Opn Journ of Civi Enginring, 3, 3, 88-93 http://dx.doi.org/.436/oj.3.333 Pubishd Onin Sptmbr 3 (http://www.sirp.org/journ/oj) A w Mthod for Prditing th UL of Cirur CFST Coumns Xinmng Yu *, Bohun Chn Cog of Civi Enginring, Fuzhou Univrsit, Fuzhou, Chin Emi: * xinmngu@gmi.om, bohunhn@fzu.du.n Rivd Apri 7, 3; rvisd M 7, 3; ptd Jun 5, 3 Copright 3 Xinmng Yu, Bohun Chn. This is n opn ss rti distributd undr th Crtiv Commons Attribution Lins, whih prmits unrstritd us, distribution, nd rprodution in n mdium, providd th origin work is propr itd. ABSTRACT Conrt fid st tub struturs hv gind booming dvopmnt in rnt dds, spi in Chin. Simpifid mthods hv bn proposd in dsign ods, suh s th Eurood 4 (EC4) nd th Chin nginring nd onstrution spifition (). In EC4, th onfinmnt fft is rsonb rtd to sndrnss nd od ntriit. Th mthod is muh stright forwrd in tht th sndrnss rtio nd od ntriit r trtd s indpndnt rdution ftors. To mk us of th dvntgs of both th nd th EC4 mthods, th mthod is modifid to onsidr th onfinmnt fft ssoitd with sndrnss nd od ntriit. It is shown tht th proposd mthod n prdit w th utimt od pit of irur stion onrt fid st tub oumns. Kwords: Conrt Fid St Tub Coumn; Utimt Lod Cpit; Simpifid Mthod; Rdution Ftor. Introdution Conrt fid st tub (CFST) oumns hv bn wid usd in high ris buidings nd bridgs. Prvious rsrhs hv shown tht th mutu strngthning mhnism of th st tub nd th onrt or hps to gin highr od pit, spi in irur CFST oumns. This mhnism hs ttrtd signifint rsrh fforts on th dvopmnt of simpifid mthods to prdit th utimt od pit (UL) of CFST oumns. Th outoms hv bn inorportd into dsign ods, suh s EC4 [], LRFD [], AIJ [3], [4], DL/T [5] nd so on. Th phiosoph bhind ths mthods m b diffrnt; howvr, th ur of thm is rsonb in tht th r mor or ss bsd on sttisti nsis on vib tst dt. o doubt, this is right w in sintifi rsrh nd ppition. Howvr, sin h mthod hs its own mtri proprtis nd mthodoog, th quivn bhind thm sms vgu. It is mningfu to dvop nw mthod whih mks th bst of th pros but ons of th mthods. This rsrh ims to driv nw UL prdition mthod bsd on nd EC4 rosswis. * Corrsponding uthor.. Simpifid UL Prdition Mthods in nd EC4 In, th UL of CFST oumn is utd b = () u whr is th ross stion rsistn drivd from imit quiibrium stt [6]; nd r indpndnt rdution ftors onsidring stbiit nd od ntriit, rsptiv, obtind from rgrssiv nsis on tst dt. fa + () for L/D 4. 5 L D 4 for L/ D 4 (3) if. 55 85. / r r (4) 3. if. 55 /r 4. r ot tht thr is no ntriit imit in Eqution (4). In EC4, th UL of CFST oumn is utd b EC4 EC4 (5) Copright 3 SiRs.
