EXERIMENTAL AND NUMERICAL STUDIES OF HOLLOW FLANGE CHANNEL BEAMS SUBJECT TO WEB CRILING UNDER ETF AND ITF LOAD CASES Keerhan oooganahan, Mahen Mahendran * and Edard Seau Schoo of Civi Engineering and Bui Environmen, Science and Engineering Facu, Queensand Universi of Technoog (QUT) Brisane, Queensand 4000, Ausraia. *Emai: m.mahendran@qu.edu.au ABSTRACT This paper presens he deais of experimena and numerica sudies on he e cripping ehaviour of hoo fange channe eams, knon as LieSee eams (LSB). The LSB has a unique shape of a channe eam ih o recanguar hoo fanges, made using a unique manufacuring process. Experimena and numerica sudies have een carried ou o evauae he ehaviour and design of LSBs sujec o pure ending acions, predominan shear acions and comined acions. To dae, hoever, no invesigaion has een conduced ino he e cripping ehaviour and srengh of LSB secions under ETF and ITF oad condiions. Hence experimena sudies consising of 28 ess ere firs conduced in his research o assess he e cripping ehaviour and srenghs of LSBs under o fange oad cases (ETF and ITF). Experimena e cripping capaci resus ere hen compared ih he predicions from AS/NZS 4600 and AISI S100 design rues, hich shoed ha AS/NZS 4600 and AISI S100 design equaions are ver unconservaive for LSBs under ETF and ITF oad cases. Hence improved equaions ere proposed o deermine he e cripping capaciies of LSBs. Finie eemen modes of he esed LSBs ere hen deveoped, and used o deermine he easic ucking oads of LSBs under ETF and ITF oad cases. Ne equaions ere proposed o deermine he corresponding easic ucking coefficiens of LSBs. Fina suiae design rues ere aso deveoped under he Direc Srengh Mehod forma using he es resus and ucking anasis resus from finie eemen anases. KEYWORDS Cod-formed See, We Cripping, ETF and ITF Load Cases, Hoo Fange Channe Beams. INTRODUCTION Cod-formed see (CFS) srucura memers are ide used in modern consrucion due o he man advanages he offer in comparison ih conveniona ho-roed see secions. The are usua hin-aed memers ih arge idh-o-hickness raios. Ligheigh, high srengh and siffness, accurae secion dimensions, eas prefaricaion and mass producion are some of he quaiies of cod-formed see memers ha creae cos savings in consrucion. Since ear 1990s, Ausraian manufacuring companies (OATM, 2008) have inroduced innovaive cod-formed hoo fange secions, and one of hem knon as LieSee eams (LSB) is shon in Figure 1. The deveopmen of his hoo fange channe secion as ased on improving he srucura efficienc adoping orsiona rigid recanguar hoo fanges, minimising oca ucking of pae eemens eiminaing free edges, disriuing maeria aa from he neura axis o afford greaer ending siffness han conveniona cod-formed secions, and opimising manufacuring efficienc. The LSB secions ere produced from a singe see srip using a comined dua eecric resisance eding and auomaed coninuous ro-forming process (OATM, 2008), primari for use as foor joiss and earers in residenia, indusria and commercia uidings. The ase see used for LSB producion has a ied srengh of 380 Ma and a ensie srengh of 490 Ma. Hoever, due o cod-forming, he nomina ied srenghs of he e and fange eemens are 380 and 450 Ma, respecive (OATM, 2008). The manufacuring process aso inroduces residua sresses and iniia geomeric imperfecions hich differ from hose of common cod-formed and ho-roed see secions. Due o he geomer of he LSB, as e as is unique residua sress characerisics and iniia geomeric imperfecions resuan of manufacuring processes, much of he exising research for common cod-formed see secions is no ike o e direc appicae o he LSB. 368
