ON THE ANALYSIS OF A COLD FORMED STEEL PROFILE ARCH STRUCTURE

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1 Proceedings of the Annual Symposium of the Institute of Solid Mechanics and Session of the Commission of Acoustics, SISOM 2015 Bucharest May ON THE ANALYSIS OF A COLD FORMED STEEL PROFILE ARCH STRUCTURE Viorel ANGHEL 1, Ştefan SOROHAN 1, Nicolae CONSTANTIN 1, Ioan STOICA 2 1 Strength of Materials Department, University Politehnica of Bucharest 2 dipl. engineer This paper describes briefly the structural analysis of a thin-walled cold formed steel arch which is used as solution for buildings and roofing structures. Some numerical calculations are presented in order to discuss the stress and stability analysis of such a structure subjected to the usual snow and wind loads. A beam model and a shell finite element representation of the analyzed structure have been considered. Keywords: Cold Formed Profile, Arch Structure, Buckling, FEM 1. INTRODUCTION Cold formed steel sections are at present increasingly used for industrial buildings as storages military hangars or shelters. They are in fact frameless arches, self-supporting cover panels obtained in a simple and fast way (manufactured on site ) by using movable panel forming and curving machine - ABM (Automatic Building Machine). A current system consists in strips of curved arches which are transversally connected by folding and sealing the edges along the length of these arches using a fold seaming machine. In this way the drilling of the sheet or the welding are no more necessary and the assembling time is shorter. The thickness of the sheet can be less than 1 mm still allowing K-span arches having a span of the order of m, [1]. Usually the thicknesses for the cold formed steel sections are between 0.8 and 1.5 mm. This kind of structures were especially used by U.S army, now they have an increasing presence in Europe (civilian domain), several such a structures are now built in Romania. In literature one can find experimental analysis such in [1], [2] and numerical static or stability approaches [3], [4]. This paper deals with some static and stability numerical tests using FEM for such an arch configuration subjected to the usual snow, wind and combined loads. Beam models or shell type finite element representations of the analyzed structures have been used. 2. COMPUTATIONS USING A BEAM MODEL As a real structure consists in many adjoining modules of individual arches, for a fast estimation of the behaviour under applied loads one can assume that the calculation of an unit module arch is relevant for the entire structure. For this reason, at this stage only a semi-cylindrical individual clamped arch having a radius R=7.1 m was considered. The figure 1 presents the cross-section of the arch highlighting the shear center and gravity center positions. The data of this cross-section correspond to the profile LS obtained starting from coil having the width of 1000 mm and 1 mm thickness. In this manner the inner radius of the arch will be around 7 m and the height of the arch is considered equal with the radius. The resulting corrugations in the forming and curving process are not taken into account. These corrugations lead in some losses concerning the bending and axial stiffness but have positive effects on local buckling, [4]. First, the beam model will be presented for the static stress state assessment of the structure in order to compare several possible load cases. In literature many applications are according to American design

2 100 Viorel ANGHEL, Ştefan SOROHAN, Nicolae CONSTANTIN, Ioan STOICA codes. However in Europe there are sometimes different load conditions and standards, [5]. Figure 2 presents two snow load distributions (one symmetric and one asymmetric) and a wind pressure distribution coefficient. The numerical data considered for loads where: p = kn/m 2 for snow and kn/m 2 for the wind (estimated acc. to SREN: CR 1-1-3/2012 and CR 1-1-4/2012). Five load cases were analyzed: symmetric snow, asymmetric snow, wind only, wind + asymmetric snow and combined asymmetric snow with reverse wind. The calculations are performed using the FE code ANSYS, [6]. Figure 3 shows results for the two snow load cases and Figure 4 shows results for the wind load case and for a combination between the reversed wind and asymmetric snow loads. a) In plane cross-section b) Cross-section properties Figure 1. Cross-section characteristics a) Snow load distribution profiles b) Wind load distribution coefficient Figure 2. Symmetrical and asymmetrical profiles of the snow loads; Wind load The first finite element model is a simple one consisting in 36 elements (BEAM188) for the whole length of the clamped ends semicircular arch. The material data are: Young modulus E = 210 GPa and Poisson ratio 0.3(used in FE models). Other data are: the yield stress 269 MPa and the ultimate tensile stress 349 MPa. The first two load cases with the snow are presented in figure 3, together with the reactions and the maximum total displacement. Some other results are reported in the table 1.

