On the weak storey behaviour of concentrically braced steel frames

Transcription

1 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 Porto, Portugal, 0 June - July 0 A. Cunha, E. Caetano, P. Rbero, G. Müller (eds.) ISSN: -900; ISBN: On weak storey behavour of concentrcally braced steel frames D.B. Merczel,, H. Somja, J.-M. Arbert, M. Hjaj, J. Lógó Insttut Natonal des Scences Applquées de Rennes, Laboratory of Structural Mechancs, 0 Av. des Buttes de Coesmes 5000 Rennes, France Budapest Unversty of Technology Economcs, Department of Structural Mechancs, Műegyetem rkp. -9. Budapest, Hungary emal: dmerczel@nsa-rennes.fr, hsomja@nsa-rennes.fr, arbert@nsa-rennes.fr, mhjaj@nsa-rennes.fr, logo@ep-mech.me.bme.hu ABSTRACT: Ths artcle deals wth concentrcally braced frames that are prone to exhbt weak storey behavor n case of a sesmc event. After ntroducton of key features of sesmc desgn of braced frames accordng to Eurocode 8 causes of weak storey behavour are presented. Ths s followed by descrpton of new desgn crtera that am to prevent occurrence of weak stores. The sutablty of new method s proved by numercal examples. KEY WORDS: concentrcally braced frame; sesmc desgn; weak storey; wavelet transform; plastc analyss INTRODUCTION Concentrcally braced frames (herenafter referred to as CBFs) are among most common structural systems for resstng lateral forces. They represent an economcal structural form for provdng lateral resstance for varous types of actons. For wnd effects, low return perod sesmc actons or for sesmc actons n buldngs of a hgh mportance class desgn behavour s elastc. Due to r geometry CBF-s counteract horzontal forces by truss acton that entals prmarly axal forces n members. The large resstance stffness lmts drfts vbratons n braced buldngs, refore provdes occupancy comfort mpedes damages n non-structural parts. Therefore CBF-s may be favoured over moment resstng frames [][] as MRF-s exhbt larger deformatons that mples second order effect problems excess damages. On or h CBF-s are generally consdered to have a worse performance than MRF-s [][] n case of a more destructve sesmc event, where return perod of earthquake s sgnfcantly larger than expected lfe cycle of buldng. In CBF-s large majorty of connectons splces are pnned as structure s stff stable wthout moment resstng connectons. Consequently level of statcal ndetermnacy s low, thus only a lmted number of members, mostly braces, can be dsspatve members n a CBF. Furrmore t has to be ensured that braces undergo plastc deformatons on each floor n order to utlze maxmum avalable capacty of dsspaton. Because of se adverstes allowed behavour factor used to be small. The current sesmc desgn practce codes penalze nondsspatve members wth hgh overstrength dem, n complance wth prncples of capacty desgn, to safeguard occurrence of plastcty n braces only. In followng structure specfc requrements of Eurocode 8 several mult-storey CBF structures desgned respectng se provsons are presented. Ths s followed by analyss of dynamc behavour of CBF-s when subjected to earthquakes. Upon descrpton of behavour a redesgn method s elaborated, results of whch are presented at end of artcle. SEISMIC DESIGN OF CBF-S BY EUROCODE 8. Eurocode 8 desgn crtera for CBF-s In desgn of buldng structures Eurocode 8 []. provdes two basc concepts for sesmc analyss. Earthquake resstant buldngs can er have a low-dsspatve or a dsspatve behavour. In a dsspatve structure controlled nelastc deformatons are expected to dsspate consderable energy damp response of structure. The behavour factor that accounts for ths effect s for CBF-s, whch s lower boundary of hgh dsspaton class (DCH) structures. In Eurocode 8 crtera for verfcaton of dsspatve structures follow capacty desgn phlosophy. Plastc deformatons are strctly requred to occur n dsspatve members that are to be desgned wth suffcent ductlty, whereas yeld or collapse of non-dsspatve zones