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

• Analytical solutions are derived for global buckling of prismatic columns.
• The derived solutions are based on shell model.
• Shear deformations are considered.
• Critical force formulae are presented in various options.
• The derived formulae are discussed through theoretical considerations and numerical studies.

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.