AN IMPROVED CAPACITY SPECTRUM METHOD BASED ON INELASTIC DEMAND SPECTRA

Size: px

Start display at page:

Download "AN IMPROVED CAPACITY SPECTRUM METHOD BASED ON INELASTIC DEMAND SPECTRA"

Elwin Hensley
5 years ago
Views:

1 4th Intrnational Confrnc on Earthquak Enginring Taipi, Taiwan Octobr 1-13, 006 Papr No. 30 AN IMPROVED CAPACITY SPECTRUM METHOD BASED ON INELASTIC DEMAND SPECTRA Xiao Mingkui 1, Dong Yinfng, Liu Gang 3, an Chng Guangjun 4 ABSTRACT Th capacit spctrum mtho which intrvns btwn static inlastic analsis an lastic namic analsis is a simplifi mtho to analsis th lastoplastic rspons an valuat th prformanc of rgular structurs unr strong groun motions to a crtain xtnt of approximation. To arss th xisting problms, two aspcts of improvmnts ar ma on th prsnt capacit spctrum mtho. irstl, b using th il strngth factor as an lastoplastic inx, th inlastic man spctra corrsponing to th sign acclration rspons spctra spcifi in th Co for Sismic Dsign of Builings in China ar fin an formulat, whil in th convntional mthos th lastic man spctra of high amping ratio ar commonl us an can not rflct th structural lastoplastic rspons man prcisl. Sconl, accoring to th nrg quivalnt critrion th il isplacmnt an il forc of th quivalnt SDO sstm ar trmin bas on th structural sign paramtrs irctl which ar usuall trmin b bilinar moling of Pushovr curvs of structurs unr ara quivalnt assumption in som prsnt cos as EMA-356 an Euro Co 8 spcifi. Th comparison of th rsults shows th improv mtho is mor simpl an prcis which can b asil carri out in structural sismic sign. Kwors: Capacit spctrum mtho, Inlastic man spctra, Enrg quivalnt critria INTRODUCTION Th lastoplastic static analtic mtho is th primar simplifi mtho for valuating prformanc of sismic structurs, which inclus th pushovr mtho an th capacit spctrum mtho. or th capacit spctrum mtho, th pushovr mtho must b rli on to valuat th prformanc of sismic structurs an it can b viw as an improvmnt on th pushovr mtho. Th vlopmnt an improvmnt of both th simplifi mthos is kston to carr out th prformanc bas sign in practic. Th capacit spctrum mtho (rman t al., 1975; Mohl, 199; ajfar, 1999) which intrvns btwn static inlastic analsis an lastic namic analsis is a simplifi mtho to analsis th lastoplastic rspons an valuat th prformanc of rgular structurs unr strong groun motions to a crtain xtnt of approximation. Th mtho is mainl implmnt b suprposition of th capacit spctrum curv an th inlastic man spctra curv to valuat rsponss prformanc of structurs. 1 Profssor, Collg of Civil Enginring, Chongqing Univrsit, Chongqing, P. R. China, xmkx@ahoo.com.cn Instructor, Collg of Civil Enginring, Chongqing Univrsit, Chongqing, P. R. China, hvhson@cta.cq.cn 3 Instructor, Collg of Civil Enginring, Chongqing Univrsit, Chongqing, P. R. China 4 Instructor, Collg of Civil Enginring, Chongqing Univrsit, Chongqing, P. R. China

