Seismic failure mode control of tall steel buildings by strengthening the weaker-members

Transcription

1 October -17,, Beng, Chna Sesmc falre mode control of tall steel bldngs by strengthenng the weaker-members Sn Af 1 and O Jnpng 2 (School of Cvl and Hydralc Engneerng, Dalan Unversty of Technology, Dalan, 14, Chna) ABSTRACT: Ths paper manly stdes sesmc falre mode analyss and sesmc falre mode controllng of steel tall bldngs. Frstly, the strctral nonlnear calclaton model and the crteron of falre mode are gven. Secondly, tall steel bldngs sesmc falre mode control method that based on smltaneos falre prncple strengthenng weaker- members n the weakest falre mode tme after tme s presented. Thrdly, the analyss methods of strctral ntegral sesmc capacty and capacty storages respectvely correspondng to desgn capacty and yeld capacty are presented. Fnally, the falre mode, ntegral sesmc capacty and capacty storage correspondng to weakest falre mode are obtaned by employng a -story steel frame bldng for lmt tme hstory analyss nder typcal earthqake grond moton and lmt Pshover analyss. And controllng method of sesmc falre mode of tall steel bldngs n ths paper s verfed practcable. The research n the paper show that tall steel bldngs sesmc falre mode can be control effectvely by strengthenng weak-members n the weakest falre mode tme after tme. 1. Abstract Large-scale complex strctres have many knds of falre modes. So t s dffclt commonly to enmerate all knds of these falre modes. Bt only several falre modes work mostly for strctral falre. They are called manly falre mode [1]. The concept of the weakest falre mode s pt forward foremost by O Jnpng etc. The weakest falre mode s defned as the falre mode correspondng to most large event set nder snge random sorce load. The practcal meanng of the weakest falre mode s that the weakest falre mode alone appears or any other falre modes appear nevtable conont the weakest falre mode [2]. Accordng to practcal meanng of the weakest falre mode, the falre mode wth mnmm strctral ntegral sesmc capacty (appear foremost) s strctral weakest falre mode. So practcal meanng of falre mode control s that searchng and controllng the weakest falre mode and accordngly mprovng strctral ntegral sesmc capacty. Desgn method of smltaneos falre [] s sed of reference n the paper. Strengthen strctral weaker-members by makng members of the weakest story n the weakest falre mode and referenced story fal synchronosly. We expect to acheve obectve of controllng strctral weakest falre mode by strengthenng strctral weaker-members repeatedly sch-and-sch and to mprove strctral ntegral sesmc capacty. In the paper, falre modes of tall steel bldngs are analyzed by employng a -story steel frame strctre for lmt tme hstory analyss nder typcal earthqake grond moton and lmt Pshover analyss. Then tall steel bldngs sesmc falre mode control method that based on smltaneos falre prncple strengthenng weakermembers n the weakest falre mode tme after tme s presented. And orgnal frame and controlled frame are all carred ot ntegral sesmc capacty analyss. 2. Sesmc falre mode analyss method of tall steel bldngs 2.1Sesmc falres mode analyss method 2.1.1Analyss model Frame plastc hnge model s sed n the paper. Plastc hnges se steel hnge property n FEMA5. Beams are ntercalated bend hnge and shear hnge. Colmns are ntercalated copled axal force-bend hnge and shear hnge. Geometry nonlnearty ndced by P-delta effect and large deformaton effect s consdered.

