Performance of lightweight thin-walled steel sections: theoretical and mathematical considerations

Transcription

1 Availal onlin at.plagiarsarchlirar.com lagia Rsarch Lirar Advancs in Applid Scinc Rsarch, 0, (5: ISSN: ODEN (USA: AASRF rformanc of lightight thin-alld stl sctions: thortical and mathmatical considrations arin Louis Nilsn, Md Azr Othuman Mdin and Mahuddin Ramli Dpartmnt of ivil and Environmntal Enginring, Univrsit of Illinois at Urana- hampaign 05 North Maths Av., Urana, IL 680-5, USA School of Housing, Building and lanning, Univrsiti Sains Malasia, 800, nang, Malasia ABSTRAT Gloall, thin-alld stl sctions hav n xtnsivl mplod as prim load-aring mmrs, such as all studs, floor joints, columns and ams, in lo to mdium-ris uildings such as offics, hotls, flat locks and houss. In spit of th accssiilit of stl sctions, thr ar still vital arrirs that rstrain its rcognition and xcution in th construction industr. rhaps on of th major arrirs is that th uilding industr is in gnral disinclind to xcut altrnativ uilding mthods and matrials unlss it dmonstrats ovious and comprhnsil qualit or prformanc nfits. It can found that th haviour of thin-alld stl sctions, including local uckling, distortional uckling, gloal uckling and shar uckling hav n ll undrstood and appropriat dsign mthods xistd. Th thortical and mathmatical quations prsntd in this papr ill aid futur rsarchrs in dsigning satisfactor thin-alld stl structurs holisticall. Kords: thin-alld, stl sction, lightight framing, local uckling, distortional, mathmatical modl, gloal uckling, shar uckling INTRODUTION During th last ars, thin-alld stl sction construction has n a srious rival to th mor traditional ood fram sstm and has gaind ground all ovr th orld, particularl in Europ countris, Australia, anada, Unitd Stats and som Asian countris for application in lo ris rsidntial and commrcial constructions. Th rason for this groing application of thin-alld stl is primaril asd on svral advantags driving from high strngth to ight ratio, high stiffnss, as rction and installation compard to thickr hot-rolld stl mmrs, homognous qualit, trmit proof and non-comustiilit. Th main structural componnts utilizd for housing ar roof raftrs, dcks, all studs, sla joists, ciling joists, and roof trusss. In spit of th availailit of coldformd stl sstm, thr ar still crucial arrirs that hold ack its accptanc and implmntation in th construction industr. rhaps on of th prim ostacls is that th uilding industr is in gnral disinclind to implmnt altrnativ uilding mthods and matrials unlss it dmonstrats apparnt and undrstandal qualit or prformanc nfits. Givn that thin-alld sctions ar slndr; this ill incras th havioural occurrncs, hich ar not rgularl found in th hot-rolld sctions sstm. First of all, hn thin-alld sctions ar xposd undr comprssion, local uckling ill tak plac caus th plat idth to thicknss ratio is vr high. This local uckling ffct ill diminish th mmr stiffnss against ovrall flxur and torsion. Fig. dmonstrats th ffct of local uckling in column. Flat lmnts in comprssion that hav oth dgs paralll to th dirction of strss stiffnd a, flang, lip or stiffnr ar rfrrd to as stiffnd lmnts. Scondl, distortional uckling at tims occurs in comprssd lippd channl sctions of intrmdiat lngth. Distortional uckling of a lippd channl tpicall lagia Rsarch Lirar 847