2 Two curvs ar n in th capacit spctrum mtho. On is th inlastic man spctrum curv which rprsnts th man for sismic capacit of structurs unr a givn groun motion. Using th tim-histor analsis mtho, a givn groun motion is input to a sris of SDO sstms with th natural frquncis istribut in a crtain rang, thn th corrsponing isplacmnt, vlocit an acclration rsponss can b foun rspctivl. Th man spctrum curv, in which th abscissa an th orinat ar th isplacmnt an acclration rsponss sparatl, can b foun b timhistor analsis. Anothr curv is th capacit spctrum curv which rprsnts th capacit of latral rift of a structur. irst, th top isplacmnt an bas shar forc can b foun b using th pushovr analsis mtho in which som pattrn of latral forcs ar loa to th structur grauall until it is stro. Thn, th top isplacmnt an bas shar forc is convrt to th acclrationisplacmnt curv of th quivalnt SDO sstm call capacit spctrum curv. Th prformanc an failur stat of sismic structurs can b valuat qualitativl with th intrsction point of th two curvs. In convntional capacit spctrum mtho (rman t al., 1975), th lastic man spctrum is oftn aopt, which woul la to th man for sismic capacit of a structur is ovrvalu. Thrfor, a varit of improvmnt mthos,.g. lastic man spctra with high amp ratio, ar propos b man rsarchrs in th worl (Mirana t al., 1994; Kowalsk t al, 1995; Calvi, 1999). Th lastic man spctra with high amp ratio mans that th issipation of nrg il b inlastic formation of sismic structurs is quat b incrscnt amp ratio, so that th ffcts of lastoplastic rspons can b tak into account. Th isavantag of this mtho is no corrsponing rlationship xists btwn th Hstrtic Enrg an high amp ratio. Compar with th high amp ratio lastic spctrum, th simplifi ruction cofficint spctra suggst b othr rsarchrs, which us uctilit ruc cofficint R µ to moif th lastic spctra, such as isplacmnt cofficint mtho in EMA73,inlastic spctra with uctilit ruc cofficint R µ b ajfar t al. (1999), ar mor thorticall rasonabl. But it is ifficult to fin uctilit cofficint of whol structur. Thrfor, a qustion for iscussion is how to fin lastoplastic spctra in which iffrnt kins of influncing factors ma b covr. Th trmination of namic cofficint of th quivalnt SDO sstm must b iscuss whil th top isplacmnt an bas shar, foun b using pushovr mtho, is convrt to th acclrationisplacmnt curv of th quivalnt SDO sstm. Thr ar various iscussions about namic cofficin of th quivalnt SDO sstm (EC8, 003; EMA356, 000). But th iscussions ar impropr in trmination of initial rigiit an il isplacmnt. Thr ar som qustions n to iscussion about th mtho for trmination of initial rigiit an il isplacmnt in EC8 an EMA356. To arss th xisting problms, two aspcts of improvmnts ar ma on th prsnt capacit spctrum mtho in this papr. irstl, b using th il strngth factor as an lastoplastic inx, th lastoplastic man spctra ar riv an formulat bas on th sign acclration rspons spctra spcifi in th Co for Sismic Dsign of Builings in China. Sconl, accoring to th nrg quivalnt critrion th il isplacmnt an il forc of th quivalnt SDO sstm ar trmin bas on th structural sign paramtrs irctl which ar usuall trmin b bilinar moling of pushovr curvs of structurs unr ara quivalnt assumption in som prsnt stanars as EMA356 an EC8 spcifi. ELASTOPLASTIC DEMAND SPECTRA To ovrcom th isavantags of using lastic man spctra with high amp ratio an ruction cofficint, b using th il strngth factor as an lastoplastic inx, th lastoplastic man spctra ar riv an formulat bas on th sign acclration rspons spctra spcifi in th Co for Sismic Dsign of Builings in P.R.China (001). Th SDO sstms with natural prio of vibration rang s an arthquak wavs with promination prio rang s ar slct for computing lastoplastic man spctra b tim-histor mtho. Th lastoplastic

3 acclration an isplacmnt ar foun an lastoplastic man spctra ar shown in ig. 1. Limit to spac of th papr, onl two figurs ar shown. Sa(m/s/s).00 Tg=0.9,Amax=.,p=0.01,ζ= ξ=0. ξ= ξ= ξ=0.5 ξ= S(m) Sa(m/s/s).00 Tg=0.55,Amax=.,p=0.01,ζ= ξ= ξ=0.3 ξ= ξ=0.5 ξ= S(m) igur 1. Elastoplastic Dman Spctrum THE DISCUSS ABOUT EQUIVALENT YIELD DISPLACEMENT IN BILINEAR MODELING O PUSHOVER CURVES Th bas shar an top isplacmnt foun b using pushovr mtho can b convrt to bilinar moling capacit spctrum curv an quivalnt il isplacmnt can b foun in bilinar moling capacit spctrum curv in EC8 (003). irstl, th top isplacmnt an bas shar can b foun b using pushovr mtho which loa with stat istributing along th hight of b structurs loas. Th cofficints of th quivalnt SDO sstm ar givn b n n b =, =, Γ= mφ / mφ, j j j j j= 1 j= 1 Γ Γ whr Γ is th cofficint concrn with vibration mos, usuall onl th first orr cofficint is slct. curv as shown ig.. is orinat valu corrsponing to maximum valu in th curv. Th curv is simplifi to ializ bilinar curv in which horizontal lin is ma through an intrsct with lin which graint is k. Th abscissa magnitu of point of intrsction is. Th trmination of inclination k an shoul b mt th conition that th m k m igur. Ialization of Pushovr curv in EC8 ara nclos b bilinar curv an abscissa shoul qual to th ara nclos b abscissa. /1. 5,morovr m = t t = S ( T a / 4π ) T Tc curv an

