HIGHER MODE EFFECT ON LATERAL FORCE DISTRIBUTIONS FOR BASE-ISOLATED STRUCTURES

Transcription

1 3 t World Coferece o Eartuake Egeerg acouver, B.C., Caada Augut -6, 004 Paper o. 736 IGER MODE EECT O LATERAL ORCE DISTRIBUTIOS OR BASE-ISOLATED STRUCTURES C. S. Ta, Bo-Je Ce, Tu-Ceg Cag 3, We-Se Pog 4 SUMMARY Te ue of te ae olator to legte te atural perod of a tructure for reducg te trao of eergy fro te groud to te tructure a ee recogzed a a effectve ea y te egeerg profeo eartuake proe rego. Te ec deg of ecally olated tructure aly govered y te Ufor Buldg Code (UBC-97). Te UBC code upple a ple, tatcally euvalet deg etod ere y dplaceet for a olated tructure are cocetrated at te olato level. Terefore, te upertructure early ove a a rgd ody, ad te deg force of eleet aove olator are aed o te eavor of olator at te deg dplaceet. oever, te UBC code, te dtruto of ertal (or lateral) force over te egt of te upertructure aove olato a ee foud to e over-coervatve for ot olated tructure. I t paper, four ple ad reaoale deg forulae, aed o te frt ode of te ae-olated tructure, for te lateral force dtruto o te olated tructure ave ee valdated y ae-olated teel tructure teted o te akg tale. Moreover, to ota ore accurate reult for rregular tructure c ger ode cotruto are ore lkely epected durg eartuake, aoter four ertal force dtruto forulae are alo propoed to clude te ger effect t paper. Bede te eperetal verfcato troug akg tale tet, te recorded floor accelerato of te USC Uverty optal durg te ortrdge eartuake ere alo adopted to vetgate te utalty of te propoed deg forulae coderg te ger ode effect. ITRODUCTIO Profeor, Departet of Cvl Egeerg, eg Ca Uverty, Tacug, Taa, R.O.C.. Eal:cta@fcu.edu.t P. D., Atat Reearc ello, Eartuake Proof Syte, Ic., Tacug, Taa, R.O.C.. E-al:jc@url.co.t 3 P. D. Caddate, Graduate Ittute of Cvl & ydraulc Egeerg, eg Ca Uverty, Tacug, Taa, R. O. C.. E-al:rckcag00@yaoo.co.t 4 Atat Profeor, Scool of Egeerg, Sa racco State Uverty, U.S.A.. E-al:pog@fu.edu

2 Te ec upgrade deg of ecally olated tructure aly govered y te Ufor Buldg Code (recetly edto UBC-97) puled y te Iteratoal Coferece of Buldg Offcal (ICBO) [-3]. Te UBC code epaze tat te dplaceet for a ae-olated tructure are cocetrated at te ae olato level, ad tat te upertructure alot ove a a rgd ody ad deged for force calculated ug te effectve tffe of te olato yte at te deg dplaceet. A euvalet tatc aaly procedure ay e ued for degg te earg ad te upertructure. evertele, te dtruto of lateral deg force over te egt of te upertructure propoed te UBC-97 o te a of a verted tragular force dtruto tat geerally ued for fed-ae tructure. T dtruto a ee foud to e te oud repoe of ot olated tructure coervatvely, eve e ger ode are ected y yteretc eavor or large value of effectve dapg of te olato yte [3]. I recet year, t dtruto of ertal (or lateral) force over te egt of te upertructure aove olato a ee foud to e te oud repoe of ot olated tructure coervatvely, eve e ger ode are geerated y olearte, large value of effectve dapg or te effect of frcto te olato yte. Ta et al. [4-5], aalytcally aed o te frt ode of te ae-olated tructure tout cople calculato, ave propoed to ple ad reaoale deg forulae for te lateral force dtruto o a olated tructure. Tee to propoed deg forulae aue tat te vertcal dtruto of erta force o a olated tructure ould e a fao of te frt ode of te aeolated tructure rater ta a verted tragular force dtruto uggeted y te UBC code. urterore, te UBC code, te egt of te ae floor gored, c ll overetate te ertal force ad au aolute accelerato o eac floor. Te propoed deg forulae y Ta et al. [4-5] alo reaoaly corporate te fluece of te ertal force o te ae floor to calculate accurately te vertcal dtruto of ertal force o a ae-olated tructure. I t paper, to ota ore accurate reult for rregular tructure c ger ode repoe are epected durg eartuake, tere are aoter four ertal force dtruto forulae propoed y coderg ger ode of te ae-olated tructure ad te upertructure aed o te teory of tructural dyac [6-0]. Te effect of te frt to ode of te ae-olated tructure ad te upertructure are cluded to prove accuracy of te lateral force dtruto tout urrederg plcty. To copare te lateral force dtruto coputed fro te propoed deg forulae ad UBC code provo, te eperetal verfcato of a ultple-ay ae-olated teel tructure te akg tale tet at te atoal Ceter for Reearc o Eartuake Egeerg Taa a ee carred out []. Bede te eperetal verfcato troug akg tale tet, te recorded floor accelerato of te USC Uverty optal durg te ortrdge eartuake ere alo adopted to vetgate te utalty of te propoed deg forulae coderg ger ode effect t paper [-3]. LIEAR TEORY O BASE-ISOLATED STRUCTURES I order to ga gt to te eavor of ae-olated tructure, te lear teory of ae olato a already ee developed y J. M. Kelly ug a ple -DO odel t lear prg ad lear vcou dapg [6-7]. A o g., oe te degree of freedo of te upertructure, ad te oter te degree of freedo of te ae olator. T -DO yte ca e olved troug odal decopoto to provde gt to te repoe of ae-olated tructure. Te euato of oto rtte a atr otato M& C& K Mr & () u& g

