SEISMIC RESPONSE AND BEHAVIOUR FACTOR OF DUAL ECCENTRICALLY BRACED SYSTEMS DESIGNED BY EUROCODE 8

Transcription

1 SEISIC RESPONSE AND BEHAVIOUR FACTOR OF DUAL ECCENTRICALLY BRACED SYSTES DESIGNED BY EUROCODE 8 elna BOSCO 1, Arelo GHERSI 2, oardo. ARINO 3 and Per Paolo ROSSI 4 ABSTRACT The athors consder dal strctres consttted by eccentrcally braced fraes and oent resstng fraes and desgn these strctres accordng to rles that are the natral extenson of those proposed n Erocode 8 for dal strctres consttted by concentrcally braced fraes and oent resstng fraes. The procedre consders that the dal eccentrcally braced strctres ay be desgned by eans of a sngle vale of the behavor factor and that the lateral forces are dstrbted between the braced and oent resstng fraes accordng to ther lateral stffness. In addton, a new desgn procedre s proposed, whch slghtly odfes that of Erocode 8 n order to fll gaps and ake the new procedre consstent wth the ntent of the code. To evalate the effectveness of the rles proposed for the applcaton of the capacty desgn prncples and the adeqacy of the behavor factor, the sesc response of the desgned systes s evalated throgh ncreental non-lnear dynac analyss. To ensre the general valdty of the reslts, the desgned bldngs are consdered to be fonded on hard or soft sol and are charactersed by dfferent vales of the lnk length and nber of storeys. INTRODUCTION The sesc response of steel systes can beneft fro the nteracton between oent resstng fraes (RFs) and braced fraes. The oent resstng fraes belongng to the dal syste were frst conceved as backp fraes to the braced frae,.e. they were ntended to provde strength and stffness so as to prevent the collapse of the strctre n the occrrence of an ntense and rare grond oton (AISC, 2005). For ths reason, sesc codes reqred that the braced fraes were sbjected to the entre sesc load and that the oent resstng fraes were desgned to resst sesc actons correspondng to the 25 per cent of the desgn base shear. Recently ths concepton has changed (Hnes and Fahnestock, 2010) and oent resstng fraes are consdered to be part of the prary lateral syste. Consstently wth ths concepton, Erocode 8 (2005) reqres that dal strctres are desgned by eans of a sngle behavor factor and that the horzontal actons are dstrbted between the dfferent fraes accordng to ther elastc stffness. Despte the potental benefts dervng fro the adopton of a dal strctre, Erocode 8 consders only dal strctres consttted by oent resstng fraes and concentrcally braced fraes. Frther, the provsons and desgn crtera reported n other sesc codes cannot be drectly transferred nto the Eropean code becase of the dfferent expected perforance levels. These lacks 1 PhD, Departent of Cvl Engneerng and Archtectre, Catana, Italy, bosco@dca.nct.t 2 Fll Prof., Departent of Cvl Engneerng and Archtectre, Catana, Italy, agehrs@dca.nct.t 3 Assstant Prof., Departent of Cvl Engneerng and Archtectre, Catana, Italy, earno@dca.nct.t 4 Assocate Prof., Departent of Cvl Engneerng and Archtectre, Catana, Italy, pross@dca.nct.t 1

2 lt the possblty of adoptng these strctral types or nderne the safety of the bldngs becase ther desgn s entrsted exclsvely to the experence of the strctral desgners. The athors consder here dal strctres consttted by eccentrcally braced fraes (s) and oent resstng fraes (RFs) and desgn these strctres accordng to rles that are the natral extenson of those proposed n Erocode 8 for other dal systes. The sesc response of these fraes s analysed n order to evalate the effectveness of the rles proposed for the applcaton of the capacty desgn prncples and the adeqacy of the behavor factor consdered. DESIGN OF DUAL ECCENTRICALLY BRACED OENT RESISTING FRAES The desgn procedre reported n Erocode 8 for dal systes reqres that the dal strctre