X. M. YU, B. C. CHE 89 whr is th ross stion rsistn onsidring th infun of onfinmnt fft, whih is rtd to od ntriit nd sndrnss. 4 EC A f A f A f 5. (6) whr nd r th st strngth rdution ftor nd onrt strngth nhnmnt ftor (du to onfinmnt fft), rsptiv, whn D nd 5. ; is th rtiv sndrnss of th CFST oumn. Othrwis, th strngthning fft is ngtd. D ; (7) 5. 3 t f ; D ; D f (8) 49. 85. 7 is nogus to th oumn buking rsistn rdution ftor drivd thorti from st oumn with initi out-of-strightnss dftion t mid-hight with itt modifition [7]. whr is prmtr dpnding on intrn rinforing brs. Whn th xi rinforing rtio is no grtr thn 3%, 5... (8) Apprnt, th EC4 pproh is diffrnt from in tht th od ntriit is no ongr n indpndnt prmtr, nithr is th sndrnss fft. Thrfor, th phiosoph bhind nd EC4 is diffrnt. In ddition, th strss-strin rtionships of onfind onrt r diffrnt. In, noninr rstrind onrt proprt is mpod. (7) f f 5. p f p f (9) In EC4, th rstrining fft n b xprssd in th foowing form s prsribd in EC [8]. f C C p f () whr C nd C dpnds on th tr onfinmnt prssur, p. Tht is f EC 5 for 5 4.. p f p. f 5. 5. p f for p 5. f () From th iustrtion bov, it is r tht th mthod is muh simpr. Howvr, th ffts of od ntriit nd sndrnss on th strngth of onrt r not r in. This triggrs th motiv of this rsrh to dvop mthod whih bsorbs th mrits of ths two mthods: inhriting th simp frmwork of th mthod, but xpiit nrihing th rdution ftors with th onfinmnt hrtristis prsribd in th EC4. 3. Dvopmnt of Simpifid Mthod for UL Prdition of Cirur CFST Coumns 3.. Th Cross Stion Rsistn of CFST Coumns In imit quiibrium stt, th st tub rhs its utimt strngth, i.., gts idd. From Eqution (), it is known tht th onrt strngth is funtion of tr prssur govrnd b th stt of th st tub. Th UL of th CFST oumn stion is th mximum ombintion of th strsss in st nd onrt. It is ssumd hr tht th strss distributions on th onrt stion nd th st stion r both uniform. Th strss distribution in thin w st tub n b rsonb ssumd to b pnr. Whn th tub gts idd, ording to th Von Miss id ritrion, w hv f () whr nd r prinip strsss in xi nd tr dirtions; f is th id strngth of tub st. ot n, whr n is th xi omprssiv strss. It n b drivd tht D t p D p (3) t A 4t And (4) A D Substituting Equtions (3) nd (4) into Eqution () nd rrrnging, w hv A f 3 p A A n A p (5) Thrfor, t utimt imit stts, th od rsistn of th ross stion n b xprssd s A A fccp f A f 3 p pa A (6) Th mximum vu of rquirs d dp A 3A p A A C A f p A (7) Copright 3 SiRs.
9 X. M. YU, B. C. CHE Thrfor, t utimt imit stts, th tr prssur on th onrt or is p k f (8) whr is th onfinmnt fft ftor, A f A f, nd 5. 3. 57 for p. 5 f k 3 C 555 for 5. p. f (9) In nginring prti, suh s in CFST bridgs, 9., hn k. 57 () It n b si drivd from Equtions (6), (8) nd () tht And A k f. f. f () 3 n 3 57 79 A. 5A f. 85A f A f. 5 () Whn ntri oding nd stbiit r not onsidrd, i.., ;, Eqution (5) n b simpifid s A f. A f 975 (3) It n b sn from Equtions () nd (3) tht th ross stion rsistn utd using this proposd mthod is bout 5. A f grtr thn tht obtind from EC4 mthod. This diffrn n b rgrdd s onsrvtiv simpifition in EC4. Th omprison of th ross stion rsistns utd b this mthod nd nd EC4 mthods is shown in Figur. Th diffrn mong thr mthods is not signifint. It shoud b pointd out tht th mthod is onsrvtiv simpifition from fa. s iustrtd in [6]. /(Af) 6 5 4 3.5.5 (A f )/(A f ) Currnt Mthod 8:9 EC4 (Rtiv SLR=) Figur. Comprison of th ross stion rsistns utd with diffrnt mthods. 