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Buckling Behavior of Cold Formed Steel Columns
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Buckling Behavior of Cold Formed Steel Columns
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5169 BUCKLING BEHAVIOR OF COLD FORMED STEEL COLUMN UNDER AXIAL LOADING Gokulpriya Malayandisamy1, Nirmalraj. S2 1Student, Department of Civil Engineering, Dr.Mahalingam College of Engineering and Technology, Pollachi- 642003, Coimbatore, Tamil Nadu, India. 2Assistant Professor, Department of Civil Engineering, Dr.Mahalingam College of Engineering and Technology, Pollachi -642003, Coimbatore, Tamil Nadu, India. ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - This Project work presentsthebucklingbehavior of Cold-formed steel column under axial loading. Thepresence of imperfection and their effect on the buckling behavior is important to be considered in CFS sections while designing. These imperfections may be theoutcomeofthemanufacturing process, shipping, and storage, or any other construction process. They require accurate examination in order to find the buckling behavior of cold-formed structures and calculate failure load. To study the buckling behavior of CFSC section with the factors like initial imperfection, the effect of stiffening, width to thickness ratio and to evaluate the load- bearing capacity of the member using the finite element software package, ANSYS. For the parametric study, four different geometric cross sectionswithuniformthicknesswere considered along with three different column length as 230, 950 and 1900mm stating that short, intermediate and long columns. Also, the influence of stiffeningelementandthickness of 1.0, 1.15, 1.2, 1.5, 1.6 and 2.0mm are studied. Also, a comparative study is made with the member withandwithout imperfection. The comparison shows that for a member with 10% of initial imperfection had a significant loss in its load carrying capacity and its efficiency is reduced toanaverage of 27%. Overall, the section S2 providesbetterbucklingbehavior, compared to the other three sections in this analysis by considering all the above parametric effects. Key Words: Cold formed steel, buckling behavior, initial imperfection, stiffening elements. 1. INTRODUCTION Cold -formed steel (CFS) is a common term, whose product was made by rolling (or) pressing steel into semi-finished or finished goods at relatively low temperature i.e. at the room temperature. When compared to the hot rolled sections its yield strength was increased by 15% to 30% due to the pre- work. Now a day’s CFS plays a major role in the construction field for panel constructions, roofing and wall system, formation of corrugated sheets, steel racks etc,. The strength of the elements used in the design was usually governed by buckling. One of the major difficulties with CFS design was to prevent the member frombuckling,becauseof its low width to thickness ratio; the member can buckle first before yielding. The factors that cause a compression member to buckle are, slenderness ratio, eccentric loading, boundary conditions, imperfections etc,. Therefore cold- formed steel design should involve considerations for local, distortional, and global buckling. Cold formed channel sections are fundamental parts for the structural elements of many engineering applications and have been studied extensively. A lot of research work has been done on different mechanical behavior of cold formed channel sections.[1] made a study on plain and lipped channel section under axial compression loading by considering imperfection in FEM and the results were compared with direct strength method. In the article [2] determination of initial geometric imperfection was done. The magnitudes for the local, distortional and global imperfections were taken as L.0 = 0.1t, D.0 = 0.1t and G.0 = L/1000.4. [3] carried a FEM to study the influence of type 1 imperfection by using ABAQUS. Accordingly, Type1 imperfection was defined as maximum local imperfection in a stiffened element, such as a web. They concluded that the local imperfection can have a significant effect on the buckling strength of the member, and this cannotbeignored in its design process. On average, the reduction can be up to 25.13% from the strength of the member without imperfection. at the suggested design level , this reduction can be as severe as 35.91%. [4] says that, beams with the short and the intermediate overall slenderness ratios were sensitive to the imperfect shape that comprise compression flange local buckling. However, for long beams, the overall buckling mode (lateral– torsional buckling) was the most sensitive mode. [5] analyzed a problem using the software ANSYS, in which for Pined- ended boundary condition, top section was identical to the bottom Section, except for the translational degree of freedom in the axial direction This was not restrained. [6] presented numerical linear and nonlinear buckling analysis of a conventional pallet racking system Nonlinear buckling analysis with material nonlinearity and the effect of plasticization is used to investigate post buckling behavior. [7] carried an elastic analysis using open source Constrained Finite StripAnalysis Software CUFSM 4.05 Then, the finite element analysis software ABAQUS 6.12 is employed to investigate the post buckling mechanics and use the magnitude of initial imperfection as 0.1times of thickness of the section for their numerical investigation.[8] undergoneFEMbasednumerical study on influence of initial imperfection of thin walled cold
