Determination of Lateral-Torsional Buckling Load of Simply Supported Prismatic Thin-walled Beams with Mono-symmetric Cross-sections Using the Finite Difference Method

Abstract

In this paper, the lateral-torsional stability of simply supported thin-walled beams with mono-symmetric section subjected to bending loads has been studied by means of a numerical method based on the finite difference method (FDM). To fulfill this purpose, the equilibrium equations for elastic thin-walled members with linear behavior are derived from the stationary condition of the total potential energy. In the applied energy method, effects of initial stresses and load eccentricities from shear center of cross-sections are also considered. Finite difference method is one of the most powerful numerical techniques for solving differential equations especially with variable coefficients. Between various computational methods to solve the equilibrium equation, finite difference method requires a minimum of computing stages and is therefore very suitable approach for engineering analysis where the exact solution is very difficult to obtain. The main idea of this method is replacing derivatives present in differential equations and boundary condition equations with finite difference expressions. Finally, the critical buckling loads are then derived by solving the eigenvalue problem. In order to present the accuracy of the proposed method, several numerical examples including lateral-torsional behavior of prismatic beams with mono-symmetric sections are considered. In order to illustrate the correctness and performance of FDM, the evaluated results are compared to the finite element simulations and other available methods.