After a brief review of the fundamental concepts concerning distortional -buckling and Generalized Beam Theory (GBT), the paper addresses a GBT-based general approach to derive "quasi-analytical" distortional buckling formulae for cold-formed steel members with arbitrary cross-section shapes and four end conditions. For illustrative purposes, this approach is used to obtain formulae for a family of thin-walled members with singly/point symmetric five/seven wall cross-sections, including a wide variety of cross-section shapes, such as rack-sections, hat-sections or channel and Z-sections with single/return lips. Finally, the accuracy, versatility and range of validity of the derived formulae are illustrated and discussed, on the basis of a set of numerical results (distortional buckling stresses) concerning members with different (ⅰ) cross-sections, (ⅱ) end conditions and (ⅲ) loadings. These results are compared with "exact values", obtained from exact GBT linear stability analyses, and, if possible, also with predictions yielded by other available formulae.
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