Hieu suat sup khung be tong cot thep chju dja chan SLF dung phan tich tmh phi tuyen Ngay nhan bai: 9/12/2013 Ngay siia bai: 23/12/2013 Ngay chap nhan dang: 27/12/2013 T O M TAT: Bai bao trinh bay mot quy trinh danh gia hieu suJt sup cua kit cau cilia tren quy trinh ky thuat dpng dat dila vao hieu suat (PBEE) cua Trung tam nghien cdu dpng dat Thai Binh DilOng (PEER) sd dung ca phan tich dpng va phan tich tinh phi tuyen. Do tin cay cda philong phap tinh da dilOc kiem chiing cho cac khung phang be tong cot thep chiu momen 4, 8, 12 va 20 tang, chiu mpt bp 40 tran dpng dat manh co xac suat xay la 2% 50 nam. Ket qua cua quy trinh sd dung philOng phap tinh dilOc so sanh vcri kit qua til philong phap dpng cho thay mpt sii xap xi rat tot va tinh hieu qua cda phflong phap nay. TCl khoa: Ky thuat dpng dat dila vao hieu suat PBEE, hieu suat sup do, phan tich dpng gia tang (IDA), phan tich tinh phi tuyen (NSP). ABSTRACT This paper presents an approach to evaluate collapse performance of building based on the Performance-Based Earthquake Engineering (PBEE) methodology of the Pacific Earthquake Engineering Research Center (PEER) by using both Nonlinear Static Procedure (NSP) and nonlinear dynamic procedure. The reliability of NSP is evaluated for 4-, 8-, 12-, and 20-story reinforced concrete special moment frame (RC-SMRF) buildings, which are subjected to 40 strong ground motions having 2% probability of being exceeded in 50 years. The results of NSP are compared with nonlinear response history analysis (NL-RHA) method, demonstrating that NSP requires only a small fraction of the computational effort inherent in exact IDA and still achieves highly accurate results. Keywords: Performance-Based Earthquake Engineering (PBEE), collapse performance, Incremental Dynamic Analysis (IDA), Nonlinear Static Procedure (NSP). KSUVanKhi Khoa Ky thuat xay dilng, Trfldng Dai hoc Bach khoa TP HCM 268 Ly Thilclng Kiet, phfldng 14, Quan 10, Tp Ho Chi Minh Di dong: 093.943.0555 Email: levankha_datminh_lp@yahoo.com.vn TS Nguyin Hong An dneinnnn'nsi'i 01.2014 Le Van Kha, Nguyen Hong An Gidi thilu Ky thuit ddng dat dUa vio hieu suit (Performance-Based Earthquake Engineering, PBEE [1]) la mdt quy trinh kit hpp cic cip dp hieu suit mpng mudn vio qui trinh thilt kl, cung cip eac kiln thflc can thilt cho viee thilt kl, dinh gii va quin ly cdng trinh ed hilu qui, nham cii thien va quin ly nhflng rfli ro thilt hai ddng dat. Phien ban dau tien cfla quy trinh PBEE (ATC-40 [2] v i FEMA-273 [3]) da danh dau mdt bfldc tiln Idn Si chuan hda eic khii niem ve y tfldng hieu suat thflc hinh thilt ke dpng dat nhilu nam [1]. Cac phit trien tiep theo cfla PBEE la FEIVIA356 [4] va FEMA-350 [5] nhflng van tdn tai nhilu han chi. Sau dd, Trung tam nghien cflu ddng dit Thai Blnh Duong (PEEI?) [6] da cd nhflng cil tiln quan trpng phuong phip PBEE. Khudn khd hieu suit cfla PEER eung cap mdt phflflng phip rd rang, cd co sd khoa hpc manh me Si xic djnh hieu suit cdng trinh dfla tren xic suit theo mdt tiln trinh tflng