Shear Lag Analysis of Simply Supported Box Girders Considering Axial Equilibrium and Shear Deformation

Abstract

The conventional methods used to analyze the shear lag effect in simply supported box girders assume that the neutral axis of the section coincides with the centroid, which does not strictly satisfy the axial equilibrium condition. To address this problem, this study proposes an analysis method in which three independent functions for the shear lag are employed to define the different shear lag strengths of the top slab, the bottom slab, and the cantilever slab. To fulfill the axial equilibrium condition of the box girder and to automatically locate the neutral axis position, the longitudinal displacement of the web is introduced. The shear deformation of the box girder is also considered. The governing differential equations and corresponding boundary conditions for displacement variables such as deflection and rotation of the box girder are derived through the application of the principle of virtual work. The differential equations are solved by utilizing the boundary conditions to obtain the analytical expressions of the shear lag function, longitudinal displacement of the web, rotation, deflection, and neutral axis position. Furthermore, after performing the finite element analysis, the effectiveness of the proposed method is verified by comparing the results with those obtained from conventional methods and finite element analysis. Furthermore, the influence of the axial equilibrium condition is quantified on axial force and stress difference ratios under three methods. Finally, extensive parametric analysis is carried out to investigate the effect of different parameter ratios on the ratios of the stress difference of the flanges. The results show that when the axial equilibrium condition is not considered, the axial stresses in the upper flange of the simply supported box girder are underestimated, especially at the intersection of the top, cantilever slab, and web, and the axial stresses in the lower flange are overestimated. As a result, the method in this study is able to calculate the axial stresses and deflections on simply supported box girders more accurately.

Analytical Method of the Shear Lag Effect in Thin-Walled Box Girders Based on the Shear Flow Distribution Law

“…Additionally, the web's longitudinal displacement was added to satisfy axial equilibrium conditions, and independent shear lag warping displacement functions were employed in different flanges [24,25]. Zhu [26] also considered axial force balance when formulating the shear lag displacement model of the single-cell box girders and pointed out that considering axial force balance yields more precise results.…”