s desgned by eans of a sngle vale of the behavor factor and that the lateral forces are dstrbted between the two sbsystes accordng to ther lateral stffness. The sggested vale of the behavor factor s eqal or slghtly hgher than the lower vale recoended for the two sbstrctres. In the case of dal eccentrcally braced oent resstng fraes, ths n vale s eqal to 5α /α 1, where α dentfes the ltpler of the sesc desgn actons correspondng to the developent of the overall strctral nstablty and α 1 dentfes that correspondng to the frst yeldng of ebers. However, recent stdes on eccentrcally braced fraes (e.g. Bosco et al., 2014) have rearked that ths vale of the behavor factor shold be redced. For ths reason, a behavor factor q d eqal to 5 s assed. The dal strctres are desgned so that yeldng takes place n lnks, n beas of RFs and at the base of the colns of the frst storey of RFs. For ths reason, whle these ebers are desgned to resst the nternal forces provded by the sesc desgn acton, all the other eleents are desgned based on capacty desgn prncples accordng to the provsons stplated for the two sbstrctres ndependently consdered. The desgn nternal forces of the lnks ay be obtaned fro ether the lateral force ethod of analyss or odal response spectr analyss. Lnk sectons are selected so that the desgn shear force and bendng oent (V, ) are not hgher than the correspondng plastc resstances (V p, p ) calclated accordng to Erocode 8. Lnks are defned as short, nteredate and long dependng on the vale of the echancal length ev p / p, e beng the lnk length; specfcally, f plastc hnges are expected at both ends of the lnk, lnks are short f the echancal length s not greater than 1.6 and long f ths rato s not lower than 3. To acheve a global dsspatve behavor of the strctre, Erocode 8 recoends that the ndvdal vales of the lnk overstrength factor do not exceed the n vale n by ore than 25% of ths n vale. The lnk overstrength factor at the th storey of the bldng s defned by eans of the followng relatons 1. 5V p for short lnks (1) V 1. 5 p for nteredate and long lnks (2) Braces and colns of the braced fraes are verfed n copresson by consderng the ost nfavorable cobnaton of axal force and bendng oent. Ther secton and steel grade are selected so that the followng relaton s verfed N, V N,G 1. ovn N, E Rd 1 (3) where N,G s the copresson force de to the non-sesc actons nclded n the sesc desgn staton; N,E s the copresson force de to the sesc desgn acton; γ ov s the ateral 2

3 . Bosco, A. Ghers, E.. arno and P.P. Ross 3 overstrength factor and N Rd s the axal desgn resstance n accordance wth Erocode 3, takng nto accont the nteracton wth the bendng oent and the shear force V. These nternal actons are calclated as the s of the contrbtons of gravty loads and sesc forces to the desgn nternal forces n the sesc desgn staton,.e. =,G +,E and V = V,G + V,E. Beas of RFs are desgned so that the desgn bendng oent at the ends of these ebers s not greater than the plastc bendng oent pl,rd. The selected sectons are sch that the desgn shear and axal forces do not decrease the fll plastc oent and the rotaton capacty at the plastc hnge. The desgn nternal actons of the colns of the RFs are derved by the followng relatons N N,G. 1 1 N (4) ov RF n,e,g. 1 1 (5) ov RF n,e V V,G. 1 1 V (6) ov RF n,e RF where n s the n of the ratos plrd, /, calclated for all the beas of the RFs n whch dsspatve zones are located. The coln cross-sectons are selected so that the desgn bendng oent s lower than the flexral strength N,Rd redced by the axal force and the desgn axal force s lower than the bcklng resstance redced by the desgn bendng oent. Both flexral and bcklng resstances are calclated accordng to Erocode 3 (2005). Note that the desgn nternal forces de to the sesc actons are aplfed becase of P-Δ effects