تجزیه و تحلیل تجربی و عددی رفتار سازه ای تیرهای فولاد سرد شکل گرفته

A research study on the structural behaviour of cold formed steel beams with C-, I-, R- and 2R-shaped cross-sections at ambient temperature is presented, based on the results of a large programme of experimental tests and numerical simulations. Firstly, several four-point bending tests were carried out in order to assess mainly the failure loads and failure modes of the beams. Secondly, a suitable finite element model was developed to compare with the experimental results, and finally, a parametric study was undertaken in order to investigate the influence of the thickness, height and length of the beams on its structural behaviour.

Studies on the structural behaviour of cold-formed steel (CFS) beams are increasingly popular in the last decades. Instability phenomena, such as local, distortional, lateral-torsional buckling and their interactions, are the most interesting and complex subjects within this research field [1], [2], [3] and [4]. Understanding and dealing with these phenomena has been the central focus of recent research efforts. These buckling modes are mostly responsible for the ultimate strength of the compression members as they may occur even before parts of the cross-section yield. The low torsional stiffness, the high slenderness and the geometric imperfections that are characteristic of CFS members are some of the main causes for their high susceptibility to buckling [5]. It is further noticed that the cross-section’s walls have a high width-to-thickness ratio (the thickness is usually less than 3 mm), that the most cross-sections are open and/or asymmetric; in other words, there is no coincidence between the shear centre and the centroid of the section. Finally, the amplitudes of the geometric imperfections are normally of the same order of magnitude or higher than the thickness of the steel plates. Therefore, cold-formed steel members are usually classified as class 3 or 4 cross-sections, according to EN1993-1.1 [6]. The majority of studies in this field emphasise further the structural behaviour of these members by means of analytical approximations and purely numerical methods. The effective width method (EWM), which was included in the EN1993-1.3 [7], is an example of an analytical approximation method, whereas the commercial software ABAQUS [8] and the free software CUFSM [9] and [10] are examples of numerical methods. As numerical techniques for finding approximate solutions to partial differential equations and their systems, as well as integral equations, the programs ABAQUS and CUFSM use respectively the finite element method (FEM) [11] and the finite strip method (FSM) [12] and [13]. Furthermore, the direct strength method (DSM) [14], which was included in Appendix 1 of the North American Specification for the design of cold-formed steel structural members (AISI S100-2007) [15], and the effective section method (ESM) [16] are examples of combining both analytical approximations and numerical methods in order to assess the axial compressive and the flexural strength of the CFS members. It is noticed that the EWM and the DSM are the design methods commonly used by designers, although their application is not easy. The EWM performs a reduction of the plates that constitutes a cross-section based on the stability of the individual plates for the prediction of the local buckling strength. In addition, this method considers distortional buckling by using a reduced thickness in the calculation of the effective area of the edge stiffener under compression. The thickness reduction factor depends, among other parameters, on the elastic buckling stress of the edge stiffener and the material yield strength. This distortional buckling strength is obtained by an iterative procedure, especially for flexural members since the stress distribution over the new effective cross-section may be different from the effective cross-section previously calculated. On the other hand, a linear elastic stability analysis is the main idea behind the DSM. First, all elastic instability modes for the gross cross-section are determined (local, distortional and global buckling mode). Subsequently, based on reduction factors for the corresponding buckling curves, the predictable strength of the CFS members is calculated. Here, the designers have to get computational tools for the calculation of the elastic buckling loads of the members, which can be determined either by FEM software such as ABAQUS or, in a speedier way, using CUFSM. The essential difference between these two methods is the replacement of plate stability with member stability. Most of the studies in the literature only take into account the structural behaviour of CFS members with just one profile and the majority of them are of numerical nature [17], [18] and [19]. The present paper reports on a series of flexural tests at ambient temperature focused on cold-formed steel beams consisting of compound cross-section CFS profiles which are often used in roofs of industrial buildings. The study involved both experimental and numerical investigations. The main objective of this research was to compare the structural response of the different kinds of beams and also to compare the results with the predictions from available design rules. To conclude, in the near future, this work will be followed by an experimental and numerical study on the behaviour of such beams under fire conditions with the purpose of developing simplified calculation methods for fire design of cold-formed steel beams since there is nothing related to the fire design of these elements in EN1993, parts 1.2 [20] and 1.3 [7].

An experimental and numerical investigation into the behaviour of cold-formed steel C-, lipped I-, R- and 2R-section beams under bending conditions at ambient temperature has been presented. A total of twelve four-point bending tests and fifty-two numerical simulations performed with the finite element program ABAQUS were made. Lastly, the suitability of design methods established by EN1993-1.1 for the buckling moment capacity was also investigated using the developed finite element model. As it was expected, cold-formed steel beams are very sensitive to local, distortional and global buckling and also their interactions. It was observed that the failure loads of the beams with C- and lipped I-shaped cross-sections corresponded to the lateral-torsional buckling modes, whereas the distortional buckling was the responsible buckling mode for the failure loads of the R and 2R beams. In order to improve the structural behaviour of these two types of beams, the authors suggested, for instance, that the U profiles of these beams are replaced by lipped U profiles like the C profiles, but with the lips towards the exterior side of the profile. In other words, the U profiles should be replaced by hat (omega) profiles [29]. As well as that, the use of sigma profiles instead of C profiles might improve the behaviour of cold-formed steel beams against the lateral-torsional buckling. All beams should also be reinforced with extra screws, maybe of a larger diameter or improved steel class. Another important conclusion to be drawn was that the use of two or more profiles in a beam can increase its strength-to-weight ratio. From the tested beams, the 2R beams showed the best ratio. However, it seems that this ratio tends to be constant for beams comprised of more than four profiles. The good agreement between the experimental and numerical results and between the respective failure buckling modes proves that the finite element analysis is a reliable tool to get quite accurate results. The finite element results showed that the strength-to-weight ratio of the simulated beams decreases a lot when their span increases, especially, from 3.0 to 4.0 m. It is also shown that EN1993-1.3 predictions may be conservative for beams comprised of two or more CFS profiles or even over-conservative as it was observed in some studied cases. However, these design guidelines may give unsafe results for these beams with spans longer than 4.5 m. Hence it is recommended that further experimental and numerical research is needed to developed new design guidelines for lateral-torsional buckling of cold-formed steel beams comprised of more than one profile and connected by screws.