Keywords: cold-formed steel lipped channel beams, local buckling, distortional buckling, local-distortional mode interaction, elastic post-buckling, elastic-plastic post-buckling, shell finite element analysis.

Most cold-formed steel members display slender thin-walled open cross-sections, a feature making them highly prone to buckling phenomena characterised by the sole occurrence of cross-section deformations (the member axis remains undeformed), namely (i) local buckling (wall transverse bending only) and/or (ii) distortional buckling (both wall transverse bending and cross-section distortion). Moreover, since the most commonly used cold-formed steel member geometries (unrestrained length and cross-section shape and dimensions) often lead to very similar local (L) and distortional (D) buckling stresses, their post-buckling behaviour, ultimate strength and failure mechanisms are likely to be strongly affected by coupling-interaction effects involving these two buckling modes.

The aim of this paper is to present and discuss numerical results concerning the elastic and elastic-plastic post-buckling behaviour of cold-formed steel lipped channel beams (uniform major axis bending) affected by L/D mode interaction and with local buckling triggered by either (i) the compressed flange (most common case - B_F-beams) or (ii) the web (high beams with narrow flanges - B_W-beams). In order to address the two situations, one analyses beams with (i) two cross-section dimensions and (ii) lengths selected to ensure virtually identical L and D critical buckling moments. In either case, one analyses otherwise identical simply supported beams containing initial geometrical imperfections (i) with different shapes (various combinations of the competing L and D buckling modes) and (ii) sharing the same overall amplitude - 10% of the wall thickness t. Each "acceptable" imperfection shape lies on a unit radius circle and is characterised by an angle theta: (i) theta=0° and theta=180° are D imperfections with inward and outward flange-lip motions, and (ii) theta=90° and theta=270° are L imperfections involving mid-span inward and outward compressed flange bending (B_F-beams) or outward and inward web bending (B_W-beams).

All the numerical results presented were obtained using ABAQUS shell finite element analyses with (i) fine member discretisations (element length-to-width ratio comprised between 1 and 2), and (ii) the simple supports (end sections locally/globally pinned and free to warp) modelled by imposing null transverse displacements at all end nodes.

The results presented and discussed consist of (i) elastic and elastic-plastic post-buckling equilibrium paths, (ii) figures showing the evolution, along the elastic paths, of the beam deformed configurations, (iii) ultimate moment values and (iv) figures providing information about the beam plastic strain evolution and collapse mechanism characteristics.

Finally, note that it was found that the most detrimental initial imperfections (i.e., those leading to the lowest beam post-buckling strengths and ultimate moments) are either pure local (B_F-beams) or pure distortional with outward flange-lip motions (B_W-beams).

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