3 ere ad alo M c 0 k 0 M $ C $ K () 0 c 0 k M v v $ r 0 (3) $ v u u g $ v u u (4) ere ad repreet te a of te upertructure (.e., tout ae la) ad te a of te ae floor, repectvely; c ad k are te lear vcou dapg coeffcet ad effectve tffe of te ae olator, repectvely; c ad k depct te dapg coeffcet ad tffe of te upertructure, repectvely; u, u ad u g deote te aolute dplaceet of te upertructure, ae olator ad te groud, repectvely; M dcate te total a of te upertructure plu tat of te ae floor; v repreet te tertory drft of upertructure; v llutrate te olato yte dplaceet relatve to te groud. If te upertructure ove a a rgd ody, te atural freuecy of te olated tructure ca e gve y: M (5) Te atural freuecy of te fed-ae tructure (.e., tout ay olato yte) (6) To portat paraeter are defed a, (7) M Moreover, te dapg factor β ad β gve y c c β, β (8) M Wt te ad of E. () ad (), te aalytcal oluto of atural freuece of te ae-olated tructure ca e gve y [6-7]: ( ), ( ) (9) ad ode ape are, k k (0) ( )

4 If <<, E. (0) ca e rertte a [6-7]:, [ ( ) ] () A o g., te upertructure early ove a a rgd ody te frt ode ape ; erea te ecod ode ape, te dplaceet of te upertructure ad te ae olator are oppote drecto. We te to ode, ad, are otaed, relatve dplaceet, v ad v, ca e rtte a v, v () ere, are te-depedet odal coeffcet. I ot tructural applcato t aued tat te dapg all eoug ad tat effect of te offdagoal copoet eglgle. Te atr euato () reduce to [6-7] && & L u& β g (3) && & L u& β g (4) ere / 3 β β β β, β (5) / ( ) ad te partcpato factor, L ad L, for te frt to ode tee euato are gve y [6-7] L, L (6) Te, te au value of ad ca e gve y L S (, β ) a D, L S (, β ) a D (7) ere S D (, β ) te dplaceet repoe pectru for te groud oto, u& & g, at freuecy ad dapg rato β. If oe oralze te ode ape of tertory drft of te upertructure eual to. A o g. 3, t te ad of E. (0), te te ode ape of te -DO odel ca e gve y ( ), (8) Te vector of euvalet tory ear force ca e rtte, aed o te teory of tructural dyac, a [8] f M a f

