# Shear Lag Effect of Ultra-Wide Box Girder under Influence of Shear Deformation
## 1 Introduction
Many domestic and international scholars have also established sophisticated bridge finite-element models, verifying their simulation results through dual validation against experiments ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). In the literature, the theoretical methods for flexural analysis of thin-walled box girders mainly focus on the shear lag effect of the box girders, whereas research on flexural and shear deformation is lacking ([PERSON] et al., 2020). In particular, the theoretical correlation between the elementary beam theory and spatial mechanics analysis theory of box girders under the influence of shear deformation of each plate is limited. In this study, the flexural displacement function of a box girder under the influence of shear deformation of each plate is proposed, and the spatial mechanics analysis theory of box girders is improved. This paper will also conduct a comparative analysis of the deflection stress calculation results and propose a cantilever displacement correction for the bending deflection function of thin-walled box girders considering the effects of shear deformation in each plate. A solid model of a single-box three-chamber box girder will be established using MIDAS/FEA NX 2021 finite-element software to analyze the factors influencing the shear lag effect under different loading conditions. The theoretical solution for the shear lag effect in the bent box girder will be provided based on the energy variation method to analytically derive the deflection function. Factors affecting the shear lag effect will be introduced to modify the formula for the shear lag effect in a single-box three-chamber box girder, addressing the workload issue in internal force calculations for box girders. The innovative aspects of this article include theoretically deriving the deflection function of thin-walled box girders under bending, influenced by the shear deformation of each plate, due to uneven shear flow transfer. This also leads to a theoretical analysis of wide-span box girders under the effect of uneven shear flow transfer. The theoretical solutions and influencing factors of the shear lag effect in bent box girders are solved using the energy variation method. Using Origin, an empirical formula for the shear lag effect in a single-box three-chamber girder is fitted, addressing the problem of calculating internal forces in box girders. Analysis of Flexural Displacement Function of Flexural Box Girder under Shear Deformation of Plates  
Considering the main girder with a single box and three chambers as the object of analysis, the force diagram of a thin-walled box girder under an arbitrary vertical load distribution is shown in Figure 1. The section coordinates and dimensions of the box girder are shown in Figure 2, where the center of the cross-section is the origin of the coordinate system, and the main inertial axes of the section are the coordinate axes. In thin-walled box girders, stress is assumed to be uniformly distributed along the wall thickness direction. For the study of thin-walled box girders, the position of any point on the section can be represented by the coordinates of the flow curve along the centerline of the thickness of the box wall, and the section of the thin-walled box girder can be simplified. A simplified section of the thin-walled box girder is shown in Figure 3, wherein the right-hand flow coordinate system is formed using \(n\), \(s\), and \(z\); \(u\) represents the displacement of the longitudinal \(z\)-axis of the girder body, and \(v\) represents the displacement of the circumferential \(s\)-axis of the girder wall. The following basic assumptions were made according to the flexural theory of a box girder [24; 25]:  
(1) Under small-deformation conditions, the contour projection of the box girder section does not deform. (2) The strain \(\varepsilon_{s}\) at the midpoint of each plate is zero; that is, for each plate of the box girder, \(\partial v/\partial s=0\).