3.. Th Infun of Sndrnss In EC4, th rtiv sndrnss,, is usd to onsidr th infuns of sndrnss: ) th onfinmnt fft rdus with inrs of ; ) th stbiit drss with inrs of. In, ths two mhnisms r ombind togthr into ftor,, whih is obtind rgrssiv from rg numbr of tst dt, dopting LD s so prmtr, ngting th onfigurtion of Dt nd mtri proprtis; Whn LD, th UL of CFST oumn is ssumd to b govrnd b Eur buking rsistn. As mntiond bov, both mthods r ibrtd from tst dt. Th diffrnt trtmnt on th sndrnss infun btwn EC4 nd mks in Equ- tion (5) grtr thn in Eqution (). If th infun of on th onfinmnt fft is onsidrd, i.., ;, thn n quivnt prmtr n b drivd, tht is Af. 5 Af (4) Th omprison of th stbiit rdution ftors of EC4 (ngting th imit of 5. ) nd is shown in Figur. It n b sn from this figur tht: ) vus (th dsh urvs) r pproximt th mirror of vus (th soid urvs) ong th urv; ) Dt hs signifint infun on th rdu- tion ftor; 3) whn LD rhs, th urvs go togthr, whih indits LD is divid for Eur buking. Thr for, nd EC4 gr with h othr gin in this point, though th onfinmnt fft is onsidrd on whn 5.. From Figur, it n b onudd tht th infun of Dt is signifint nd thrfor shoud b onsidr d in th rdution ftor. B obsrving th sinusoid Stbiit Rdution Ftor.9.8.7.6.5 A: D= & t= B: D= & t=4 C: D=5 & t=8 EC4-B EC4-A EC4-C Rtiv sndrnss>.5 4 8 6 L/D EC4-A EC4-C EC4-B Figur. Comprison of stbiit rdution ftors of χ (EC4-A, B & C), (EC4-A, B & C) nd (unit of D nd t: mm). Copright 3 SiRs.
X. M. YU, B. C. CHE 9 shp of th EC4 urvs, nw mthod for prditin g th stbiit rdution n b obtind, s shown in Eqution (5). 4t L π L n sin (5) D D 5 D Th prmtr n in Eqution (5) govrns th shp of th urv. Through urv fitting, th urvs gr w with both EC4 nd urvs whn n., s shown in Figur 3. This ftor, i.., Eqution (5), in- orports th dvntg of, with xtndd sndrnss boundr, nd EC4, whih inuds th infun of Dt. Lod Entriit Rdution F tor.8.6.4. EC4-A EC4-B EC4-C Currnt-A Currnt_B Currnt_C A: t/d=/, f=4, f=35 B: t/d=4/, f=4, f=35 C: t/d=8/5, f=4, f=35..4.6.8 /r 3.3. Th Efft of Lod Entriit As th onfinmnt strngthning fft rdus with ntri oding, rdution ftor is usd to ount for this hng. This ftor in n b usd in wid rng of ntriit onditions, s shown in Eqution (4), whih stms from th M- urv nsis foowd b urv fitting [6]. Howvr, in EC4, th od ntriit indud infun is intgrtd into th ution of ross stion rsistn whn D. Simir to, n quivnt ftor,, n b obtind b tting ;. 