Figure 1 LieSee eams Figure 2 We cripping faiures of LSBs We earing is a form of ocaized faiure ha occurs a poins of ransverse concenraed oading or suppors of hin-aed see eams (Rhodes e a., 1998). LSB joiss and earers ha are unsiffened agains his pe of oading are aso vunerae o e earing/cripping faiures (see Figure 2). The compuaion of he e earing srengh means of heoreica anasis is quie compex as i invoves man facors such as oca ieding in he oading region, insaii of he e eemen, and man ohers. Hence he curren design rues in mos codformed see srucures codes are empirica in naure deveoped ased on more han 1200 ess of conveniona cod-formed see secions such as C-, Z- and ha secions and ui-up secions (Winer and ian; 1946, Waker, 1972; Khan and Waker, 1975; raakaran, 1993; Young and Hancock, 1998 and Macdonad e a., 2011) for he four pes of e cripping oading condiions shon in Figure 3: End-One-Fange Loading (EOF), End- To-Fange Loading (ETF), Inerior-One-Fange Loading (IOF) and Inerior-To-Fange Loading (ITF). Since 2005, unified e earing capaci equaions have een deveoped ha define specific e cripping coefficiens for he ke parameers infuencing he e earing capaci of C-, Z-, Ha and ui-up secions, name, cear e heigh o hickness raio (d 1/ ), inside en radius o hickness raio (r i/ ), earing engh o hickness raio ( / ), in addiion o e hickness ( ) and ied sress (f ). Hoever, hese capaci equaions are no appicae o he LieSee eams (LSB) due o he presence of o recanguar hoo fanges insead of he conveniona fange pae eemens. Effecs of he presence of hoo fanges incuding he higher roaiona resrain a he LSB e-fange juncure have een successfu incuded in he shear capaci design rues of LSBs (Keerhan and Mahendran, 2010 and 2011). Hoever, such an approach has no een deveoped e for he e cripping capaci of LSBs. Hoo fange channe secions such as LSBs can e used as fexura memers in see uiding ssems, for exampe, foor joiss and earers. For hem o e used as fexura memers, heir fexura, shear and e cripping capaciies mus e knon. Recen research sudies have invesigaed he fexura (Anapaan and Mahendran, 2011 and 2012) and shear (Keerhan and Mahendran, 2010 and 2011) ehaviour and capaciies of LSBs. Hoever, no invesigaion has een conduced ino he e cripping ehaviour and srengh of LSB secions. In his research e cripping ehaviour and srengh of LSBs under ETF and ITF oad cases as invesigaed using experimena and numerica sudies. Experimena sud as used o deermine he uimae e cripping capaciies hie finie eemen anases ere used o deermine heir easic ucking oads for hese o oad cases. Using hese resus, improved design rues are proposed incuding he direc srengh mehod ased design rues. This paper presens he deais of hese sudies, and he resus. 369
