End condition effect on distortional buckling of cold-formed steel columns with arbitrary length

Usual design practice for distortional buckling considers a lower bound solution as the actual buckling load. In reality, this practice is inconsistent with actual case since the obtained buckling load is a constant value no matter how long the column is and whatever the end condition is. According to available literature, the research dealt with such a problem is found quite rare. In this scenario, this paper presents an analytical approach to establish a new distortional buckling formula, which takes both the effects of column length and end condition into consideration. The formula was derived based on an edge stiffened plate model. The model was assumed to be pin-ended and fix-ended so as to investigate their effects. The Galerkin method was employed to derive the distortional buckling formula. Further, simplifications to the rigorous formula were made to allow them to be easily used by the engineers. Subsequently, in order to verify the accuracy of the derived formula, the results obtained from the derived formula were compared with the numerical results obtained from the computer software GBTUL. In addition, the performance of the derived formula was further verified by comparing the corresponding ultimate strength based on Shafer's DSM expressions with numerical result from the literature. The comparison and validation result shows that the derived formula (i) can be used successfully in estimating the distortional buckling load for both pin-ended and fix-ended columns with practical length and (ii) can general more rational buckling strength estimation due to the consideration of column length and end condition effect.