bfldc, cung cap cie thude hieu suat de djnh luong tdn that kinh te, rfli ro thflong vong (casualty risk) v i thdi gian cdng trinh tam ngflng boat ddng (downtime) giup cic ben liln quan cd nhilu thdng tin eg t h i hon de dat duoc muc tieu hieu suit mong mudn [7,8]. Quy trinh danh gia hieu suit cua PEERdi duoc i p dung rpng rii trin t h i gidi. Nghien cflu dfla theo nhflng chi din danh gii hilu suit cua PEER. Mdt nhflng muc tieu cdt Idi cua quy trinh danh gia hieu suit cua PEER la djnh Iflong hieu suit sup hay danh gia rfli ro sup cfla cdng trinh (di tdn tai hoac dang qua trinh thilt kl). Sup d diy dflpc hieu l i mat on djnh ddng tdng t h i (Global Instability, Gl) khi ning chju t i i ngang suy giim kit cau bj hu hdng bdi lire ddng dat vi inh hfldng cfla hi|u flng P-i. Hai dai dien chp sfl tiem an sup dp l i xae suit sup dp (P[Collapse|IIVl])vi tan suat trung binh hang nim efla sir sup (\„,,pj,,) tflong flng vdi cap dp dpng dat quan tim [9]. B l bio v l cdng trinh khdi sup va lim co sd cho vi§c fldc tinh cic hfl hai va ton that (tii chinh, thflong vong .) ddng dit trpng tflong lai, viec tinh toin ehinh xae hai dai Iflong niy l i rat quan trpng. Cd nhilu phuong phap dflpe phit triln Si giii quylt van de nay, dd cd ci phuong phap ddng va phuong phip tinh. Phflong phip phin tfch ddng gia tang (Incremental Dynamic Analysis, IDA [10]) d i dflpc dUa vao tilu chuan dja chan hien dai (FEMA 350), dflpc xem nhfl l i phflong phip fldc tinh ehinh xae nhit cic trang thai gidi han cfla cdng trinh, dd cd sfl sup dd mat dn djnh ddng tdng thi. Vi l i phflong phip ddi hdi mdt chuoi cie phin tich ddng phi tuyln theo ljch sflthdi gian (Nonlinear Response History Analysis, NLRHA) eho nhilu cap dp khac efla cic dao ddng nen, nln viec ip dung phuong phip IDA ddi hdi mdt quy trinh tuong ddi phflc tap gdm nhilu bfldc va tdn nhilu thdi gian, ngudn lfle. Sfl dung thuit toan thich hop (vidu hunt-and-hill-tracing [10,11]) ed the lim giim sd I'an phan tich NL-RHA can thilt de tao moi dfldng cong IDA tfl mdt dao dpng nen rieng 1^, nhien sd Iflpng phan tich van l i rat Idn (Chopra etal. [12]). Trong IDA phflc tap va tdn n h i l u thdi gian, mot sd phuang phap don g i i n dfla t r i n phan tich tinh phi tuyen (Nonlinear Static Procedures, NSP) van la sfl lfla chpn k h i thi v i ed t h i dflpc i p dung trpng thue hanh thiet k l m i khdng can cung cap cie dap ddng nen. D i e biet la d i n h g i i k h i n i n g sup S6 mat dn djnh ddng cua k i t cau, NSP trd nen chinh x i c hon sfl sup dflOc chi phdi chu y l u bdi dang dao ddng dau tien (mode 1) [13]. Phuang p h i p tinh don g i i n , nhanh chdng hon, giup xap xi flng xfl cfla he n h i l u b i c t u (MDOF) bdi md hinh he mdt b i c t f l (SDOF) tflong dflong cd dfldng cong k h i nang (backbone curve) phu hop vdi dfldng cong day d i n tTnh (SPO) eua he k i t cau. Tuy cd n h i l u phuong p h i p gidng nhu v i y tdn tai nhflng thfldng sd dung dang dudng cong k h i n i n g la song t u y l n tinh (bilinear) [14,15]. Nghiln cflu sfldung phflong phap