4 T 1 Tc t = S a 1 + ( q 1) 4π q T t is targt isplacmnt whil loaing in pushovr analsis, whr n a j j j= 1 T Tc q S /( / m ), m mφ. = = B sam pushovr mtho, th bas shar an top isplacmnt an quivalnt il isplacmnt in th bilinar capacit spctrum curv ar foun in EMA356. But thr ar iffrncs onl in ciing of bilinar curv. It is suggst b EMA356 that th initial stiffnss stimat is govrn b th rquirmnt that th actual an ializ curvs intrsct at 0.6, an post-il stiffnss is govrn b th rquirmnt for th curvs to mt at th targt isplacmnt. an ar slct b trial an rror so as to giv approximatl qual aras unr bilinar curv an curv in th targt isplacmnt, as shown in ig. 3. b 0.6 α k k t m igur 3. Ialization of Pushovr curv in ma356 Th targt isplacmnt unr sign sismic wav is slct b th following formula: =ΓS ( T /4 π ) T T t a c T 1 T 1 ( 1) c t =Γ Sa q T Tc, 4π q + < T whr T is ializ lastic prios, S a is acclration rspons spctra corrsponing to T, Tc is promination prios of groun movmnt. b vibration mo cofficint Γ rspctivl. an can b foun if an ar multipli Th isavantags of th mthos propos b EC8 an EMA356 ar computing trial an rror is n, an bcaus thr ar iffrnc of initial stiffnss slct b using EC8 mtho an EMA356 mtho rspctivl, th valu of T gottn b EC8 mtho is gratr than that gottn b EMA356. If pushovr curv is trilinar tp, th ifficult problm of computing trial an rror occur to both EC8 an EMA356 mtho. It is suggst that th nonlinar charactristic of sismic structurs ar not b th floor strngth cofficint ξ in th papr. ξ Y Y is xprss as following ξ u() i u() i V() i Y() i = η p = =, (1) u () i u () i V () i p whr η is an incrscnt cofficint of floor lastoplastic isplacmnt. Th valu is from 1.3 to. p for multi-stor frams. u (), i V () i ar floor lastic isplacmnt an lastic shar which ar foun

