Determining the Maximum Lateral Displacement Due to Sever Earthquakes without Using Nonlinear Analysis

Transcription

1 Word Academ of Science, Enineerin and Technoo 5 9 Determinin the Maximm Latera Dipacement De to Sever Earthqake withot Uin Noninear Anai Ma Mahmodi Abtract For Seimic dein, it i important to etimate, maximm atera dipacement (ineatic dipacement) of the trctre de to ever earthqake for evera reaon. Seimic dein proviion etimate the maximm roof and tore drift occrrin in major earthqake b ampifin the drift of the trctre obtained b eatic anai bjected to eimic dein oad, with a coefficient named dipacement ampification factor which i reater than one. Here, thi coefficient depend on vario parameter, ch a dctiit and overtrenth factor. The preent reearch aim to evaate the vae of the dipacement ampification factor in eimic dein code and then trie to propoe a vae to etimate the maximm atera trctra dipacement from ever earthqake, withot in non-inear anai. In eimic code, ince the dipacement ampification i reated to force redction factor hence; thi apect ha been accepted in the crrent td. Meanwhie, two methodooie are appied to evaate the vae of dipacement ampification factor and it reation with the force redction factor. In the firt methodoo, which i appied for a trctre, the ratio of dipacement ampification and force redction factor i determined direct. Wherea, in the econd methodoo that i appicabe jt for / moment reitin frame, the ratio i obtained b cacatin both factor, eparate. The acqired ret of thee methodooie are aike and etimate the ratio of two factor from to.. The ret indicate that the ratio of the dipacement ampification factor and the force redction factor differ to thoe propoed b eimic proviion ch a NEHP, IB and Iranian eimic code (tandard no. 8). Keword Dipacement ampification factor,, Force redction factor, Maximm atera dipacement. I. INTODUTION STIMATING the maximm atera dipacement of the E trctre in the wake of maive earthqake i conidered to be wide important for eimic dein. Thee incde: etimatin minimm eparation joint width to avoid pondin, etimatin maximm tore drift to avoid detrction of non-trctra eement and performance of p- deta anai. De to economic reaon, the preent eimic code often aow trctre to ndero ineatic deformation in the event of tron rond motion. oneqent, the demand atera trenth i ower than the reqired trenth to maintain the trctre in the eatic rane. M. Mahmodi, ivi Enineerin Department, Shahid ajaee Teacher Trainin Univerit, Tehran, Iran, phone and Fax: 9897, e-mai: m.mahmodi@rtt.ed. The demand atera trenth i obtained b dividin the reqired f eatic trenth to the force redction factor (). A ch, the dipacement (or drift), cacated b anazin trctre nder the atera dein force i not the rea dipacement, rather it i e than the maximm trctra dipacement drin tron motion. Seimic dein proviion, etimate the maximm roof dipacement and tore drift b amentin the dipacement and drift obtained from eatic anai b dipacement ampification factor ( ): Δ max = Δ e () Where Δ max i the maximm ineatic dipacement (roof or tore drift), Δ e i the dipacement cacated b eatic anai and i the dipacement ampification factor. Since, depend on force redction factor (), therefore, it i important to evaate the ratio of both dipacement ampification factor (DAF) and force redction factor (FF). Here, two approache are eected to evaate / ratio. The firt approach enera determine the ratio of / for a trctre, bt the econd approach, which i jt acceptabe for / moment reitin frame, obtain the vae of and eparate and then cacate their ratio. II. FIST APPOAH: DIET EVALUATION OF THE ATIO Fi. how the acta repone enveope and ideaized eato-patic repone crve and the foowed b three qantitie []: Bae Shear e Ideaized Δ w Δ Δ Δ e Drift, Fi. Genera Strctra epone Acta 6