(a) End o fange (ETF) Loading () Inerior o fange (ITF) oading (c) End one fange (EOF) oading (d) Inerior one fange (IOF) oading Figure 3 Loading condiions for e cripping ess (AISI, 2008) WEB CRILING TESTS Ten eigh ess ere conduced o invesigae he e cripping ehaviour of LSBs under ETF and ITF oad cases. Tae 1 presens he deais of he e cripping es specimens. I incudes he measured e hicknesses ( ), cear e heighs (d 1), and ied sresses (f ) of he e eemens of esed LSBs. Since he ouside of he inner en corners (r i) is fied ih ed maeria unike in open cod-formed channe secions, he inner en radius (r i) of LSB as considered as zero (see Figure 1). Figures 4 (a) and () sho he es se-up used in he e cripping ess of his research for ETF and ITF oad cases, respecive, ui ased on he recommended AISI sandard es mehod shon in Figure 3 (a) and (). I is saed in he AISI S909 es mehod (AISI, 2008) ha he specimen engh shoud e a eas equa o hree imes he fa porion of cear e heigh for he ETF oad case hie i shoud e a eas equa o five imes he fa porion of cear e heigh for he ITF oad case. Hence five imes he secion deph as seeced for oh ETF and ITF oad cases. (a) ETF Load Case () ITF Load Case Figure 4 We cripping es se-up A he LSB ess ere conduced using an Insron esing machine. Three differen sizes of earing paes (50 mm, 100 mm and 150 mm) ere used o aain hree pes of esing condiions for oh ETF and ITF oad cases. The suppor ssem as designed o ensure ha he es eam had pinned suppors a he op and oom. The appied oad is he imporan parameer. The measuring ssem as se-up o record he appied oad and associaed es eam dispacemens. The cross-head of he esing machine as moved a a consan rae of 0.7 mm/minue uni he es eam faied. Figures 5 (a) and () sho he e cripping faiure modes of 200x45x1.6 LSBs under ETF oad and ITF cases, respecive (earing engh = 100 mm). No fange crushing faiures ere oserved in he ess. Experimena uimae e cripping capaciies are compared ih he predicions from he design equaion (Equaion 1) ased on AS/NZS 4600 (SA, 2005) and AISI S100 (AISI, 2012) in Tae 1. For he predicion of e cripping capaciies, suppor and fange condiions ere aken as Unfasened, Siffened or paria 370
siffened fanges and To-fange oading or reacion and he corresponding e cripping coefficiens are as foos. Therefore 2 r i R C f s i n 1 C r 1 C 1 C C = 13, C r = 0.32, C = 0.05, C = 0.04 for ETF oad case C = 24, C r = 0.52, C = 0.15, C = 0.001 for ITF oad case d 1 (1) Tae 1 We cripping capaciies of esed LSBs and comparisons ih AS/NZS 4600 design rues We Cripping We Cripping Capaci LSB d 1 Capaci (kn) Raio f No. (mm) (mm) Bearing Load Tes/ Secions (Ma) Lengh Case AS/NZS roposed Tes/roposed Tess (AS/NZS 4600 Eq. Eqs 4600) 1 150x45x1.6 1.59 118.4 454.2 50 ETF 12.52 8.43 9.51 0.67 0.89 2 150x45x2.0 2.03 119.5 437.1 50 ETF 20.26 16.57 16.63 0.82 1.00 3 200x45x1.6 1.60 168.9 452.1 50 ETF 11.34 6.89 6.79 0.61 1.02 4 250x60x2.0 1.97 209.4 446.0 50 ETF 16.55 10.86 9.66 0.66 1.12 5 200x60x2.5 2.50 160.0 443.3 50 ETF 29.97 21.70 23.42 0.72 0.93 6 150x45x1.6 1.60 121.0 454.2 100 ETF 13.75 9.60 11.08 0.70 0.87 7 150x45x2.0 1.97 119.3 437.1 100 ETF 20.60 19.93 17.91 0.97 1.11 8 200x45x1.6 1.56 167.8 452.1 100 ETF 11.72 7.14 7.39 0.61 0.97 9 250x60x2.0 1.97 209.2 446.0 100 ETF 17.94 11.82 11.18 0.66 1.06 10 200x60x2.5 2.50 160.0 443.3 100 ETF 32.24 25.38 26.80 0.79 0.95 11 150x45x1.6 1.59 118.5 454.2 150 ETF 14.52 11.43 12.30 0.79 0.93 12 150x45x2.0 2.00 119.7 437.1 150 ETF 22.49 24.22 20.43 1.08 1.19 13 200x45x1.6 1.58 169.1 452.1 150 ETF 12.79 7.85 8.44 0.61 0.93 14 200x60x2.5 2.50 160.0 443.3 150 ETF 33.98 31.82 29.40 0.94 1.08 Mean 0.76 1.00 COV 0.19 0.098 15 150x45x1.6 1.60 119.3 454.2 50 ITF 50.86 15.43 17.62 0.30 0.88 16 150x45x2.0 2.00 118.4 437.1 