Keywords: cold-formed steel members, finite element method, non linear analyses, distortional buckling, local-plate buckling, distortional post-buckling behaviour, local-plate post-buckling behaviour, local-plate/distortional mode interaction.

Most cold-formed steel members display slender thin-walled open cross-sections, a feature making them highly susceptible to local buckling phenomena, characterised by the sole occurrence of cross-section (in-plane) deformations and classified into two major categories: (i) local-plate buckling and (ii) distortional buckling. The former concerns flexural displacements alone and the latter involves flexural and membrane displacements, including fold-line motions leading to cross-section distortions. Figures 99.1(a) and 99.1(b) show the deformed configurations of rack-section column segments experiencing local-plate and distortional buckling, respectively. Moreover, whenever cold-formed steel members display cross-section geometries and length values leading to similar local and/or global (flexural-torsional or flexural) critical buckling stresses, their structural behaviour is affected by mode interaction effects, namely coupling between (i) local-plate and distortional or (ii) local and global buckling modes (the cross-section geometry determines the nature of the local mode).

In the presence of relevant mode coupling and/or spread of plasticity effects, the "exact" structural behaviour of thin-walled steel members can only be determined by employing sophisticated numerical methods, such as the FEM, which require a computer power only routinely available in (well equipped) research institutions. Although this situation is rapidly changing, as attested by the number of commercial computer codes which are now readily available to perform complex geometrically and physically non linear structural analyses, it was only recently that it became feasible to use FEM analyses to investigate local buckling effects in slender thin- walled members. They will be very useful to validate and/or calibrate easy-to-use design methodologies, thus paving the way to a progressive replacement of several experimental tests by much more convenient computer simulations. Moreover, the above design methodologies are only rational (physically based) and efficient if the member local-plate and/or distortional post-buckling behaviour are accurately known.

This paper presents, discusses and illustrates the application and efficiency of an unified approach to the use of FEM analyses to investigate the local buckling, post- buckling and mode interaction behaviour of cold-formed steel thin-walled members, both in the elastic and elastic-plastic ranges. Initially, a number of relevant modelling and numerical implementation issues are briefly addressed, namely related to (i) the finite element and mesh discretisation choice, (ii) the incorporation of the initial geometrical imperfections, (iii) the modelling of the local boundary conditions or (iv) the numerical solution techniques. Next, in order to assess how the FEM approach is able to handle the aforementioned problems, several aspects dealing with the non linear structural behaviour of rack section members are investigated. At this point, one should mention that all the numerical results displayed are obtained by means of analyses performed using the commercial code ABAQUS [1]. Moreover, in order to validate such FEM results, some of them are compared with values available in the literature, most of which have been obtained by means of finite strip analyses. The different types of (non linear) analyses dealt with are:

(i)

Elastic buckling (linear stability) analyses, involving the solution of standard eigenvalue problems and yielding critical stress values and buckling mode configurations. Attention is paid to the influence of the applied stress distribution and local support conditions.

(ii)

Elastic and elastic-plastic local post-buckling analyses, concerning members which bifurcate in either the local-plate or distortional buckling modes. Such analyses (ii) account for the influence of initial geometrical imperfection, (ii) can only be performed by resorting to incremental-iterative numerical techniques and (ii) lead to the determination of non linear (post- buckling) equilibrium paths, which relate the evolutions of the applied stress value and the displacement component better suited to describe the member deformed configuration.

(iii)

Elastic and elastic-plastic (local) mode interaction analyses, concerning the behaviour of members with similar local-plate and distortional buckling stress values. Such analyses also yield non linear equilibrium paths and particular attention is paid to identifying (iii) the configuration of the (elastic) coupled buckling mode and (iii) the nature of the elastic-plastic deformed configuration.

1

Hibbit, Karlsson and Sorensen Inc., "ABAQUS Standard" (Vrs. 5.8), 1998.

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