Signature Curve for General Thin-Walled Members

Signature curve is widely used in stability design of cold-formed steel members, since it provides with a simple way to determine critical loads for local, distortional and global buckling, which then can be used in predicting member capacity. Signature curve is created by calculating critical loads by systematically changing the length of the thin-walled member while assuming that the load is uniform along the length and the transverse displacement is one single sine half-wave. Mathematically, these conditions are closely related to the semi-analytical finite strip method, while, practically, correspond to a member with pinned end supports subjected to two concentrated loads at the ends, equal in magnitude but opposite in direction. This definition of signature curve cannot easily be applied to more general cases, however, a possible generalization is presented in the paper. Numerical examples are also shown, by employing the constrained finite element method. If the proposed procedure is applied for basic members, the calculated generalized signature curve exactly coincides with the classic signature curve. It is also shown, however, that meaningful generalized signature curve can be calculated for various loading and supports, or even for members with holes.

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