Flexural, Torsional and Distortional Buckling of Single-Cell Thin-Walled Box Columns

Abstract

Instability is an important branch of structural mechanics which examines alternate equilibrium states associated with large deformations. In this study, Varbanov's generalized strain fields and Vlasov's displacement equations were used to obtain a set of equations for neutral equilibrium of axially compressed single-cell box column with deformable cross-sections. The study involved a theoretical formulation based on Vlasov's theory as modified by Varbanov and implemented the associated displacement model in generating series of ordinary differential equations in distortional displacement V(x). The initial result of the formulation was in form of total potential energy functional, which was then minimized using Euler-Lagrange equation. Minimization of the total potential energy functional resulted to a set of governing equations of equilibrium in matrix form. The longitudinal warping displacement functions U_(x) were eliminated from the governing equations of equilibrium in different forms to obtain the following equations: two fully uncoupled ordinary differential equations in V₁ and V₂ representing flexural buckling about the two axis of symmetry; a fully separated ordinary differential equation in V₄ representing distortional buckling about the longitudinal ox-axis; a pair of coupled simultaneous ordinary differential equations in V₃ and V₄ representing torsional – distortional buckling mode. This study has resulted in better understanding and separation of distortional mode from the other stability modes. The results show that the effect of deformation can be substantial and should not be disregarded by assuming rigid cross-sections. This present work has also simplified instability analysis and design of thin-walled box columns with deformable single-cell cross-sections on the basis of Vlasov's theory by deriving precise equations for all the possible buckling modes.