2 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: involvs rotation of th flangs and th lips around th flang- junctions. Figur illustrats th tpical distortional uckling mod of a lippd channl sctions. Figur. Local uckling of comprssion lmnts in column Figur. Distortional uckling mod of a lippd channl sction Thirdl, thin-alld stl columns ar mor simpl to fail in flxural uckling as th alas hav a largr slndrnss compard to th sam lngth of hot-rolld columns. Fourthl, givn that svral thin-alld sctions hav ithr no, or onl on, axis of smmtr (as shon in Fig., this mans that ths sctions hav a natural inclination to tist undr load. Thus th ill mor simpl to fail in torsional uckling or flxural-torsional uckling. Finall, a thin-alld stl sction ma fail in shar uckling oing its small thicknss. To sum up, hn compard to hot-rolld stl sctions, cold-formd thin-alld stl sctions ar mor possil to fail in local uckling, distortional uckling, various gloal uckling and shar uckling. Figur : Tpical cold-formd stl sctions. THEORETIAL AND MATHEMATIAL ONSIDERATIONS FOR THIN-WALLED STEEL SETIONS. Local uckling Local uckling is prdominantl common in thin-alld sctions and is charactrisd th fairl short uckling avlngth of individual plat lmnts. For ach plat, th local uckling capailit dpnds on th ffctiv ara of th plat, hich is quivalnt to th ffctiv idth of th plat multiplid its thicknss. Th ffctiv idth of lagia Rsarch Lirar 848

3 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: a plat dpnds on th strss distriution in th plat, th supporting stat and th idth to thicknss ratio of th plat. Fig. 4 shos th form of strss distriution rgularl ncountrd across th dcisiv sction of a homognousl comprssd plat. Th utmost strss occurs at th supportd plat dgs hilst strsss nar th profoundl uckld plat cntr ar comparativl small, such that it can considrd that th ffctivnss of th plat in nduring loading is confind to th supportd plat dgs. Th ffctiv idth concpt assums that th portions of a plat lmnt (.g. ff / in Fig. 4 nar th supports ar compltl ffctiv in rsisting load and th rmaindr of th lmnt is compltl inffctiv as shon in Fig. 4. Actual strss distriution Simplifid quivalnt strss ff σ ff σ ff σ ff Figur 4: Effctiv idth ff of a plan lmnt stiffnd along oth dgs. Wintr s quation [] is tpicall adoptd diffrnt dsign mthods. It givs: ff = if λ 0.67 ( ff 0. = ( if λ > 0.67 ( λ λ in hich th plat slndrnss λ is dfind : λ = Ys σ cr =.05 t Ys Ek σ hr, is th plat idth; ff is th ffctiv idth of th plat; σ cr is th critical uckling strss of th plat, and Y s is th maximum dg strss of th plat and ma takn as th dsign ild strss of th plat. E is th Young's modulus; k is a uckling factor, hich is a function of th plat supporting condition. k = 4.0 for a simpl supportd plat in uniform comprssion and 0.4 for an outstand plat lmnt ith on dg fr. Th xprssion for ffctiv idth in BS5950 art 5 (998 is: ff Ys 4 0. = [ 4( 0.5 ] (4 σ cr. Distortional uckling Distortional uckling has onl nl rcivd th concntration of rsarchrs and a numr of analtical mthods hav n dvlopd for dtrmining th lastic distortional uckling strss of individuall smmtric crosssctions. f x o Shar cntr of flang and lip unit ff ( h h x o l x ntroid of flang and lip unit Figur 5. ross-sction of a lippd channl lagia Rsarch Lirar 849

4 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: With rfrnc to Fig. 5, sinc distortional uckling primaril involvs th rotation and latral nding of th flangs, stimatd xprssions can drivd considring th flangs in isolation, assuming that th ar undistortd. [] hav givn an analtical xprssion and a straightforard mthod to calculat th distortional uckling strss of thin-alld lippd channl sction columns. Th dsign formulas ar shon lo: E = {( α α ± [( α α 4α ]} (5 cr hr, cr is th distortional uckling load. η K φ α = ( β 0.09Jλ β βηe (6 β α = η(i 0 β (7 η α = η( αi β β (8 (I x I β = h x A (9 β = I I x (x 0 h x (0 β = I (x h ( x 0 x 4 = β ( 0 h [I ( 0 h β β ] ( Eβ4 0.5 β4 0.5 λ = π( = 4.80( ( D t π η = ( (4 λ ' Et. λ K φ = [ ( ] 5.46( 0.06λ EAt λ (5 ' η is otaind from Eqn..5 ith α = ( β 0.09Jλ β (6 cr Th distortional strss is σ d = (7 A Et In quations 5-7, E is th Young s modulus of stl; D is th lippd flang flxural rigidit, D = ; ϖ is ( ν th oisson s ratio; I x and I ar th scond momnts of ara of th lippd flang aout x, axs, rspctivl; I x is th product scond momnt of ara of th lippd flang aout th x, axs; I is th arping constant of th lippd flang; J is th torsion constant of th lippd flang; A is th cross-sctional ara of th lippd flang; t is th thicknss of th flang; is th dpth of th ; h x and h ar th x, coordinats of th flang/ junction; x 0 and 0 ar th x, coordinats of th shar cntr, as shon in Fig. 5. In Fig. 5, th origin of th x- axs is at th cntroid of th flang and lip unit. Kon and Hancock (99 rportd a sris of comprssion tst rsults on lippd channl sctions ith fixd nds and proposd to dsign quations, hich ma usd to xplicitl considr distortional uckling in dsign calculations. Th first is an xtnsion of th arlir quations givn Lau and Hancock (988 asd on th column-uckling philosoph. Th formulations ar: f f σ max = f(- if σd (8 4σ d f f f σ max = f if σd (9 4 d σ hr σ d is th lastic distortional uckling strss, givn σ d in quation 7, f is th ild strss. lagia Rsarch Lirar 850

5 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: Th scond is a modification of plat-strngth curv and is asd mainl on th plat-strngth dsign approach as usd for distortional uckling in th AISI spcification hn th lip is not adquat to full support th flang []. Th formulation is givn : ff =, λ 0.56 (0 ff 6 σd 0.6 σd 0. = ( ( 0.5(, λ 0.56 ( f f Th distortional uckling slndrnss is dfind as: f λ = ( σ d Ths to proposd dsign quations ar consistnt hn prdicting distortional uckling load, ut th scond on is asir to comin ith currnt cod dsign mthods to prdict th failur load for mixd local and distortional uckling modl including th cas hr local uckling occurs for distortional uckling. Th gnralizd Bam Thor (GBT has com a usful tool to stud distortional uckling of thin-alld columns. Davis and Lach [,4] gav mor dtails. Sparat and comind individual uckling mods can associatd ith load componnts in GBT. Th asic quation of GBT is k k '''' k k '' k k k E V G D V B V= q ( in hich th scond-ordr ffcts ar xcludd. Ignoring th shar ffct, th quation for mod k is E k k V '''' k k '' k k ijk i j ' ' k G D V B V k( W V = q (4 i j hr k dnots mod k; k is th gnralizd arping constant; k D is th gnralizd torsional constant and k B is th transvrs nding stiffnss. Th gnralizd sction proprtis dpnd onl on th cross-sction gomtr. ijk k is a thr dimnsional arra of scond-ordr trms hich taks account of th intractions tn in-plan strsss in th facs and out-of-plan dformations. k V and k W ar th gnralizd dformation and arping strss rsultants in th i th mod, rspctivl. E and G ar th modulus of lasticit and shar modulus. k q is th uniforml distriutd load and n is th numr of mods in th analsis. Th critical strss i W, can otaind if k q is zro. If assuming that th mmr ill uckl in a half sin av of avlngth λ, th critical strss for singl-mod uckling, hich is valid for uckling in an individual mod, is [4]: i,k k π k k λ W = E [ ] G D B[ ] ijk (5 k λ π As th avlngth is varid, th minimum critical strss rsult is: i,k k k k W = ( E B G D (6 ijk k and th corrsponding half-avlngth is k k E 0.5 λ = π( (7 k B From quations 5, 6 and 7 it can sn that th distortional critical strss rsultant for mod k is onl dpndant on th scond-ordr coupling trm ikk k hn th load is applid in a diffrnt mod i and th half