Behaviour and DSM design of stiffened lipped channel columns undergoing local-distortional interaction
Introduction
Generally, cold-formed structural systems are made of high-strength steel and exhibit open cross-section members that are structurally very efficient (high strength-to-weight ratios) but, on the other hand, are highly susceptible to instability phenomena involving cross-section deformation and/or rigid-body motions, namely local (L), distortional (D) and/or global (G) buckling – Fig. 1(b)–(d) show buckled shapes of lipped channel cross-sections with web and flange intermediate stiffeners (hereafter termed “WFSLC”) associated with column local (web-triggered), distortional and global (flexural-torsional and flexural) modes. However, the assessment of the structural efficiency of slender thin-walled members cannot be based exclusively on information concerning their “pure” (individual – L, D or G) buckling and post-buckling behaviours, since interactions involving these three instability phenomena may occur, namely L-G, L-D, D-G or L-D-G interaction – this work deals solely with L-D interaction.1 While L-G interaction is already quite well understood and adequately codified in most modern specifications for the design of cold-formed steel structures, the mode interaction phenomena involving distortional buckling are far less studied and further research is needed before it is possible to establish efficient (accurate and safe) design rules for members experiencing those phenomena. In particular, a key challenge facing the technical and scientific communities working with cold-formed steel structures consists of establishing guidelines aimed at assessing when these interaction effects are relevant, taking into account that it is well known that neglecting them may lead to unacceptably low reliability indices, i.e., to a high likelihood of reaching unsafe designs. The practical relevance of L-D interaction is due to the fact that a fair number of commonly used cold-formed steel members exhibit geometries (cross-section shape/dimensions and length) leading to close local and distortional critical buckling stresses. This closeness is responsible for a more or less substantial ultimate strength erosion, particularly for high-strength steels, that, unfortunately, is not yet adequately accounted for by the cold-formed steel specifications.
In order to alter this situation, a fair amount of research has been recently devoted to the structural response and failure load of cold-formed steel columns affected by L-D interaction, comprising experimental investigations, numerical simulations and design proposals – the latter mainly through the development/improvement of Direct Strength Method (DSM) approaches. Originally proposed by Schafer and Peköz [2], with the roots in the work of Hancock et al. [3], the DSM is already included in the current versions of the Australian/New Zealand [4], North American [5] and Brazilian [6] cold-formed steel specifications to cover (i) columns, and (ii) beams (major and/or minor-axis bending) with and without perforations. However, the vast majority of the available results concern columns with “plain cross-sections” (i.e., without intermediate stiffeners), mostly lipped channels. For instance, the works of Kwon and Hancock [7], Loughlan et al. [8], Young et al. [9] and Dinis et al. [10] provide experimental evidence of L-D interaction, while those of Silvestre et al. [11], Dinis and Camotim [12] and Martins et al. [13] showed numerically the occurrence of this phenomenon – in particular, the last of these works assesses the relevance of L-D interaction, by establishing combinations of (i) local and distortional buckling stresses and (ii) yield stresses that lead to a visible ultimate strength erosion and/or a change in the failure mode nature (mechanical characteristics), which can be local, distortional or “mixed” local-distortional. For practically all the above cross-section shapes, local buckling is triggered by the web, where most of the L-D interaction takes place. This situation changes when intermediate stiffeners (e.g., “v-shaped” stiffeners) are added to the web, since local buckling is bound to be triggered by the flanges. In this regard, and exclusively for web-stiffened lipped channel (WSLC) columns, Kwon and Hancock [7], Yap and Hancock [14] and He et al. [15] observed experimentally flange-triggered L-D interaction, while Martins et al. [16] numerically investigated the influence of the L-D interaction in the behaviour and design of WSLC columns exhibiting a wide variety of ratios between the local and distortional (buckling) and yield stresses – it was shown that earlier findings [13], for “plain cross-section” columns, can be extended to columns exhibiting flange-triggered L-D interaction. The situation may change again when both the web and flanges are stiffened, since local buckling is also triggered by the web (like in “plain cross-sections”). Concerning WFSLC columns under L-D interaction, and to the authors' best knowledge, the only available results are the tests reported by Yang and Hancock [17]2 – the aim of the present work is to fill this gap, at least partially.
The objectives of this work are two-fold: (i) acquire in-depth understanding on the mechanics of L-D interaction in fixed-ended WFSLC columns, and also (ii) provide a contribution towards their efficient DSM design. The results presented and discussed, obtained from ABAQUS (Simulia Inc. [20]) shell finite element analyses, concern the (i) post-buckling behaviour (elastic and elastic-plastic), (ii) ultimate strength and (iii) failure mechanism of WFSLC columns previously selected to undergo more or less severe L-D interaction. The columns analysed exhibit various geometries and yield stresses, ensuring a wide variety of combined ratios between the (i) distortional and local critical buckling stresses, and (ii) yield stress and higher of the two buckling stresses – the latter is relevant to capture the effects of the so-called “secondary bifurcation L-D interaction”, which may occur in columns with the above critical buckling stresses quite apart. Special attention is paid to comparing the ultimate strength erosions, due to L-D interaction, exhibited by the WFSLC columns studied here and the “plain cross-section” and WSLC columns investigated earlier [13], [16]. Then, the experimental failure loads collected from the literature, for WFSLC columns failing in L-D interactive modes, are also used to assess the quality of their estimates by means of the existing and proposed DSM-based design approaches. Finally, the paper closes with some considerations about the impact of the findings reported in this work on the design of (plain and stiffened) cold-formed steel columns undergoing different levels of L-D interaction, including the reliability assessment of the predictions provided by the above DSM-based approaches for the experimental and/or numerical failure load data considered.
Section snippets
Buckling analysis – column geometry selection
In order to investigate the behaviour and ultimate strength of fixed-ended WFSLC columns affected by different levels of L-D interaction, it is indispensable to begin by selecting column geometries (cross-section dimensions and length) associated with different “levels of closeness” between the local and distortional critical buckling stresses (i.e., RDL = fcrD/fcrL values). As done earlier [13], [16], the column geometry selection was made through a “trial-and-error” procedure involving the
Direct Strength Method (DSM) design
The Direct Strength Method (DSM), based on an original idea of Hancock et al. [3] and first proposed by Schafer and Peköz [2], has been shown to provide an efficient and general approach to obtain efficient (safe and accurate) estimates of the ultimate strength of cold-formed steel columns and beams on the sole basis of the steel yield stress and elastic critical local, distortional and global buckling stresses. For columns, the DSM nominal strengths against local (fNL) and distortional (fND)
Concluding remarks
A numerical investigation on the influence of L-D interaction on the post-buckling behaviour, ultimate strength and DSM design of cold-formed steel fixed-ended web-flange-stiffened lipped channel (WFSLC) columns, exhibiting web-triggered critical local buckling, was reported in this work. The numerical results presented and discussed were obtained through ABAQUS geometrically and materially non-linear shell finite element analyses. Initially, GBT buckling analyses were performed to identify
Acknowledgements
The first author gratefully acknowledge the financial support of FCT (Fundação para a Ciência e a Tecnologia – Portugal), through the doctoral scholarship SFRH/BD/87746/2012.
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