975. / D /D. /D. (6) It is sn from Eqution (6) tht is funtion of both nd D. Howvr, in, on th ntriit is onsidrd (s Eqution (4)). Th ompr- son of nd is shown in Figur 4. in whih th D is owd to xtnd to.. Athough thr is hug diffrn bt wn ths two mthods to d with Stbiit Rdution Ftor.9.8.7.6.5.4 A: D= & t= B: D= & t=4 C: D=5 & t=8 Rtiv sndrnss>.5 EC4-A EC4-B EC4-C Currnt-A Currnt-B Currnt-C 4 8 6 L/D Figur 3. Comprison of stbiit rdution ftors of (urrnt), nd (unit of D nd t: mm). Figur 4. Comprison of th od ntriit rdution f- tors of φ, nd. od ntr iit, th trnd of rdution with ntriit is simir. On ompromis to this disgrmnt is to rt n xponnti funtion with both nd D s its prmtrs, s givn in Eqution (7). xp m D (7) Th in Eqution (7) is tkn from Eqution (3). Th prmtr m is usd to ibrt urv fitting. It is found tht whn m 85., th grs w with both nd, s shown in Figur 4. 4. Th UL of CFST Coumns Prditd b Currnt Mthod From prvious drivtion, it is thrfor proposd tht th UL of CFST oumn to b prditd b u L D r L D (8) whr, nd n b utd from Equtions (), (5) n d (7), rsptiv. Whn LD, th UL is govr nd b th Eur buking rsistn. 4.. Th UL of Entri Lodd CFST Coumns In ordr to undrstnd th bhviour of ntri odd CFST oumns, Chn t. [9] tstd 8 spimns with vrious od ntriit nd Dt rtios. Th spimn dtis, tst rsuts nd UL prditions using diffrnt mthods r istd in Tb. It is r from Tb tht whn th od ntriit is ow, th EC4 prdition is fir onsrvtiv. Whn th od ntriit is high, th -M urv hs to b usd. Th UL prditd b urrnt mthod is osd to but bttr thn thos prditd b, whih n b usd vn whn th od ntriit is high. Copright 3 SiRs.
9 X. M. YU, B. C. CHE Tb. Comprison of th prditd nd msurd utimt o d rsistns of ntri odd onrt fid st tub oumns. s.n. L D t f (MP) * f (MP) (mm) UL (K) Tst EC4 ** Currnt 38.9 989 8 3578 3445 37.6 5 45 56 43 53 3 39.8 5 86 33 9 96 9 6 4 38.9 75 333 89 58 44 5 36. 96 4 995 6 36. 5 77 69 733 7 3.9 93 69 73 65 8 3.4 5 646 766 98 6 9 33. 5 36 784 479 633 35 33. 75 987 784 99 78 3.4 669 766 997 98 3.4 5 579 766 86 765 9 4 3 35. 98 7 867 73 4 36.3 5 695 87 33 5 36.3 5 5 87 558 746 6 34.8 75 7 83 34 338 7 36. 85 87 6 97 8 36. 5 /A 87 95 87 Stndrd Dvition (Prditd/Tst).753. 57. 49 ot: * f is onvrtd from ubi strngth b f. 67 f ub ** ; Th imit of rtiv sndrnss in EC4 mthod, whih is.5, is not onsidrd. 4.. UL of CFST Coumn with Vrious L/D A numbr of CFST oumn tsts with L/D vr from 3 to 5 wr ondutd during 98 to 983 b Ci t. Th spimn nd tst dtis n b found in [6]. On th tst rsuts of spimns in Bth II r tkn hrb. Th UL of th spimns prditd b urrnt mthod s w s thos utd using nd EC4 r omprd in Figur 5. Agin, th EC4 prdition is onsrvtiv nd th proposd mthod givs th bst nd smooth prdition rsuts. 5. Conusions Th UL of irur CFST oumns n b prditd b vrious simpifid mthods with diffrnt onsidrtion on onfinmnt fft. Ths mthods hv thir pros nd ons. Th EC4 mthod onsidrs th infun of od ntriit nd sndrnss on th onfinmnt fft. Th mthod is simp nd stright forwrd, sut Prditoin / Tst R.4..8.6 4/t s/t urr/t 3 4 5 6 Spimn umbr Figur 5. Comprison of th UL prdition of CFST oumns b thr diffrnt mthods. but rs ss on th ross stion prmtrs. A simpifid mthod is dvopd b inhriting th simp frmwork of th mthod, but nrihing th sndrnss nd od ntriit rdution ftors Copright 3 SiRs.