2 October -17,, Beng, Chna 2.1.2Lmt tme hstory analyss Lmt tme hstory analyss method s defned that tme hstory analyss s made step by step by ncreasng acceleraton peak vale of npt earthqake ntl reachng strctral lmt state. (1)Damp model Relay damp model s sed n tme hstory analyss. Relay damp model s denoted as: C= α M + α 1 K 1 Here, M s strctral mass matrx. K s strctral stffness matrx. K s strctral ntal stffness matrx can be sed. ξ ξ + 1 2( ) ϖ ϖ + 1 2( ξ + 1ϖ + 1 ξϖ ) α = α1 = ϖ ϖ ϖ ϖ + 1 Here, ϖ ϖ + 1 ( ξ, ξ + 1)strctral random two border pon self-vbraton crclar freqency. The frst crclar freqency ϖ 1 and the second crclar freqency ϖ 2 correspondng to strctral ntal stffness can be sed. Damp rato of steelξ1 andξ 2 s.2 nder small earthqake acton and.5 nder large earthqake acton [4]. (2)Nmercal ntegral method formlas. Newmark method s sed becase of accracy and stablty. Newmark method s denoted by the followng {} = {} + (1 γ ){} t+ γ{} t t+ t t t t+ t {} t+ t = {} t + {} t t+ ( β){} t t + β{} t+ t t 4 2 Here,γ and β are parameters. In the paper,γ eqal to 1/2 and β eqal 1/ Lmt Pshover analyss Pshover analyss method s a knd of statc elastc-plastc analyss method. Pshover analyss method s defned that loadng to strctres wth monotone ncremental horzontal load ntl reach target dsplacement of reference pont or bldngs collapse. In Pshover analyss horzontal load s monotone ncreased ntl strctres reach lmt state. Control method of Pshover analyss ncldes dsplacement control and load control. Dsplacement control s sed n the paper [11]. 2.2Crteron of sesmc falre mode Falres of tall steel bldngs manly nclde onts falre, members falre and strctral collapse. The assme that onts don't fal s made n the paper. Members falre cased by materal yeld s consdered n the paper. Strctral collapse s that strctres lose whole stablty. When too many plastc hnges n members appear, strctres wold become mechansms and collapse [5~] Falre crteron of members When materal ntensty of members reaches yeld lmt state, members wold fal. Yeld lmt state nclde three knds. They are separate copled axal force-bend lmt state, shear stress lmt state and torson shear stress lmt state. The three lmt state of materal are not separate correlatve and shold be respectvely checked [7] Falre crteron of strctres Strctral falre s defned that strctres lost load-carryng capacty or can not work for se normally. The two falre crterons sed for dstngshng strctral lmt states. When anyone of two falre crterons s satsfed, strctres wold be determned havng reached strctral lmt state [7]. 1 Strctral total stffness matrx snglarty. When whole strctre system or local strctre becomes mechansm, strctral total stffness matrx snglar appears. It can be denoted by the followng formla. K = 5 Here strctres have reached strctral lmt state. 2 Strctral total dsplacement or local dsplacement overrn. Dsplacement control condton s denoted by the followng formla. [ ]

3 October -17,, Beng, Chna When above neqaton s not ftted, strctres wold be determned havng reached strctral lmt state. Here [ ]s strctral control dsplacement lmt vale. Code for sesmc desgn of bldngs n chna [8] control strctral deformaton by restrctng story drft.. Sesmc falre mode control method of tall steel bldngs Sesmc falre mode control of tall steel bldngs s acheved by strengthenng strctral weaker-members n the weakest falre mode tme after tme. The strengthenng method s that members of the weakest story n the weakest falre mode and conslted story are reqred to start fal(yeld) smltaneosly by strengthenng members of both of the two stores or anyone of the two stores, that colmns of the weakest story n the weakest falre mode s frst consdered for beng strengthened and colmns of conslted story may be strengthened or not be strengthened and that only beams of the story falng earler between the two stores may be strengthened. The conslted story s a story selected from the two conont stores of the weakest story n the weakest falre mode. Selecton method s that the story below the weakest story s frst selected and that the story above the weakest story s selected f members of the story below the weakest story and members the weakest story start fal smltaneosly before strengthened. If members of the two conont stores of the weakest story and members of the weakest story start fal smltaneosly before strengthened. The conslted story wll be selected from the two stores separated by a story wth the weakest story accordng to above selecton method. If s the weakest story n the weakest falre mode and s conslted story, the followng formlas shold be ftted. When θ eqalsθ, then y θ = θ 7 Q Q θ = θ = k h k h y 8 Formla(7) can be denoted by formla(). k Q h θ y = k Q h θ y Here k s lateral story stffness of and shold be calclated throgh story shear beng dvded by story drft. Q s story shear of. h s heght of. θ s story yeld drft rotaton of. y Whether colmns or beams, when strengthened, same knd of member of same shold be strengthened all together. When colmns strengthened, cross sectons of colmns shold are bgger than cross sectons of colmns of below conont story. When beams strengthened, smaller cross sectons shold be sed. When members of 2 s reqred to be strengthened, colmns of both bottom and 2 shold be frst consdered f need to be strengthened. When beams of 2 need to be strengthened, beams of both bottom and 2 shold be strengthened wth same cross sectons all together except specal demand. Whether the weakest falre mode determned by lmt tme hstory analyss method or the falre mode determned by lmt Pshover analyss method (only one falre mode) can be controlled or can be mproved by sng above strengthenng method tme after tme ntl the weakest falre mode determned by lmt tme hstory analyss method s elmnated or the falre mode determned by lmt Pshover analyss method s mproved for obtanng expected strctral ntegral sesmc capacty. Correspondng analyss method of strctral ntegral sesmc capacty wll be dscssed therenafter. 4. Integral sesmc capacty analyss of sesmc falre mode of tall steel bldngs 4.1Analyss method Strctral ntegral sesmc capacty s defned as earthqake acton endred by the strctre before the strctre reach lmt state. For lmt tme hstory analyss strctral lmt ntegral sesmc capacty can be represented by acceleraton peak vale of npt grond moton. For lmt Pshover analyss strctral lmt ntegral sesmc capacty can be represented by strctral base shear. Strctral safety can be evalated by sng capacty storage. Strctral capacty storage coeffcent s defned as rato of lmt ntegral sesmc capacty to yeld capacty or of lmt ntegral sesmc capacty to large earthqake desgn capacty. Strctral capacty storage coeffcent may be calclated respectvely by formla (1) or formla (11).

