# Shear Lag Effect of Ultra-Wide Box Girder under Influence of Shear Deformation
## 1 Introduction  
Considering the development of bridge structures using light thin-wall, long-span, wide-web spacings and wide cantilever plates, problems related to the spatial mechanics caused by thin-walled structures have become increasingly prominent [1, 2, 3]. When the thin-walled box girder is in a flexural state, the flexural function of the wing plate is no longer applicable to the assumption of the plane section owing to the influence of shear deformation; the resulting warping phenomenon is called the \"shear lag effect\" [4, 5, 6]. The analytical method based on the principle of energy variation is a research approach rooted in the theory of elasticity. Among various methods employed for analyzing the shear lag effect in box girders, the energy variation method stands out as the most commonly utilized. This method involves treating the difference between the longitudinal displacements of the girder body and the longitudinal displacements of the wing plates as unknowns. By applying the minimum potential energy theory to resolve the governing differential equations, the deflection of the girder body and the transverse distribution of normal stresses can be obtained. [PERSON] et al. [7] expressed the shear lag deflection function using the maximum shear deformation difference function, and combined it with the energy variation method to investigate the shear lag effect in curved box girders. [PERSON] et al. [8] assumed the shear lag deflection functions of box beams on the cantilever, top, and bottomplates. Based on spline finite points and the principle of energy variation, they discretized the structure using B-spline curve equations, thus revealing the variation law of shear lag effect in box girders. [PERSON] et al. (2019), on the foundation of energy variation theory, introduced spatial girder element functions and derived the Euler girder matrix equation. By considering the influence of shear deformation, they derived the stiffness matrix of Timoshenko beams. Through extensive exploration by numerous scholars, the domain of energy variation methods has been further expanded. From rectangular box sections to curved box girder sections, and then to box girders utilizing composite materials, it has been discovered that employing the energy variation method to solve for the shear lag effect is indeed feasible. This paper also aims to investigate the shear lag effect in thin-walled box girders using the energy variation method. The key issue lies in accurately determining the form of the deflection function, as it directly affects the precision of solving for the shear lag effect. Currently, the flexural displacement function is primarily based on artificial assumptions and has been considered quadratic parabola, cubic parabola, quadric parabola, cosine function, and catenary-type ([PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020) functions. [PERSON] et al. (2020) reported that the shear lag effect of thin-walled box girders was essentially caused by shear deformation. By studying the shear flow of a box girder under a vertical load, they proposed a flexural displacement function with shear deformation. [PERSON] et al. (2020). represented the shear strain of a steel-concrete composite girder with a cosine function and established a mechanical analysis model of a steel-concrete composite girder considering the influence of shear deformation and interface slip between the concrete and steel plate ([PERSON] et al., 2020). The proposed model was verified by comparing the obtained results with solutions of elastic analysis and finite-element results. [PERSON] et al. (2020) introduced boundary correction factors to the cantilever plate to reflect the influence of different boundary constraints on the shear lag deflection. By utilizing spatial finite-element software to compute the results, the values of the boundary correction factors for the cantilever plate were determined.