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5170 formed lipped channel beams. The results of manual calculations are considerably lower than the results of simulation processbyabout 35-45%comparedtotheresults obtained from finite element program ABAQUS. [9] carried out the experimental investigation and finite element analysis on buckling behavior of irregular section cold- formed steel columns under axially concentric loadingandit says that due to the deviation of the shear center, the buckling behavior of such the sectionalwaysshowsbuckling mode coupled with torsional response. [10] presented the study on thin walled beam, and gives the ideology that according to the theory of thin-walled beams does not take the effect of local buckling into account, and that the Resulting critical global forces do not correspond to the actual behavior of the beam. The FEM gives the value of the critical force by taking the effect of the local buckling into consideration and concluded that, for the C-section beam, the plane load does not go through the shearcentreandhere buckling and torsion appear simultaneously, so the rigidity of the plate, through which the load get transferred, had an influence on the value of the critical load. [11] contributed the guidance on the choice of most unfavorable geometric imperfection representedby theEigenmodeshapes,forFEM GMNIA. [12] investigated an non-linearbuckling behavior by considering both the geometric and material non linearity’s into account. PUT IN SAME BRAKET. [13] carried out non linear buckling analysis with initial imperfection whose magnitude was 10% to the thickness of the member. [14] and [15] provides an definition for the plastic Load, PP, was defined as the load corresponding to the intersection of the Collapse limit line and the load-deformation curve. They used twice elastic slope and tangent intersectionmethods to predict the inelastic buckling Load. 1.1 Torsional Buckling In the flexural buckling, the members deform by bending in the plane of one of the principle axes. However columns as well as beams also buckle by twisting or by a combination of bending and twisting. These modes offailureoccurwhenthe torsional stiffness of the member is very small or if bending and twisting are coupled so that one necessarily produces the other. Thin walled open sections usually have very low torsional rigidity and are therefore especially prone to torsional buckling. Combined bending and twisting occurs in axially loaded members, such as angles and channels, whose shear center axis and centroidal axis do not coincide. For single symmetric, the section usually has two buckling modes one for the pure flexural buckling and theotherforthecombined torsional-flexural buckling. And for channels and angles the torsional-flexural buckling load can be significantly below the Euler load, and torsional- flexural buckling must be considered for the design. 2. NUMERICAL INVESTIGATION 2.1 Euler Buckling for Solid Section The finite element analysis (FEA) program ANSYS was used to predict the critical buckling loads for doubly symmetric section. It uses the solid square cross section of 100mm x 100mm with the length of 1m and it takes the young’s modulus value as 2x 105 N/ mm2 Table -1: Boundary condition details for FEA S. no Boundary condition At Top At Bottom 1 Both ends are pinned (K=1) RZ and UY are free RZ free 2 One end fixed other free (k=2) free fixed 3 One end fixed other end hinged (k=0.707) UY free fixed 4 Both ends are fixed (k=0.5) UY is free in 6DOF fixed 2.2 Singly Symmetric Channel Section Euler buckling load is for the doubly symmetric section, where pure flexural buckling occurs. For the singly symmetric sections like channel sections , there are two possible modes of failure where the buckling can occur either by bending in lane of symmetry or by combination of twisting and bending which depends mainly on the dimension of the section. For channel sections, torsional flexural buckling load can be lower than the Euler flexural buckling load. Hence, Euler formula for finding out the critical load will not valid here. The theory of thin walled members does notconsiderthelocal buckling(imperfection) effects into account, where its critical load does not match with the experimental values. Hence the FEM was introduced here to know the buckling behavior of CFS channel column whichincludesall imperfectionand material non linearity (GMNIA). (A) Section Analyzed At first 12 specimens were undergone for non-linear to Know the effect of initial imperfection, W/T ratio, and the stiffening effect. Later other 6 specimen of section S1 with length L1 are analyzed with the effect of knowing the thickness effect.
