EXPERIMENTAL STUDY OF A SEISMICALLY ISOLATED BUILDING STRUCTURE SUBJECT TO TRIAXIAL GROUND MOTIONS

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1 171 EXPERIMENTAL STUDY OF A SEISMICALLY ISOLATED BUILDING STRUCTURE SUBJECT TO TRIAXIAL GROUND MOTIONS Jenn-Shn HWANG 1 And Tng-Yu HSU 2 SUMMARY Un-lateral, b-lateral and tr-axal shakng table tests are conducted to study the sesmc response of a three story base-solated steel structure. The lateral force dstrbuton formulas specfed n the desgn specfcatons are evaluated expermentally. A method to calculate the lateral force dstrbuton s proposed and expermentally verfed. Sesmc responses of the test model to the un-lateral, b-lateral and tr-axal ground exctatons are compared. The effects of vertcal ground acceleraton on the maxmum acceleraton of the superstructure and the maxmum dsplacement of the solaton system are nvestgated. The maxmum dsplacements of the solaton system under b-lateral and tr-axal ground motons are compared wth those determned from the drecton combnaton rule. INTRODUCTION In the past two decades, base-solated structures have been constructed to passvely control ther sesmc response. Extensve studes have been conducted n laboratores to verfy and to enhance the desgn and analyss theores. Numerous shakng table studes for the sesmc responses of base-solated buldng structures have been performed n the past. Kelly et al. [198] have conducted shakng table tests of a base-solated buldng structure wth a fal-safe system on whch the superstructure s carred when the bearngs are dsplaced beyond ther stablty lmt. Kelly et al. [1986] have tested a base-solated rgd block to the roll-over of the lead-rubber bearngs. Grffth et al. [1988] have evaluated the effect of column uplft on the sesmc response of a basesolated buldng. Al-Hussan et al. [1993] have performed a seres of tests on a base-solated buldng wth the frcton pendulum system. Hwang and Ku [1997] have correlated the expermental results of a rgd block solated by hgh dampng rubber bearngs wth those predcted by an analytcal model. However, these shakng table studes are all lmted to un-lateral or un-lateral plus vertcal ground exctatons. In ths study a three story steel structure solated by lead-rubber bearngs and natural rubber bearngs wll be tested usng a three-axs shakng table. Un-lateral, b-lateral and tr-axal ground shakngs wll be used to nvestgate the sesmc responses of the test structure. 2. TEST MODEL AND TEST PROGRAM A three story base-solated steel structure shown n Fg. 1 s assumed to be a.4-scale model. The superstructure s composed of three moment resstng frames n the longtudnal (X) drecton whle two exteror steel dual systems together wth a central moment resstng frame are desgned n the transverse (Y) drecton. Smallest locally avalable rolled sectons are selected for the constructon of the test structure. The superstructure s orgnally desgned as a fxed-base structure accordng to the sesmc desgn specfcatons of buldng structures. 1 2 Professor,, Natonal Tawan Unv of Scence and Tech Nat Center Research on Equake Eng Tawan. JSH@mal.ntust.edu.tw 2. Grad Research Asst, Dept of Constructon Eng, Natl Tawan Unv of Scence and Tech, P.O. Box 9-13, Tape, Tawan

2 A B C 2.2m 2.2m A B C 2.2m 2.2m m 2.m 1.2m 1.2m 1.m H12X12 Typcal Floor Plan Elevaton Frame 1, m 2.m m 2.m 1.2m 1.2m 1.m H1X1 H12X12 1.2m 1.2m 1.m TUBE34. TUBE42.7 TUBE42.7 H12X12 Elevaton Frame B Elevaton Frame A, C Fgure 1: Typcal plan and elevaton of the test superstructure Shear Force (kn) Dsplacement (mm) Dsplacement (mm) Dsplacement (mm) Fgure 2: Typcal hysteress loops from cyclc loadng tests n Tawan [Sesmc 199], and the reducton of force demand due to the ncorporaton of the base solaton system s not consdered. Lead brcks weghng N each are attached to the floors of the test model to smulate the sesmc reactve mass. The weghts from the base floor to the roof are approxmately equal to 113 kn, 92 kn, 92 kn, 7 kn, respectvely. The total weght of the superstructure above the solaton system s estmated to be 367 kn. The solaton system s composed of 8 crcular lead-rubber bearngs and one natural rubber bearng for the tests. The dameter of the crcular lead-rubber bearng s 12 mm. The bearng s composed of 16 rubber layers and 1 steel shm plates. The thckness of each rubber layer s 3. mm and the thckness of the steel plates s 1 mm. The dameter of the