Stability of Axially Compressed Single-Cell Mono-Symmetric Thin-Walled Closed Column

Abstract

Compared with conventional structural columns, the pronounced role of instabilities complicates the behaviour and design of thin-walled columns. This study investigated the stability of axially compressed single-cell thin-walled column with mono-symmetric non-deformable cross-sections. The work involved a theoretical formulation based on Vlasov's theory with modification by Varbanov and implemented the associated displacement model in analysing flexural and flexural-torsional (FT) buckling modes. The initial result of the formulation was in form of total potential energy functional, which was then minimized using Euler-Lagrange equation to obtain a set of differential equations of equilibrium in matrix form. The elements of the coefficient matrices of the governing differential equations of equilibrium were determined for the mono-symmetric cross-section by first generating and plotting the generalized strain fields. Technique of diagram multiplication was then used in determining the elements of the coefficient matrices from the generalize strain mode diagrams. The substitution of the determined coefficients back into the governing equations of equilibrium resulted to one uncoupled ordinary differential equation representing flexural behaviour and a pair of two interactive (coupled) ordinary differential equations representing the flexural-torsional (FT) behaviour. These equations were then solved using direct closed-form approach for the uncoupled flexural behaviour and Varbanov's trigonometrical series with accelerated convergence (TSWAC) for the coupled flexural-torsional behaviour. The results are presented in form of stability matrices and the numerical results are presented on tables (1) and (2). Comparison of the two tables' results indicates that the flexural behaviour will control design.