Equations for Tapered Thin‐Walled Beams of Generic Open Section

Abstract

This paper presents a detailed treatment of the formulation for buckling and dynamic instability analysis of tapered thin‐walled beams of generic open section. The theory developed is limited to small strains, moderate deflections, and small rotations. Shear straining of the midsurface of the member wall is neglected. Rigorous expressions for strains based on membrane theory of shells is obtained through which the effect of nonlinear tapering is considered. Computer solutions for classical buckling and vibration analysis by the finite‐element method is discussed. Numerical integration by using Gaussian quadrature over the cross section for the computation of section properties and stress resultants and over the length for the computation of flexural, geometric, and mass matrices is suggested. Critical buckling loads and the natural frequencies and the corresponding buckled and mode shapes are obtained by using Jacobi iteration procedure.