f the nterstorey drft senstvty coeffcent θ, calclated accordng to the followng eqaton, s larger than 0.1 (Erocode 8, 2005) and lower than 0.2. Ptotdr (7) V h tot In Eqaton (7) P tot s the total gravty load at and above the storey consdered n the sesc desgn staton, V tot s the total sesc storey shear, h s the nterstorey heght and d r s the desgn nterstorey dsplaceent at the storey nder consderaton. In Erocode 8 ths latter paraeter s sggested to be calclated as a fncton of the desgn behavor factor q d. DESIGNED BUILDINGS The desgn procedre descrbed n the prevos secton s appled to 2-, 4-, 8- and 12-storey bldngs fonded on hard to soft sols (sol types A, C and D accordng to Erocode 8). The plan s sqareshaped (24 x 24 2 ) and the nterstorey heght h s eqal to 3.3 (Fg. 1). The strctral schee s consttted by the ntersecton of two sets of for three-bay plane fraes dsposed along two orthogonal drectons. Two eccentrcally braced fraes are located on the pereter of the bldng along each of the two orthogonal drectons. The eccentrc braces are dsposed n the central span n the splt K geoetrc confgraton. The lnk length e s assed to range fro 0.1 to 0.4 tes the length L of the braced span. Ths range of vales s consdered to evalate the sesc response of bldngs n whch the nelastc response of lnks s governed by ether shear (short lnk) or flexre (long lnks), or by both shear and flexre (nteredate lnks). To nllfy the nteracton between deck and lnks, two bea ebers are ntrodced at each level of the s nstead of the tradtonal sngle secton (Bosco et al., 2014). Whle the frst sstans the vertcal loads transtted by the deck, the second ressts the horzontal actons and constttes the lnk tself. Colns are contnos n elevaton and orented as shown n Fgre 1. Conseqently, the stffness provded by the oent resstng fraes s greater along the x-drecton becase the colns labelled as C2 n Fgre 1 are generally charactersed by greater cross sectons. Connectons between colns of the braced fraes and beas or fondaton are pnned. All the other connectons, ncldng end connectons of braces,

4 C1 C0 C0 C1 C0 C2 C2 C C0 C2 C1 C h = 3.3 β Sesc force along the x- drecton Sesc force along the y- drec ton Fgre 1. Layot of the dal strctre are rgd and fll strength. The geoetrc and ass propertes of the bldngs are eqal at all storeys. Vertcal dead and lve loads n the non-sesc desgn staton are eqal to 9.2 kn/ 2. In the sesc desgn staton, the sesc acton s calclated on the bass of asses correspondng to a ean vale of the gravty loads eqal to 5.0 kn/². The nternal forces de to the desgn sesc acton are calclated by eans of ether the odal response spectr analyss (RSA) or the lateral force ethod of analyss (LFA) on the bass of the elastc response spectr proposed by the Erocode 8 and scaled to a peak grond acceleraton eqal to 0.35 g. In order to report synthetcally the an propertes of the desgned strctres, the ltate avalable plastc rotaton angle of the lnk of each storey s calclated frst accordng to the relatons provded by Erocode 8,.e rad evp p rad evp p 3. 0 lnear nterpolaton between the vales above for 1. 6 ev p p 3. 0 (8) Second, the ean plastc rotaton capacty of the lnks of the whole strctre s calclated. Ths latter paraeter s eqal to 0.08 rad f all the lnks are short and eqal to 0.02 rad f all the lnks are long; nteredate vales are representatve of systes wth nteredate length lnks n at least one storey. Fnally, the n, ean and ax vales of the noralsed overstrength factors (Fg. 2) of each syste are reported as a fncton of. Dashes dentfy the n and ax vales of the lnk noralsed overstrength whle trangles, rhobses and crcles pnpont the ean vale of the sae paraeter n the lnks of systes fonded on dfferent sol types. The ax noralsed overstrength factor s always lower than 1.25 for the s arranged along the