EQUATIONS FOR TAPERED THIN-WALLED-BEAMS OF GENERIC OPEN SECTION

This paper presents a detailed treatment of the formulation for buckli ng and dynamic instability analysis of tapered thin-walled beams of ge neric open section. The theory developed is limited to small strains, moderate deflections, and small rotations. Shear straining of the mids urface of the member wall is neglected. Rigorous expressions for strai ns based on membrane theory of shells is obtained through which the ef fect of nonlinear tapering is considered. Computer solutions for class ical buckling and vibration analysis by the finite-element method is d iscussed. Numerical integration by using Gaussian quadrature over the cross section for the computation of section properties and stress res ultants and over the length for the computation of flexural, geometric , and mass matrices is suggested. Critical buckling loads and the natu ral frequencies and the corresponding buckled and mode shapes are obta ined by using Jacobi iteration procedure.