SPO-to-IDA (the Static Pushover-to-lneremental Dynamic Analysis, SP02IDA [16,17]) phat t r i l n bdi Vamvatsikos va Cornell, cho phep sfl dung cic dang dfldng cong k h i nang tfl song t u y l n tinh d i n t f l t u y l n tinh (quadrillnear) phflc tap, giup tao cac dfldng cong IDA chinh x i c hon, cho phep ngfldi sfl dung dat dflOc nhflng fldc tinh chinh x i c ve c i c thdng sd p h i n flng (Engineering Demand Parameter, EDP) va k h i ning (Intensity Measure, IM) efla k i t cau cho cac trang t h i i gidi ban quan tam, ed m i t on djnh ddng tdng the (Gl). 2. Quy trinh danh gia hieu suHt sup theo PEER Hieu suit sup dd theo quy trinh PBEE cfla PEER dac trflng bdi hai dai Iflong P[Collapse|IM] v i \„^ ^. Quy trtnh d i n h gia bao gdm bfldc [9]. ""^ Bfldc 1: Phin tich rui ro vj tri (Hazard Analysis). M i l u t i x i c s u i t x i y cua cac t r i n dpng dat tai c i c vj tri cu the, d i e trflng bdi biln dac cfldng dp (IM). Sfl dung phd gia tdc, Sa(T1, (,), tfldng flng vdi ti sd c i n {(.) va chu ky d mode dao ddng dau t i l n (Tl) cfla he k i t eau n h f l l i mdt dai dien ehinh cho IM. Trong dd X[IM] la tan s u i t trung binh h i n g n i m cfla sfl vflpt mdt cfldng dp dap ddng n l n cu the, la mdt ham cua IM. Bfldc dfloc thflc hien bdi c i c ky sfl dja chan [8], cung cap: (1) mdt p h i n tich x i c suit nguy hiem dja chan (Probabilistic Seismic Hazard Analysis, PSHA) cho vj tri cu the, (2) mdt p h i n flng (Uniform Hazard Spectrum, LJHS) cho c i c cap dp dpng dat khac (vi du x i c suit x i y 2% 50 n i m ) , v i (3) vdi mdi cap dp nhfl viy, cung cap mdt bp gdm n dap ddng nen de sfl dung p h i n tieh ddng phi t u y l n d bfldc t i l p theo. K i t q u i quan trpng n h i t cOa bfldc n i y la c i c bd dao ddng n l n dai di§n cho k I' u vflc x i y dung cdng trinh va dfldng cong nc ^iem dja chan (Hazard Curve) the J^n he gifla IM vdi X[IM] dat dupc hidn m t f l PSHA. Bfldc 2: Phan tich phan flng k i t eau. Mdt md hinh chi t i l t efla k i t eau cd ke d i n phi t u y l n hinh hpc v i vat lieu dupe tao ra, c i c dao dpng n l n cung cap t f l bfldc dflpc sfldung trpng md phdng bang IDA v i p h i n flng cua k i t c i u dflpc xac djnh b i n g eac thdng sd yeu cau ky t h u i t , c h i n g ban nhudp trdi t i n g d m i i , ^ , dflpc x i c djnh nhfl l i chuyin vj m i i chia chp chilu eao cdng trinh; hoac g i i trj Idn nhat cfla dp trdi t i n g d tat e i eac tang, 6^^^ xac djnh bang cich chia dp trdi cho chieu cao mdi tang. Cudng dp dao ddng n l n gay sup (do m i t on djnh dpng) cdng trinh dupe gpi la cudng dp sup dd hay"khi n i n g sup dp"(Sa;.) cua cdng trinh [18].Thdng ke t i t c i c i c gia trj Sa^. d l tao dfldng cong p h i n phdi x i c suit (Cumulative probability function, CDF) sup P[Collapse|IM]. Tan suit trung blnh hang nam cua sfl sup i\„^^^ J dupe tinh t o i n bang c i c h lay tieh p h i n dudng eong P[Collapse|IM] efla cdng tnnh vdi dfldng eong nguy hiem dja chan thu dupc tfl bfldc theo phflong trtnh (1) (Ibarra 2003, phflong trinh (7.10) [19]). ^collapse = j"p[Sac) 