50 ITF 72.87 30.14 29.03 0.41 1.04 17 200x45x1.6 1.57 168.5 452.1 50 ITF 48.87 13.03 13.28 0.27 0.98 18 250x60x2.0 1.99 210.0 446.0 50 ITF 73.50 22.48 20.91 0.31 1.08 19 200x60x2.5 2.50 160.0 443.3 50 ITF 110.21 42.42 43.65 0.38 0.97 20 150x45x1.6 1.59 119.3 454.2 100 ITF 59.82 16.14 18.67 0.27 0.86 21 150x45x2.0 1.97 118.4 437.1 100 ITF 83.57 32.16 29.96 0.38 1.07 22 200x45x1.6 1.57 168.5 452.1 100 ITF 58.15 13.26 14.30 0.23 0.93 23 250x60x2.0 1.97 210.0 446.0 100 ITF 85.05 23.16 21.75 0.27 1.06 24 200x60x2.5 2.50 160.0 443.3 100 ITF 128.54 43.68 46.39 0.34 0.94 25 150x45x1.6 1.64 118.2 454.2 150 ITF 70.77 16.91 21.30 0.24 0.79 26 150x45x2.0 1.98 119.7 437.1 150 ITF 94.08 34.52 31.67 0.37 1.09 27 200x45x1.6 1.58 168.4 452.1 150 ITF 65.99 14.18 15.34 0.21 0.92 28 200x60x2.5 2.50 260.0 443.3 150 ITF 142.29 48.81 36.20 0.34 1.35 Mean 0.31 1.00 COV 0.21 0.135 Noe: AS/NZS 4600 and AISI S100 design rues are idenica. For ETF oad case, he mean vaue of es o prediced e cripping capaci of LSB AS/NZS 4600 is 0.76 hie he corresponding coefficien of variaion (COV) is 0.19. For ITF oad case, he mean vaue of es o prediced e cripping capaci of LSB AS/NZS 4600 is 0.31 hie he corresponding COV is 0.21. Tae 1 resus sho ha AS/NZS 4600 (SA, 2005) and AISI S100 (AISI, 2012) design equaions are considera unconservaive for LSB secions, in paricuar under ITF oad case. Since AS/NZS 4600 (SA, 2005) and AISI S100 (AISI, 2012) design equaions ere deveoped for open cod-formed see secions, ne e cripping capaci equaions shoud e deveoped for LieSee eams (LSBs) ih recanguar hoo fanges. Deais of he proposed e cripping capaci equaions for LSBs are given in he nex secion. 371
(a) ETF oad case () ITF oad case Figure 5 We cripping faiure modes of 200x45x1.6 LSBs under ETF and ITF oad cases (Bearing Lengh = 100 mm) Since he curren avaiae e cripping capaci equaions are unsafe for LSBs, ne design equaions are proposed o predic he e cripping capaciies of LSBs ased on experimena resus. This approach is simiar o ha used in he curren cod-formed see design codes (SA, 2005 and AISI, 2012) in hich Equaion 1 is proposed ih modified e cripping coefficiens C, C r, C and C. Since he inside en radius (r i) as considered as zero, C r as aken as zero. Equaions 2 and 3 sho he proposed design equaions for he e cripping capaciies of LSBs (R ) hie Tae 2 shos he associaed, modified e cripping coefficiens. Experimena uimae e cripping capaciies are compared ih he predicions from he proposed Equaions 2 and 3 in Tae 1. For ETF oad case, he mean vaue of es o prediced e cripping capaci raio is 1.00 ih a COV of 0.098. For ITF oad case, hese vaues are 1.00 and 0.135. I shos ha he e cripping capaciies prediced Equaions 2 and 3 agree e ih he experimena e cripping capaciies of LSBs under ETF and ITF oad cases. 2 R 12. 5 f 1 0. 12 2 R 25. 7 f 1 0. 04 1 0. 07 1 0. 06 d 1 d 1 (2) (3) Tae 2 roposed e cripping coefficiens Load Case Equaions C C r C C Mean COV ϕ ETF AS/NZS 4600 13.0 0.32 0.05 0.04 0.76 0.159 0.90 roposed 12.5 0 0.12 0.07 1.00 0.098 0.87 ITF AS/NZS 4600 24.0 0.52 0.15 0.001 0.31 0.206 0.80 roposed 25.7 0 0.04 0.06 1.00 0.135 0.83 ELASTIC BUCKLING FINITE ELEMENT ANALYSES Theoreica easic ucking anasis approaches ere aemped in he pas o invesigae he ucking ehavior of see secions under concenraed oads (Waker, 1975). The ideaized he es of cod-formed see secions