s to be evaded. To ensure elastc behavour of non-dsspatve zones r sesmc requstons are amplfed n desgn wth a suffcent overstrength. In CBF-s braces are meant to be dsspatve members. Therefore CBF-s are desgned so that yeld of dagonals takes place before falure of connectons or columns or beams. For sake of homogeneous dsspatve behavour a smultaneous yeld of braces on every floor has to be ensured. Eurocode 8 ams to promote ths by a condton gven for overstrength factors, Ω, realzed on dfferent floors, makng m closely unform. It needs to be verfed that maxmum overstrength does not dffer from mnmum by more than 5%. N pl, Rd, Ω = Nbr, Ed, () Ωmax.5 Ω () mn For desgn of columns beams Eurocode 8 requres fulflment of followng condton: ( ) N M N +. γ Ω N () pl,rd Ed Ed,G ov Ed,E 8

2 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 where N pl,rd (M Ed ) s desgn bucklng resstance takng nto consderaton smultaneous bendng, N Ed,G N Ed,E are axal actons from non sesmc sesmc actons respectvely. The global overstrength factor s defned as: Ω = mnω () The overstrength factor, Ω, accounts for reserve n dsspatve members. It ensures that resstance of nondsspatve members s adequate untl frst plastc deformatons occur. The γ ov factor accounts for rom varablty of materal propertes. Its recommended value s.5. The factor. represents ncrease of yeld stress of dsspatve members due to stran-hardenng. In addton Eurocode 8 defnes lmtatons to nondmensonal slenderness: λ 0. (5) for X-braced confguratons also:. λ (6) where non-dmensonal slenderness s a rato between slenderness elastc lmt slenderness: λ E λ = wth λ = π (7) λ f y The upper bound defned n Eq. (5) s mposed to reduce plastc out of plane deformaton of gusset plates whch are prone to low-cycle fatgue falure. Furrmore ths lmtaton evades sudden mpact-lke loadng at end of straghtenng phase of buckled dagonals. The lower bound assures bucklng of dagonals.. Desgn of CBF-s of varous heghts Wth am of better understng behavour of CBF-s subjected to sesmc acton, a seres of concentrcally braced steel frame structures were desgned. The buldngs are dentcal n plan, see Fgure. The spacng of two adjacent columns s 6 metres n both drectons. There are four bays n both drectons gvng m m plan layout. Out of four bays nner two are braced concentrcally on four facades. The elevaton of buldngs dffers n terms of storey number. The number of floors s four, sx eght n buldngs denoted by CBF, CBF6 CBF8 respectvely. The storey heght s metres on every floor n each buldng. The columns n braced bays are pnned at base, but orwse contnuous throughout whole heght y are postoned n a way that r strong axs partcpates n lateral resstance. Consequently lateral load resstng system s same n both drectons. All or columns are pnned at both ends. The beams are smply supported I secton beams. The rectangular hollow secton braces are placed dagonally y are hnged at both ends. The loadng s dstrbuted between steel members va concrete floor slabs, but composte acton s not taken nto consderaton. The dead load s a unform loadng of 6.77 kn/m. The buldngs are consdered to have an offce occupaton where mposed loadng of B category n EC gves kn/m evenly dstrbuted loadng on slabs. The ψ combnaton factor was taken to be 0. refore 0% of lve loadng s concurrent wth sesmc acton. The earthquake acceleraton response spectrum s consdered to be type one n EC8 assumng B type sol condtons. The desgn ground acceleraton s taken to be 0.5g, where g s acceleraton of gravty. The behavour factor, q, s n agreement wth structure-specfc regulatons of stard. To obtan a more realstc accurate desgn, wnd loadng s also taken nto consderaton n calculaton structural members are verfed not only n sesmc desgn stuaton, but n ultmate servceablty lmt states also. In followng table appled cross-sectons are presented. The nteror exteror columns are lsted separately. Furrmore relatve slenderness λ overstrength factor, Ω, are also ndcated. Table. Sectons of members, slenderness overstrength results of desgned CBF-s Int Int Int HEM HEM Ext Ext Ext HEM Beam Brace λ Ω Beam Brace λ Ω Beam Brace λ Ω

