Nonlinear Buckling Analysis of Thin-Walled Box Beams considering Shear Lag

Abstract

In this work, a general geometric nonlinear model of straight thin-walled box beams (STBBs) under combined eccentric and axial loads is established. In order to accurately reflect the behavior of STBB, the additional shear lag warping is added to enrich the displacement field. It is necessary to define the section shape function to describe the local section deformation. Therefore, extension, bending, torsion, distortion, and shear lag effects are expressed by the generalized coordinate method. Based on the stability of transverse unconstrained box beam theory, meaningful higher-order solutions can be obtained by defining a set of coupled deformation modes. The equilibrium equation is discretized by the Galerkin method, and the Newton–Raphson incremental method is used to derive and solve the nonlinear governing equations. On this basis, the analytical expression of stiffness matrix is established. For solving the stability problem, the effectiveness of the proposed method is verified by comparing the calculation results of shell element (Ansys) with other theories. Numerical examples even show that the proposed method can not only get the influence of shear lag but also obtain the variation of lateral buckling of the beam model.