as simp suppored recanguar hin paes aong he edges and sujeced o oca disriued in-pane edge compressive forces. Hoever, some siffened compression eemens i no fai hen he easic ucking oad is reached u i deveop pos-ucking srengh means of redisriuion of sresses. The pos-ucking srengh compuaion is raher compex, especia ih he ineracion of e and fange eemens. Mos of he pas heoreica sudies simp ignored his and considered i as a pae eemen. This secion presens he deveopmen of finie eemen modes o invesigae he easic ucking ehaviour of LieSee eams under concenraed oads. Finie eemen modeing sofare ABAQUS as used o perform his ask. ABAQUS has severa eemen pes o simuae he ucking ehaviour of eams. Bu among hem, S4R she eemen as seeced as i has he capaii o simuae he inear ucking ehaviour of LSBs. LSB secions ere meshed in o 5 mm x 5 mm, excep he secion s corners. These corners ere modeed ih 1 mm x 5 mm mesh o accurae represen he infuence of ouside corner radius (r o). Figure 6 shos he deveoped finie eemen mode of LSB under ITF oad case. 372
Tae 3 Criica ucking oad using FEA and k-facors (ETF and ITF oad cases) LSB Secion Load Case (mm) cr(fea) k FEA k prop k FEA/k prop 150x45x1.6 ITF 50 18.17 2.94 2.95 1.00 200x45x1.6 ITF 50 12.50 2.87 2.79 1.03 250x60x2.0 ITF 50 19.44 2.82 2.78 1.01 200x60x2.5 ITF 50 49.78 2.82 2.81 1.00 150x45x1.6 ITF 100 19.43 3.14 3.18 0.99 150x45x2.0 ITF 100 37.55 3.11 3.05 1.02 200x45x1.6 ITF 100 13.12 3.01 3.02 1.00 250x60x2.0 ITF 100 20.50 2.92 2.98 0.98 200x60x2.5 ITF 100 52.22 2.95 2.99 0.99 150x45x1.6 ITF 150 20.82 3.37 3.35 1.01 200x45x1.6 ITF 150 13.83 3.17 3.19 0.99 200x60x2.5 ITF 150 53.84 3.05 3.13 0.97 Mean 1.00 COV 0.02 150x45x1.6 ETF 50 10.60 1.72 1.76 0.97 150x45x2.0 ETF 50 20.36 1.69 1.76 0.96 200x45x1.6 ETF 50 6.58 1.51 1.41 1.07 200x60x2.5 ETF 50 26.79 1.52 1.58 0.96 150x45x1.6 ETF 100 14.66 2.37 2.36 1.00 150x45x2.0 ETF 100 27.95 2.32 2.30 1.01 200x45x1.6 ETF 100 8.72 1.99 2.01 0.99 200x60x2.5 ETF 100 35.30 2.00 2.06 0.97 150x45x1.6 ETF 150 17.83 2.89 2.83 1.02 150x45x2.0 ETF 150 33.82 2.80 2.71 1.03 200x45x1.6 ETF 150 10.73 2.46 2.47 1.00 200x60x2.5 ETF 150 43.06 2.43 2.43 1.00 Mean 1.00 COV 0.03 Tae 4 roposed coefficiens for ucking coefficien (k) k C C,r C, C, C, Mean COV k ETF 0.432 0.0 0.6 0.5 0.2 1.00 0.03 k ITF 0.489 0.0 0.2 0.2 0.5 1.00 0.02 Loading as direc appied means of noda forces in he op e-fange juncion o represen he oad appied hrough oading pae. The op fange nodes ih he appied equivaen noda forces ere prevened from moving aong he ransverse and ongiudina direcions (axes 1 and 3). Ever node on he oom earing engh (end span secion in ETF and mid-span secion in ITF oad cases) as prevened from moving aong he ransverse (axis 1), verica (axis 2) and ongiudina (axis 3) direcions. (a) Load and Boundar Condiions () Bucking Mode Figure 6 Finie eemen mode of 200x45x1.6 LSB under ITF oad case 373
