Mixed variational formulation for thin-walled beams with shear lag

Abstract

A mixed variational principle for thin-walled prismatic structures is formulated and a solution method is proposed. In this principle, the cross section of the thin-walled prismatic structure is assumed to be rigid in its own plane, but flexible out of plane, and both the stresses and displacements are considered to be unknown variables in this function. The solutions are expanded in a series of coordinate functions and the governing equations of the unknown functions are derived. The coordinate functions for bending problems can be deduced systematically and the solutions can be obtained in simple closed form. This method can be applied to members with rows of openings and to problems involving shear lag phenomena. Numerical examples show that only the first two terms in the solution series will give an approximate result in which the shear lag phenomenon has been reflected, while a three-term solution will give a satisfactory result in comparisons with the finite strip method.