lead plug s 2 mm. The dmensons of the natural rubber bearngs are completely the same as those of the lead-rubber bearngs wthout a lead-core. Based on the average axal load exerted on the solaton system by the dead load of the superstructure, an axal load of 4 kn s mposed to each bearng for the performance test conducted n a cyclc manner. Very smlar hysteress characterstcs have been observed for the entre set of lead-rubber bearngs as shown n Fg. 2. Addtonally, some other tests are also conducted wth a varyng axal load. The test results have ndcated that the characterstc strength Q d, effectve stffness K eff and energy dsspaton capacty EDC [Gude 1999] of these lead-rubber bearngs are dependent on the axal load. Ths result s consstent wth what were reported by Tyler and Robnson [1984]. Sx recorded earthquakes shown n Table 1 are used to nvestgate the three dmensonal sesmc responses of the test structure. The superstructure and the solaton system are so arranged to yeld a symmetrc-plan system. Four 2 171

3 tests are conducted for each recorded earthquake. The two horzontal acceleraton components of each earthquake are nput to the shake table separately n the frst two tests, followed by a b-lateral and a tr-axal exctatons. The orgnal tme step of.2 second of all ground motons s scaled to.12 second accordng to the scalng factor of the test model. Table 1: Earthquake records used for shakng table tests Earthquake Names 1% 194 Imperal Valley, El Centro, Irrgaton Dstrc, N-S(X), E-W(Y), up(z) 1% 198 Loma Preta, Captola, Fre Staton, 36 (X), 9 (Y) and up(z) % 199 Hanshn, Kobe, JMA Staton, N-S(X), E-W(Y) and up(z) 12% 1989 Loma Preta,Corraltos, Eureka Canyon Road, 36 (X), 9 (Y) and up(z) 6% 1994 Northrdge, New Hall, 36 (X), 9 (Y) and up(z) 2% 192 Kern Contry, Taft, Lncoln School Tunnel, S69E(X), N21E(Y) and up(z) Dsplacement transducers and accelerometers are nstalled at the corner and center columns of each story of frame A and frame 3 to measure the sesmc responses of the test structure. Nne axal-shear load cells are mounted beneath the solaton bearngs to measure the shear forces and to montor the axal force varaton of the bearngs. 3.1 Un-lateral Tests 3. TEST RESULTS Both the fxed-base and base-solated condtons of the model are tested usng random whte noses to determne ther natural frequences. In order not to cause the yeldng of the lead-rubber bearngs, a small peak ground acceleraton of.3 g s selected for the whte nose ground moton. For the base-solated condton, the frst mode natural frequences determned from the transfer functons are equal to 2.16 Hz, 4.96 Hz and 12. Hz respectvely n the longtudnal (X), transverse (Y) and vertcal (Z) drectons. For the fxed-base model, the frst mode natural frequences are equal to 2.97 Hz and 4.96 Hz correspondng to the longtudnal and transverse drectons. The results from un-lateral tests ndcate that the hysteress loops of all lead-rubber bearngs are not the same or smlar to one another. A typcal example obtaned from the longtudnal test wth the Captola record s shown n Fg. 3 from whch t s seen that the EDC, Keff and Q d of the hysteress loops are qute dfferent. Ths result s not the same as what has been observed from the cyclc loadng tests n whch all lead-rubber bearngs reveal very smlar hysteress characterstcs. The reason for ths dfference may be due to the fact that the statc axal loads exertng on the bearngs under exteror center columns (e.g. the center bearng of frame A) are larger than those on the bearngs under corner columns (e.g. the corner bearng of frame A) The average statc axal loads exertng on the bearngs under the center columns of frames A and C, the center columns of frames 1 and 3, and the corner columns are measured to be equal to 49 kn, kn and 2 kn, respectvely. Snce the shear forcedsplacement relatonshp of the bearngs s dependent on the axal load [Tyler and Robnson 1984], the energy dsspaton of the bearngs under the center columns s larger than that under the corner columns. However, the dependency of the hysteress loops on the axal load s often not consdered n the practcal desgn n whch the hysteress loops of lead-rubber bearngs wth a same lead core dameter and bearng dmenson are usually presumed to be the same. The UBC [unform 1997] has requred desgn engneers to consder the effect of axal load when modelng the behavor of solaton bearngs for a dynamc tme hstory