avlngth dpnds onl on th cross-sction proprtis k and k B hich ar indpndnt of th load. [5,6] hav carrid out a dtaild caliration for distortional uckling prdiction against mor accurat hol-sction analsis offrd GBT. Th pointd that th rotational rstraint stiffnss k φ in quation (5 ma com ngativ ith incrasing dpth of th from quation 5 and if th uckls arlir than th flang, this ma rsult in a lo prdiction of th distortional uckling strss. Thrfor, for this cas, a simpl uckling modl hr th rotational rstraint tn th flang and th can tratd as zro can stalishd and th uckling strsss in th flang and can analsd sparatl. As th uckling load of th flang alon can otaind ith k φ takn as zro in quation 5, th uckling strss of th plat is: lagia Rsarch Lirar 85

6 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: π D λ σ = (8 4 t λ Whn th uckling strss in th is smallr than that in th flang, thr is som uckling intraction and th man uckling strss can calculatd approximatl : ' σ cr = ( σt / Ag (9 hr, A g is th ara of hol cross-sction. In th AISI Spcification [7], th failur of th dg stiffnr to prvnt distortional uckling is considrd rducing th local uckling cofficint of th plat lmnt supportd th stiffnr to a valu lo 4.0. In this mthod, th uckling cofficint (k σ can chosn from Tal. Tal. Buckling cofficint k to considr distortional uckling ffct S Buckling cofficint k σ 0.5 < / f 0.8 / f 0.5 S 4 t 5L Is < < S k = (4.8 ( t Ia 5L Is / 5 S k = (4.8 ( t I L s 0.5 σ kσ =.57( Ia L s / σ kσ =.57( a Ia I I d L Figur 6. Elmnts ith dg stiffnr In ENV99-- [9[, distortional uckling is takn into account assuming that th dgs of th intrmdiat stiffnrs hr distortional uckling ma occur, hav as comprssd struts on lastic foundations. Th lastic foundation is rprsntd a spring hos stiffnss dpnds upon th nding stiffnss of th adjacnt parts to th plat lmnt of th cross-sction undr considration and on th oundar condition of th lmnt. Th spring stiffnss of th stiffnr ma dtrmind appling a unit load pr unit lngth to th cross-sction at th location of th stiffnr, as illustratd in Fig. 7. Th spring stiffnss K pr unit lngth ma dtrmind form: K = u / δ (0 hr δ is th dflction of th stiffnr du to a unit load u acting in th cntroid of and L. For an dg stiffnr, th dflction can otaind from; δ ( µ f (- ν = θ f Et θ = µ / ith f θ Thrfor, th spring stiffnss k can statd as: lagia Rsarch Lirar 85

7 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: K Et = ( 4(- ν 0.5 k f hr,, ar th distanc from th -to-flang junction to th cntr of th ffctiv ara of th dg stiffnr of flang and, rspctivl, as shon in Fig. 7; f is th flang idth, is th dpth; k f =0 for a am in A k = for a am in axial comprssion, k f = for a smmtric am. ff nding, f A ff Th critical uckling strss can drivd as: KEI A s σ cr = ( s in hich, A s and I s ar th ffctiv cross-sctional ara and th scond momnt of ara of th stiffnr, as shon in Fig. 8. f θ µ δ L µ δ (a Actual sstm K L µ ( Equivalnt sstm (c alculation of δ in comprssion cas Figur 7. Dtrmination of th spring stiffnss K according to ENV99-- [9] f a a L L f / t 60 A s, I s K Figur 8.Effctiv cross-sctional ara of an dg stiffnr Th rotational stiffnss ma xprssd as th summation of th lastic and strss-dpndnt gomtric stiffnss trms ith contriutions from th flang and th, hich ill zro if distortional uckling appars. Th rotational stiffnss ma xprssd as: K φ f (K ~ t (K φf K φ (K φf K φ g = (K φf K φ - φf K = 0 = φ Thrfor, th critical uckling strss ( σ cr is (4 lagia Rsarch Lirar 85