5 M a M ( ) a ( C D ) ( ( C ) ( D ) ) a ( ( C ) ( D ) ) a a a a ere C (f << ) (0) ( ) D [ ( ) ] (f <<) () [ ( ) ] ere f ad f repreet te ae ear ad tory ear force, repectvely. a RATIOAL DESIG ORMULAE OR ERTICAL DISTRIBUTIO O LATERAL ORCES I te UBC code, te lateral force are aued to e dtruted over te egt of te upertructure aove te olato terface accordace t te forula [-3]: () depct te erta force at level aove te olato level; ad repreet te egt at level ad level, repectvely;, are te egt of te t ad t tory aove te olato, repectvely; te lateral ec ear force; te total uer of tore of te upertructure. Te upertructure aove te olato yte deged ad cotructed to ttad a u ear force,, ug te forula ere (9) (3) RI K D (4) D, a repreet te deg force for te upertructure ad te eleet elo te olato terface; D D depct te deg dplaceet of ae olato; K te au effectve tffe of te ae D, a olator at te deg dplaceet; R I portray te deg force reducto factor (ductlty factor), c teded to accout for te elatc repoe te upertructure. It evdet tat E. () lead to a tragular vertcal dtruto of te erta force over te egt of te upertructure. urterore, te erta force o eac floor aove te ae floor coputed fro E. () ee to e overetated ecaue te egt of te ae floor eglected. I ve of t, Ta et al. [4-5] ave propoed to ratoal ad ple deg forulae for te vertcal dtruto of te lateral D

6 force over te egt of te upertructure le oly coderg te fluece of te frt ode of te ae-olated tructure. Te erta force at eac floor gve a (a o g. (a)) [4-5] 0 (5) ad ( ) [ ] ( ) [ ] 0 (6) ere (ee E. 7) te rato of atural freuece, ad alo repreet te rato of te dplaceet at te top of upertructure relatve to te ae floor to tat of te ae floor (ee g. (a)); repreet te total egt of te ae-olated tructure aove olato level; ( ) repreet te frt ode ape of te fed-ae tructure (.e., tout ay olator); ( ) ad ( ) decre te value of te frt ode ape at level ad level, repectvely, e te upertructure rgdly fed. It ould oted tat te value of te frt ode ape at te top of te upertructure, ( ), ould e oralzed ad eual to. Moreover, f ger order ter of ad value are codered, E. (5) ad (6) ca e rertte a: 0 (7) ad ( ) ( ) 0 (8) IGER MODE EECTS O ERTICAL DISTRIBUTIOS O LATERAL ORCES Te aforeetoed four deg forulae ca ota atfactory predcto of te vertcal dtruto of erta force uder cae otly retrcted to te upertructure tat are alot rgd ody oto ad tat te freuece of te frt ad ecod ode o olated tructure are ell-eparated. Up to o, o ay reearcer accout for te cotruto of ger ode to te lateral force dtruto of aeolated tructure f te upertructure rregular or uyetrcal ad te tructural yte are full of varete. To overcoe tee lato, utale vertcal dtruto forulae for erta force y coderg te ecod ode cotruto of a ae-olated tructure are propoed t paper. Wt te ad of E. (9), to deg forulae are gve a:

7 ( ) ( ) 0 a a a a (9) ad ( ) ( ) ( ) ( ) ( ) ( ) 0 a a a a (30) ere te au value of ad ca e otaed y uercal aalye [8]. I E. (9) ad (30), oe cooe te ae g of ad to eure te flelty of te upertructure, ad t alo cofored to actual vertcal dtruto of erta force o olated tructure. Moreover, E. (8) ad (30), oe ca preue tat te deflected ape of te upertructure relatve to te ae floor te frt ode ape ( ) of te fed-ae tructure (.e., tout ay olator). oever, uc atfactory predcto are retrcted to ore lke regular tructure. It very a portat ue for a rregular tructure to reaoaly redtrute erta force o te upertructure y coderg te cotruto of ger ode o te upertructure [9]. To overcoe tee ltato, everal reearcer ave propoed adaptve force dtruto to provde etter etate of te fed-ae tructure [9-0]. Copra ad Goel [9] ave developed a proved odal puover aaly (MPA) procedure. Ja et al. [0] ave propoed a alteratve etod to ply etate te lateral force dtruto of g-re uldg y cog cotruto fro te frt ad ecod ode. Baed o propoed deg forulae for te fed-ae tructure y Copra [8-9] ad Ja et al. [0], oe ca coe te frt- ad ecod-ode cotruto to ota a dtruto vector of te lateral force of te upertructure, ad te dtruto vector copoet gve a [8-0]: ( ) ( ) ( ) ( ) a a a a α $ ( to ) (3) ere ad depct te frt- ad ecod-ode atural freuece of te fed-ae tructure, repectvely; ad decre te egt at level ad level, repectvely; ( ) ad ( ) repreet te frt- ad ecod-ode ape of te fed-ae tructure at level, repectvely; ( ) ad ( ) are te frt- ad ecod-ode ape of te fed-ae tructure at level ad are oralzed to. It ould oted tat te value of te vector copoet at te roof level, α, ould e eual to ; ad ( ) ( ) a a,, ξ ξ D D Γ Γ (3)