analyss. However, dffcultes arse from the fact that the leadrubber bearngs from dfferent manufacturng processes or manufacturers may reveal dfferent axal load dependency. From ths nvestgaton, t s concluded that the effect of the axal load on solaton bearngs nstalled at dfferent locatons of a base-solated structure should be consdered for practcal desgn. In addton to the aforementoned, the hysteress loop of each bearng shown n Fg. 3 s not skew-symmetrc as what has been seen from the cyclc loadng test result. Ths s because the overturnng moment of the superstructure undergong a ground exctaton has ntroduced an axal load varaton nto the bearngs. For example, dscrepancy s observed between the traces a - b - c and c - d - e of the hysteress loops of the center 3 171

4 bearng of frame A as shown n Fg 3(b). Correspondng to these two loop traces, the axal load on the bearng s, ' ' ' ' ' varyng from traces a - b - c to c - d - e as shown n Fg.3(c). Snce the loadng varaton trace c ' ' ' - d - e shows ' ' ' an ncrease on the compressve axal load whle the load loadng varaton trace a - b - c depcts a decrease on the compressve axal load, the area encased n the loop trace c - d - e s larger than that covered by the loop trace a - b - c. The effect of axal load nduced by the overturnng of the superstructure should also be consdered n the practcal analyss. Shear (kn) Dsplacement (mm) Shear (kn) d e Dsplacement (mm) a c b Varaton of Axal Force (kn) 4 3 d' 2 c' 1 a' e' -2 b' TIME (sec) Fgure 3: (a) Hysteress loops of corner bearng; (b) Hysteress loop of center bearng and (c) axal load varaton on the center bearng From un-lateral tests, the normalzed peak story acceleraton wth respect to the maxmum shakng table acceleraton s shown n Fg. 4. In the follows, these maxmum story acceleratons and dsplacements ncludng those measured at the base floor wll be used to correlate the expermental results wth the lateral force dstrbuton formulas gven n the current desgn specfcatons such as UBC [Unform 1997]. The lateral force dstrbuted over the heght of the structure above the solaton nterface s specfed by the UBC as wxhx Fx = Vs (1) n Σ w h =1 where V s = the mnmum force should be consdered for the desgn of the superstructure above the solaton nterface, whch s determned from dvdng the maxmum base shear force transmtted by the solaton system, V b, by a reducton factor R I ; w, w x = the weght located at story level or x ; and h, h x = the heght of story level or x above the base floor. Accordng to the formula, two anomales arse: (1) The formula was adopted based on an assumpton that the frst mode shape of an elastc mult-story fxed-base buldng structure can be approxmately proportoned by the heght of the story level above the base [Chopra 199]. Ths assumpton s recognzed to be acceptable for most mult-story fxed-base buldng structures, because the desgn base shear force V s s obtaned by reducng the elastc base shear force by a factor such as R w of UBC. However, for a base-solated structure, the total lateral force V s s calculated based on a reducton on the nelastc desgn base shear force V b whch s determned from an equvalent lnear analyss procedure [Hwang and Chou 1996]. The equvalent lnear analyss s adopted accordng to the recognton that the maxmum nelastc dsplacement response of a structure can be approxmated by the maxmum elastc dsplacement response obtaned from an equvalent lnear system. Therefore, the frst mode shape of a base-solated structure may not be able to be represented by the proporton of the story heght as what s usually done for a fxed-base buldng structure; and (2) As can be seen from Eq. (1) where the ndex s startng from = 1, the nerta force exertng on the base floor should be excluded from the total base shear force V b when calculatng the desgn base shear force of the superstructure V s. However, accordng to UBC, the desgn base shear force exertng on the superstructure s obtaned by drectly reducng the nelastc base shear force transmtted the solaton system V b by an R I factor. The nerta force on the base floor s not excluded. To llustrate these aforementoned dscussons, the measured base shear force n the solaton system s substtuted for V s of Eq. (1) (.e. R I s set to 1) and the calculated acceleraton dstrbutons are compared wth those measured from the tests n Fg. 3. From the fgure, t s clear that the predcted dstrbutons of the peak story acceleraton are qute dfferent from the measured dstrbutons both n shape and n magntude. In ths study, a procedure to calculate the lateral force dstrbuton on a base-solated buldng structure wll be proposed n the follows. The procedure does not follow the UBC formula n whch the desgn base shear force of the superstructure s calculated by reducng the maxmum nelastc shear force of the solaton system by a 4 171