3 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 NTHA at end, we can see that all braces have a trangular buckled shape. At md secton of bracng bars plastc hnges form due to local bucklng of plates. In repeated cycles cumulatng plastc deformatons gradually facltate bucklng by rotaton of plastc hnge. Eventually ths leads to angular buckled shape. In meantme plastc elongatons ncrease network length of bars. Consequently dagonals have to be n compresson after sesmc acton when buldng s laterally unloaded. Plastc elongatons refore furr amplfy trangularty of braces. Also we can notce that magntude of trangular mperfecton ntroduced to system by plastc strans may vary on dfferent floors. Fgure. Plan layout sde vew of -storey CBF. BEHAVIOUR OF ANALYSED BUILDINGS. Dynamc behavour of CBF-s under sesmc effect For verfcaton of CBF desgns a Nonlnear Tme Hstory analyss (henceforth NTHA) program has been carred out. For analyss seven artfcal accelerograms were selected. The length of each exctaton s 0 seconds spectra of ground motons were ftted to desgn spectrum. The used accelerograms are benchmarks n RFCS OPUS research program conducted wth cooperaton of several European unverstes [5]. Ths selecton of artfcal records comples wth correspondng parts of Eurocode 8. The acceleraton records were scaled by multplyng peak ground acceleraton by a scale factor rangng from 0. up to.0. The analyss was conducted on planar beam models wth FnelG nonlnear fnte element software. The members were dvded nto multple beam elements appled materal model was Guffré Menegotto Pnto cyclc law [6]. The masses smultaneous loads were appled n ntersectons of beams columns. The ntal mperfecton of braces was provded by dstrbuted loadng along dagonals. The dynamc behavour can be well nvestgated by lateral dsplacement hstory deformatons of buldngs. By smply lookng at deformed shape of - storey CBF model n Fgure that we get as a result of an Fgure. Resdual deformatons after sesmc acton. The larger trangular-lke mperfecton mples larger relatve lateral drfts on partcular storey whch ndcates formaton of a weak storey. The weak storey yeld mechansm s related to large relatve dsplacement of adjacent floors, sgnfcant plastc elongaton rotaton of plastc hnge. Therefore to dentfy occurrence of a weak storey lateral dsplacements of slabs nterstorey drft results have to be examned. The lateral dsplacements of floor slabs as a result of one of 0 second exctatons are depcted n Fgure. It can be seen that top floor exhbts dsproportonally large dsplacements compared to or three storeys. The maxmum nterstorey drft rato results presented n Fgure are even more convncng that on top a weak storey developed. The nterstorey drft rato s nterstorey drft dvded by storey heght: X X IDR = (8) H where lateral dsplacement of floor slabs s denoted by X, H s storey heght s storey ndex. Lateral dsplacement (m) 0,06 0,0-0,0-0,06-0,0 Tme (0-0 sec) Fgure. Horzontal dsplacements of floor slabs. 85

4 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 Maxmum IDR,0%,5%,0%,5%,0% 0,5% 0,0% Tme (0-0 sec) Fgure. Maxmum nterstorey drft ratos. In presented tme seres weak storey phenomenon can be dentfed on top floor, refore we furr analyse ts dsplacements. The man objectve of wavelet transformaton s to decompose an arbtrary functon nto elementary contrbutons [7]. The wavelet transform measures smlarty of analysed sgnal functon a seres of wavelets wth dfferent translaton n tme resoluton n frequency doman. The wavelet transform of sgnal x(t) by defnton s nner product n Hlbert space of functon a famly of wavelets: * t b W ( a,b) = g x() t dt a a (9) where g*(t) s mor wavelet functon whch generates famly of wavelets. The mor wavelet s dlated by