2 Word Academ of Science, Enineerin and Technoo 5 9 = Δ / () max Δ = e / () = / (4) Where = tem dctiit factor, = dctiit redction factor, = trctra overtrenth factor, Δ = tem ied dipacement, e = f eatic bae hear ratio, = ied trenth eve and = firt inificant ied eve bae hare ratio. It i hown [] that the force redction and dipacement ampification factor, for workin tre dein cae, can be expreed a: = Y (5) = Y (6) d Y = / w (7) Where Y denote aowabe tre factor appied for workin tre dein and, w i correpondin dein force eve. The force redction and dipacement ampification factor, for timate trenth dein cae, cod be expreed a: = (8) d = (9) Where the vae of Y i eqa to one. ( w = ). oniderin the eqation (5) to (9), the ratio of and i th: d Y = or ) = Y ( () Eqation () how that the ratio of / for timate trenth dein and workin tre dein are the ame hence; it wod be better to evaate the ratio of intead of /. It i concded that the ratio of / depend on the dctiit factor and the parameter affectin, ch a tem dctiit factor, fndamenta period of trctre, materia oad-dipacement mode, dampin ratio, ite effect and the characteritic of earthqake (PGA, dration and freqenc content) []. A. Determination of ratio With reard to eqation (), it i th feaibe to evaate the ratio of intead of. Severa forma have been eted a force redction factor ( ) b Newmark and Ha [], idde [], Krawinker [4] and Miranda [5]. The factor, propoed b Newmark-Ha, depend on dctiit factor ( ) and trctra fndamenta period (T): = T. 5 () = T >. 5 At the ame time, dctiit factor and trctra fndamenta period ao affect on the forma propoed b idde: * = + * T = T > T * * T T () Where * and T* are determined from the tabe propoed b idde in term of tem dctiit factor. Krawinker factor depend on fndamenta period of tem (T), dctiit factor ( ) and train hardenin ratio (α ). It i amed the vae of train hardenin ratio i eqa to zero in thi paper: / = [ ( ) + ] () a T b = + a T + T Accordin to Krawinker Tabe, when α=, the vae of a, and b are eqa to one and.4 repective. The force redction factor a eted b Miranda depend on dctiit factor ( ), trctra fndamenta period (T), predominant period of the rond motion ( T ) and ite characteritic. The crrent paper th appie the forma for rock ite a: = + (4) Φ Φ = + T T exp[ T (n T Fi. to how the ratio of to ) 5 ] ( ) (or DAF/FF) which have been cacated in term of and T. Fi. indicate reationhip between the ratio of and tem fndamenta period a determined b aforementioned forma. Baed on Fi., evera concion can be drawn. The minimm vae of i abot.85, extracted b Miranda eqation. The maximm vae for i.5, which i reated to the eqation of Miranda and Krawinker. It i fond that the ratio of i hih when the vae of the period i ow and become eqa to one when the period i hih. 7

3 Word Academ of Science, Enineerin and Technoo 5 9 Fi. -6 how the ratio of, which wa compted in eqation and ha aread been expained above for =, 4, 6 and 8 repective. The minimm vae for a cae i approximate.8. The vae increae with increain dctiit factor. The ratio of i hiher than one when the fndamenta period i e than.7 ec. The atio of DAF to FF Period () Fi. The ratio The atio of DAF to FF IDD. KA. MIA. ver fndamenta period for tem dctiit factor= Period () Fi. The ratio The atio of DAF to FF IDD. KA. MIA. ver fndamenta period for tem dctiit factor= Period () Fi. 4 The ratio IDD. KA. MIA. ver fndamenta period for tem dctiit factor=4 The atio of DAF to FF Period () Fi. 5 The ratio The ratio of DAF to FF IDD. KA. MIA. ver fndamenta period for tem dctiit factor=6 4 Period () Fi. 6 The ratio IDD. KA. ver fndamenta period for tem dctiit factor=8 Fi. 7 hihiht the variation of the in term of dctiit factor for T=.. A ch, the fire how that the ratio tron depend on dctiit factor. The minimm vae i one for a forma. Fi. 8 to how the reationhip between the ratio in term of dctiit factor compted a T=.,.5,, and 4 ec. The minimm vae for the ratio in Fi. 8 and 9 i one and eqa to.9 and.85 in Fi. and, repective. Meanwhie, the maximm vae of the ratio increae with increain dctiit factor and decreae with increain T. The atio of DAF to FF IDD. KA. MIA. ver tem dctiit factor for Fi. 7 The ratio fndamenta period=. ec. 8