5 reducton factor. Instead, the lateral force dstrbuton on the whole base-solated structure ncludng the base floor s calculated frst based on the maxmum nelastc shear force transmtted by the solaton system. Then, the lateral force exertng on the superstructure may be reduced by R factor f desred. For dong so, t s ntended frst to ascertan whether the dstrbuton of the maxmum lateral story dsplacements can be used to calculate the lateral force dstrbuton as what s usually done for an elastc fxed-base structure. The followng formula s proposed to calculate the lateral force dstrbuton and to correlate wth the expermental results wx x Fx = Vb (2) n Σ w = where V b = the total base shear force transmtted by the solaton system;, x = the relatve dsplacement of each story ncludng the base floor to the ground. For =, w = the weght of the base floor and = the relatve lateral dsplacement of the solaton system to the ground whch s the desgn dsplacement of the solaton system denoted as D D n the UBC. Usng Eq. (2) and the measured maxmum story dsplacements, the lateral acceleraton dstrbuton of the test structure subjected to varous ground motons can then be calculated. From Fg. 4, t s seen that the calculated maxmum story acceleratons compare well wth the measured peak story acceleratons. Therefore, t can be concluded that, even though the sesmc response of a base-solated structure s nelastc, the maxmum story dsplacement can be used as the mode shape to calculate the lateral force dstrbuton as what s usually done for an elastc fxed-base structure. One should be cautous that the weght and the lateral dsplacement of the base floor are nvolved n the above calculaton usng Eq. (2). However, n the practcal desgn, these story dsplacements except the relatve dsplacement (or desgn dsplacement) of the solaton system s not known pror to the calculaton of the lateral force dstrbuton. In order to facltate the procedure for practcal analyss, t s proposed that the story dsplacements and x can be calculated pror to the determnaton of the lateral force dstrbuton usng the total base shear force V b and a assumed lateral force dstrbuton gven by wx f x = Vb (3) n Σ w = n whch f x = the assumed lateral force dstrbuton to calculate the lateral dsplacement and x. Usng Eq. (3), the story dsplacement can then be calculated usng a smple elastc analyss. Ths s because the total base shear force and the maxmum nelastc dsplacement of the solaton system predcted by Eq. (3) are exactly equal to V b and D D so that the stffness of the solaton system can be represented by the effectve stffness. Based on Eqs. (2) and (3), the correlaton between the calculated results and the expermental results s K eff shown n Fg. 4. From ths fgure, t suggests that the proposed procedure be adopted for the calculaton of the lateral force dstrbuton of a base-solated buldng. Once the lateral forces on the superstructure s determned, I Roof Measured Eq. (2) Proposed UBC Code (a) (b) (c) 2nd sotry 1st story they can be reduced by R I, f desred, to obtan the desgn force of the superstructure. Fgure 4: Measured and predcted normalzed story acceleraton (a) El Centro test; (b) Captola test; and (c) Newhall test 3.2 B-lateral and Tr-Axal Tests Base Ground Normalzed Peak Story Acceleraton 171

6 Among the b-lateral and tr-axal test results, the peak story acceleraton and the maxmum dsplacement of the solaton system are of partcular nterest. Ths s because the peak story acceleraton s related to the nerta force exertng on the superstructure and the maxmum dsplacement of the solaton system s mportant for the desgn of the solaton bearngs, utltes and gaps. The normalzed peak story acceleratons measured n the longtudnal drecton reveal that the dfference among the un-lateral, b-lateral and tr-axal test results s nsgnfcant. Ths may be explaned by the fact that, under b-lateral and tr-axal exctatons, the solaton bearngs may yeld n any lateral drecton once the total shear