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5171 Table -2: Dimension of channel section (B) Procedure for Numerical Analysis Initially, elastic buckling analysis called as Eigen value buckling analysis was carried out to obtain the linear critical load and corresponding mode shape. Later the non -linear analysis is carried out with the material and geometric non – linearity’s. Using a nonlinear buckling analysis makes it possible to include such features as initial imperfections, plastic behavior, contact, large- deformation response, and other nonlinear behavior. Nonlinear buckling analysis with material nonlinearity and the effect of imperfection is used to investigate post buckling behavior Nonlinear buckling is more accurate than Eigen value buckling and is therefore recommended for the design or evaluation of structures. In addition, the buckled mode shapescanbeusedas an initial geometric imperfection for a nonlinear buckling analysis in order to provide more realistic results. Nonlinear buckling analysis employs a nonlinear static analysis with gradually increasing loads to seek the load level at which a structure becomes unstable and is a time consuming process. (B) Code for Initial Imperfection The following code is used for carryingthenon -linearEigen value buckling analysisalongwithinitial imperfection where the buckled mode shape from linear Eigenvalueanalysiscan be used as an initial geometric imperfection for a nonlinear buckling analysis. /prep7 UPGEOM, 1, 1, 1, file,rst cdwrite,db,file,cdb Where, first numerical in the second line of code represents the value of imperfection, here 1 resembles the magnitudeof 100% of thickness (1t) for imperfection second numerical represents the load step which is time dependent third numerical represents the buckled mode shape number (i.e) at which mode the an initial geometric imperfection is considered. 3. RESULTS 3.1 Comparison of Euler load with Numerical Load Table -3: Theoretical and analytical comparison of Buckling load for long column 3.2 Parametric Analysis for Channel Section (A) Influence of Initial Imperfection: The average ratio of zero imperfection with 10% of initial imperfection is 1.27862. The below chart shows, the linear and non -linear critical load with and without initial imperfection for 4 sections with 3 lengths of thickness1.5mm. Chart -1: Comparison of Individual Limit Loads For Members Analysed For Imperfection Effect. Boundary conditions Critical Buckling load (KN) Analytical (KN) FEA (KN) Error % Both pinned 16449 16186 1.6 Fixed free 4112.4 4121.1 0.23 Fixed hinged 32908 32243 2.02 Both Fixed 65942.4 60746 7.88
4.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5172 (B) Influence of W/T Ratio: Load carrying capacity increases with decrease inw/tratio were t is constant as 1.5mm and web length (w) varies. In average w/t 83.33(S2) is 1.748 times the capacity increased. Chart -2: Comparison of Individual Limit Loads For Members Analysed For The Effect of W/T Ratio. (C) Effect of Stiffening Element: Section S2 shows the better carrying capacity of 2.12, 1.09, and 2.07 times the other sections of short, intermediate and long column. More Stiffer the element, capacity is more and reduction in occurrence of distortional mode where failure occurs quickly. Chart -3: Comparison of Individual Limit Loads For Members Analysed For Stiffening Effect. (D) Effect of Thickness: It is clear that the capacity of section increases with increase in thickness this is due to increase in the stiffness. Chart -4: Comparison of Individual Limit Loads for Members Analysed For Thickness Effect Table -4: Comparison of Axially Loaded Capacity Between with And Without Initial Imperfection For Varying Thickness. SECTION S1 L1 FINITE ELEMENT ANALYSIS Thickness(mm) Linear N.L (0t) N.L(0.1t ) P0t/P0.1 t SHORT COLUMN 1 12.2 11.8 8.4 1.40 1.15 18.2 17.8 12.2 1.46 1.2 20.57 19 14 1.36 1.5 39.28 38 26 1.46 1.6 46.4 44 31 1.42 2 86.66 85 63 1.35 AVERAGE 1.16 3.3 Buckling Behavior (A) Short Column It possess higher load carrying capacity than the intermediate and long column Buckling mode is local buckling,followedbydistortional buckling. (B) Intermediate Column Buckling mode is distortional. (C) Long Column It possesses flexural buckling for un-lipped section distortional buckling is followed by flexural phenomenon.