4 Word Academ of Science, Enineerin and Technoo 5 9 The atio of DAF to FF Fi. 8 The ratio The atio of DAF to FF Fi. 9 The ratio The atio of DAF to FF IDD. KA. MIA. ver tem dctiit factor for fndamenta period=. ec IDD. KA. MIA. ver tem dctiit factor for fndamenta period=.5 ec Fi. The ratio The atio of DAF to FF IDD. KA. MIA. ver tem dctiit factor for fndamenta period= ec Fi. The ratio IDD. KA. MIA. ver tem dctiit factor for fndamenta period=4 ec. III. SEOND APPOAH: SEPAATE EVALUATION OF D AND FATOS In thi approach, vae of the dipacement ampification factor and the force redction factor are determined in eqation (5) and (6) eparate and then their ratio are obtained. = Y (5 repeat) = Y (6 repeat) d The preent reearch evaate the vae of and for / moment reitin frame hence; it i necear here to cacate the vae of dctiit factor, overtrenth factor, force redction factor and afet factor. The cacation and their vae for trctre with one to fifteen torie are preented in [6], [7]. A. Determination of the Force edction Factor Step : determination of member rotationa dctiit factor otationa dctiit factor for beam and comn ( ) i expreed a foow: = (5) Where i the timate rotation for patic hine and it vae wi be eected accordin to FEMA (Federa Emerenc Manaement Aenc) hown in Tabe I [8]. TABLE I THE VALUES OF Member Beam. omn.5 i the ied rotation and cacated accordin to FEMA-7. In Tabe II the vae of i preented for a frame (beam and comn eparate) [8]. TABLE II THE VALUES OF MEMBES OTATION DUTILITY ( ) (no. of torie) Beam omn

5 Word Academ of Science, Enineerin and Technoo Step : acation of oba dctiit factor The reationhip between oba dctiit factor ( ) and oca dctiit factor ( ) for / moment reitin frame are a foow []: A- eation between oba dctiit and beam dctiit factor: = ab ( b.4) + (6).4. a b =.+ (7) N N B- eation between oba dctiit and comn dctiit factor: = ac ( c.4) + (8). 57 a c =.85 + (9) N Where N i the nmber of torie, b and c are the critica beam dctiit and critica comn dctiit repective in moment reitin frame. The minimm vae of in eqation 6 to 9 i a the oba dctiit factor of frame ( ).Tabe III how the vae of oba dctiit factor for a frame. Step : determination of Uin determined in tep and amin tre hardenin (α ) eqa to. (a=, b=.7) and in eqation, the force redction factor de to dctiit ( ) are cacated. The vae of ( ) i preented in Tabe IV. TABLE III GLOBAL DUTILITY FATOES (no. of (no. of torie) torie) TABLE IV FOE EDUTION FATOES DUE TO DUTILITY (no. of torie) (no. of torie) Step 4: acation of overtrenth factor In ref. [], the overtrenth factor ( ) wa determined for a frame. The vae of overtrenth factor i preented in Tabe V. TABLE V OVESTENGTH FATOES (no. of torie) (no. of torie) Step 5: Determination of afet factor The vae of afet factor depend on ampification oad factor and trenth redction factor. For exampe, in AI89 code, the vae of afet factor eqa to.4 (..7.75=.4). Step 6: Evaation of the force redction factor In the previo ection the item affectin on force redction factor (, andy ) were determined. Uin thee factor, the vae of i cacated accordin to eqation 5 and hown in Tabe VI. B. Determination of the dipacement ampification factor The vae of dipacement ampification factor ( d ) i obtained in eqation 6. The vae of d i hown in Tabe VI. The ratio of the force redction factor and the dipacement ampification factor i preented in Tabe VI too. TABLE VI FOE EDUTION FATOS, DISPLAEMENT AMPLIFIATION FATOS AND THEI ATIO (no. of / torie