4 October -17,, Beng, Chna R R a s = ay a s = am R F s = (1) Fy R F s = (11) Fm Here a, a and a are separate acceleraton peak vale of npt earthqake when strctres reach strctral y m lmt state, strctres start yeld and large earthqake desgn demand. F, F and y are separate strctral base shear when strctres reach strctral lmt state, strctres start yeld and desgned accordng to large earthqake. 4.2Falre mode control can mprove ntegral sesmc capacty Strctral sesmc falre mode s controlled n order to elmnate the weakest falre mode determned by lmt tme hstory analyss method and mprove falre mode determned by lmt Pshover analyss method for mprovng strctral ntegral sesmc capacty. So feasblty of control method of sesmc falre mode shold be verfed by dgng f strctral ntegral sesmc capacty can be mproved. 5. Example 5.1Analyss parameters The employed strctre s a -story steel frame bldng wth bays. The strctre s reglar. Each span s.m. The heght of bottom story s 4.2m and heght of other stores s all.m. Strctral calclatng dagram s showed by fgre 1. Vertcal dstrbted dead load on beams s 21.kN/m. Vertcal dstrbted lve load on beams s.kn/m []. Sesmc fortfcaton s ntensty 8. The ste-class s.desgn earthqake grop s the second grop. Elastc modlar of steel s E = N/mm 2. Materal property of steel s Q. The fnte program SAP2 s sed for strctre desgn and nonlnear fnte element analyss. Three typcal grond motons fttng ste s selected for tme hstory analyss. They are Elcentro(NS), Sgs w and Tangshan. The strctre s desgned accordng codes [8~1]. Strctral member secton types are lsted n table1. F m Fg.1 Strctral calclatng dagram Members Table 1 Member sectons Sectons Colmns of 1, Colmns of, Colmns of 5~8 5 5 Colmns of ~1 5 5 Colmns of 11~

5 October -17,, Beng, Chna Beams of 1~ H 5 5.2Falre mode analyss The strctre s carred ot lmt tme hstory analyss nder typcal earthqake grond moton and lmt Pshover analyss respectvely accordng to each of above two falre crterons. In lmt Pshover analyss the strctre s loaded by sng nverse trangle dstrbton pattern. (1) Strctral whole falre mode When whole strctre system or local strctral part becomes mechansm, the strctre whole falre mode appears. Crteron of strctral whole falre mode s that strctral whole stffness matrx snglar appears. In lmt tme hstory analyss, when acceleraton peak vales of Elcentro(NS), Sgs w and Tangshan reach respectvely 21gal, gal and 145gal, the strctre becomes geometrcal nstable system. Correspondng falre mode s showed n fgre 2. In lmt Pshover analyss, when strctral base shear force s 1.kN before the strctre becomes geometrcal nstable system. Correspondng falre mode s showed n fgre 2. (a)elcentro npt (b) Sgs w npt (c) Tangshan npt (d) Pshover analyss Fg.2 Mode of overall falre (2) Strctral dsplacement overrn falre mode Code for sesmc desgn of bldngs n chna control strctral deformaton nder large earthqake by restrctng elastc-plastc story drft of weak story. For steel bldngs lmt elastc-plastc story drft rotaton s [ θ p ] =1/5. In crtcal tme hstory analyss, when acceleraton peak vales of Elcentro(NS), Sgs w and Tangshan reach separate 1gal, 1gal and 55gal, the strctre falre all becase of dsplacement overrn. Correspondng elastc-plastc story drft rotatons of weak story are separate.22,.2 and.2. Strctral story drft rotatons are showed by Fgre. In lmt Pshover analyss, when strctral base shear s 224.4kN, elastc-plastc story drft rotatons of weak story reach.2. Strctral story drft rotatons are showed by Fgre.