X. M. YU, B. C. CHE 93 with ross stion onfigurtion infuns in ordn with thos impid b th EC4 mthod, so s to nb finr tuning pbiit thn in. Thrfor, th proposd mthod mks th bst of both EC4 mthod nd mthod. Th proposd mthod is drivd from mtri proprtis in th imit quiibrium stt, dopting th rstrind onrt proprtis prsribd in EC nd xtnding th boundr of od ntriit nd rtiv sndrnss imit in EC4. Vidtion ginst sris of tsts shows tht th proposd mthod n prdit th UL of irur CFST oumns with good ur. REFERECES [] Eurood 4 (EC4), Dsign of Composit St nd Conrt Struturs, Prt.: Gnr Rus nd Rus for Buidings, Commission of Europn Communitis, Brusss, 4. [] Amrin Institut of St Constrution (AISC), Mn- St Tubur Struturs, u for Strutur St Buidings: Lod nd Rsistn Ftor Dsign (LRFD), Chigo, 5. [3] AIJ, Rommndtions for Dsign nd Constrution of Conrt Fid Arhittur Institut of Toko, Jpn, 997. [4] Chin Assoition of Enginring nd Constrution Stndrdiztion- 8:9, Spifition for Dsign nd Constrution of Conrt Fid St Tubur Struturs, Chin Pnning Prss, Bijing, 99. [5] Th Etri Powr Industr Stndrd of PRC: DL/T 585-999, Cod for Dsign of St-Conrt Composit Strutur, Issud b Stt Eonomi nd Trd Commission of PRC, 999. [6] S. H. Ci, Modrn St Tub Confind Conrt Struturs (Rvisd Edition), Chin Communitions Prss, Bijing, 7. [7] J. Y. R. Liw nd D. X. Xiong, Efft of Prod on th Axi Cpit of Conrt-Fid Composit Coumns, Journ of Constrution St Rsrh, Vo. 65, o. 3, 9, pp. 79-7. doi:.6/j.jsr.8.3.3 [8] Eurood (EC), Dsign of Conrt Struturs, Prt -: Gnr Rus nd Rus for Buidings, Commission of Europn Communitis, Brusss, 4. [9] B. C. Chn, Z. J. Ou, L. Y. Wng nd L. H. Hn, Exprimnt Stud on Crring Cpit of Conrt Fid St Tubur Coumn undr Entri Lod, Journ of Fuzhou Univrsit-tur Sin Edition, Vo. 3, o. 6,, pp. 838-844. omnturs A : St r of th ross stion of CFST oumn (mm ) A : Conrt r of th ross stion of CFST oumn ( mm ) D: Outr dimtr of CFST oumn (mm) : Loding ntriit (mm) E, E m : Young s Moduus of st nd snt moduus of onrt EI : Bnding stiffnss of CFST oumn, ff 6 EI E I. E I ff m L: Efftiv ngth of CFST oumn (mm) i : Cross stion rsistn of CFST oumn utd b mthod i i u : Utimt od pit of CFST oumn utd b mthod i : Psti rsistn of th ross stion of CFST pr oumn, A f A f pr r : Eur buking rsistn of CFST oumn, EI L r ff I, I : Sond momnt of inrtis of st tub nd onrt or stion P: Ltr onfinmnt prssur on onrt or r : Rdius of onrt or, : Currnt stbiit rdution ftor nd od ntriit rdution ftor i i, : Stbiit rdution ftor nd od ntriit rdution ftor of mthod i : A ftor onsidring th infun of intrn xi rinforing brs in EC4 : Stbiit rdution ftor in EC4 : Rtiv sndrnss, pr r A f r, : Prinip strsss in xi nd tr dirtions : Confinmnt fft ftor, A f A f, : Strngth djustmnt ftors for st nd onrt, rsptiv, in EC4 Copright 3 SiRs.