y-drecton. Only sporadcally, the ax noralsed overstrength factor s greater than 1.25 for hgh storey systes wth long lnks arranged along the x-drecton. Indeed, n these few cases the stffness provded at the top storeys by the oent resstng frae s not neglgble also n the elastc range of behavor, ths the sesc forces at the pper storey are anly sstaned by the oent resstng fraes. Frther, the lnk cross secton has not been redced becase the HEB 120 secton has been selected as the n lnk cross secton. As rearked n Bosco et al. (2014), the expresson provded n Erocode 8 to evalate the lnk overstrength factor Ω s not perfectly consstent to that sggested n the past by Popov et al. (1992). Specfcally soe dfferences ay be fond when at soe storeys the lnk echancal length s close to 1.6 becase, as also reported by other researchers (azzolan et al., 2009), the lnk overstrength factor defned n Erocode 8 s dscontnos at ths specfc vale of the echancal lnk length. 4

5 . Bosco, A. Ghers, E.. arno and P.P. Ross 5 Sol A Sol C Sol D ns= ns= ns= Ω/Ω n Desgned by RSA Ω/Ω n Desgned by LFA φ 0.08 Ω/Ω n φ 0.08 Ω/Ω n φ φ 0.08 Fgre 2. ax noralsed overstrenght factors calclated accordng to Erocode 8 for systes analysed along the x-drecton, y-drecton Desgned by RSA Desgned by LFA Ω/Ω n Ω/Ω n φ 0.08 Ω/Ω n φ 0.08 Ω/Ω n φ φ 0.08 Fgre 3. ax noralsed overstrenght factors calclated accordng to Popov et al. (1992) for systes analysed along the x-drecton, y-drecton

6 Sol A Sol C Sol D ns= ns= ns= θ Desgned by RSA 0.30 θ Desgned by LFA φ θ φ θ φ φ 0.08 Fgre 4. Interstorey drft senstvty coeffcents for systes analysed along the x-drecton, y-drecton To show these dfferences, the noralsed overstrength factors calclated accordng to the relaton provded by Popov et al. (1992) are plotted n Fgre 3. Ths fgre shows that n soe systes,.e. those charactersed by n the range , the ax noralsed overstrength factors ay ncrease over 1.25 f the relaton proposed by Popov s adopted. Slarly, the ax, n and ean vales of the nterstorey senstvty drft coeffcent are reported n Fgre 4. The ax vale of the nterstorey drft senstvty coeffcent θ along the heght of the bldng generally ncreases as the echancal length of the lnk ncreases (.e. as the vale of decreases). However, θ s always lower than 0.2. NUERICAL ANALYSES The sesc response of the dal systes s obtaned by ncreental non-lnear dynac analyss. The sngle non-lnear dynac analyss s carred ot on two-densonal odels by eans of the OPENSEES progra (azzon et al., 2007). The vscos dapng forces are obtaned throgh the forlaton proposed by Raylegh. In partclar, a vscos dapng rato eqal to 0.05 s fxed for the frst and thrd odes of vbraton of the 4-, 8- and 12-storey strctres, and for the frst and second odes of the 2-storey strctres. For each strctre, the analyss s perfored ncldng P-Δ effects and consderng the sesc force acton along ether x- or y-drecton. Lnks are odelled by eans of three eleents connected n seres (Bosco et al., 2014). The central eleent has the sae length and oent of nerta of the lnk and slates the flexral behavor of the lnk (the shear stffness of ths eleent s nfnte). The two endng eleents are zero length and connect the bea segents otsde the lnk to the flexral eleent of the lnk. The nodes of these endng eleents are allowed to have only relatve vertcal dsplaceents. The stffness of the translatonal sprng that allows ths relatve oveent s defned so as to slate the shear deforablty of half a lnk. The post-elastc behavor of the shear and flexral eleents of the lnk s 6