8 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: (K (K ~ φf Kφ σcr= t (5 K φf φ hr, K f and K fg ar th lastic rotational stiffnss of th flang and th gomtric rotational stiffnss of th flang, rpctivl; K and K g ar th lastic rotational stiffnss of th and th gomtric rotational stiffnss of th, rspctivl. Analtical modls ar ndd for dtrmining th rotational stiffnss contriutions from th flang and th. For th flang, cross-sctional distortion is not important; hnc th flang is modlld as a column undrgoing torsional-flxural uckling. For th, cross-sctional distortion must considrd, so th is modlld as a singl finit strip. Thrfor, th transvrs shap function is a cuic polnomial. Th longitudinal shap functions of th flang and ar matchd using a singl half-sin av for ach. Th final rotational stiffnss trm for th flang and th ar prsntd as: 4 π I xf π K φ f = EI xf (x of h xf Ef E (x of h xf GJ f (6 L I f L ~ π Ixf Ixf k φfg = Af (x of h xf 0 (x of h xf h xf 0f I xf I (7 f L I f I f Et K φ = (8 6 ( ν ~ π t k φ g = (9 L 60 Th critical lngth can also found and it is a function of th gomtric trms. It can calculatd : 4 6π ( ν Ixf L cr = Ixf (x0f hxf I (x0f h xf (40 t If hr, E is lastic modulus; G is shar modulus; ν is poisson s ratio; t is th plat thicknss; is th idth; L is th distanc tn rstraints hich limit rotation of th flang/ junction; A f is th gross ara of th comprssion flang; I xf and I f ar th scond momnts of ara of th flang along x and dirction, rspctivl; I is arping constant of th flang. x of is x-distanc from th flang/ junction to th cntroid of th flang; h xf is x- distanc from th cntriod of th flang to th shar cntr of flang, as shon in Fig..9. h xf x of k xf L of K f h f x k φf Figur.9.Flang modl (Schafr and k z 999 Each mthod for prdicting th lastic distortional uckling strss has n compard [9,0]. Th mthod givn in ENV 99-- is quit rough and somtims givs inaccurat rsults for -sctions and plats ith intrmdiat stiffnss hil th mthod dvlopd Lau and Hancock [] corrlats ttr ith th rsults otaind numricall.. Gloal uckling For a thin-alld stl column undr comprssion, th column ma undrgo diffrnt forms of gloal uckling, including flxural uckling, torsional uckling and comind flxural-torsional uckling. Th local uckling and lagia Rsarch Lirar 854

9 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: distortional uckling caus rduction in th ffctiv stiffnss of th mmr and thus affct th ovrall flxural and torsional-flxural uckling strngth of th columns and latral uckling strngth of th ams. Thrfor, th ultimat failur of a thin-alld column undr comprssion ma a comination of local and ovrall uckling or distortional and ovrall uckling. In dsign calculations, local and distortional ucking mods ar considrd first valuating th ffctiv cross-sction of th structural mmr. Gloal uckling is thn chckd using proprtis of th ffctiv cross-sction, hich ar otaind from local or distortional uckling haviour. Du to local and distortional uckling, th cntroid of th ffctiv cross-sction and th gross cross-sction ma not coincid. In this situation, th ffct of a shift in th cntroid should includd, hich can sn in Fig. 0. This shift in nutral axis is to introduc a nding momnt in an axiall loadd mmr. Figur 0.Nutral axis shift In BS5950 [], for sctions smmtrical aout oth principal axs or closd cross-sctions hich ar not sujct to torsional flxural uckling, or ar racd against tisting or columns ith fixd nd conditions, th flxural uckling load ma calculatd as: c 0.5({cs ( ηe } [{cs ( ηe } 4cs E ] = (4 E π EI = (4 L η = 0.00 (L / i 0 (4 In hich, cs is th cross-sctional capacit for local uckling; I is th scond momnt of ara of th cross sction; L is th ffctiv lngth of th mmr; i is th radius of gration of th gross cross-sction corrsponding to E. For cross-sctions ith a singl smmtr axis, th