6 October -17,, Beng, Chna (a) Inpt Elcentro (b) Inpt Sgs w (c) Inpt Tangshan (d) Pshover analyss Fg. Story drfts rotatons Accordng to above analyss, we fnd that strctral lmt load-carryng capactes correspondng to dsplacement overrn are smaller than strctral lmt load-carryng capacty correspondng to strctral whole falre n both lmt tme hstory analyss and lmt Pshover analyss. Ths shows that dsplacement overrn falre crteron s strcter than whole falre crteron. Strctral weakest falre mode In lmt tme hstory analyss the strctre has three dfferent sesmc falre modes when acted by three dfferent earthqake s. Falre mode correspondng to mnmm acceleraton peak vale s the weakest falre mode. So the strctral weakest falre mode s falre mode nder Tangshan acton. Strctral ntegral sesmc capacty correspondng to the weakest falre mode nder Tangshan acton s 145gal whole falre crteron or 55gal(dsplacement overrn falre crteron). For lmt Pshover analyss only one falre mode can be obtaned correspondng to each falre crteron, so weakest falre mode can t be determned. 5.Falre mode control From above analyss we can fnd that the weakest falre mode correspondng to smaller strctral ntegral capacty s dsplacement overrn falre nder Tangshan acton (see table2). So dsplacement overrn falre nder Tangshan acton s obect for falre mode control. In the weakest falre mode the weakest story s see table. The conslted story selected s 5. Colmns of shold be frst consdered for beng strengthened. Bt colmns of have same sectons type wth colmns of below 5. Frthermore lateral story stffness break s not great. And colmns of wll not be strengthened here for makng less members beng strengthened. Colmns of 5 are not very mpartment for beng strengthened. So colmns of 5 wll not be strengthened here. Beams of 5 wll be strengthened becase they fal before beams of fal. Members shold be strengthened wth less secton when ensrng members of 5 and members of starts fal smltaneosly. The strengthened member secton types are lsted n table 4. The strengthened frame s carred ot lmt tme hstory analyss nder typcal earthqake grond moton and lmt Pshover analyss. The strengthened frame s made to respectvely reach strctral lmt state correspondng to mnmm lmt load-carryng capacty. In lmt tme hstory analyss the weakest falre mode s dsplacement overrn falre nder Tangshan acton. Strctral ntegral sesmc capacty s 58gal. In lmt Pshover analyss strctral falre mode s also dsplacement overrn falre when strctral base shear reach 27.8kN. Strctral story drft rotatons are showed by fgre4. Above analyss shows that strctral weakest falre mode sn't elmnated. Accordng to the method strengthenng the strctre after strengthened tme after tme ntl the weakest falre mode s elmnated. Strctral ntegral sesmc capactes and the weakest stores after every tme strengthened are showed respectvely n table2 and table. Members strengthened every tme are showed n table 4. Members of the frame after controlled (the frame after 11 th tme strengthened) are showed n table 5. The frame after controled fals frst becase of story dsplacement overrn n both lmt tme hstory analyss nder typcal earthqake grond moton and lmt Pshover analyss. In lmt tme hstory analyss the weakest falre mode of controlled s story dsplacement overrn falre nder Sgs w acton. Correspondng strctral ntegral sesmc capacty s 71gal. In lmt Pshover analyss strctral ntegral sesmc capacty s 8.kN. Strctral story drft rotatons are showed by fgre 5.