7 . Bosco, A. Ghers, E.. arno and P.P. Ross 7 elasto-plastc wth kneatc stran hardenng. Braces, colns of the braced fraes and bea segents otsde lnks are odelled by eans of elastc eleents becase they are non-dsspatve ebers; beas and colns belongng to the oent resstng fraes are odelled as bea wth plastc hnges eleents. Wthn the plastc hnge length (eqal to the heght of the cross secton), the cross secton s sbdvded n fbres. The enegotto-pnto odel s sed to slate the steel ateral. The sesc npt s consttted by three sets of ten accelerogras that are artfcally generated and copatble wth the elastc response spectr proposed by the Erocode 8 for sol A, C or D, respectvely. These accelerogras are charactersed by a total draton of 30.5 s and are enveloped by a copond fncton. The draton of the statonary part of the accelerogras s set eqal to 7.0 s on the bass of a prevos nvestgaton n whch natral and artfcal accelerogras were copared n ters of npt energy spectra, Aras ntensty, freqency content and nber of eqvalent cycles (Aara et al., 2014). The peak grond acceleraton a g s scaled n step of 0.04g n order to estate the peak grond acceleraton correspondng to hgh daage n the strctral eleents (a g ). The latter reference level of daage s charactersed by assgned plastc rotatons of lnks, beas and dctle colns belongng to the RFs and assgned nternal forces of non-dsspatve ebers (beas and colns of the s, colns of the RFs when sbjected to hgh axal forces). DEFINITION OF THE STRENGTH OR DUCTILITY CAPACYTY OF EBERS Lnks, beas of the RFs and colns of the RFs charactersed by axal forces lower than 0.3 tes the axal plastc resstance are dctle ebers. For lnk ebers the dctlty capacty s gven by Eqaton (8). As reported n Erocode 8 Part 3, the nelastc deforaton capacty for beas and colns n flexre s expressed n ters of the plastc rotaton at the end of the eber, as a ltple of the chord rotaton at yeldng θ y 6 2 y y secton class1 secton class 2 (9) θ y s calclated as a fncton of the plastc flexral resstance redced becase of the axal force Rd,N, the shear span L V, the oent of nerta of the cross secton I and the odls of elastcty E Rd,NLV y 3EI (10) Ths, to assess the daage of these ebers, the ax plastc rotatons experenced for the sesc event scaled to the assgned vale of a g are noralsed to the plastc rotaton capacty above. The obtaned ratos are ndcated by the sybol R. Braces, colns of s and bea segents otsde lnks are non-dsspatve ebers. Ther capacty s expressed n ters of the flexral strength N,Rd redced becase of the axal force and n ters of the bcklng resstance N b,rd () redced becase of the bendng oent. Ths, the safety levels of these ebers for both yeldng and nstablty phenoena are evalated by the ratos S and B between nternal flexral or axal forces to the correspondng capacty. Fnally, colns of the RFs that drng the sesc event are sbjected to axal forces N hgher than 0.3 N pl,rd are non-dsspatve. For these colns, the rato S cannot be calclated as reported above. In fact, these ebers are odelled as bea wth plastc hnge eleents and the ax bendng oent never reaches the flexral strength N,Rd becase of the gradal yeldng of the sngle fbres of the hnge secton. Ths, for these ebers, the safety level for yeldng phenoenon S s calclated as the rato of the ax reqred crvatre χ ax to the crvatre at yeldng χ y,.e as

8 Sol A Sol C Sol D ns= ns= ns= a g /g a g /g φ φ 0.08 Fgre 5. Peak grond acceleraton correspondng to the frst acheveent of the ltate lt state: dal fraes desgned by RSA; LFA S ax ax (11) y EI Rd,N ULTIATE RESPONSE OF THE BUILDINGS For each desgned dal strctre and for the sngle consdered accelerogra, the peak grond acceleraton a g correspondng to the frst acheveent of the ltate lt state,.e. to the frst acheveent of a ntary vale of the ratos R, S or B defned n the prevos secton, s deterned. Then, the vale of a g s averaged over the vales correspondng to the ten accelerogras and copared to the desgn peak grond acceleraton (.e. 0.35g). In Fgre 5, the n peak grond acceleraton a g obtaned along the x- or y-drecton s plotted as a fncton of the ean vale