Global buckling of thin-walled simply supported columns: Analytical solutions based on shell model

In this paper global buckling (i.e., flexural, pure torsional, or flexural–torsional buckling) of thin-walled columns is discussed. The considered problem is the most basic one: the column is simply supported and subjected to a uniform concentric compressive force. The columnʹs cross-section is an arbitrary open thin-walled cross-section. For the critical forces of this problem classical analytical solutions are known. In the presented research alternative formulae are derived on the basis of modeling the member as a set of flat plane elements (or strips). As it is found, the derivations can be carried out in various ways, among which eight options are considered. The resulted critical force formulae are briefly discussed in this paper. Extensive numerical studies are also completed; these studies are summarized in a companion paper.