ffcts of movmnt of th ffctiv nutral axis should takn into account. Th ultimat load carring capacit for flxural uckling should calculatd as: M c c c = (44 (M c c s hr M c is th lastic nding momnt capacit of th cross-sction, c is th flxural uckling capacit in hich th nutral axis shit has not n considrd and s is th distanc tn th gomtric nutral axis of th gross cross-sction and that of th ffctiv cross-sction. In 99-- [8], diffrnt uckling curvs, hich should chosn in accordanc ith th tp of cross-sction and axis of uckling, should usd to dtrmin th flxural uckling capacit. c = χa ff f / γ M (45 ff = Σtff = Σtρ = βaa (46 A χ = ( φ [ φ λ ] 0.5 λ = ( λ λ [ βa ] (48 λ i (49 = L 0.5 λ = π[e / f Y ] (50 In AISI, th asic quation (5 can usd to dtrmin th various gloal uckling load. A F c = ff n (5 lagia Rsarch Lirar 855

10 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: hr, F n is dtrmind as: F = f ( f / 4F for F > f / and F = F for F f / (5 n For flxural uckling, F is π E π E F = = (L / i (KL / i (5 hr, A ff is th ffctiv ara of th cross-sction and K is th ffctiv lngth factor, hich is rlatd to th oundar condition. If th cross-sction of a column has onl on axis of smmtr and ithout latral racing against tisting, th column ma fail into torsional or torsional uckling mod. Th load carring capacit for torsional or torsionalflxural uckling in BS5950 art 5 (BSI 998 can calculatd as: n c = 0.5({ cs ( TF } [{ cs ( η TF } 4cs TF ] = 0.5({ } [{ } 4β ] EX T EX T EX T / η (54 TF β (55 EX EI X L π = (56 π E T = (GJ i 0 L (57 x 0 β = ( i ( (ix i x0 i = (59 η = 0.00( αl / i 0 (60 for > = (6 for EY / EY TF, α ( TF EY TF α = < (6 In hich, I x is th scond momnt of ara aout th x axis; G is th shar modulus; J is th St Vnant torsion constant for th cross-sction hich ma takn as th summation of t / for all lmnt, hr is th lmnt flat idth and t is th thicknss; is th arping constant for th cross-sction; x 0 is th distanc from th shar cntr to th cntroid masurd along th x axis and i x and i ar th gration aout th x and axs, rspctivl. In ENV99-- [8], uckling curv is usd to dtrmin th torional or torsional-flxural uckling capacitis. Th asic quation is th sam as Eqn. 45, providd cofficint χ is dcidd as: χ = (6 0.5 φ [ φ λ ] λ = ( fy σcr [ βa ] (64 σ cr = σcr,tf, ut σcr σcr,t (65 π E For torsional uckling, σ cr,t = [GJ ] (66 A i L g 0 in hich, th calculation of i o can sn in quation 58. For torsional-flxural uckling, σ cr,tf = [( σcr,x σcr,t ( σcr,x σcr,t 4βσ cr,xσcr,t ] (67 β σ cr,x = π E /(l /ix (68 In AISI (996, th asic quation 5 is also n usd to dtrmin th ultimat torsional-flxural uckling capacit. F can calculatd as: lagia Rsarch Lirar 856

11 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: F = [( σcr,x σcr,t ( σcr,x σcr,t 4βσ cr,xσcr, T ] (69 β hr, σ cr, x and σ cr, T can calculatd using quations.66 and.68, rspctivl. Som comprssion mmrs ar also sujctd to nding and th latral uckling capacit should chckd. Equations 70-7 hav n usd to chck th latral uckling capacit in BS5950 art 5 (BSI 000. N c N c c x M M X Mx Fc ( x,ff M X M M x cr EX MY M Nc YM,ff ( EY M Y M N ( c EY Y M,ff (70 (7 in hich, M cr is th lastic latral uckling rsistanc momnt; M x,ff is th lastic nding momnt capacit of th cross-sction aout th x axis in th asnc of N c and M ; M,ff is th nding momnt capacit of th crosssction aout axis in th asnc of N c and M X; x, ar th cofficint dfining th variation of momnts along x and axis; N c is th axial comprssion load, M x and M ar th nding momnt aout x, axis, rspctivl; M x and M ar th additional nding momnts aout th x-x and - axs du to nutral axis shifts. Whn using ENV99-- (00, a am-column should