of the ltate plastc rotatons of the lnks of the whole strctre. The fgre shows that, when the bldngs are desgned by the odal response spectr analyss (Fg. 5a), vales of a g larger than the desgn vales are obtaned only for soe of the systes charactersed by larger than The range of dal systes wth satsfactory behavor s redced frther when the lateral force ethod of analyss s sed (Fg. 5b). Indeed, n ths case only 2- or 4-storey dal systes wth larger than reach the ltate lt state for a g larger than 0.35g. In order to nvestgate the reasons of ths nsatsfactory behavor, the nber of accelerogras that lead to falre n lnks (R = 1), colns of RFs (S or B = 1) or bea segent otsde lnks (S or B = 1) s evalated. In all the other ebers (braces and colns of s and beas of RFs) the sesc deand never exceeds the ltate capacty. Fgre 6 shows the reslts for soe of the desgned strctres (4- and 12-storey dal systes fonded on sol A and D desgned by RSA). Ths fgre shows that the ltate lt state s generally reached n lnks for dal systes n whch the lnk length e s eqal to 0.10 L. In the other systes, the ltate lt state s often attaned n the bea segents otsde lnks and n non-dsspatve colns of oent resstng fraes earler than n other ebers. Ths, the code provsons for the applcaton of the capacty desgn prncple do not always ensre the expected collapse echans. The vales of the ratos R, S or B correspondng to a sesc event wth peak grond acceleraton a g are averaged at each storey over the vales correspondng to the ten accelerogras consdered n the nercal analyses. The n, ean and ax vales of the paraeter R obtaned for lnks are reported n Fgre 7 as fncton of for systes analysed along the y- drecton. The fgre shows that only n systes endowed wth short lnks and desgned by odal response spectr analyss the ean vale of R s hgh, whch ples that the lnk daage s farly nfor n elevaton. In nearly all the other cases, the ean vale of the lnk daage n the bldng s odest and dentfes nsatsfyng sesc perforances. Ths behavor can fnd two dfferent reasons. In soe cases (e.g. n strctres wth short lnks and desgned by the lateral force ethod of 8

9 . Bosco, A. Ghers, E.. arno and P.P. Ross L 0.40 L 4-storey systes 0.30 L 0.20 L 0.10 L 0.30 L 0.20 L 0.10 L n acc L 0.40 L Lnk 12-storey systes 0.30 L 0.20 L 0.10 L 0.30 L 0.20 L 0.10 L Col RF Bea n acc. Fgre 6. Nber of accelerogras that lead to falre n lnks, bea segents otsde lnks and colns of RFs (sesc force along the y-drecton): dal fraes standng on sol A; sol D. analyss), the ltate lt state s acheved n lnks bt the lnk daage s scattered n elevaton. In other cases (e.g. n strctres endowed wth nteredate or long lnks) the ltate lt state s acheved n non-dsspatve ebers rather than n lnks and ths the lnk daage s everywhere ch lower than nty. Fgre 8 shows that the plastc rotatons n beas of the oent resstng fraes are always low. In fact, the ax vale of R obtaned for the beas of RFs s always lower than PROPOSAL OF ODIFICATION OF THE DESIGN PROCEDURE On the bass of the reslts descrbed n the prevos secton, a new desgn procedre s proposed. Ths procedre s obtaned odfyng that of Erocode 8. Soe of the proposed odfcatons have recently been proposed for the desgn of eccentrcally braced fraes (Bosco et al., 2014), other odfcatons are related to the desgn of oent resstng fraes (Elghazol, 2009). The frst odfcaton s related to the defnton of the lnk overstrength factor. In partclar, whle the forlaton of the overstrength factor reported n Erocode 8 calclates how ch the ltate lnk strength exceeds the desgn nternal force, the proposed overstrength factor Ω s referred to the frst yeldng of lnks. In fact, Ω s defned as the n between the followng shear and flexral overstrength factors V V p, V V,E,,G, 1 de, 1 d r, (12) p,,e,,g, 1 d e, 1 d r, (13) where d e s the nterstorey dsplaceent obtaned fro the strctral analyss adopted n desgn and the rato 1 d e, d r, 1 s sed to redce the P-Δ effects to those correspondng to the frst yeldng of lnks. Ths correcton s not reqred f the nterstorey drft senstvty coeffcent θ s not hgher than 0.10 becase no addtonal strength s reqred by the code to conterbalance P-Δ effects