8 ere te t-ode partcpato factor, ere ( ) Γ, gve y [8-0] T ( ) ν ( ) T ( ) Γ (33) dcate te t-ode ape of te fed-ae tructure; repreet te a atr of te fed-ae tructure; D repreet te t-ode pectral dplaceet; ξ deote te t-ode dapg rato of te fed-ae tructure; ν depct te fluece vector. If oe oly coder te fluece of te frt ode of te ae-olated tructure ad ultaeouly coder te frt- ad ecod-ode cotruto of te upertructure, te deg forula gve a: α (34) α 0 Bede, to ota ore accurate reult, oe ca take to accout te fluece of te ecod ode of te ae-olated tructure ad te ger ode cotruto of te upertructure, ad te deg forula ca e epreed a: ( ) a α α a (35) ( ) a α α 0 a EXPERIMETAL ERIICATIO OR A MULTIPLE-BAY BASE-ISOLATED STRUCTURE I order to verfy te accuracy ad utalty of propoed deg forulae coderg ger ode cotruto of te olated tructure, a ere of akg tale tet of a ultple-ay olated tructure ere carred out, ad gve a a eaple to vetgate te dtcto aog tee propoed deg forulae, te UBC code provo, ad eperetal reult. A o g. 4 ad 5, a 40% cale tree-tory ae-olated teel tructure cotructed a a oet-retg frae. Te tructure ued for outg ae olator rectagular ape, rg 4.5 vertcally ad occupyg a plae of orzotally. Te egt fro te ae floor to te roof ere approately etated eual to 08, 93, 93, ad 85k, repectvely. Te olato yte a copoed of fve laated ruer earg (RB) ad four trrup ruer earg (SRB) [], a o g. 5. gure 6 o tat te type of laated ruer earg teted 46 daeter ad 84 egt. Tey cot of 0 ruer layer of 5 tcke eac, 9 teel plate of tcke eac ad 3 ruer cover, ad eac ed plate.5 tck t olted coecto. gure 7 o tat te type of trrup ruer earg (oted a SRB) teted alo 46 daeter ad 84 egt. Eac earg cot of a lup of ruer ateral of 54 tcke, 4 eteral teel rg of 6, 3 ruer cover, ad a plate of 5 tcke at eac ed t olted coecto. Te SRB earg reearc coducted y Ta Taa, eperetal eaato va te copoet ad akg tale tet, dcate tat te SRB earg poee ger dapg rato at ger tra, ad loer orzotal effectve tffe ta oter kd of ruer earg eve e te vertcal aal load lgt.