5 onl b lastic analsis or b lastic rspons spctra vibration mo composition mtho. B vibration mo composition mtho in which lastic rspons spctra corrspon to th Co for Sismic Dsign of Builings in China ar mplo, th valu of u (), i V () i in statistical sns can b foun. Th floor il isplacmnt an il shar V () i can b foun irctl b th sign cross sction an sign rinforcmnt numbr of th structur mmbrs. Thn th quivalnt il shar ar foun accoring to first orr vibration mo iφi =. () Γ Th quivalnt lastic bas shar is foun b bas shar mtho. Thn, th il strngth cofficint of quivalnt SDO sstm is ξ = / = /. (3) or consiring th affct of all kins of arthquak wavs, svral iffrnt kins of arthquak wavs ar chosn an tim-histor mtho is mplo to fin th lastic maximum isplacmnt of frams. Thn th lastic isplacmnt of quivalnt SDO sstm is foun accoring to first vibration mo, an Eq. 3 is mplo to fin 1 an ξ. It is obsrv that th lastoplastic analsis o not n if th mtho propos b th papr is us. Evn if th ffcts of all kins of arthquak wavs ar rquir to consir, onl lastic tim-histor analsis mtho is n. Th rationalit of th mtho is valiat b intification mtho bas th nrg quivalnt critrion. Yil isplacmnt of quivalnt lastoplastic SDO sstm ar intifi b th critria that th hstrtic nrg pr unit mass of original fram qual to that of th quivalnt SDO sstm. Th formula which ar crat b Akiama (1985 an 1988) an tim-histor mtho ar mplo to comput th hstrtic nrg. Th valiat rsult is shown lattrl b an xampl. THE IMPROVED CAPACITY SPECTRUM METHOD BASED INELASTIC DEMAND SPECTRA AND ANALYTIC PROCESS Th improv capacit spctrum mtho, in which th inlastic man spctra ar riv from th sign acclration rspons spctra spcifi in th Co for Sismic Dsign of Builings in China an th il isplacmnt an il forc of th quivalnt SDO sstm ar trmin bas on th structural sign paramtrs irctl accoring to th nrg quivalnt critrion, is propos in this contribution. Th analtic procss of improv capacit spctrum mtho is basicall sam as th analtic procss of traitional capacit spctrum mtho. Th iffrnt procss ar th lastoplastic man spctrum shoul b chosn accoring to th charactristic prio T g of a givn sit firstl, thn th pushovr curv shoul b ializ to bilinar capacit spctrum curv b fining ξ of th quivalnt SDO sstm using th mtho propos in th papr. Th subsqunt procss is to suprpos bilinar capacit spctrum curv an man spctrum curv, fin th intrsction of two curvs an isplacmnt man magnitu b th intrsction point. Thn convrt isplacmnt man magnitu into top isplacmnt of fram structur givn b δ =Γ φ D (4) targt 1 N1 t. Th pushovr analsis shoul b carri out again bas on th targt isplacmnt δ targt. Th formation of vr mmbr of sismic fram structur unr targt isplacmnt δ can b foun b loaing to th sismic fram structur grauall until th top isplacmnt of sismic fram structur is to targt isplacmnt δ. Th prformanc of sismic fram structur is valuat b targt targt th formation of vr mmbr of sismic fram structur unr targt isplacmnt δ. targt

6 EXAMPLE ANALYSIS To compar th iffrncs btwn th improv capacit spctrum mtho propos in th papr an th mthos in EC8 an EMA356, th ξ valu of th quivalnt SDO sstm of a 5-floor, 3- ba fram is calculat unr th arthquak wav for T = 0. 4 with th capacit spctrum mtho an tim-histor mtho rspctivl. Th rsults of th quivalnt paramtrξ ar shown in Tabl 1. Tabl 1. Th valu of g ξ calculat b intifing mtho of quivalnt nrg Earthquak Wavs USA01385 USA00631 USA01083 USA01945 USA0138 CHI00056 ξ Th rsults of th quivalnt mass valu, prio an il isplacmnt paramtrs of th fram ar shown in Tabl. Tabl. Cofficints of quivalnt SDO Tabl shows that th prios of th quivalnt SDO sstm is clos to th natural prio of th fram 1.06s, an ξ is about 0.4. It is obsrv from Tabl that th rsults obtain b th mtho of th papr ar closr to th rsults obtain b th mtho in th EMA356. Consiring th ffcts of arthquak wavs, svral iffrnt kins of arthquak wavs ar chosn an tim-histor mtho is appli to fin th lastic isplacmnt an ξ of fram. Th rsults ar shown in Tabl 3. Th rsults show thatξ varis with iffrnt arthquak wavs, whil th man valu has a littl iffrnc with th rsult comput b th mtho in EMA356 an EC8. If mor arthquak wavs ar chosn as input ata whn tim-histor mtho is carri out, mor accurat stimat of ξ in statistical sns can b foun. Thrfor, it is suggst that th mtho can b us in computing ξ of th quivalnt SDO. Rsults obtain b th propos mtho ( foun b bas shar mtho) Rsults obtain b th mtho in EMA356 Th ovrla of th capacit spctrum curv, which is ma b convrting th bas shar an top isplacmnt of th fram comput b pushovr mtho with invrt triangl loaing pattrn, an lastoplastic man spctra curv, is shown in ig. 4. Th abscissa valu of th intrsction of th two curvs is 0.061, whil ξ =0.4, can b foun in ig.4. Th first mo cofficint of th fram Γ 1 is 1.4, b substituting Γ = to Eq. 4, th targt isplacmnt or top isplacmnt of th fram is Rsults obtain b th mtho in EC8(003) T(s) D (m) D t (m) (kn) ξ M(kG)