parameter a translated by b whch vary contnuously so that a seres of son wavelets are created. One possble choce as mor wavelet s Morlet functon whch s a modfed verson of Gabor wavelet. β ( t b) π( t b) g () t = exp cos (0) a a Ths expresson defnes a harmonc functon that decays exponentally on both sdes over a tme nterval around t=b. The parameter β defnes length of envelope wave. By evaluatng Eq. (9) on a seres of son wavelets n a fxed tme frequency doman we can map nstantaneous frequency components of analysed sgnal. The dagram depctng results s called a scalogram whch s analogue wth spectrogram created by Fourer transformaton but tme frequency axes are both varables, refore results are represented by a colormap. In our case sgnal s horzontal dsplacement of a selected floor slab comng from an earthquake exctaton. The wavelet transform of dsplacements does not show sharp margns n Fgure 5, shape s more cloud-lke. Ths s due to fact that exctaton dsplacement both mss any knd of harmonc regularty. Furrmore dsplacement dagram only has a few waves over 0 second tme seres ths leads to a bad resoluton. Noneless local maxma are denoted by a whte lne on wavelet transform dagram ths lne shows that after frst second of featureless nose characterstc frequency decreases from about 0,77-0,80 Hz to 0,5-Hz throughout seres. Fgure 5. Wavelet transform of top floor slab.. Causes of observed behavour So far t has been shown that under a sesmc exctaton dagonals of a CBF are prone to gradual deteroraton that leads to a trangular mperfect shape. In meantme dsplacements of floor slabs become dsproportonal, even unsynchronzed when CBF exhbts weak storey behavour. It can be assumed that rreversble deteroraton of braces that are man horzontal load bearng elements results n a sgnfcant alteraton of dynamc behavour of structure. To verfy ths assumpton a seres of natural frequency analyses were conducted on elastc model of four-storey braced frame [8]. The perfect model wth two straght bracng bars was altered. At mdpont of two braces on same floor dfferent magntudes of mperfecton were ntroduced. The mdponts of dagonals were pulled perpendcularly to bar by 0 centmetres at each step up to 50 centmetres. Ths resulted trangular shape braces. The trangular alteraton of dagonals was done at every floor separately to analyse effect of developed weak storeys. Also same mperfectons were appled on every floor smultaneously whch corresponds to development of global yeld mechansm. Furrmore natural frequency analyss was run on perfect model wth one dagonal on every floor, neglectng buckled bar n compresson, n accordance wth Eurocode 8. In Table natural frequency results for more relevant frst second modes are lsted. The rows of table correspond to dfferent levels of ntroduced mperfecton whle columns dffer n storey of mperfecton. For sake of comparson t s noted that frequences of perfect model wth only one bar yelded 0.8 Hz.6 Hz respectvely. Table. Natural frequences of mperfect models. st mode all 0 cm cm cm cm cm nd mode all 0 cm cm cm cm cm

5 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 One can see n results of table that wth concurrent deformaton of all braces decrease of frequences n two modes s roughly proportonal. However ths s not case when trangular modfcaton s done to braces of one floor only. Consequently t s not only frequency of modes that changes. The ntroduced mperfecton of braces modfes stffness matrx of structure. It decreases stffness values correspondng to end nodes of altered braces only. Hence new stffness matrx of structure s not proportonal to orgnal, whle mass matrx remans same. Therefore mode shapes have to change also. Fgure 6 depcts frst two modes of vbraton correspondng to -storey CBF wth 0 cm brace mperfecton on thrd floor. extrapolaton of elastc behavour of ths SDOF system gves an upper bound approxmaton of actual nonlnear behavour. Ths approach s vsualzed