9 Te ae-olated tructure a ujected to te 940 El Cetro eartuake U. S. A. ad te 995 Koe eartuake Japa. Te frt to atural freuece are.9z ad.9z te logtudal drecto of te tructure tout olator. Te a rato ( M ) eual to I t tudy, te a goal of eperet to proe to te vertcal dtruto of lateral force ad verfy te e propoed deg forulae coparo t te UBC code provo. Terefore, te deg force reducto factor R I ot cluded (.e., R I ) t tudy. Te agtude of te ( ) value troug te akg tale tet are 0.5 ad 0.38 durg te El Cetro ad Koe eartuake, repectvely. It o te effectvee of te ruer earg outed o t tree-floor teel frae. Tale ad dplay te coparo of reult coputed fro te propoed deg forulae, te UBC code provo, ad te eperetal tude te logtudal drecto of te ae-olated frae durg te El Cetro ad Koe eartuake. It llutrated tat te propoed deg forulae ca ell predct te vertcal dtruto of te peak accelerato o te olated tructure durg eartuake. I te UBC code, te egt of te ae floor gored, c ll overetate te au aolute accelerato o ger floor. gure 8 ad 9 depct te oralzed peak accelerato o eac floor calculated y E. (5) ad (35), te forula provded y te UBC code, ad eperetal reult troug akg tale tet. ro tee fgure, t prove tat reult otaed fro propoed deg forulae are good agreeet t te eperetal reult. Moreover, t ll e ore accurate y coderg ger ode effect of te ae-olated tructure ad te upertructure. ERIICATIO O PROPOSED ORMULAE TROUG RECORDED DATA I addto to te eperetal verfcato, recorded floor accelerato for te Uverty optal of te Uverty of Souter Calfora durg te 994 ortrdge eartuake, a o g. 0 ad [-3], are adopted to vetgate dtcto aog te propoed deg forulae, UBC code provo, ad recorded data. Te peak free-feld ad peak foudato accelerato te ort-out drecto ere 0.49g ad 0.37g, repectvely. Te au floor accelerato ere recorded at te ae ad te roof of te optal to e 0.3g ad 0.g, repectvely. Te peak floor accelerato ere alo recorded at te 4t floor ad 6t floor to e 0.0g ad 0.g, repectvely. I t tudy, lear terpolato utlzed to ota oter floor accelerato tout truetato. Te a fro te ae floor to te roof ere eual to 33.75, 4.874, 3.709,.354,.33,.46, 9.769, 8.897, 0.94 kp ec /, repectvely. Te frt to atural freuece are approately.93z ad 4z te ort-out drecto of te fed-ae USC Uverty optal. Te a rato ( M ) eual to 0.74, ad te agtude of te ( ) value eual to 0.5. Tale 3 et te coparo of reult calculated fro te UBC code provo, te propoed deg forulae, ad te recorded accelerato data te ort-out drecto of te USC Uverty optal. It llutrated tat te vertcal dtruto of peak accelerato coputed y propoed deg forulae are good agreeet t te recorded floor accelerato. gure llutrate te oralzed peak accelerato o eac floor calculated y E. (5) ad (35), te forula provded y te UBC code, ad te recorded accelerato data. It deotrate tat te propoed deg forulae ca ell predct te vertcal dtruto of peak accelerato actual eartuake. We te ger ode effect codered, etter agreeet t te recorded data oerved. urterore, t alo deotrate tat te accelerato at eac floor calculated y te UBC code provo a ee foud to e dtct coderaly cotrat t te recorded accelerato data ad too coervatve.

