Load carrying capacity of innovative Cold Formed Steel column.
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1 IOSR Jounal of Mechanical and Civil Engineeing (IOSR-JMCE) ISSN: : Load caing capacit of innovative Cold Fomed Steel column. Savade S.M. 1, Savade M.M. 1 (Depatment of Stuctual Engineeing, VJTI Mumbai, India) (Depatment of Civil Engineeing, Fabtech Technical Campus College of Engineeing, Sangola, India) ABSTRACT: Cold Fomed Steel is an excellent altenative to the taditional hot-olled steel section as it is ve light in weight and has a high stength to weight atio. Consideable eseach has esulted in a simplified method of CFS design known as Diect Stength Method (DSM). This method is now well established in the codes of pactices fo the design of CFS because of its simplicit. With ecent advances in the manufactuing technolog of CFS, it is possible to manufactue sections with pefoations which ae utilised fo plumbing, electical and an othe functional pupose. Cuent DSM method is validated mainl fo the sections without pefoations. Due to its simplicit in pedicting the capacit of the section, this method is emploed to calculate load caing capacit of innovative CFS column sections with pefoations b developing Finite Stip Models and using Diect Stength Method. Feel available Finite Stip ogam, CUFSM, is used fo analsis. Kewods: Cold Fomed Steel, CUFSM, Diect Stength Method, Finite Stip Analsis, and efoations. 1. INTRODUCTION In counties like India, whee thee is scacit of shelte, paticulal fo the economicall backwad class, thee is a need to povide an altenative which will povide an economical solution. Cold Fomed Steel has the potential to be that solution as it has Attactive appeaance, Fast constuction, Low maintenance, Eas extension, Lowe long-tem cost, Non-shinking and non-ceeping at ambient tempeatues, No equiement of fomwok, Temite-poof and ot poof, Unifom qualit, Non combustibilit. Also it is a ecclable mateial. Cold fomed steel beams and columns ae tpicall manufactued with pefoations to enhance thei functional use. Fo example, in low and midise constuction, holes ae pepunched in columns to accommodate the passage of utilities in the walls and ceilings of buildings as shown in Fig In case of cold-fomed steel stoage ack columns, pefoations allow fo vaiable shelf configuations as shown in Figue 1.. Cuentl, Membes with discete holes, ae limited to cetain hole sizes, shapes, and configuations. It geatl hampes an enginee s design flexibilit and deceases the eliabilit of coldfomed steel components whee holes exceed these pesciptive limits. Figue 1.1 efoations atten [1] 7 age
2 Figue 1.1 Hole pattens in stoage ack columns [1]. DIRECT STRENGTH METHOD DSM is elativel new and epesents a majo advancement in Cold Fomed Steel design because it povides enginees and cold fomed steel manufactues with a tool to pedict the stength of a membe with an geneal coss section. Cold-fomed steel membes ae manufactues fom thin sheet steel, and theefoe membe esistance is influenced b coss-section instabilities (e.g. plate buckling and distotion of open coss section) in addition to the global buckling influence consideed in thicke hot olled steel sections. DSM explicitl defines the elationship between elastic buckling and load defomation esponse with empiical equations to pedict ultimate stength. To calculate the capacit of cold fomed steel membe with DSM, the elastic buckling popeties of a geneal cold fomed steel coss-section ae obtained fom an elastic buckling cuve. This cuve is geneated b emploing the finite stip method..1 Finite Stip Method The Finite Stip Method (FSM) is the basis fo the DSM. Simila to the Finite Element Method (FEM), the FSM consists of segegating a membe into longitudinal stips ove the coss-section as shown in Figue.1. Once a membe is divided into stips, a numeical stabilit analsis is pefomed utilizing conventional matix techniques. Figue.1.1 Coodinates, Degees of Feedom, and Loads of a Tpical Stip [] Fo a given distibution of edge tactions on a membe the geometic stiffness scales lineal, this leads to the stabilit eigenvalue poblem of inteest, which fo a single eigen (buckling) mode, φ, and eigen(buckling) value λ ma be expessed as Keφ = λkgφ (.1) Both Ke and Kg ae a function of the stip length, a. Theefoe, the elastic buckling value and the coesponding buckling modes ae also a function of a. The poblem can be solved fo seveal lengths, a, and thus a complete pictue of the elastic buckling value and modes can be detemined. The minima of such a cuve can geneall be consideed as the citical buckling loads and modes fo a membe. CUFSM follows this implementation and an example is povided in Figue. 8 age
