Keywords: cold-formed steel, rounded corners, direct strength method.

The direct strength method (DSM) is a relatively new proposal for the design of cold-formed steel members [1]. It simplifies the thin-walled member strength calculations by only requiring the engineer to provide the elastic buckling load for the three characteristic buckling classes: local, distortional, and global, along with the squash load or yield moment. Even for common member geometry elastic buckling calculations can sometimes lead to ambiguous predictions. The constrained finite strip method (cFSM) is presented as a potential solution to this problem [2]. However, cFSM does not provide identically the same solution as the semi-analytical finite strip method (FSM), which was used for the calibration and verification of the DSM formulae.

The differences between FSM and cFSM are caused by two reasons. One is the mode coupling which has already been investigated by the authors [3], concluding that the cFSM-based DSM predictions slightly overestimate the local and distortional resistance.

This paper focuses on the other important source of the FSM/cFSM differences, namely: the rounded corners, always existing in cold-formed steel profiles. Rounded corners cannot directly be considered in cFSM, since separation of local and distortional buckling is possible only if the cross-section is modelled with sharp corners. To investigate the problem parametric numerical studies have been completed. Z and C cross-section beams with a wide range of geometrical dimensions are analyzed: section properties and critical stresses are calculated by using sharp and rounded corners, and by using FSM and cFSM.

Based on the results of the studies performed a simple method is proposed, which uses sharp-cornered cross-sections only, therefore the advantage of cFSM can fully be utilized, while keeps the simplicity of the original DSM approach. Cross-sectional properties and critical stresses calculated for the sharp-cornered cross-section are to be modified by appropriate factors to consider the effects of mode coupling and rounded corners.

The proposed cFSM-DSM method is validated by comparison to test data. The results show that the proposed method is statistically equivalent to the original FSM-DSM approach, leading to reasonably accurate moment capacity predictions. Further studies are necessary to extend the proposed method to cover other loading cases and other cross-section shapes.

1

B.W. Schafer, "Review: The Direct Strength Method of Cold-formed Steel Member Design", International Colloquium on Stability and Ductility of Steel Structures, Lisbon, Portugal, 49-66, Sept. 6-8, 2006.

2

S. Ádány, B.W. Schafer, "A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method", Journal of Constructional Steel Research, 64(1), 12-29, 2008. doi:10.1016/j.jcsr.2007.04.004

3

S. Ádány, Z. Beregszászi, "Local and Distortional Buckling of Thin-Walled Members: Numerical Study to Compare Conventional and Constrained Finite Strip Method", Fifth International Conference on Thin-Walled Structures, Brisbane, Australia, 1121-1128, June 18-20, 2008.

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