Analysis of self-weight induced collapse of long-deep beams

A numerical procedure is developed in this paper for analysing the collapse of long-deep thin-wall beam-type structures caused by distributed loads like their self-weights. It is based on the first-order shear deformation plate theory, and the critical load is determined by a linear buckling eigenvalue problem. A two-step analysis is involved in the procedure of which the first is to determine the pre-buckling in-plane stress distribution and the second is to solve an eigenvalue problem, which is formed with the structural stiffness and geometric stiffness matrices of which the latter is constructed with the obtained in-plane stress distribution. As an example, the load factor of the self-weight induced lateral–torsional buckling of a long-deep tee beam in lifting is calculated using the procedure.