7 October -17,, Beng, Chna Above analyss shows that strctral weakest falre mode of has been elmnated and strctral ntegral sesmc capacty has been mproved by carred ot falre mode control. Table Strctral ntegral sesmc capacty Strctres Lmt tme hstory analyss /gal Lmt Pshover Inpt Elcentro Inpt Sgs w Inpt Tangshan analyss /kn Orgnal frame st strengthened frame nd strengthened frame rd strengthened frame th strengthened frame th strengthened frame th strengthened frame th strengthened frame th strengthened frame th strengthened frame th strengthened frame th strengthened frame Table2 the Weakest Strctres Lmt tme hstory analyss Lmt Pshover Inpt Elcentro Inpt Sgs w Inpt Tangshan analyss Orgnal frame st strengthened frame nd strengthened frame,4 4 rd strengthened frame 4,8 4 4 th strengthened frame 1, th strengthened frame 1,11,4 4 th strengthened frame,4 1, th strengthened frame th strengthened frame 4 1,11 4 th strengthened frame , 4 1 th strengthened frame , th strengthened frame ,7 5 Table4 Every tme strengthened frame Members Strengthened members Members and sectons 1 st strengthened Members Beam of 5: H nd strengthened Members Beam of : H 5 Colmn of 1,2: rd strengthened Members Colmn of : Colmn of 4: Beam of : H th strengthened Members Beam of 4: H 5 Beam of 7: H th strengthened Members Colmn of 1,2: Colmn of : th strengthened Members Colmn of 4: Beam of : H th strengthened Members Beam of 1,2: H 5 8 th strengthened Members Colmn of 5: Beam of 4: H 5 5 th strengthened Members Beam of 1,2: H th strengthened Members Colmn of : 5 5 Beam of : H 5 4

8 October -17,, Beng, Chna 11 th strengthened frame Beam of 8: H 5 Colmn of 5: Colmn of 7: Beam of 1,2: H 5 5 Beam of : H 5 5 Table 4 Member sectons of frame after controlled Members Sectons Colmns of 1, Colmns of, Colmns of 5, Colmn of Colmns of 8, 5 5 Colmn of Colmns of 11~ Beam of s 1,2 H 5 5 Beam of H 5 4 Beam of 4 H 5 5 Beam of 5 H 5 5 Beam of H 5 5 Beam of 7 H 4 2 Beam of 8 H 5 Beam of s ~ H (a) Inpt Elcentro (b) Inpt Sgs w (c) Inpt Tangshan (d) Pshover analyss Fg.4 Story drft rotatons of frame by strengthened frstly (a) Inpt Elcentro (b) Inpt Sgs w (c) Inpt Tangshan (d) Pshover analyss Fg.5 Story drfts rotatons of controlled frame 5.4Integral sesmc capacty analyss Strctral lmt ntegral sesmc capacty s earthqake acton endred by the strctre before the strctre