6 Word Academ of Science, Enineerin and Technoo 5 9 Tabe VI how the ratio of dipacement ampification factor to force redction factor i eqa to one approximate, except for bidin havin hort period. IV. SEISMI POVISION OF D / Thi ection dea with / a recommended b NEHP, IB and Iranian eimic code (tandard no. 8). Tabe VII it the maximm and minimm vae of / ratio, iven b NEHP [9]. TABLE VII NEHP- EOMMENDED MAXIMUM AND MINIMUM ATIO OF D AND Maximm Minimm Strctra tem vae vae Bearin wa tem.6 Bidin frame tem.5 Moment reitin frame tem.9.69 Da tem with a pecia moment frame Da tem with an intermediate moment frame Inverted pendm trctre eimic force reitin tem Tabe IIX indicate the maximm and minimm vae for / a recommended b IB code []. TABLE VIII IB- EOMMENDED MAXIMUM AND MINIMUM ATIO OF D AND Maximm Minimm Strctra tem vae vae Bearin wa tem.67 Bidin frame tem.5 Moment reitin frame tem.9.69 Da tem with a pecia moment frame.9.5 Da tem with an intermediate moment frame Inverted pendm trctre eimic force reitin tem Iranian eimic code e on one vae for / which i eqa to.7 []. Baed on Tabe VII and IIX, it i oberved that the ratio of / i never arer than one except for inverted pendm trctre eimic force reitin tem. V. ONLUSION The preent td ha appied two methodooie to dic, in detai, abot the dipacement ampification factor and the force redction factor. In the firt methodoo, which i appied for a trctre, the ratio of dipacement ampification factor and force redction factor i determined direct. Wherea, in the econd methodoo that i jt appicabe for / moment reitin frame, two factor are cacated eparate and then their ratio have been obtained. The ret from firt method indicate that the minimm vae for the ratio of dipacement ampification and force redction factor i.8. It howed that the minimm vae increae with increain dctiit factor and decreain of fndamenta period. The ratio / cod be mch hiher than. for dctie frame tem (hih dctiit) and tiff bidin (ow fndamenta period). Meanwhie, the ratio / went p to more than.5 for ow period tem. The ret acqired from the econd methodoo how that the / ratio i abot. except for hort period bidin. With reference to the ret from thee two approache, it eem that the vae for dipacement ampification factor to be down etimated, epecia for bidin with hort period. The factor, recommended b NEHP, IB and Iranian eimic code (tandard no. 8) are ow and therefore the need to be modified, epecia for bidin havin hih dctiit and ow period. In order to cacate the maximm atera dipacement, the modified vae of dipacement ampification factor can be eted a: =. T<.5 ec. = T.5 ec. Where, T=trctra fndamenta period and =force redction factor. EFEENES [] Uan., Maarof A., Dipacement ampification factor for eimic dein proviion, Strctra Enineerin, (8):4-46, 994. [] Mahmodi M., The effect of period and overtrenth on eimic ineatic demand of / fexra frame (Perian), A thei preented for the deree of doctor of phiooph in trctra enineerin; Tarbiat Modarre Univerit; Iran; 999. [] idde, Hidao P., rz E., epone modification factor for earthqake reitant dein of hort period bidin, Earthqake Spectra, 5():57-589, 989. [4] Naar A., Oteraa J., Krawinker H., Seimic dein baed on trenth and dctiit demand, Proceedin of the Earthqake Enineerin, Tenth Word onference, Bakema, oterdam, p: , 99. [5] Miranda E., Site-dependent trenth-redction factor, Strctra Enineerin; 9(), 5-59, 99. [6] Mahmodi M., Performance Baed Dein Uin Force edction and Dipacement Ampification Factor for MF, Firt Eropean onference on Earthqake Enineerin and Seimoo, Geneva, Switzerand, -8 September 6. [7] Mahmodi M., The Primar Evaation of MF With the Aim of Performance Baed Dein, Jorna of Technoo & Edcation, Vo., No., p. 99-6, 7. [8] Federa Emerenc Manaement Aenc, (997), NEHP Gideine for Seimic ehabiitation of Bidin, FEMA 7. [9] NEHP recommended proviion for the deveopment of eimic reation for new bidin, Bd. Seimic Safet onci; Wahinton, D.., 994. [] Internationa Bidin ode (IB), Internationa ode onci,. [] Iranian code of practice for eimic reitant dein of bidin (tandard no. 8), Bidin & hoin reearch center, 999.