Flexural buckling of simply-supported thin-walled columns with consideration of membrane shear deformations: Analytical solutions based on shell model

In this paper, flexural buckling of pin-ended thin-walled columns is discussed. The classical formulae for the critical force are based on a beam model. The simplest formulae use the classical Euler–Bernoulli beam theory, but solutions based on the shear-deformable beam theory are also known. In the presented research alternative formulae are derived. The column is modeled as a set of flat plane elements, and the in-plane membrane shear deformations are explicitly considered. The derivations can be carried out in various, slightly different ways, leading to different formulae. The derived critical force formulae are discussed through theoretical considerations and numerical studies.