7 δ targt = top = m. Th Pushovr analsis is carri out again bas on th targt isplacmntδ targt. Th formations of all mmbrs of th fram structur unr targt isplacmnt δ ar foun b loaing grauall until th top isplacmnt is th targt isplacmnt δ. Wav nam Tabl 3. Rsults obtain b th propos mtho targt ξ of quivalnt SDO targt Rsults obtain b th mtho in EMA356 Rsults obtain b th mtho in EC8 USA01385 (L tp) CHI00056 (L tp) USA00631(M tp) USA01083(M tp) USA0138 (S tp) USA01945(S tp) Man-St Man Man+St Sa(m/s/s) S(m) ξ=0. ξ=0.3 ξ=0.4 ξ=0.5 ξ=0.6 Capacat curv igur 4. Capacit VS Rquirmnt spctrum of 5-stor fram CONCLUSIONS Two aspcts of improvmnts ar ma on th prsnt capacit spctrum mtho in th papr. Th inlastic man spctra b using th il strngth factor as an lastoplastic inx an corrsponing to th sign acclration rspons spctra spcifi in th Co for Sismic Dsign of Builings in China ar fin an formulat. Accoring to th nrg quivalnt critrion, th quivalnt SDO sstm ar trmin bas on th structural sign paramtrs irctl which ar usuall trmin b bilinar moling of pushovr curvs of structurs unr ara quivalnt assumption in som prsnt cos as EMA356 an EC8 spcifi. Th comparison of rsults shows th improv mtho is mor simpl an prcis which can b asil carri out in structural sismic sign.

8 ACKNOWLEDGMENTS This rsarch is sponsor b National Natural Scinc ounation of China unr Grant No REERENCES Akiama, H. (1985). Earthquak Limit-Stat Dsign for Builings, Univrsit of Toko Prss. Akiama, H. (1988). Earthquak Rsistant Dsign Bas on th Enrg Concpt, Procings of 9 th WCEE, , Calvi, G.M. (1999). A Displacmnt-Bas Approach for Vulnrabilit Evaluation of Classs of Builings, Journal of arthquak Enginring, 3, CEN. (003). EN1998 Euroco 8: Dsign of structurs for arthquak rsistanc, British Stanars & Eurocos, part1 EMA. (000). Rport EMA 356:Prstanar an commntar for th sismic rhabilitation of builings. ajfar, P. (1999). Capacit Spctrum Mtho Bas on Inlastic Dman Spctra, Earthquak Enginring an Structural Dnamics, 8, rman, S.A., Nicoltti, J.P., an Trll. (1975). Evaluation of Existing Builings for Sismic Risk-A Cas Stu of Pugt Soun Naval Shipar Brmrton, Procings of 1 st U.S. National Confrnc on Earthquak Enginring, Washington, Kowalsk, M.J., Pristl, M.J.N., an Macra, G.A. (1995). Displacmnt-bas sign of RC brig columns in sismic rgions, Earthquak Enginring an Structural Dnamics, 4, MINISTRY O CONSTRUCTION P.R.China. (00). Sismic Structur Dsign Co GB Mirana, E., an Brtro, V.V. (1994). Evaluation of Strngth Ruction actors for Earthquak-Rsistant Dsign, Earthquak Spctra, 10, Mohl, J.P. (199). Displacmnt-bas sign of R/C structurs subjct to arthquaks, Earthquak Spctra, 8(3),

Development of Shear-key Consisted of Steel Disk and Anchor Bolt for Seismic Retrofitting

Development of Shear-key Consisted of Steel Disk and Anchor Bolt for Seismic Retrofitting Dvlopmnt of Shar-ky Consist of Stl Disk an Anchor olt for Sismic Rtrofitting. Takas & T. Ika Rsrch Institut of Tchnology, TOISHIMA Corporation, Japan. agisawa, T. Satoh & K. Imai Tchnological vlopmnt,