n Fgure 7, where dsplacement, δ, s plotted aganst sesmc effect, a gr denotng peak ground acceleraton. Accordng to Ballo Sett [9][0] q factor s rato of sesmc effect correspondng to frst yeld n structure.e. end of elastc stage at pont B, ntersecton of curves representng lnear nonlnear post-yeld behavour, pont C. A desgn n accordance wth Eurocode 8 s elastc refore t corresponds to a sesmc effect at pont A, lower than elastc lmt, a el,u. Consequently actual desgn effect, whch s q-tmes larger than elastc effect, s smaller than ntersecton at q tmes a el,u, beyond whch dynamc nstablty can be expected. In ths case lnear extrapolaton of dsplacements obtaned by lnear analyss certanly gves a safe estmaton, pont D, of real values, pont E. Ths approach can safeguard adequacy of desgn. Conversely verfcaton of a dsplacement obtaned by analyss of an equvalent SDOF system may not mean that dsplacements are under a requred lmt on every floor. If behavour of buldng s global wth equal drfts on all floors curve number one on Fgure 7 corresponds to behavour of all storey drfts. Fgure 6. Modes of vbraton of mperfect model. The frst mode exhbts a quas rgd bodly movement above weak storey neglgble dsplacements below. Ths fundamental mode also has a large mass partcpaton, almost 60 %, refore t governs response of buldng. Consequently plastc deformaton caused mperfecton of braces results an adverse rearrangement of horzontal nerta forces n a way that ths nflcts an ncrease n storey shear on floor already subjected to plastc strans. Ths ncrease of storey shear causes a recurrng cycle as t wll lead to occurrence of furr cumulatng plastc deformaton on floor under consderaton, whch s concatenated wth growth of brace mperfecton change of dynamc response. Hence development of weak storey mechansm can be regarded as a gradual, auto exctng amplfyng phenomenon n case of cyclc sesmc acton. In presented numercal example weak storey occurred on fourth floor. The wavelet transformaton ndcated that n begnnng moton of ths storey can mostly be descrbed by a 0,77-0,80 Hz vbraton after gradual decrease ths frequency becomes about 0,5-0,5 Hz. These result are n good agreement wth modal analyss results of -storey model, as frequency of fundamental mode of perfect model s 0.8 Hz mperfect model wth 50 cm brace mperfecton on top floor yelded 0.50 Hz for frst mode.. Contradcton of behavour EC8 hyposes The Eurocode procedure somehpw reduces MDOF structure to an equvalent SDOF problem assumes that Fgure 7. Generalzed dsplacement acceleraton curve. If ths perfect behavour s altered however by effects not taken nto consderaton n desgn curves of dfferent floors devate, t s possble that certan floors follow curve number two for example that causes early falure. Unfortunately realty s second scenaro, see numercal example above, where nterstorey drfts of dfferent floors are not equal, not even closely related. In authors opnon unformty condton gven by Eq. () s not able to evade local mechansms. However desgn shall only be modfed by ntroducton of new crtera that prevent occurrence of excess storey drft dfferences wth ths condton orgnal dea of desgn wth q behavour factor can be successfully appled. The unformty condton mposed to overstrength factors of every floor by Eq. () s an attempt n Eurocode to evade occurrence of localzed dsspaton on a weak storey by promotng smultaneous yeldng of braces on multple, or f possble, on every floor. Both a smplfed desgn modal response analyss of a CBF eventuates 87