9 October -17,, Beng, Chna reaches strctral lmt state. Strctral lmt ntegral sesmc capactes of orgnal frame and controlled frame are lsted n table. Strctral lmt ntegral sesmc capactes of control frame have been mproved. Table Lmt sesmc resstance capacty Strctres Lmt tme hstory analyss /gal Lmt Pshover analyss /kn Orgnal frame Controlled frame Strctral yeld capacty s earthqake acton endred by the strctre when strctral member yeldng appear frstly. Strctral yeld capacty can be expressed by peak vale of acceleraton of nptted grond moton or by total basc shear force. By nonlnear tme hstory analyss nder typcal earthqake grond moton and Pshover analyss Strctral yeld capacty may be calclated. Strctral yeld capacty of orgnal frame and controlled frame are lsted n table 7. Strctral yeld capactes of control frame have been mproved. For sesmc fortfcaton 8 ntensty, peak vale of large earthqake desgn acceleraton of grond moton s 4gal. In Pshover analyss, strctral total basc shear force correspondng to performance pont obtaned by desgn response spectrm and demand spectrm of large earthqake s large earthqake desgn earthqake acton. Large earthqake desgn earthqake actons of orgnal frame and controlled frame are separate 147.5kN and 8.kN. Strctral capacty storage coeffcents correspondng to yeld (lsted n table7) and correspondng to large earthqake desgn (lsted n table8) have been calclated by formla (1) and (11). Mnmm capacty storage coeffcents correspondng to yeld of orgnal frame and controlled frame are separate 1.4 and 1.2. The case that mnmm capacty storage coeffcents correspondng to yeld of controlled frame dmnsh s that extent ncreased of yeld capacty s bgger than extent ncreased of ntegral sesmc capacty. Mnmm capacty storage coeffcents correspondng to large earthqake desgn of orgnal frame and controlled frame are separate 1.8 and Mnmm capacty storage coeffcents correspondng to large earthqake desgn of controlled frame are ncreased.. Conclsons Table 7 Yeld capacty Strctres Lmt tme hstory analyss /gal Lmt Pshover analyss /kn Orgnal frame Controlled frame Table 8 Capacty storage coeffcent correspondng to yeld Strctres Lmt tme hstory analyss Lmt Pshover analyss Orgnal frame Controlled frame Table Capacty storage coeffcent correspondng to large earthqake desgn Strctres Lmt tme hstory analyss Lmt Pshover analyss Orgnal frame Controlled frame controllng method of sesmc falre mode of steel tall bldngs. The followng conclsons are made. 1 In nonlnear tme hstory analyss, by npttng more grond motons more strctral falre modes can be obtaned. Seqent the weakest falre mode can be determned. In Pshover analyss, only one strctral falre mode can be obtaned, so the weakest falre mode can t be determned. 2 Strctral ntegral sesmc capacty may be determned accordng to strctral falre mode. When tme hstory analyss method s sed, acceleraton peak vale of npt grond moton represents strctral ntegral sesmc capacty. When Pshover analyss method s sed, strctral base shear represents strctral ntegral sesmc capacty. Strctral ntegral sesmc capacty storage coeffcent correspondng to yeldng capacty or correspondng to large earthqake desgn s mportant for estmatng strctral safety storage.

10 October -17,, Beng, Chna Strctral whole falre and story dsplacement overrn of strctral weak story are two knds falre crterons sed n the paper. By analyzng strctral falre mode and strctral ntegral sesmc capacty, we fnd the strctre sally story dsplacement of strctral weak story breaks bond before the strctral becomes mechansms and collapse. 4 The weakest falre mode n tme hstory analyss can be elmnated, or the falre mode n Pshover analyss can be mproved, and strctral ntegral sesmc capacty s mproved by based on smltaneos falre prncple strengthenng weak members n the weakest falre mode tme after tme. ACKNOWLEDGMENTS The athors grateflly acknowledge the fnancal spport provded by the Natonal Maor Fndamental Research Program nder grant Nos. 27CB71422 and 27CB714. REFERENCES [1] Ho Ganglng. Relablty ndex vectors,random pshover analyss and strctral system relablty doctorate dssertaton [D].Harbn harbn nsttte of technology,21. [2] O Jnpng Dan Ybo. Sesmc relablty analyss and optmm desgn of tall bldngs[j]. Eartqake engneerng and engneerng vbraton,,vol.(1):1~1. [] Qan Lx. Optmm desgn of engneerng strctres [M]. Beng:Chna WaterPower Press,18. [4] Chna Accentre technology research nsttte. JGJ-8 Techncal specfcaton for steel strctre of tall bldngs [S]. Beng:Chna archtectre & bldng press,21. [5] Lv Xln, Zho Deyan, L Smng etc. Bldng strctre sesmc desgn theory and example [M]. Shangha: Tong nversty Press, 22. [] L Goqang. mlt and tall steel bldng desgn[m]. Beng: Chna archtectre & bldng press,24. [7] O Jnpng Dan Zhongdong Xao Yqng. offshore platform strctre safety evalaton theroy, method and applcaton[m].beng Scence Press, 2. [8] Mnstry of constrcton P.R.Chna. GB Code for sesmc desgn of bldngs [S]. Beng: Chna archtectre & bldng press,21. [] Mnstry of constrcton P.R.Chna. GB5-21 Load code for the desgn of bldng strctres [S]. Ben :Chna archtectre & bldng press, 21. [1] Mnstry of constrcton P.R.Chna. GB517-2 Code for desgn of steel strctres [S]. Beng: Chna archtectre & bldng press,21. [11] Sn Af, O Jnpng. Lateral acton patterns and ther effects on Pshover sesmc analyss of steel tall bldngs [J]. Eartqake engneerng and engneerng vbraton,,vol.(4).