satisf th folloing quations 7-7. χ χ min lat N f A N f A ff ff / γ / γ M M k(m f W k χ X ff,x,com (M f W LT LT Mx kz(m / γ f W X M Mx / γ ff,x,com M ff,,com k Z(M f W M / γ M M ff,,com / γ M (7 (7 in hich, χ min is th lss of χ and χ x, hr χ and χ x ar th rduction factors of uckling aout and x axis; χ lat is th rduction factor for latral torsional uckling; k x and k ar modification factors to account for nding momnt distriutions in th column aout th x-x and - axs; W ff,x,com and W ff,,com ar th lastic modulus of th ffctiv sction.. THIN-WALLED STEEL WALL-STUDS Th diaphragm racing of stl all-studs using gpsum oards and othr matrials as invstigatd Simaan and kz []. Th usd an nrg approach including th shar rigidit and rotational rstraint of th diaphragm to dvlop a dsign procdur and approximat solution for th uckling of diaphragm-racd all-studs. Th AISI [7] Spcification is asd on this rsarch. Th maximum load that can carrid all-studs is govrnd column uckling tn fastnrs in th plan of th all, flxural and/or torsional ovrall column uckling out-of-plan, and shar failur of th shathing. According to AISI [7], it can found that incrasd stud spacing incrass th ovrall shar rigidit and rsults in incrasd strngth prdiction for oth th ovrall diaphragm-racd uckling mods and shar failur of th shathing itslf. Hovr, uckling tn fastnrs is indpndnt of stud spacing. Millr t al (994 studid th haviour of gpsum-shathd cold-formd stl all studs asd on xprimntal analsis. Th found that incrasing alloard thicknss and th dg distanc to th fastnr ould incras th failur load pr fastnr and th failur mod ould chang from alloard cracking and taring to sharing of th scrs. Th also pointd out that th tst rsults contradictd ith th shar-diaphragm modl, th dformations of gpsum alloard panls (in tnsion r localizd at th fastnrs and not distriutd throughout th panl. This rsarch ld to th imposition of som limitations (.g. maximum stud spacing AISI [7]. [0] studid th haviour of gpsum-shathd prforatd stl all studs asd on th stud column tsts and all stud assml tsts. Th found that th gpsum oard connction improvd th in-plan uckling rsistanc ut it could not full rstrain th rotation of th flang and th lip. Thir calculatd strngth valus according to ENV99-- [8] ar aout 0% consrvativ for th intraction of comprssion and nding momnt if th stud is assumd latrall racd and rotational support of th fastnrs is ignord. Th concludd that ths support conditions ma usd in dsign and ould on th saf sid. lagia Rsarch Lirar 857

12 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: [] prsntd dtails of tsts of a total of 0 full-scal all frams, four ing unlind, ight ing lind on on sid hil th rmaining ight ing lind on oth sids. Each panl consistd of thr studs spacd at 600 or 00mm. Th hight of th frams as st at.4m. For th lind frams, 0mm plastroard as usd. Th found that th plastroard lining should fastnd to th studs at smallr spacing to al to gain an additional strngth. Th AISI mthod is unal to prdict th failur mod of som cass and is inadquat in prdicting th failur loads of studs lind on on sid. [4] usd diffrntial quations of quilirium to driv a mathmatical mthod to calculat th axial strngth (flxural and flxural-torsional uckling loads for gpsum-shathd cold-formd stl all stud composit panls. In thir analsis, axial load as assumd to applid to th cntroid of th gross cross-sction of ach -shapd stud ith racing action of th alloard and connction of scrs r prsntd lastic springs. Thir formulations prdictd that th panl strngth as indpndnt of stud spacing ut rflctd th localizd natur of th alloard dformation. [5] rportd 0 panls tsts, in hich 0 