6 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 thatt desgn s made to a lateral load pattern that s nverted trangular refore corresponds to global yeld mechansm. In desgn nternal forces are calculated by use of ths loadng from normal forces n dagonals formaton of supposed behavour s verfed. Brefly, development of globall yeld mechansm s verfed by use of nternal force results that already suppose ts presence. In authors opnon elgblty of provdng proof to formaton of one phenomenon by analyss of ts effects s questonable. Conversely t s more desrable to prove that structure s susceptble to exhbt plastc behavour on multple floors even f subjected to varous, more rom-lke lateral load patterns as ths entals development of a dstrbuted dsspatve behavour eventually. The crteron of Eurocode 8 s necessary but not suffcent to prevent development of weak storeyss as t proves global plastc mechansm by supposng t.. Performance of desgns The man objectve of verfcaton of presented desgns by NTHA s to see wher desgns are prone to weak storey behavour or not. For analyss each buldng s loaded by seven acceleraton records scaled from 0. to.0, for each scale factor average of seven dfferent results s calculated at end. Ths comples wth regulatons of Eurocode 8. Prevously we have seen that maxmum nterstorey drft well ndcates exstencee of a weak storey. By plottng maxmum nterstorey drfts aganst scale factor we can observe development of weak storey phenomenon. In Fgure 8 maxmum nterstorey drft results of 6-storey CBF are presented. For sake of comparablty of all buldngs maxma mnma are dstngushed for three scale factors se are depcted by bar charts n Fgure 9. The selected scales are 0.5 whch s half strength,.0 whch s desgn strength.5. In Fgure 9 we can observe that maxmum nterstorey drft s tendentously multple tmes larger than mnmum. The dfference s large even at half strength though n case of smaller, -storey buldng maxmum mnmum rato becomes smaller for hgher scale factors, n larger buldngs dfference escalates.,5 6,0 storey 5,5 MAX,0 Maxmum IDR [%],5,0 0,5 MIN 0,0 0,00 0,,5 0,75,00,5,50,75,00 Scale factor Fgure 8. Maxmum IDR dagram of 6-storey CBF. CBF- The large dfferences ndcate that n every case manfold of curves correspondng to dfferent floors s rar broad just lke n Fgure 8. The buldngs refore do not exhbt a dstrbuted dsspaton, ree are storeys that undergo lot larger plastc excursons than ors. As results ndcate an adverse behavour n every buldng we can conclude that CBF-s desgned accordng to Eurocode 8 are susceptble to develop weak storeys even when subjected to sesmc actons that are smaller than desgn level. Maxmum IDR [%] 0,00,5 050 CBF-6,00,5 CBF-8,00 Fgure 9. Maxmum IDR results of desgned CBF-s.,5 PROPOSED REDESIGN METHOD. Defnton of method In order to establsh an approprate redesgn crteron nstead of usng a perfect elastc model exhbtng global behavour, a plastc model penalzed wth mperfectons r consequental effects should be used. Frst foremost we assume that structure exhbts weak storey phenomenon on one floor. Moreover we suppose that bars are deterorated by tensle yeld deformaton of md secton n a way that lateral stffness on weak storey decreases. A great loss of stffness sgnfcantly changes fundamental mode so that dsplacements above weak storey are closely rgd bodly, under neglgbly small. The acceleratons comng from such a dsplaced shape can be well approxmated by constant acceleraton above weak storey nothng under. The horzontal loads determned from ths acceleraton are refore proportonal to masses of slabs. If masses are equal on every storey, equvalent load pattern that we can use for analyss s constant above zero under weak storey, see Fgure 0. Fgure 0. Equvalent horzontal loadng of mperfect CBF model plastc collapse mechansms. 88