0.15 Hlnti 1. Cic dildng cong IDA cda khung BTCT chjumdmen4 tang (ID1010) dildl 40 tran dong dat Moi diem trdn t r i n hinh tflong flng vdi mdt p h i n tich NL-RHA cho mdt cap cfldng dp eua mdt dao ddng n l n va sfl mat dn djnh dpng tpng the b i l u h i l n bdi d i e tinh n i m ngang (flatline) cfla mdi dfldng cong IDA nay, d dd p h i n flng dja c h i n cua k i t cau (6 J t i n g oi.2oi4Bnnicdai 107 Oill (c) 0.02 0.03 DO M i t i n g m i l (6!,^) O.OOS (d) 0.01 0.01 S 0.02 B9 trai t i n g mai (£>„,,) Hinh 2. Cac ducrng cong SPO vdi 4dang phan phoi tai: (a) Ichung 4tang (IDIOIO); (b) khung Stdog (101024): (c) Uiimg 12 tang (101015); va (d) khmg20 tdng (101020) 3500 3M0 2500 ^ 2000 ^ 1500 • Duimg l ; tUAng hOa'vy^ .1 •>^ 1000 - •- • —•—Ci»n 500 < ' '-^ X X -»—' dung he mdt b i c t u dp (SDOF) tflOng dflong de xap xi cho he n h i l u bac t f l (MDOF), cic k i t q u i p h i n vj IDA eho he SDOF thu dupe tfl SP02IDA ed the dflpc sfl dung d l xap xi chinh x i c flng xfl dja chan cfla he MDOF Phflong phap ddi hdi sfl dung he SDOF cd dfldng cong k h i nang phu hop nhat vdi dfldng cong SPO"te nhat" cfla he MDOF de xap xi chinh xie p h i n flng ddng cfla nd. Dfldng cong dflpe tao b i n g c i c h thflc hien cic phan tich diy d i n tinh tflong flng vdi cie dang p h i n phdi t i i ngang cung cap bdi FEMA 356 hoac c i c dang t i i d l xuat bdi Vamvasikot v i Cornell [14]. Budng cong SPO "te n h i t " se tflong flng vdi trfldng hop cdng trtnh sup dd b i l n dang la it nhit. Thuc hien ly tudng hda dudng cong n i y de thu dflpc dfldng cong k h i nang cho he SDOF tflong dflong, va cudi cflng c i c p h i n vj IDA 16%, 50% va 84% cua he MDOF se dfloc fldc tinh. Hinh the hien c i c dfldng cong SPO eua bdn khung tren vdi mdt v i i trudng hop t i i tflong flng nhfl: (1) p h i n bd theo Iflc ngang tflong dflong (ELF); (2) p h i n bd theo dang dao ddng dau tien (first mpde); (3) theo dang c i n b i c hai cua tdng cae blnh phflong cfla hai dao dpng dau tien (twio modes SRSS); (4) la dang nghjch d i o cfla trfldng hop (3) (tw/o modes SRSS, then inverse), quan s i t c i c b i l u dd thi trfldng hop se cho dfldng cong SPO "te nhat". Sfl dung phflong p h i p 1;^ tfldng hda cfla Chopra et al. [8], dfldng cong kha nang tflong flng eho he SDOF tflong dflong cua cic khung dupe the h i l n tren hinh 3.Tfldd cic dfldng phan vj IDA 16%, 50% va 84% eho cie khung va c i c diem eudng dp sup Sa,. tuong flng Suae Udc tinh (hinh 4). Dp phan t i n (6) va trung binh logarit t u nhien (p) cfla nd dflpc tinh theo phflong trinh (3) [19]. :i|nfM%L = l"(>'50%) (c) 02 0.4 0.6 0.8 Chuydn vj mdi [m] 1.2 02 0.4 0.6 0.8 Chuydn \n mat [m] Hinh3.fluc(ng cong SPO'te nhaf'va dirdng ly tirdng hda tiwng dng: (a) khung 4tang (IDIOIO); (b) khang tdng (101024); (c) khung 12 tdng (101015); va (d) khang 20 tang (101020) vd ban vdi mdt sfl t i n g r i t nhd eua cfldng dp dap dpng n l n Sa(T1,0, cfldng dp sup dp (Sa^) tuong flng the hien bdi cie d i l m cudi efla moi dfldng cong IDA. Cie dfldng eong p h i n phdi xac