10 COCLUSIOS Te deg of ecally olated tructure aly govered y te Ufor Buldg Code (UBC) puled y te Iteratoal Coferece of Buldg Offcal. evertele, te vertcal dtruto of lateral force over te egt of te upertructure te UBC code provo o te a of a verted tragular force dtruto. It a ee foud to e te oud repoe of ot olated tructure coervatvely, eve e ger ode cotruto are geerated. Te deg forulae propoed t paper ca reaoaly corporate te fluece of te ertal force o te ae floor to accurately calculate te lateral force dtruto o olated tructure va te verfcato of te eperetal ad recorded data. Meale, te propoed deg forulae coderg ger ode effect are good agreeet t te actual vertcal dtruto of lateral force o rregular ae-olated tructure. ACKOWLEDGEMET Specal tak gve to te atoal Scece Coucl, Taa, R. O. C., for facal upport for t reearc (SC 90--E ). Te atace fro te atoal Ceter for Reearc o Eartuake Egeerg Taa ad KP Coultg Egeerg U. S. A. are apprecated. REERECES [] Ufor Buldg Code, Iteratoal Coferece of Buldg Offcal, Wlter, Calfora, 997. [] ERP Gudele for te Sec Realtato of Buldg, ederal Eergecy Maageet Agecy, EMA-73, 993. [3] ERP Gudele for te Sec Realtato of Buldg, ederal Eergecy Maageet Agecy, EMA-74, 994. [4] C. S. Ta, Bo-Je Ce ad Tu-Ceg Cag Eperetal ad Coputatoal erfcato of Reaoale Deg orulae for Bae-Iolated Structure. Eartuake Egeerg ad Structural Dyac, ol. 3, [5] C. S. Ta, Bo-Je Ce ad Tu-Ceg Cag Reaoale Lateral orce Dtruto o Iolated Structure. Te 00 ASME Preure eel ad Ppg Coferece, Sec Egeerg 00, acouver, Brt Colua, Caada, ol., pp. 9-36, Augut 00. [6] Jae M Kelly Eartuake-Retat Deg t Ruer. Secod Edto, Sprger-erlag, Lodo, 997. [7] arzad ae ad Jae M. Kelly Deg of Sec Iolated Structure: ro Teory to Practce. Jo Wley & So, Ic., 999. [8] Al. K. Copra Dyac of Structure: Teory ad Applcato to Eartuake Egeerg. Pretce-all, Ic., 995. [9] Al. K. Copra ad Rake K. A Modal Puover Aaly Procedure for Etatg Sec Dead for Buldg Eartuake Egeerg ad Structural Dyac, ol. 3, pp , 00. [0] T. S. Ja, M. W. Lu ad Y. C. Kao Puover Aaly ad Sec of Structure to ear ault Eartuake. A Reearc Report of atoal Coucl of Taa, Report o: SC 90--E , Sept. 00. [] C. S. Ta, Bo-Je Ce, Tu-Ceg Cag ad Gua-g Lee Eperetal Study of a Multple Bay Structure Iolated Wt yrd Bearg. Te 003 ASME Preure eel ad Ppg Coferece, Sec Egeerg 003, Clevelad, Oo, U.S.A., pp , July 003. [] Jeffero W. Aer, Davd R. a olkurg, Roald L. Maye, Trevor Kelly, Bjor I Sveo ad Saf ua Sec Iolato Deg of te USC Uverty optal Proceedg of ourt U.S. atoal Coferece o Eartuake Egeerg, Pal Sprg, Calfora, U. S. A., ol. 3, May, 990. [3] Petro Koodroo Sec Iolato for Eartuake-Retat Structure. WIT Pre, Soutapto, Boto.

11 Ta. Accelerato Coparo of Reult Otaed fro Propoed Deg orulae, UBC Code Provo, ad Eperet Logtudal Drecto of Bae-Iolated Structure durg El Cetro Eartuake Ut: g Ta. Accelerato Coparo of Reult Otaed fro Propoed Deg orulae, UBC Code Provo, ad Eperet Logtudal Drecto of Bae-Iolated Structure durg Koe Eartuake Ut: g

12 Ta. 3 Accelerato Coparo of Reult Otaed fro Propoed Deg orulae, UBC Code Provo, ad Recorded Accelerato Data ort-sout Drecto of USC Uverty optal durg Groud Moto Bae E. (5) E. (6) E. (7) E. (8) E. (9) E. (30) E. (34) E. (35) UBC Code Recorded Data /A Ut: g g. To-Degree-of-reedo Bae Iolato Syte (a) () g. 3 Mode Sape of To-Degree-of-reedo Bae Iolato Syte (a) () g. Mode Sape of To-Degree-of-reedo Bae Iolato Syte g. 4 Teted Bae-Iolated Structure

13 Roof 3 A,50 B,50 C 50X50X9X4 5X60X6X8,000 Bae 90X0 L90,000 Groud UBC E. (5) E. (35) Eperet RB SRB Bae loor Ut : g. 8 Coparo of oralzed Peak Story Accelerato of Multple-Bay Iolated Steel Structure uder El Cetro Eartuake (PGA0.600g) g. 5 Locato of Ruer Bearg Roof 40 Ut:.5 Bae oud g. 6 Sceatc of Laated Ruer Bearg (RB) 46.5 Gr UBC E. (5) E. (35) Eperet g. 9 Coparo of oralzed Peak Story Accelerato of Multple-Bay Iolated Steel Structure uder Koe Eartuake (PGA0.7008g) 40 Ut: g. 7 Sceatc of Strrup Ruer Bearg (SRB) g. 0 USC Uverty optal loorpla

14 Bae Groud UBC E. (5) E. (35) Recorded g. Recorded loor Accelerato of USC Uverty optal g. Coparo of oralzed Peak Story Accelerato of USC Uverty optal uder 994 ortrdge Eartuake