7 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN 0 As structural model s n non-elastc range we shall conduct plastc analyss of structure to calculate magntudes of loadng [], defned by load parameter λ, that correspond to dfferent plastc collapse mechansms. Our am s to provde a condton that can ensure that structure s ultmately drven towards a dstrbuted dsspaton on every floor f possble nstead of a weak storey collapse, even n presence of a developed weak storey. The basc dea of new crteron s that f load parameter correspondng to a local storey collapse mechansm s larger than load parameter of global collapse mechansm, weak storey collapse on analysed floor may not occur as plastc yeld of multple dagonals precedes t. For complete analyss of whole buldng we need to verfy ths condton n an n-storey CBF n tmes, whch gves n load parameter pars. On se pars followng nequalty has to be met to prevent development of weak storeys: λ λ () loc, glob, Ths condton does not necessarly ensure hard-torealze smultaneous plastcty of every dagonal. Conversely t defnes a barrer wthn whch plastc deformatons can be realzed n dagonals of multple storeys. It assures that CBF tends to exhbt dstrbuted dsspaton regardless of loadng hstory any nstantaneous plastcty scheme. Furrmore comparson of load parameters defnes an nternal condton n structure that can be evaluated wthout ground acceleraton or any or parameter that descrbes magntude of desgn sesmc effect. Therefore ntroduced crteron s loadng ndependent, t shows wher structure s prone to weak storey behavour or not. The structure that fulfls condton s deemed to be robust n terms of beng able to exhbt a controlled dsspatve behavour under any sesmc effect wthn ts strength range of desgn. For ths reason authors have chosen to call redesgn procedure as Robust Sesmc Brace Desgn (henceforth RSBD) method. As method s ndependent of loadng, a CBF has to be desgned frst accordng to provsons of Eurocode 8. Then desgn can be verfed or modfed by evaluatng Eq. () not respectng unformty yeld condton or requrement for columns.e. Eq. () () any longer. The ntroduced crteron s necessary to evade weak storey collapse but not suffcent to keep dfferences of nterstorey drfts on all floors wthn an acceptable lmt. The reason s followng. The nequalty condton defned n Eq. () can be satsfed by enlargng er brace or column sectons as y are both nvolved n plastc resstance of a certan storey. If n an extreme case resstance s only gven by brace columns are neglgble, load of frst yeld on storey s equal to ultmate plastc resstance. As RSBD method ams to prevent attanment of ultmate resstance, frst yeld wll not be reached er storey remans elastc throughout sesmc effect. Conversely, f all resstance comes from plastc hnges on top on bottom of columns braces are neglected, lateral dsplacement on ths certan floor wll be a lot larger than of all or floors as bent floor s a lot more flexble than ones stffened by braces. Brefly, local load parameter can be modfed by both braces columns. As se two exhbt dfferent behavour n terms of dsplacement an addtonal condton has to be ntroduced for sake of a good selecton of brace column sectons. To resolve ths problem Brace Partcpaton Rato (henceforth BPR) s ntroduced. The BPR s shortly product of plastc overstrength.e. rato of local global load parameters, an expresson descrbng nvolvement of brace n lmtng lateral dsplacements by use of plastc work of braces columns. BPR λ W loc, pl, br = λglob, Wpl, br + τ Wpl, col () where W pl,br s plastc work of braces W pl,col s work n column cross sectons n local plastc mechansm. To take nto consderaton that columns wth two contnuous ends or wth one or two pnned ends do not lmt lateral dsplacement same way, plastc work of columns s multpled by τ parameter. Ths parameter s.0 for contnuous columns, 0.6 for one-pnned-end columns. The BPR has to be determned for every floor ndependently. To obtan a dstrbuted dsspatve behavour n whch every floor partcpates, a unformty condton s mposed to BPR smlarly to Eurocode requrement for storey overstrength factors. The maxmum mnmum BPR has to be n a 0 % range.. Performance of redesgned structures In Table modfcatons to prevously ntroduced desgns are presented. The changed brace or column cross sectons are hghlghted also storey overstrength factor, plastc load parameters of RSBD method BPR results are lsted. In Fgure maxmum nterstorey drft rato dagram of redesgned 6-storey CBF