s u i t sup dd (vdi tdng dp p h i n tan aLN,Total x i c djnh theo phflong trtnh (3)) tflOng flng cfla bdn khung n g h i l n cflu x i c djnh bang phflong p h i p IDA va SP02IDA duqc trinh bay va OSBWniCHB.'l 01.2014 so sanh d phan sau. 5. Phflong phap phan tich tfnh phi tuyen SP02IDA l i mpt phflong p h i p dua tren sfl k i t ndi gifla dfldng cong day dan tmh (SPO) vdi dfldng cong IDA t h i hien mdi quan he gifla cfldng dp dap ddng nen (Sa(Tl ,0) vdi p h i n flng cua k i t eau (S^J. Thdng qua mdt phflong phap tflong t u nhfl FEMA 273, dfla t r i n nguyen ly sfl (3) yx•^6%J Trong dd, x84%, x50% v i x16% tflong flng vdi c i c g i i trj cua SaC,84%, SaC,50%vi SaC,16% (cic diem cham trdn) tren hinh 4. 6. Ket q u i nghien culu Hinh trtnh bay eac dudng eong phin phdi xae s u i t sup dd cfla bdn khung BTCT chju mdmen nghien cflu n i y t f l phflong phip ddng IDA (Haseltpn et al. [9]) va phflong phip tinh d l x u i t (SP02IDA), sai sd gifla hai phflong phap t h i hien tren hinh 6. Tfl dd, eac g i i trj \oii.p« ^^dc fldc tinh bang c i c h lay tieh phin theo phflong trinh (1) eua moi dfldng cong vdi dfldng cong nguy hiem dja chan cho khu vuc x i y dflng edng trinh [9]. K i t q u i so sinh d i y dfl hon gifla hai phflong p h i p duoc trtnh b a y t r o n g B i n g 1. 7. Ket luan: Trong bai b i o nay, mdt nghien cflu so sanh gifla viec ap dung phflong phap tinh SP02IDA vdi phflong p h i p ddng IDA v i o quy trtnh danh g i i hieu suat sup dd cfla Trung t i m n g h i l n cflu ddng dat T h i i Blnh Dflong (PEER) da dfloc sup va hieu suit sup dp (bing 1) c i ddi vdi edng trtnh eao t i n g (20 ting). Su ehinh xie efla phflpng p h i p tTnh SP02IDA phu thudc chfl y l u vao viec lua chpn cic dang p h i n phdi tai ngang. Tuy nhien c i c dang t i i la khdng nhit, vl vay viec xem xet mpt vai dang t i i khic sfl dung phuang p h i p l i c i n thiet. (a) OJ02 OJ04 0.06 0.08 0.1 0.12 0.14 00 trolling I n n h j t « u 0.02 0.04 0.06 0.08 0.1 (c) OOtrOi ting kSn n i l * («!,„) 0.12 (d) 0.02 0.04 0.06 0.08 BO troi ting kin nhit ( f t j Hinh Cac dudng phan vj IDA taSP02IDA: firj khung tdng (101010);(b) khung tdng (101024); (c) khang 12 tdng (101015); vd (d) khung 20 tdng (101020) — IDA-Haseltonetal.[9] -SP02IDA-Ticgii Safn=0.86)[g] (c) Sa(n=2.13s)Ig] (d) S a a i =2.635) [g] Hinh 5. eucmg cong CDF sup xac dinh bdi SP02IDA va IDA: (a) khang 4tdng (IDIOIO); (bj khung tdng (101024); (c) khung 12 tdng (101015); va (d) khang 20 tdng (101020) thflc hien cho eic khung BTCT chju mdmen ba nhjp, 4, 8, 12 va 20 tang chju 40 t r i n ddng dat vdi xac suat xay 2% trpng 50%. Phuong phap SP02IDA eho k i t q u i ude tinh kha chinh xac cfldng dp sup eua edng trinh (eac g i i trj p h i n vj 16%, 50%, 84% cua SaC) va cie gia trj P[Collapse|Sa(T1,5%)] va XCollape. Sai sd Idn n h i t gifla hai phflong p h i p la rat nhd. K i t qua n g h i l n cdu cho t h i y : phuc"'" p h i p SP02IDA don g i i n v i nhanh chdng, ed t h i thay t h i tdt eho phuong p h i p IDA viee d i n h g i i hieu s u i t sup cfla edng trtnh