5.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5173 4. CONCLUSIONS This project work was conducted with a total17 specimens including four different cross sections with three different lengths of 230mm, 950mm, 1900mm stating of short, intermediate and long column respectively, with a constant thickness of 1.5mm and other five dealing with varying thickness of 1.0, 1.15, 1.2, 1.6 and 2.0mm which were analyzed for carrying the buckling behavior of cold formed steel column channel section. The above mentioned 17 specimens were undergone withnon-linearanalysisforboth of perfect specimen and the specimen with 10% of imperfection. When there wasanimperfectioninthecolumn it significantly reduce the carrying capacity of the column, hence imperfections have to be considered while designing. For a member with 10% of initial imperfection ,its efficiency is reduced to an average of 27%.It is for the section S2 the load carrying capacity is better compared to all the other three sections. The buckling behavior of sections was based on the length of the section, initially local buckling occurs first, later it is followed by the distortional buckling. For slender columns combined flexural-torsional buckling phenomenon occurs first, in case of the short column local buckling is the critical mode and in case of intermediate column the failure mode is distortional also for the cross section without the stiffening element it contributes to the distortional buckling mode resulting in the reduced load carrying capacity of the specimen. When the thicknessofthe section increases, its stiffness also consequently increases resulting in the section with increased in its load carrying capacity. 5. SCOPE FOR FUTURE WORK For more detailed and accurate study, the result from analytical work has to be cross checked with the experimental works. Also a comparative study has to be made with an AISI specification. For the next stage of work study has to be conducted on the interaction of buckling behavior of cold formed steel sections. This work can become more effective if parameters like residual stresses, loading conditions and other are involved. REFERENCES [1] Jun yea, iman hajirasoulihaa, jurgen becquea. (2018), ‘Experimental investigation of local-flexural interactive buckling of cold formed steel channel columns’, Thin- Walled Structures volno:125, pp no: 245–258. [2] Dinar camotima, pedro b. Dinisa, andré d. Martinsa ben youngb. (2017), ‘Interactive behavior, failure and DSM design of cold-formed steel memberspronetodistortional buckling’, Thin-Walled Structures. [3] Hashmi s.s. ahmed, siddhartha ghosha, mohit mangal. (2017), ‘probabilistic estimation of the buckling strength of a cfs lipped-channel section with type 1 imperfection’. [4] Bassem l. Gendy , m.t. HANNA. (2017),‘Effectofgeometric imperfections on the ultimate moment capacity of cold- formed sigma-shape Sections’, HBRC Journal (2017) vol.13, pp.163–170. [5] Y.q. wang, z.x. wang, x.g. hub, j.k. han , h.j. xing. (2016), ‘Experimental study and parametric analysis on the stability behavior of 7A04 high-strength aluminum alloy angle columns under axial compression’, Thin-Walled Structures vol no:108 , pp no:305–320,83 [6] Chandrakant n. Thombare, keshav k. Sangle, vinod m. Mohitkar, kharmale s.b . (2016) , ‘Nonlinear buckling analysis of 2-D cold-formed steel storage rack structures’, international journal of civil and structural engineering, Vol.no.6, pp.3 [7] Hareesh muthuraj, s.k.sekar, mahen mahnedran, o.p.deepak,vinay Mahajan. (2016), ‘ Post Buckling Behaviour and Strength Assessment of Cold Formed Steel Columns Failing under Local-Distortional Interaction Mode Instability’, 61st Congress of ISTAM [8] Marsel garifullina, udo nackenhorstb. (2015), ‘Computational analysis of Cold-Formed Steel Columns with Initial Imperfections’, Procedia Engineering vol no:117, pp no:1073 – 1079. [9] Chayanon hansapinyo. (2015), ‘Buckling Performance of Irregular Section Cold-Formed Steel Columns under Axially Concentric Loading’, International Journal of Civil and Environmental Engineering ,Vol:9, pp-5 [10] Diana simic penava ana radic tanja ilijaselastic. (2014), ‘stability analysis of thin-walled c- and z section beams without lateral restraints z section beams without lateral restraints’, transactions of famena xxxviii-2 [11] Z. Sadovsky, j.Krivacek, Ivanco Duricova.(2012), ‘ computational modelling of geometric imperfections and buckling strength of cold-formed steel’ Journal of Constructional Steel Research vol no:78, pp no: 1–7 [12] B. Prabu, a.v. raviprakash, n. Rathinam. (2010), ‘Parametric study on buckling behaviour of thin stainless steel cylindrical shells for circular dent dimensional variations underuniformaxial compression’,International Journal of Engineering, Science and Technology,Vol.No.4, pp. 134-149
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 5174 [13] N. Silvestre, d. Camotim and p.b. dinis. (2009) , ‘ Direct strength prediction of Lipped channel columns experiencing Local-plate/distortional interaction’, Advanced steel construction, vol no:5, pp no:49-71 [14] Martin muscat, donald mackenzie, robert Hamilton. (2003), ‘A work criterion for plastic collapse’, International Journal of Pressure Vessels and Piping vol no:80, pp no: 49–58. [15] Donald mackenzie and hongjun li. ‘A Plastic LoadCriterion for Inelastic Design by Analysis’. [16] Alexander chajes. (1974), ‘principle of structural stability theory’, department of civil engineering, university of Massachusetts, US. [17] B.W. Schafer and S. Ádány.(2005), ‘Understanding and classifying Local, distortional and global Buckling in open thin-walled Members Annual Conference Structural Stability Research Council Montreal, Canada. [18] Thomas H.-K. Kang,Kenneth A.Biggs,andChrisRamseyer. (2013), ‘Buckling Modes of Cold-Formed Steel Columns’ IACSIT International Journal of Engineering and Technology, Vol. 5, No. 4
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