Solving Flexural-Torsional Buckling Equations of Thin-Walled Columns using Stodola-Vianello Successive Iteration Method

Abstract

In this study, Timoshenko’s equations for the generalized elastic thin-walled column buckling analysis was solved by the Stodola-Vianello iteration method (SVIM). The candidate problem which is a system of three coupled ordinary differential equations (ODEs) in three displacement variables was expressed using four successive integrations as a system of three coupled iteration equations at the nth buckling mode. Boundary conditions (BCs) were applied to obtain the constants of integration. General solutions were then obtained for simply supported BCs for the general cases of: (a) unsymmetrical cross-sections, (b) doubly symmetrical cross-sections and (c) singly symmetrical cross-sections about the yy axis and zz axis respectively. It was found that for the doubly symmetric cross sections, the buckling equations are uncoupled and the least of the critical buckling loads in flexural buckling about the yy and zz axes and torsional buckling determines the failure. It was also found that the buckling types are coupled for unsymmetrical cross-sections. However, for doubly symmetrical cross-sections about the zz axis, the flexural buckling in the zz direction is uncoupled while the flexural buckling about the yy direction is coupled with the torsional buckling. For singly symmetrical cross-sections about the yy axis, the flexural buckling in the yy direction is uncoupled while the flexural buckling about the zz axis is coupled with the torsional buckling. The critical buckling load is found as the smallest of the buckling loads obtained by solving the algebraic eigenvalue problem