m i khdng can eung cap cie bp dao ddng n l n dau v i p va chi ddi hdi mdt nd liic tinh t o i n rat nhd so vdi IDA phflc tap, sfl dung n h i l u p h i n tich dpng phi tuyen theo m i l n thdi gian. Sfl sup do mat on djnh ddng eua cdng trinh chi chju chi phdi chfl y l u bdi dang dao ddng dau tien (mode 1), the hien qua dp chinh x i e cao cic k i t q u i so sinh v l cfldng dp Tiki LI|U THAM KHAO [I] Krawinkler, H., Miranda.L, (2004). Performancebased earthquake engineering. Earthquake Engineering: from engineering seismology to Performance-based earthquake engineering. Chapter 9, Bozorgni a Y, Bertero W (eds); CRC Press: Boca Raton, 9-1to 9-59. [2] ATC-40. (1996). Seismic Evaluation and Retrofit of existing concrete buildings, Report No. ATC-40, Applied Technology Council, Redwood City, CA. [3] FEMA-273. (1997). NEHRP guidelines for the seismic rehabilitation of buildings. Report No. FEMA-273, Federal Emergency ManagementAgency, Washington, D.C. [4] FEMA-356. (2000). Prestandard and commentary for the seismic rehabilitation of buildings. Report No. FEMA-356, Federal Emergency ManagementAgency, Washington, D.C. [5] FEMA-SAC (2000). Recommended seismic design criteria for nev^ steel moment-frame buildings. Report No. FEMA350, SAC Joint Venture, Federal Emergency Management Agency, Washington, DC. [6] PEER, Pacific Earthquake Engineering Research Center: Strudural Performance Database, University of California, Berkeley, Available at http://nisee.berkeley.edu/spd/ [7] Deierlein, G. (2004). "Oven/lew of a comprehensive framework for earthquake performance assessment". Proceedings Inter Workshop on Performance Based Design, Bled, Slovenia, June. [8] Cornell, A. (2004). "Hazard, ground motions, and prababilistic assessments for PBSD". Proceedings Inter. Workshop on Performance Based Design, Bled, Slovenia, June. [9] Haselton, CB. and G.G. Deierlein (2007). "Assessing seismic collapse safety of Modern Reinforced Concrete Frame Buildings', PEER Report 2007/08, Pacific Engineering Research Center, University of California, Berkeley, California. [10] Vamvatsikos D, Cornell CA (2002). "Incremental dynamic analysis". Earthquake Engineering and Structural Oynamics;31(3):491-514. [II] Vamvatsikos D, Cornell CA (2004)."Applled incremental dynamic analysis". Earthquake Spectra; 20(21:523-553. [12] Han, S.W., Moon, K.H., Chopra A.K. (2010)."Application of MPA to estimate probability of collapse of structures", Earthquake Engineering and Structural Dynamics; 39:12591278. [13] Vamvatsikos 0., Aschheim M., Comartin CD. (2011). 'A targeted nonlinear dynamic procedure to evaluate the seismic performance of structures". Proceedings of the C0MPDYN2011 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece. [141 Chintanapakdee, C, Nguyen, A.H., and Hayashikawa, I (2009). "Assessment of modal pushover analysis procedure for seismic evaluation of buckling-restrained braced (rames".The lES journal Part A: Civil & Structural Engineering 2(3): 174-186. [15] Nguyen, A.H., Chintanapakdee, C, and