Stability of the in-plane bending mode of thin-walled framed structures

Abstract

The paper outlines an approach to solving the stability problem for framed structures under arbitrary transverse loading. The available methods are limited by one law of variation in the bending moment responsible for loss of stability. The equilibrium equations for a thin-walled bar are integrated assuming that the bending moment is constant. The solution of the Cauchy problem is given in normal form. The arbitrary varying bending moment is approximated by a piecewise-constant function, which will be a little different from the original if the bar is partitioned into a great number of segments. The equations of the boundary-value problem for a discretized framed structure are derived using the boundary-element method. The critical forces and moments are determined from a transcendent equation. Numerical solutions are presented to demonstrate the high accuracy and efficiency of the approach. The solutions of test problems are in agreement with those obtained by Timoshenko