3 Figue.1. FSM Output. []. DSM Equations Capacit of the column is calculated as pe DSM based upon thee limit states viz. global buckling, local buckling and distotional buckling. The Global, Local, Distotional slendeness atios ae consideed coespondingl to calculate the section capacit as pe the DSM equations. i.e...1: Flexual, Tosional, o Tosional-Flexual Buckling. The nominal axial stength, ne fo flexual, o tosional- flexual buckling is, c c ne Fo, 1.5; Fo, c 1.5; ne...(..1) c c = ce A F g Whee, ce= Minimum of the citical elastic column buckling load in flexual, tosional, o tosional-flexual buckling...: Local Buckling. The nominal axial stength, nl, fo local buckling is, Fo, 0.776; l nl ne cl cl Fo, l 0.776; nl ne...(..) ne ne = l ne cl cl = Citical elastic local column buckling load...3: Distotional Buckling. The nominal axial stength, nd, fo distotional buckling is Fo, 0.561; cd cd Fo, d 0.561; nd (..3) = d d nd cd cd= Citical elastic distotional column buckling load. 9 age
4 3. ROOSED SECTION The equations of DSM wee modified b Moen C.D.[] to accommodate the influence of holes. He poposed six altenatives out of which following equations pedicted the column capacit moe accuatel. Equation (..3) was modified as, Fo,, d d1 nd net net fo, nd net d d1 d d d d1 d d cd cd fo d d, nd (3.1) 0.4 net When, d ; d ; net d 10.5 d d Othe equations emain same povided that the the citical elastic buckling loads cl, cd, and ce ae calculated including the influence of holes. Following membe coss-section is poposed fo the stud. The thickness of the section is 3 mm and oveall length is 3m. The section has holes longitudinall at 00mm c/c. Figue 3.1 oposed Coss- section 3.1 Local Buckling Local buckling in pefoated column is assumed to occu eithe buckling in goss coss-section between pefoations (clnh) o buckling of the unstiffened stips of web adjacent to a pefoation, (clh). The buckled mode shape with the lowest citical buckling load is cl. To get the value of cnh, the goss coss section is analsed in CUFSM. The pocedue followed in this case is simila to the DSM design guide fo unpefoated section. The clh i.e. net section elastic buckling cuve is geneated in CUFSM b deleting all nodes and elements in pefoated egion. Hee to isolate the local buckling fom distotional buckling, cones ae to be estained in z-diection. A efeence stess of N/mm is applied to the coss-section to geneated the buckling loads. 30 age
5 Figue 3. Geomet of poposed section in CUFSM. Fo goss coss section, Analsis input, fo 1 ksi, i.e N/mm stess, = N, Output gives load facto = and half wave length = 00 mm clnh clnh clnh kn Fo net coss section. To isolate local buckling fom distotional buckling, cones of the section ae estained in z-diection. Figue. 3.3 Net coss section in CUFSM Analsis input, stess =6.894 N/mm = N, output gives load facto =34.53 and half wave length = 60 mm, 31 age
6 clh clh clh kn cl is minimum of clnh and clh. cl = kn. 3. Distotional Buckling. The section does not have a distinct local minimum coesponding to distotional buckling (Figue 3.3), and theefoe a constained finite stip analsis (Schafe and Ádàn 006) is pefomed in CUFSM to identif Lcd (Figue 3.6). The constained finite stip analsis is pefomed with a staight cone model to obtain Lcd (Schafe and Ádàn 006). Analsis input, Stess = N/mm, = N, Output gives, Load facto = and half wave length = 00mm cd cd cd kn Reduced web thickness is then found out and implemented in second finite stip analsis to get coect value of cd The educed web thickness is calculated with (Moen and Schafe 009a) t L 1 L h cd 1/3 1/3 t 0 t t.896 mm Whee, Lh= length of hole. Second finite stip analsis is pefomed with the educed web thickness i.e..896 mm Analsis input, Stess=6.984 N/mm, = N. Analsis output gives, Load facto = , half wave length =00 mm. cd cd cd kn It is found that pefoations esult in 13% eduction in section capacit in distotion. 3.3 Global Buckling. To estain global tanslation in x-diection and tensional otation about z- axis, Mid-height bacing is povided. It esults in following unbaced lengths. Fo unbaced column, K=1 Lx=1500 mm Kx=1.0 L=3000 mm K=1.0 Lt=1500 mm Kt= 1.0 Holes ae povided along length at 00 mm c/c. It esults 13 nos of holes in 3000mm length. Theefoe, Lg=3000-(13x 0)=740 mm. Lnet=(13x0)=60 mm. Lxg=1370mm Lxnet=130mm Ltg=1370 mm Ltnet=130 mm As the holes ae smmeticall placed, the geometic facto T is zeo. To calculate flexual and flexual tosional buckling, weighted aveage of section popeties ae calculated as follows. 3 age
