Keywords: cold-formed steel lipped channel columns, distortional buckling, local-plate buckling, local-plate/distortional mode interaction, elastic post-buckling, elastic-plastic post-buckling, shell finite element analysis, GBT-based analysis.

Most cold-formed steel members display very slender thin-walled open cross-sections, a feature making them highly susceptible to local instability phenomena, namely (i) local-plate and (ii) distortional buckling. Moreover, since several commonly used members exhibit cross-section geometries (shape and/or dimensions) associated with rather similar local-plate and distortional bifurcation stresses, their overall structural behaviour is likely to be affected by the occurrence of mode interaction phenomena involving the above two (local) buckling modes.

The aim of this paper is to present and discuss the results of a numerical investigation dealing with the influence of local-plate/distortional buckling mode interaction on the elastic and elastic-plastic post-buckling behaviour and strength of lipped channel cold-formed steel columns. The columns analysed exhibit (i) cross-section dimensions and length values that ensure equal local-plate and distortional critical stresses, (ii) several yield-to-critical stress ratios and (iii) locally/globally pinned free-to-warp end sections. Moreover, since the main goal of this work is to assess the local-plate/distortional mode interaction effects, one must determine the post-buckling behaviour of columns with a wide variety of critical-mode initial imperfection shapes, all sharing the same overall amplitude. In this work, the initial imperfection shapes combine the three-wave local-plate and single-wave distortional critical buckling modes, multiplied by amplitudes and that are appropriately chosen to ensure an overall magnitude equal to 10% of the wall thickness (see Figure 152.1).

The analyses were performed using mostly the finite element method (code ABAQUS with columns discretised by means of fine meshes of 4-node shell elements), but also a recently developed and numerically implemented generalised beam theory (GBT) formulation, which includes shear and transverse extension deformation modes (only elastic results). The results presented and discussed consist of (i) elastic and elastic-plastic post-buckling equilibrium paths, (ii) curves describing the evolution, along the elastic paths, of the column deformed configurations and (iii) figures providing information about the effect of the initial imperfection shape on the spread of plasticity and column elastic-plastic failure mode (see Figure 152.2).

Among the conclusions drawn from this investigation, it is worth mentioning: (i) in the advanced post-buckling stages, all the elastic and elastic-plastic equilibrium paths "merge" into two curves, associated with predominantly distortional coupled modes; (ii) when the imperfection is predominantly local-plate, a "snap-through" occurs along the column elastic equilibrium path; (iii) in the GBT-based post-buckling analyses, it is more meaningful to view the initial imperfections as combinations of deformation modes; (iv) in spite of the fairly good qualitative agreement between the finite element method (FEM) and GBT-based elastic post-buckling results, some quantitative differences remain to be explained; (v) the elastic-plastic failure may be triggered by the onset of yielding (low-to-moderate ) or preceded by a "snap-through" phenomenon and a subsequent strength increase (high ) and (vi) the pure distortional initial imperfections are the most detrimental ones - they correspond to the lowest column strengths (elastic or elastic-plastic).

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