Hayashikawa, oi.2oi4J5Dni:[|9i Bing 1: So sinh k i t qua gifla SP02IDA va phflong p h i p chinh xae IDA Cic g i i tri tinh t o i n Cdng trtnh Phflong p h i p Sac.so%(g) tang (IDIOIO) Sting (IDI 024) 12 t i n g (ID1015) 20 tang (ID1020) IDA SP02IDA Saisd IDA SP021DA Saisd IDA SP021DA Saisd IDA SP021DA Saisd 2.24 2.25 0.45% 0.72 0.72 0% 0.62 0.6 3.23% 0.48 0.48 0% Saci6%(g) Sac84%(g) 1.47 1.42 3.52% 0.483 0.48 -0.55% 0.419 0.39 7.09% 0.33 0.3 10.4% 3.41 3.2 6.14% 1.07 1.04 3.18% 0.92 0.88 3.9% 0.69 0.7 1.7% Sa(n=0.8es)(g] lb) OlnTotal 0.65 0.64 0.89% 0.64 0.632 1.25% 0.63 0.645 2.32% 0.62 0.655 5.7% M 0.806 0.811 3.41% -0.329 -0.329 0% -0.48 -0.511 6.86% -0.732 -0.734 0.3% San'1=1.71s)lg] "8 .1 , I . -1 - ^ ^ -? (c) Saai=2.13s)[g] (d) Sa(n =2,635) lg) Hinh 6. Sai so giiia SP02IDA va IDA tinh toan dudng cong CDF sup do: (a) khung tang (IDIOIO); (b) khung tang (101024);(cj khang 12 tdng (101015); va (d) khung20 tdng (ID1020) T. (2010). "Assessment of current nonlinear static procedures for seismic evaluation of 6RBF buildings". Journal of Construdional Steel Research 66(8-9):1118-1127. [16] Vamvatsikos, D. and Comell, C (2005). "Dired estimation of seismic demand and capacity of multidegreeof-fi'eedom systems through incremental dynamic analysis of single degree of freedom approximation" Journal of Strudural Engineering (ASCE); 131(4): 589-599. [17] Vamvatsikos, D. and Cornell, C (2006). "Dirert estimation of seismic demand and capacity of oscillators with multi-linear static pushovers though IDA". Earthquake Engineering and Structural Dynamic; 35(91:1097-1117. [18] Zareian F, Krawinkler H (2007).'Assessment of probability of collapseand design for collapse safety". Earthquake Engineering and Structural Dynamics; 36(13):1901-19M. [19] Ibarra LF (2003). "Global collapse of frame stmctures MOlBinniEvaai 01.2014 under seismic excitations". PhD Dissertation, Departmert of Civil and Environmental Engineering, Stanford University, Stanford, CA. [20] Open System for Earthquake Engineering Simulation (Opensees). Pacific Earthquake Engineering Research Center, University of California, Berkeley, http://opensees.berkeley.edu/ [21] MATLAB (2010).The Language ofTechnical Computing. Version R2010a, The Mathworks Inc., Natlck, Massachusetts. PiCollapse] tai Sa2«,/5ii(T1,4) 0.09 0.085 0.3.41% 0.35 0.348 0.53% 0.29 0.312 7.61% 0.31 0.321 3.5% Xcollap.dO") 2.5 2.28 8.76% 16.8 16 4.76% 12.6 14 11.11% 13.8 15 11.9% . quan trpng. Cd nhilu phuong phap dflpe phit triln Si giii quylt van de nay, trong dd cd ci phuong phap ddng va phuong phip tinh. Phflong phip phin tfch ddng gia tang (Incremental Dynamic . phip fldc tinh ehinh xae nhit cic trang thai gidi han cfla cdng trinh, trong dd cd sfl sup dd do mat dn djnh ddng tdng thi. Vi li phflong phip ddi hdi mdt chuoi cie phin tich ddng phi. tilt ve eae he khung dflpc trinh bay trong Haselton et al.[9]. Phi tuyln vit lieu va hinh hpc diu duoc xlt din trong nghien cflu nay. Qng xfl phi tuyln eua kit eau dflpe phin tich bang