Flexural‐Torsional Stability of Thin‐Walled Columns

Abstract

This paper discusses the problem of flexural‐torsional stability of columns with open thin‐walled cross sections. It introduces an analytical solution technique applicable to the differential equation system describing the current problem. The approach derived is more comprehensive than those presented traditionally in the literature and is applicable in determining the value of critical load due to combined buckling modes. The system considered consists of three separate differential equations that are coupled in a general case. Various symmetries of the cross section release these couplings. This presentation is limited, for simplicity, only to columns having singly symmetric cross sections, or at least cross sections of point symmetry. Thus, there are couplings between two of the governing equations, The elastic restraints having varying stiffnesses with respect to translation, rotation, torsion and warping, separately, have been studied as boundary conditions through numerical examples. The stiffnesses of the restraints applied are chosen to cover the range from zero to infinity.