An improved method for analyzing shear lag in thin-walled box-section beam with arbitrary width of cantilever flange

The shear lag effect can significantly affect the performance of wide-box structures, and even becomes one of the most important influencing factors endangering structural safety. This paper develops a theoretical analysis method, which is designated as PM analysis for analyzing shear lag phenomenon in thin-walled box-section beam with arbitrary width of cantilever flange. In this method, the introduction of initial shear rotation (or initial shear strain) gamma(oi), due to the effect of web restraint on flanges, is innovatively proposed and further employed in describing the additional warping displacement in top lateral cantilever flanges, and a practical and straightforward procedure of coefficient alpha(3) is designed (DP) based on the proposed assumptions. In addition, a modified method to PM-DP analysis is developed for improving the defects of the hypothesis of shear-lag warping displacements in top lateral cantilever flanges, that is, PM-DP(M) analysis. The differential equations for generalized displacement w(x) and the standard magnitude of shear-lag warping displacement U(x) of the beam are deduced by means of the principle of minimum potential energy (MPE) and solved with the given boundary conditions. Numerous models of thin-walled box-section with arbitrary width of top lateral cantilever flanges under distributed load are chosen and built through a software program (ABAQUS). The results obtained from PM analysis (PM-LB, PM-DP and PM-DP(M)) are summarized into a series of curves indicating the distribution of normal stress and the displacements for various examples, and compared to those obtained from the finite element method (FEM). The study widely demonstrates the strong applicability and high precision of PM-DP(M) analysis, which can be considered as an ideal solution in predicting shear lag effect for thin-walled box-section beam with arbitrary width of cantilever flange and, possibly, be adopted as valuable reference for the design of related thin-walled structures.