Symplectic Analysis of the Shear Lag Phenomenon in a T-Beam

Abstract

The principal purpose of this paper is to develop a new analytical method for the shear lag problem of T-beams. The flange slab of a T-beam is simplified into a plane stress plate. A system of Hamilton dual equations of the flange slab using symplectic elasticity theory can be obtained. Analytical solutions of the flange slab under uniform or linear shear force applied on the entire slab length are obtained by solving the equation. Based on the solution, the cause of the positive shear lag and negative shear lag phenomenon are studied in this paper. Theoretical research indicates that the method is superior for analyzing the shear lag phenomenon. The analytical solution has been validated by comparison with the beam solution and FEM solution of a cantilever T-beam subjected to a uniform load.