force reaches the yeld surface of the bearngs. When the lead-rubber bearngs yeld, the solaton effect commences and the transmsson of the ground acceleraton nto the superstructure s lmted. Thus, the maxmum longtudnal or transverse acceleraton component s not necessary to be larger that of the un-lateral tests. On the other hand, the maxmum dsplacements of the solaton system determned from the un-lateral tests, blateral tests, tr-axal tests and drecton combnaton rule are summarzed n Tables 2 and 3 n whch ( U bx ) max = the maxmum relatve dsplacement of the solaton system measured from the un-lateral tests n the longtudnal (X) drecton; ( U by ) max = the maxmum relatve dsplacement of the solaton system measured from the un-lateral tests n the transverse (Y) drecton; and ( U b ) max = the maxmum relatve dsplacement of the solaton system n any horzontal drecton measured from the b-lateral or tr-axal tests. From Table 2, t s nterestng to note that the maxmum dsplacement responses of the solaton system measured from the b-lateral and tr-axal tests are not necessary smaller than those determned from the drecton combnaton rule. Earthquake Records Table 2: Measured maxmum dsplacement of solaton system Un-Lateral Un-Lateral B-Lateral Tr-axal ( U ) bx max Occurng Tme ( U ) by max Occurng Tme ( U ) bx max Occurng Tme ( U ) bx max Occurng Tme (mm) (sec) (mm) (sec) (mm) (sec) (mm) (sec) Captola Corraltos El Centro Kobe Newhall Taft Table 3: Calculated maxmum dsplacement of solaton system usng rule Earthquake Records rule U +.3 ( U ) by max.3 ( U ) bx max + ( U ) by max ( bx ) max (mm) (mm) Captola Corraltos El Centro Kobe Newhall Taft

7 Y Dsplacement (mm) X Dsplacement (mm) Y Dsplacement (mm) X Dsplacement (mm) (a) (b) Fgure : Dsplacement traces of solaton system from Captola test (a) b-lateral and (b) tr-axal For example, the maxmum dsplacements measured from the tr-axal tests of the Captola and Taft records are about 1% larger than those obtaned from the combnaton rule. Therefore, the desgn dsplacement of the solaton system determned usng the drecton combnaton rule may not be conservatve. In addton, t s also seen from the table that the maxmum dsplacements of the solaton system measured from the tr-axal tests are all slghtly larger than those from the b-lateral tests. In partcular, the tr-axal test wth the Captola record has generated a maxmum dsplacement at the solaton bearngs 1% larger than that of the correspondng b-lateral test. Fg. shows the comparson between the dsplacement traces of the solaton system measured from the b-lateral and tr-axal tests of the Captola record. From the comparson, the effect of vertcal ground acceleraton may have to be carefully consdered when determnng the maxmum dsplacements of the solaton system. 4. CONCLUSIONS Based on the three-dmensonal shakng table tests of a.4-scale three story base-solated steel structure, some conclusons of sgnfcance are drawn n the follows: (1) Under a un-lateral exctaton, the effects of the axal force varaton of the lead-rubber bearngs have to be carefully consdered for desgn. The axal force varaton may be nduced by the dead load dstrbuton on the bearngs at dfferent locatons n the buldng, the overturnng moment of the superstructure and the exctaton of the vertcal ground acceleraton. (2) A method dfferent than what have been specfed n the current desgn practces has been proposed to calculate the lateral force dstrbuton on the superstructure. The approprateness of the proposed method s verfed by the experment. (3) The results from the b-lateral and tr-axal tests have ndcated that the maxmum dsplacement determned from the drecton combnaton rule may not be conservatve. ACKNOWLEDGEMENTS The study s supported by the Natonal Scence Councl of Tawan under grant No. NSC Z The support s acknowledged. The authors also lke to thank the Natonal Center for Research on Earthquake Engneerng for provdng the expermental facltes for conductng ths research. REFERENCES Al-Hussan, T.M., Zayas, V.A. and Constantnou, M.C. (1994). Sesmc solaton of mult-story frame structures usng sphercal sldng solaton system. Report No. NCEER-94-7, Natonal Center for Earthquake Engneerng Research, Buffalo, New York. Chopra, A.K. (199). Dynamcs of structures theory and applcatons to earthquake engneerng. Prentce Hall, Englewood Clffs, New Jersey

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