Easic criica ucking oads cacuaed from finie eemen anases (FEA) ere comined ih he criica ucking oad equaion (Equaion 4) o cacuae he ucking coefficien (k) and he resus are summarized in Tae 3. These anases sho ha he ucking oads of he secions var ih earing engh. Based on he easic ucking anasis resus, he fooing simpe equaion (Equaion 5) as deveoped for he deerminaion of he easic ucking coefficiens of LSBs under ETF and ITF oad cases. Finie eemen anases coefficiens (k FEA) and proposed ucking coefficien (K rop) ere compared in Tae 3. The mean vaues of FEA o proposed coefficiens (k FEA/k rop) for ETF and ITF oad cases are 1.00 hie he corresponding COVs are 0.03 and 0.02, respecive. I shos ha he ucking coefficiens prediced ased on he proposed equaion (Equaion 5) agree e ih FEA ucking coefficiens for LSB secions under oh oad cases. This ucking coefficien equaion incudes he effec of inside en radius (r i), e deph (d 1), earing engh ( ), fange idh ( f) and hickness ( ) of he secions, hich is in a simiar form of AISI S100 (2012) and AS/NZS 4600 design rues for e cripping capaciies. Coefficiens for cacuaing he ucking coefficien (k) under ETF and ITF oad cases can e oained from Tae 4. (4) K rop =C (1 C,r r i )(1 C, d 1 )(1+C, )(1+C, f ) (5) C = genera coefficien, C,r = coefficien of inside en radius o hickness raio, C, = coefficien of e senderness raio, C, = coefficien of earing engh o hickness raio, C, = coefficien of fange idh o hickness raio This proposed equaion o cacuae he ucking coefficien as used o derive he e cripping capaci equaions of LSB secions under ETF and ITF oad cases in he nex secion. This mehod o predic ucking coefficiens under e cripping can e exended o oher cod-formed see secions such as ipped channes and channes ih e ris in he fuure. DIRECT STRENGTH METHOD The direc srengh mehod (DSM) is an aernaive o he radiiona effecive idh mehod and has een adoped as an aernaive design mehod in AS/NZS 4600 and AISI S100. Hoever, no forma DSM provisions exis for e cripping of cod-formed see eams. Hence suiae design rues ere deveoped for he e cripping capaci of LSBs under he DSM forma. The are proposed in a simiar manner o hose of he secion capaci of coumns in compression sujec o oca ucking (Equaions 6 and 7) using es resus. In hese equaions he DSM ased nomina e cripping capaci ( u) is proposed using he oca ucking capaci equaion (N c) here N c, N o and N ce are repaced u, cr (easic ucking capaci in e cripping) and (ied capaci in e cripping), respecive. In hese equaions, poer coefficiens of 0.78 and 0.75 are used insead of 0.4 ased on he experimena resus of LSBs for ETF and ITF oad cases, respecive. Senderness (λ) as cacuaed using Equaion 8. Equaions 6 and 7 sho he proposed DSM ased design equaions for he e cripping capaci of LSBs under ETF and ITF oad cases, respecive. u 0. 501 0. 05 cr 0. 78 cr 0. 78 (6) u cr 0. 561 0. 05 f cr 0. 75 d 1 f cr d 1 2 0. 75 (7) (8) (9) (10) 374
u u cr cr Figure 7 Comparison of e cripping capaciies of LSBs from ess and DSM ased design equaions Equaions 9 and 10 aove presen he equivaen ied capaciies in e cripping ased on a 45 oad disriuion o he midde from he earing pae edges for ETF and ITF oad cases, respecive. These equivaen e ied capaci expressions aso agree ih he ied-ine mode of Young and Hancock (2001). In order o invesigae he accurac of he proposed DSM ased e cripping design equaions for LSBs, experimena uimae e cripping capaci resus ere processed ihin he DSM forma and compared ih he proposed design equaions (6 o 10). The are shon in Figures 7 (a) and () for ETF and ITF oad cases, respecive. These figures are in a non-dimensiona forma, ie. u/ versus λ = ( / cr) 0.5. I can e seen ha he proposed DSM equaions are ae o predic he e cripping capaciies of LSBs accurae. Furher FEA ased research is coninuing o improve he proposed DSM equaions using