panls had onl on stud and 0 panls ith to studs. Th scr spacing as 00mm, 400mm and 600mm in th studs. Th oards r orintd strand oard (OSB, cmnt particl oard (B and calcium silicat oard (SB. Th numr of oards usd in thir tsts had no shathing, on-sid or to sid shathing. On point, to point or four point loads r applid on th top of th panl. Aftr tsts, all spcimns ithout oard shathing faild in ovrall flxural uckling. For th panls ith on-sid shathing, narl all of th studs faild as a rsult of torsional-flxural uckling and th sid studs faild du to flxural uckling and hav local uckling. For th panls ith to-sid shathing, th studs faild ovrall torsional-flxural uckling and local crushing nar thir nds. Th also found that th oard tp and numr and scr spacing affctd th panl load carring capacitis. Th failur loads of panls shathd ith OSB r aout 0% highr than panls shathd ith B and 70% highr than SB. Th failur loads of panls ith oth sid shathing panls r significantl highr than on-sid shathing panls. Th load carring capacit of studs incrass ith dcrasing scr spacing. ONLUSION This papr has prsntd thoroughl th thortical and mathmatical considrations for thin-alld stl sctions including th studis of th haviour of thin-alld stl structurs at room tmpratur. It can found that th haviour of thin-alld stl structurs at room tmpratur, including local uckling, distortional uckling, gloal uckling and shar uckling hav n ll undrstood and suital dsign mthods xistd. Th thortical and mathmatical quations prsntd in this papr ill assist futur rsarchrs in dsigning accptal thin-alld stl structurs holisticall. Acknoldgmnt Th authors ould lik to thank Univrsiti Sains Malasia and Ministr of Highr Education Malasia for thir financial supports undr Fundamntal Rsarch Grant Schm (FRGS. No. 0/BGN/6756. REFERENES [] Wintr, G., Strngth of thin-stl comprssion flangs. ornll Univrsit Eng. Exp. Stn. Rport No., 947. [] Lau, S.. W., Hancock, G. J., J. of Structural Enginring, ASE, 987, : [] Davis, J. M., Lach., J. of onstructional Stl Rsarch, 994, :87-0. [4] Davis, J. M., Lach., J. of onstructional Stl Rsarch, 994, :-4. [5] Davis, J. M., Jiang,., Non-linar uckling analsis of thin-alld mtal columns, rocding of Thirtnth Intrnational Spcialt onfrnc on old-formd Stl Structurs, St. Louis, Missouri, U.S.A., 996, -4. [6] Davis, J. M., Jiang,., J. of onstructional Stl Rsarch, 998, 46:74-75 [7] AISI, Th spcification for th dsign of cold-formd stl structural mmrs, Washington D: Amrican Iron and Stl Institut, 996 [8] EN, ENV 99--, Eurocod : Dsign of stl Structurs, art.: Gnral ruls, supplmntar ruls for cold formd thin gaug mmrs and shting, Europan ommission for Standardisation, Brussls, 00. [9] Ksti J., Davis J. M., Thin-alld Structurs, 999, :5-4 [0] Ksti J., Local and distortional uckling of prforatd stl all studs, hd Thsis, Hlsinki Univrsit of Tchnolog, Laorator of Stl Structurs, Espoo, 000. [] BSI, British Standard: Structural us of stlork in uilding, art 5: od of practic for dsign of cold formd thin gaug sctions, British Standard Institution, 998. [] Simaan, A.,kz, T., J. of Structural Division, 976, 0:77-9 [] Tlu, Y., Mahndran, M., J. of onstructional Stl Rsarch, 00, 57: lagia Rsarch Lirar 858

13 arin Louis Nilsn t al Adv. Appl. Sci. Rs., 0, (5: [4] L. J., Mahndran, M., Buckling haviour of thin-alld comprssion mmrs at lvatd tmpraturs, rocdings of th Sixth acific Structural Stl confrnc, Bijing, hina, 00, [5] Tian, Y. S., Lu, T. J. Barlo,. Y., Evans, J., An xprimntal stud on th load carring capacit of coldformd stl studs and panls, rocding of Sixtth Intrnational Spcialt onfrnc on old-formd Stl Structurs, 00, lagia Rsarch Lirar 859