10 Sol A Sol C Sol D ns= ns= ns= R 1.00 R f f 0.0 Fgre 7. Rato of the ax plastc rotaton to the avalable vale for lnks: systes desgned by RSA, LFA (y-drecton) 0.50 R 0.50 R f 0.0 n ths case. Note that the proposed defnton of the overstrength factor s contnos wth the echancal lnk length and takes nto accont the nternal forces cased by gravty loads. Regardng the applcaton of the capacty desgn prncples, braces, colns of the s and bea segents otsde lnks are desgned by eans of the relatons N b, Rd, V N ; N, Rd N, V f 0.0 Fgre 8. Rato of the ax plastc rotaton to the avalable vale for beas of the RFs: systes desgned by RSA, LFA (y-drecton) (14) where N N,G. 1 ov N (15) n,e,g. 1 ov (16) n,e V V,G. 1 ov V (17) n,e In the eqatons above, the nternal forces are calclated as a fncton of the ltate nternal forces of the lnks. In fact, the coeffcent 1.5 appears n these eqatons becase t s not nclded n the overstrength factor. Fnally, as sggested by Elghazol (2009) wth regard to oent resstng steel strctres, the RF atheatcal forlaton of the overstrength factor n shold take nto accont the effects of the gravty loads,.e. t shold be defned as the n of the ratos ( plrd, -,G, )/,E, calclated for all the beas of the RFs. 10

11 . Bosco, A. Ghers, E.. arno and P.P. Ross 11 Table 1. Coparson of the sesc responses of the 8-storey dal systes (e = 0.30 L, sol A) desgned by the two consdered procedres Desgn Procedre T1 (s) N acc Lnk N acc Col. RF N acc Bea (rad) ag falre falre falre Erocode g Proposed g VALIDATION OF THE PROPOSED PROCEDURE The effectveness of the proposed procedre s shown wth reference to the 8-storey bldng wth e/l eqal to 0.30 and standng on sol type A. Table 1 shows that the dal frae desgned by the proposed odfcaton s stffer than that desgned by the procedre reported n Erocode 8. In fact, the flexral rgdty of braces has been ncreased so as to redce the bendng oents n the bea segents otsde lnks and verfy the resstance reqreents (see Eq. 14) n these ebers. The lnk sectons adopted n the two copared systes are slar. In fact, the obtaned vales of are close each other. Table 1 also reports the coparson of the sesc responses of the two fraes and shows that, when the proposed odfcatons are appled, the ltate lt state s always reached n lnks and the peak grond acceleraton a g s hgher than 0.35 g. Fgre 9 shows the coparson between the two dal strctres n ters of the hghtwse dstrbton of the noralsed plastc rotatons of lnks. Specfcally, the whte crcles dentfy the noralsed plastc rotatons experenced by the lnks on the occrrence of the ten accelerogras, each scaled to a peak grond acceleraton eqal to a g,. At each floor, the black crcle pnponts the ean vale of the noralsed plastc rotatons prodced by the ten accelerogras and ths dentfes the vale of the aboveentoned paraeter R at that storey. In the dal frae desgned accordng to Erocode 8 the lnk daage s everywhere ch lower than nty becase the ltate lt state s acheved n non-dsspatve ebers. In the dal frae desgned by the proposed approach, nstead, the ax noralsed plastc lnk rotaton cased by the sngle accelerogra s eqal to nty. Frther, the ax noralsed plastc rotatons do not concentrate at the sae storey level (.e. the ns 8 desgned accordng to Erocode 8 ns 8 desgned accordng to the proposed procedre R ns R ns 8 6 Average vale Vale correspondng to the sngle accelerogra R R Fgre 9. Noralsed plastc rotaton of lnks: dal fraes sbjected to sesc acton along the x- drecton; y-drecton.