more e cripping capaci daa. CONCLUSIONS This paper has presened he deais of 28 e cripping ess conduced o invesigae he e cripping ehaviour and capaciies of hoo fange channe eams knon as LieSee eams (LSB) under ETF and ITF oad cases, and he corresponding finie eemen anases o deermine heir easic ucking oads. Comparison of he uimae e cripping capaciies from ess shoed ha AS/NZS 4600 (SA, 2005) and AISI S100 (AISI, 2012) design equaions are unconservaive for LSB secions under oh ETF and ITF oad cases. Ne equaions ere herefore proposed o accurae predic he e cripping capaciies of LSBs ased on he es resus. Ne equaions ere aso proposed o cacuae he easic ucking oads of LSBs under ETF and ITF oad cases. Suiae DSM ased design equaions ere hen deveoped for he e cripping capaci of LSBs under ETF and ITF oad cases. Furher finie eemen anases are coninuing o improve he DSM equaions. A simiar approach can e used o deveop DSM ased design equaions for conveniona open cod-formed see secions. REFERENCES Anapaan, T., Mahendran, M. and Mahaarachchi, D. (2011) Secion Momen Capaci Tess of LieSee Beams, Thin-Waed Srucures, Vo.49, pp.502-512. Anapaan, T. and Mahendran, M. (2012). Improved Design Rues for Hoo Fange Secions Sujec o Laera Disoriona Bucking, Thin-Waed Srucures, Vo.50, pp.128-140. American Iron and See Insiue (AISI S100). (2012). Norh American Specificaion for he Design of Codformed See Srucura Memers, AISI, Washingon, DC, USA. American Iron and See Insiue (AISI S909). (2008). TS-9-05 Sandard Tes Mehod for Deermining he We Cripping Srengh of Cod-formed See Beams, DC, USA. Keerhan,. and Mahendran, M. (2010). Experimena sudies on he shear ehaviour and srengh of LieSee eams, Engineering Srucures, Vo. 32, pp. 3235-3247. Keerhan,. and Mahendran, M. (2010) Easic Shear Bucking Characerisics of LieSee Beams, Journa of Consruciona See Research, Vo. 66, pp. 1309-1319. Keerhan,. and Mahendran, M. (2011). Ne Design Rues for he Shear Srengh of LieSee Beams, Journa of Consruciona See Research, Vo.67, pp.1050 1063. Khan, M. Z., Waker, A.C. (1972). Bucking of aes Sujeced o Locaized Edge Loading, Srucura Engineer, Vo. 50, pp.225-232. Macdonad, M., Heianudua, M.A., Koeko, M. and Rhodes, J. (2011). We Cripping Behaviour of Thinaed Lipped Channe Beams, Thin-Waed Srucures, Vo. 49, pp. 682-690. OneSee Ausraian Tue Mis, (OATM), Design of LieSee eams, Brisane, Ausraia, 2008. 375
raakaran, K. (1993). We Cripping of Cod-formed See Secions, rojec Repor, Deparmen of Civi Engineering, Universi of Waeroo, Waeroo, Onario, Canada. Rhodes, J. and Nash, D., (1998). An Invesigaion of We Crushing Behaviour in Thin-Waed Beams, Thin- Waed Srucures, Vo. 32, pp. 207 230. Sandards Ausraia/Sandards Ne Zeaand (SA). (2005). Ausraia/Ne Zeaand Sandard AS/NZS4600 Cod-formed see srucures, Sdne, Ausraia. Waker, A.C. (1975). Design and Anasis of Cod-formed Secions, John Wie and Sons, Ne York, U.S.A. Winer G, ian R.H.J. (1946). Crushing Srengh of Thin See Wes, Engineering Experimen, Bueinno.35, Corne Universi, Ne York, USA. Young, B. and Hancock, G.J. (1998). We Cripping Behaviour of Cod-formed Unipped Channes, roc. Of he 14h In. Specia Conference on Cod-Formed See Design and Consrucion, Missouri, USA, pp. 127-150. Young, B., and Hancock, G. J. (2001). Design of Cod-formed Channes Sujeced o We Cripping, Journa of Srucura Engineering, Vo. 127, pp.1137-1144. 376