3 On the Analysis of a Cold Formed Steel Profile Arch Structure 101 a) Symmetric snow load case b) Asymmetric snow load case Figure 3. Load distribution, total displacements and reactions for the snow load cases The critical load cases concerning the maximum stress and the total maximum displacement consist in asymmetric snow load and the combination between the reversed wind and asymmetric snow loads. The beam model displacements were restricted to the global plane XOY, so the eigenbuckling analysis gives only the global buckling modes having big values of the buckling factors. Load case Max displacement [mm] Table 1. Results using the beam model whole arch Max Von Mises stress [MPa] arch without clamped end regions Snow symmetric Snow asymmetric Wind Wind+ Snow asymmetric Reverse wind+ Snow asymmetric

4 102 Viorel ANGHEL, Ştefan SOROHAN, Nicolae CONSTANTIN, Ioan STOICA a) Wind load case b) Reversed wind+ asymmetric snow load case Figure 4. Load distribution, total displacements and reactions for the wind load cases 3. COMPUTATIONS USING A SHELL MODEL The main failure case for this type of structure is the buckling. For this reason a shell finite element model of the arch was performed using the SHELL181 element type. The arch is clamped at the two ends and on the two lateral sides are imposed symmetry boundary conditions. At the moment only the symmetric snow load case was considered. The model has nodes and elements. In the case of the eigenbuckling analysis the general eigenvalue problem has the form, [7]: K 0 (1) i K i where [K] is the structural stiffness matrix based on initial geometry and linear material properties, [K σ ] is the geometric (stiffness) matrix, depending on the applied load and boundary conditions, λ i is the buckling load factor, {Φ i } is the eigenvector corresponding to the buckling mode shapes. The critical buckling load is then obtained multiplying the value of λ i by the actual applied load. Practical importance has especially λ 1 (first buckling mode). Some selected results are reported in figures 5 to 7. Figure 5 presents the uniform snow load distribution and the resulting total displacements. The maximum obtained total displacement is mm as expected located at the middle of the arch. Figure 6 shows the Von Mises stress for the whole arch and for the arch excepting the two clamped end regions. Figure 7 gives two pictures for the first buckling mode having the factor Using this model, it is expected to obtain a smaller buckling factor in the case of the asymmetric snow load case. However, the real arch has corrugations which give a higher strength, as local buckling strength for curved panels is better with respect to plane ones.

5 On the Analysis of a Cold Formed Steel Profile Arch Structure 103 a) Snow uniform distribution load b) Total displacements Figure 5. Load distribution and resulted total displacements in the case of the shell model a) Von Mises stress (whole arch) b) Von Mises stress (arch without clamped end regions) Figure 6. Von Mises stress results in the case of the shell model a) Shape of the first buckling mode b) Detail of the first buckling mode shape Figure 7. First buckling mode in the case of the shell model

6 104 Viorel ANGHEL, Ştefan SOROHAN, Nicolae CONSTANTIN, Ioan STOICA 4. CONCLUSIONS The main objective of this work was to asses several load cases in order to analyse a simple model of a frameless arch configuration. Only finite element computations in the linear elastic domain were performed. The beam model allows the analysis in a simple manner of the global behaviour of the arch under loads. In the beam model was possible to implement several load cases, the critical one seems to be given by the asymmetric distributed snow combined eventually with the reversed wind. Only a shell model gives the possibility to estimate the local buckling characteristics. Therefore a better model representation of different type of coil corrugations has to be taken into account. For this reason, further studies can be performed using more refined FE models (linear and nonlinear) in order to include several adjacent arches, their connections by folding, representation of corrugations, proper boundary conditions and for other load cases according to the actual European standards or regulations. A practical goal can be to obtain the maximum possible span which can be allowed using such a structure having given height, coil thickness and profile, for known load conditions. REFERENCES 1. BENUSSI F., MAURO A., Half-Barrel Shells Composed of Cold-Formed Profiles, IABSE Colloquium Proceedings, Stockholm September 1986, p AIRUMYAN E. I., BOIKO O.I., Full-Scale Testingand Design of Frameless Arch Steel Roof, Structural Assessment: The Role of Large and Full-Scale Testing, edited by K.S. Virdi, F.K. Garas, J.L. Clarke, G.S.T. Armer, E&FN Spon, London, 1997, p WALENTYNSKI R., CYBULSKI R., KOZIEL K., Numerical Models of ABM K-Span Steel Arch Panels, Architecture civil engineering environment - ACEE, Silesian University of Technology, No. 4, 2011, p WALENTYNSKI R., SANCHEZ R., CYBULSKI R., Linear Buckling Analysis with Different ABM K-Span Arch Panels, Architecture civil engineering environment- ACEE, Silesian University of Technology, No. 2, 2012, p *** European Standard; Eurocode 3- Design of steel structures- Part 1-3: General rules- Supplementary rules for cold-formed members and sheeting, EN , *** ANSYS USER GUIDE, Swanson Analysis Systems Inc., September 15, SOROHAN ŞT., CONSTANTINESCU I.N.,The Practice of Finite Element Modeling and Analysis (in Romanian), Ed. POLITEHNICA Press, Bucharest, 2003.