12 accelerogras do not case the plastc rotaton capacty of the lnks to be reached at the sae storey of the bldng) and ths the ax vale of R s slghtly lower than nty. Ths reslt s encoragng bt t shold be valdated by eans of the analyss of a wde set of dal systes. CONCLUSIONS The paper evalates the effectveness of the procedre sggested n Erocode 8 for the desgn of dal strctres obtaned by coplng eccentrcally braced fraes and oent resstng fraes. The ncreental non-lnear dynac analyses perfored on the desgned dal strctres show that a vale of the behavor factor eqal to fve ensres a satsfyng ltate perforance only for strctres endowed wth short lnks and () desgned by the odal response spectr analyss or () charactersed by a low nber of storeys and desgned by lateral force ethod of analyss. In all the other cases, the peak grond acceleraton correspondng to the acheveent of the ltate lt state s lower than 0.35g. These low vales are chefly cased by the lted effectveness of the rles for the applcaton of the capacty desgn prncples. For ths reason, soe odfcatons are proposed to the desgn procedre of Erocode 8. The effectveness of the proposed odfcatons s shown wth reference to a sngle case stdy,.e. an 8- storey systes endowed wth nteredate lnk. The obtaned reslts are encoragng bt they shold be valdated by eans of the analyss of a wde set of dal systes. REFERENCES AISC 341(2005) 05-AISC 341s1-05. Sesc Provsons for Strctral Steel Bldngs ncl. Sppleent No. 1. Aercan Insttte of Steel Constrcton, Inc. Aara F, Bosco, arno E and Ross PP (2014) An accrate strength aplfcaton factor for the desgn of SDOF systes wth P Δ effects Earthqake Engneerng & Strctral Dnacs, 43: Bosco, arno E and Ross PP (2014) Proposal of odfcatons to the desgn provsons of Erocode 8 for bldngs wth splt K eccentrc braces Engneerng Strctres, 61: Elghazol AY (2009) Assessent of Eropean sesc desgn procedres, Blletn of Earthqake Engneerng, 8: Erocode 8 (2003) Desgn of strctres for earthqake resstance. Eropean Cottee for Standardsaton; pren /2/3. Hnes E, Fahnestock LA (2010) Desgn phlosophy for steel strctres n oderate sesc regons, Proceedngs of the 9th US Natonal and 10th Canadan Conference on Earthqake Engneerng, EERI/CAEE, Toronto, Canada; Jly. azzolan F, Landolfo R, Della Corte G (2009) Erocode 8 provsons for steel and steel-concrete Coposte strctres: coents, crtqes, proveent proposals and research needs, Proceedng of the Workshop on Erocode 8 Perspectves fro the Italan Standpont, azzon S, ckenna F, Scott H, Fenves GL and Jerec B (2003) OpenSEES Coand Langage anal. Pacfc Earthqake Engneerng Research Center. Unversty of Calforna at Berkeley. Popov EP, Rcles J, Kasa K (1992) ethodology for opt lnk desgn, Proceedngs of the 10th World Conference on Earthqake Engneerng, adrd, Span,