s presented. Fgure depcts same bar chart as Fgure 9, but for redesgned buldngs. Comparng Table we can see that as a result of RSBD redesgn method columns that are connected to braces had to be sgnfcantly renforced. Ths need s not realzed n Eurocode desgn as analyss of perfect structure does not yeld sgnfcant bendng of columns, refore by Eq. () requred resstance s underestmated. In Table we can also see that due to renforcement of certan braces Eq. () s not respected anymore. Neverless Fgure depcts a favourable narrow manfold for CBF-6 Fgure shows that behavour s smlar for all redesgned buldngs. Comparng Fgure to Fgure 9 we can see that mnmum drft grows whle maxmum sgnfcantly decreases n redesgned buldngs. Consequently RSBD redesgn method provdes CBF-s that exhbt a lot more dstrbuted dsspatve behavour n a sesmc desgn stuaton than ones desgned respectng Eurocode 8 provsons. Moreover by decreasng maxmum drft RSBD method decreases damages also provdes a more resstant structure that may lead to a larger allowable q factor. 89

8 Proceedngs of 9th Internatonal Conference on Structural Dynamcs, EURODYN ,5,0 Maxmum IDR [%] Table. Results of redesgn by RSBD method.,5,0 Ext. Brace Ext. Brace Ext. Brace HD HD storey 5,5,0 0,5 0,0 0,00 0,5 0,75,00,5,,50,75,000 Scale factor Fgure. Maxmum IDR dagram redesgned CBF-6. Ω λ loc λ glob % % % % Ω λ loc λ glob % % % % % % Ω λ loc λ glob BPR BPR BPR % % %. 0 7% % % % % Maxmum IDR [%] 0 CBF- RSBD,00 Fgure. Maxmum IDR results of redesgned CBF-s. 5 CONCLUSIONS In artcle three CBF-s were presented that comply wth sesmc desgn requrements of Eurocode 8. For sake of verfyng sesmc behavour resstance of se desgns NTHA calculatons were conducted. By analyss of obtaned dsplacement data seres dynamc behavour of CBF-s was examned. An explanaton was gven for observed behavour nconsstences of Eurocode hyposes actual behavour were ponted out. By analyss of three buldngs t was proved that Eurocode desgns are prone to exhbt weak storey behavour. In last secton a new redesgn method was proposed that s based on observed behavour of buldngs. By analyss of redesgned buldngs t was proved that RSBD method successfully prevents occurrence of weak storey phenomenon by t, sgnfcantly enhances performance of braced frames. REFERENCES,5 CBF-6 RSBD,00,5 CBF-8 RSBD,00,5 [] A.Y. Elghazoul: Sesmc desgn procedures for concentrcally braced frames. Proc. of Inst. of Cvl Engneers, Structures & Buldngs 56, pp. 8-9, 00. [] A. Longo, R. Montuor, V. Pluso: Falure mode control of X-braced frames under sesmc actons. Journal of Earthquake Engneerng, : do: 0.080/ [] G. A. MacRae, Y. Kmura, C. Roeder: Effect of column stffness on braced frame sesmc behavour. Journal of Structural Engneerng, Vol. 0 No., pp. 8-9, 00. do: 0.06/(ASCE)07-95(00)0:(8) [] EN 998-:00 Eurocode 8: Desgn of structures for earthquake resstance Part : General rules, sesmc actons rules for buldngs [5] Bracon A et al (0) OPUS Project fnal report. European Unon, RFCS program [6] M. Menegotto, P. Pnto: Method of analyss for cyclcally loaded renforced concrete plane frames ncludng changes n geometry nonelastc behavour of elements under combned normal force bendng. IABSE Symposum on resstance ultmate deformablty of structures acted on by well-defned repeated loads, Lsbon. 97. [7] M. Büssow: An algorthm for contnuous Morlet wavelet transform. Mechancal Systems Sgnal Processng, Vol., 007. [8] D. B. Merczel, H. Somja, J.-M. Arbert, J. Lógó: On behavor of concentrcally braced frames subjected to sesmc loadng. Perodca Poltechnca Cvl Engneerng, 57/, -, 0.do: 0./pp.c.0-.0 [9] G. Ballo: ECCS approach for desgn of steel structures aganst earthquakes. Symposum on Steel Buldngs, Luxembourg 985. IABSE-AIPC-IVBH Report, Vol.. 8, pp. 7-80, 985. [0] F. M. Mazzolan, V. Pluso: Theory Desgn of Sesmc Resstant Steel Frames. E $ FN Spon, 996. ISBN X [] S. Kalszky: Plastcty. Theory Engneerng Applcatons. Akadéma Kadó Budapest,