7 Table.3.1 Goss and Net section popeties (A) Goss Section opeties (B) Net Section opeties A g mm A net mm I x mm I xnet mm I mm I net mm x mm xnet mm. 5. mm net mm J mm J net mm C w mm C wnet mm X 0 mm. 0 X 0net mm. 0 Y 0 mm. 19. Y 0net mm I x0 mm I x0net mm I 0 mm I 0net mm x0 mm x0net mm mm net mm o mm onet mm I I I I xavg xavg avg avg avg avg xavg xavg Ix. Lxg Ixnet. Lxnet Tx( Ix Ixnet) Lx Ixavg mm 1500 I. Lg Inet. Lnet T( I Inet) L Iavg mm 300 Lg net Lnet T( net ) L avg mm 3000 x Lxg xnet Lxnet Tx( x xnet ) Lx xavg mm 1500 J J avg avg x J. Ltg J net. Ltnet Tt( J J net ) Lt J avg mm 1500 o. Ltg onet. Ltnet Tt ( o onet ) Lt mm 1500 o. Ltg onet. Ltnet Tt ( o onet ) Lt mm age
8 The waping constant, Cw, does not follow weighted aveage appoximation. It has to be calculated based upon distibuted hole egion in CUFSM o CUTW. Distibuted hole egion, dh*, is calculated as given b Moen and Schafe 009a. In this case, thee ae two pattens of holes, due to smmet, dh* is calculated as follows, h= 50-3=47 mm h 0 =h, out to out depth of element containing hole. * 1 d h dh dh ho dh ho d d C * h * h wavg mm in Global Buckling Loads. (AISI-S100-07, section C4) EI xavg ex A. K. L x avg EC t A.. x ex N/mm EI e A. K. L e N/mm wavg GJ. avg Kt Lt t N/mm =1- (AISI Eq C ) ext =1- = ext ex t ex t 4. ex. t (AISI Eq C ) ext N/mm ce ex e ce A Min (,, ) (319.65) ext ce kn 3.4 Ultimate stength calculations. Inputs ae, net=8.868 kn, =10.5 kn, cl= kn, cd= kn, ce= kn. Fom DSM Equations.(efe section.) DSM Global buckling Stength. 34 age
9 = c 105 c = = c c ne Fo, 1.5; ne ce ne kn 3.4. DSM local buckling Stength. ne l = cl l = = Fo, 0.776; Min (, ) nl Min (10.47,8.868) nl kn DSM Distosional buckling Stength. d l nl ne net d =. cd 10.5 d = = net d d net d d d d d d1 nd net d = 7.19 kn Fo,, nd kn edicted column capacit, n= Min (ne, nl, nd) n=8.868 kn. 4. CONCLUSION Diect Stength Method is simple and has wide applicabilit. It does not depend upon effective width calculations and iteations. Most impotantl it encouages enginees to optimise the section fo the most effective use. efoations poviding functional advantage geneate complexities in the analsis and design at the same time. Conventional method based upon effective width concept become tedious to appl fo innovative sections. In this pape DSM is applied to calculate load caing capacit of the innovative cold fomed steel column. It is found that thee is consideable decease in the distotional buckling and oveall column capacit due to pefoations. 35 age
10 REFERENCES 1. Moen, C.D., Diect Stength Design fo Cold-Fomed Steel Membes with efoations, h.d. Thesis, Johns Hopkins Univesit, Baltimoe, (008). Z. Li, Schafe BW, Buckling analsis of cold-fomed steel membes with geneal bounda conditions using CUFSM: conventional and constained finite stip methods, Twentieth Intenational Specialt Confeence on Cold-Fomed Steel Stuctues Saint Louis, Missoui, USA, Novembe 3 & 4, Schafe, B. W., and Adan, S. (006) Buckling analsis of cold-fomed steel membes using CUFSM, conventional and constained finite stip methods. oc., 18th Int. Specialt Conf. on Cold-Fomed SteelStuctues, 39 54, 4. Schafe B. W. (006), Designing Cold-Fomed Steel Using the Diect Stength Method, 18 th Intenational Specialt Confeence on Cold-Fomed Steel Stuctues, Olando, Floida Octobe 6-7, 006, 5. Schafe B.W., Review: The Diect Stength Method of cold-fomed steel membe design, Jounal of Constuctional Steel Reseach 64 (008) , ELSEVIER, (008) 6. Moen, C.D., and Schafe, B.W. "Expeiments on cold-fomed steel columns with holes." Thin-Walled Stuctues, 46, (008) 7. Moen, C.D., and Schafe, B.W. (009a). "Elastic buckling of cold-fomed steel columns and beams with holes." Thin-Walled Stuctues, 31(1), Moen, C.D., and Schafe, B.W. (009b). "Elastic buckling of thin plates with holes in compession and bending." Thin-Walled Stuctues, 47(1), Moen, C.D., and Schafe, B.W. (011), Diect stength design method fo design of cold fomed column with holes, Jounal of Stuctual Engineeing, Vol. 137, No. 5, Ma 1, 011 ASCE. 10. Ameican Ion and Steel Institute,AISI-S100-07, AISI Specification fo the Design of Cold-Fomed Steel Stuctual Membes. Ameican Ion and Steel Institute. Washington, D.C.(007) 36 age
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