EarthquakeProtection of Structures”, International Journal of Computer Applications inTechnology, Vol.13,No.1-2,pp. 25-41.

Kaplan, H. and Seireg, A., 2001. “Optimal Design of a Base Isolated System for aHigh-Rise Steel Structure”, Earthquake Engineering and StructuralDynamics, Vol . 30, No. 2, pp. 287-302.

Kaplan, H., 2002. “A Computer Controlled System for Earthquake Protection ofStructures”, Ph.D. Dissertation, University of Wisconsin-Madison, Madison,Wisconsin, USA, 519 p.

Kaplam, H. and Seireg, A., 2002. “A Base Isolation system for Bridges Subjectedto Seismic Disturbances”, Earthquake Engineering and Structural Dynamics,Vol. 31, No. 5,pp. 1093-1112.

Kareem, A., 1994. “The Next Generation of Tuned Liquid Dampers”, First WorldConference on Structural Control, Los Angeles, California, USA.

Koike, Y. and Murata T., 1994. ‘ Development of V-Shaped Hybrid Mass Damperand its Applications to High-Rise Buildings’ First World Conference onStructural Control, Los Angeles, California, USA.

Kuroda, T. and Saruta, M., 1989. “Verification Studies on Base Isolation Systems byFull Scale Buildings”, In Seismic, Shock and Vibration Isolation, Chung, H.and Fujita, T. (eds), Vol. 181, ASME, New York pp. 1-8

Lin, T.W., and Hone, C.C., 1993. “Base Isolation by Free Rolling Rods UnderBasement”, Earthquake Engineering and Structural Dynamics Vol. 22, No. 3,pp. 261-274.

Lin, T.W., Chern, C.C., and Hone, C.C., 1995. “Experimental Study of BaseIsolation by Free Rolling Rods”, Earthquake Engineering and StructuralDynamics Vol. 24, No. 12, pp. 1645-1650.

Matlab Version 5 User’s Guide, 2001. Prentice Hall, Englewood Cliffs, New Jersey.

Marano, G.C. and Greco, R., 2003. “Efficiency of Base Isolation Systems inStructural Seismic Protection and Energetic Assessment”, EarthquakeEngineering and Structural Dynamics Vol. 32, No. 10, pp. 1505-1531.

Matheu, E. E., Singh, M.P., and Beathe, C., 1998. “Output-Feedback Sliding-ModeControl with Generalized Sliding Surface for Civil Structures underEarthquake Excitation”, Earthquake Engineering and Structural Dynamics,Vol. 27, No. 3, pp. 259-282.

Mayes, R.L., Jones, R., Bukle, G., and Eeri, M., 1990. “Impediments to theImplementation of Seismic Isolation”, Earthquake Spectra, EarthquakeEngineering Research Institute, Vol. 6, No.2, pp. 245-263.



Mostaghel, N. and Davis, T., 1997. “Representations of Coulomb Friction forDynamic Analysis”, Earthquake Engineering and Structural Dynamics, Vol.26, No. 5, pp. 541-548.

Samali, B., Wu, Y.M., and Li, J., 2003. “Shake Table Tests on Mass Eccentric Modelwith Base Isolation”, Earthquake Engineering and Structural Dynamics Vol.32, No. 9, pp. 1353-1372.

Seireg, A., 1998. “Friction and Lubrication m Mechanical Design”, Mercel Dekker,New York, NY.

Shing, P. B., Dixon, M. E., Kermiche, N., Su, R., and Frangopol M., 1996. “Controlof Building Vibrations with Active/Passive Devices”, EarthquakeEngineering and Structural Dynamics, Vol. 25, No. 10, pp. 1019-1039.

Symans, M.D., 2002. “Base Isolation and Supplemental Damping Systems forSeismic Protection of Wood Structures: Literature Review”, EarthquakeSpectra, Earthquake Engineering Research Institute, Vol. 18, No. 3, pp. 549.

Tzan, S. R. and Pandelides. C.P., 1994. “Hybrid Structural Control UsingViscoelastic Dampers and Active Control Systems”, Earthquake Engineeringand Structural/ Dynamics Vol. 23, No. 12, pp. 1369-1388.

Wang, Y. P and Liu, C. J., 1994. “Active Control of Sliding Structures under StrongEarthquakes”, FP1-23; First World Conference on Structural Control, LosAngeles, California USA.

Wang, Y. P. and Reinhjorn, A. M., 1989. “Motion Control of Sliding IsolatedStructure”, In Seismic, Shock and Vibration Isolation, Chung, H. and Fujita, T.(eds), Vol. 181, ASME, New York.

Yang, Y.B. and Huang, W. H., 1998. “Equipment-Structure Interaction Consideringthe Effect of Torsion and Base Isolation”, Earthquake Engineering andStructural Dynamics Vol. 27, No. 2, pp. 155-171.

Youssef, N., Nuttall, B, Rahman, A., and Hata, O., 1994. “Passive Control of theLos Angeles City Hall”, FP2-54; First World Conference on StructuralControl, Los Angeles, California, USA.

Zhao, B., Lu, X., Wu, M., and Mei, Z., 2000. “Sliding Mode Control of Buildingswith Base-Isolation Hybrid Protective System”, Earthquake Engineering andStructural Dynamics Vol. 29, No. 3, pp. 315-326.

Zhou, Q. and Lu, X., 1998. “Dynamic Analysis on Structures Base Isolated by ABall System with Restoring Property”, Earthquake Engineering andStructural Dynamics, Vol. 27, No. 8, pp. 773- 791.

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APPENDIXMotion of the base and geometric relationships

Figure A-l- Motion of the base and geometric relationships

Figure A-2- Motion of the base on the spherical balls with the concave support

(A-1)

(A-2)

(A-3)



(A-4)

The vertical acceleration:

(A-5)

Total horizontal force at the base

(A-6)

Total vertical force at the base

(A-7)

where n is the number of the spherical balls.

(A-8)

(A-9)

By substituting Equation (A-9) into Equation (A-6),

(A-10)

and H can also be approximated as:

(A-11)

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