Keywords: local-distortional mode interaction, lipped channel columns, high strength steel, ultimate strength, direct strength method, yield-to-critical stress ratio.

This work concerns an investigation on the post-buckling behaviour, strength and design of pinned and fixed lipped channel columns experiencing local/distortional buckling mode interaction. Previous experimental or numerical studies provided clear evidence that the codified direct strength method (DSM) curves cannot handle this interactive behaviour and prompted proposals for novel DSM design curves specifically aimed at such members [1,2]. However, the calibration and assessment of these proposals was almost exclusively based on the strength of columns exhibiting strong local-distortional interaction: local and distortional critical stresses less than 10% apart. Thus, an important question remained open: how far apart should those critical stresses be to be acceptable ignoring these coupling effects? The main aim of this paper is contribute to answering this question on the relevance of local-distortional interaction. Moreover, a first attempt is made to develop a general DSM-based approach able to estimate the strength of lipped channel columns exhibiting or not local-distortional coupling. To achieve this goal, ABAQUS finite element analyses are performed to obtain elastic-plastic failure loads of columns with several cross-section dimensions and yield stresses, selected to ensure wide distortional slenderness and yield-to-critical stress ratio ranges. The paper includes remarks and design recommendations, drawn from comparing the "exact" strengths and estimates yielded by various DSM-based design approaches.

The relevance of the local-distortional interaction is not restricted to columns with close local and distortional critical stresses: columns with critical stresses 40% apart still exhibit strong elastic coupling, particularly if local buckling precedes distortional buckling. The effect of local-distortional interaction on the column ultimate strength depends on the critical stress closeness and yield-to-critical stress ratio: if high enough, coupling is always relevant (interaction may develop before yielding causes failure).

Based on the parametric study performed, some preliminary conclusions may be drawn:

1. Pinned columns are more affected by local-distortional interaction than fixed columns.
2. In slender and very slender columns, considerable local-distortional interaction occurs before yielding begins.
3. If f_y<2f_cr (f_y>2f_cr) the DSM distortional expression predicts well the column strength (provides unsafe strength estimates), regardless of f_crd/f_crl.
4. If f_y>2f_cr, the NDL expression provides safe strength estimates for any f_crd/f_crl.
5. The MNDL expression (fixed columns) yields mostly unsafe strengths, but with moderate errors and scatter. Further modifications must include f_y/f_cr to improve the prediction quality.

1

D. Yang, G.J. Hancock, "Compression tests of high strength steel channel columns with interaction between local and distortional buckling", Journal of Structural Engineering (ASCE), 130(12), 1954-1963, 2004. doi:10.1061/(ASCE)0733-9445(2004)130:12(1954)

2

N. Silvestre, D. Camotim, P.B. Dinis, "Direct Strength prediction of lipped channel columns experiencing local-plate/distortional interaction", Advanced Steel Construction , 5(1), 49-71, 2009.

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