# Shear Lag Effect on Box Steel Beams with Wide Curved Flanges
## 1 Introduction  
This paper examines the axial stress distribution law in curved flanges, essential for ensuring proper design and structural safety throughout the service life of the structure. Initially, the shear lag phenomenon in general is thoroughly described, discussing findings from the existing research. Subsequently, a parametric analysis is conducted, detailing both the methodology employed and the findings, followed by a discussion of the conclusions drawn from the results. When a beam with the span-height ratio larger than five is subjected to bending, it is often assumed that the [PERSON]'s hypothesis of plane sections can be applied--for a linearly elastic material, the plane cross-sections remain plane during deformation, resulting in a linear distribution of normal stresses across the height of the cross-section. This hypothesis is fully satisfied only in the case of \"pure\" bending, for a constant bending moment value along the beam, without the action of any additional transverse shear force. For cases where the beam is loaded with transverse forces, the shear stresses cause the shear deformation of the cross-sections, thus violating the abovementioned hypothesis. However, for the aforementioned beam height-length ratio, it is known that the influence of deformation due to shear stresses/deformations can be neglected, and in most cases, the calculation of stresses and deformations of the beam can be reduced to the problem of a one-dimensional element with corresponding flexural stiffness [1]. In such analyses of thin-walled cross-sections, the complex planar behavior of the flanges and webs and their shear deformability are neglected. If we consider a beam loaded with transverse forces applied in the web plane, its in-plane bending yields the longitudinalfiber displacements located at the web-flange junction. This results, then, in longitudinal normal and horizontal shear stresses, and thus transverse normal stresses (because of the prevented displacements due to cross-section symmetry). The distribution of shear loading to the web along the beam is assumed to be affine to the shear force diagram. Now, considering the flange as a separate disk loaded only with edge shear loading, for low half-width to beam span (distance between the zero points of the moment diagram) ratio (\(\text{b}_{0}/\text{L}_{\text{e}}>0.02\) according to [2]), a uniform distribution of longitudinal stresses across the flange width can be assumed (the flange behaves like a shell with load eccentricity being neglected), while for larger ratios, it is necessary to determine the distribution of longitudinal stresses across the width of the flange. Due to the shear deformability, it is expected that the flange fibers closer to the web will be more loaded than those farther away--this phenomenon is called \"shear lag\" [3]. Therefore, the concept of the effective width \(\text{b}_{\text{eff}}=\beta\times\text{b}_{0}\) is introduced, which takes into account the shear pliability by excluding the flange part farther from the junction with the web, satisfying the condition of the equilibrium of longitudinal force by integrating stresses across the flange width, as shown in Figure 1. In the wide-flange beam calculation, not taking into account shear lag leads to a great probability of underestimating the stress values at the junction of the web with the flange. Since large-span steel beams are generally composed of slender plates, a stability issue due to the action of compressive stresses (unless it is a cross-section of class 3 or less) can occur. Such slender plates have longitudinal stiffeners (open or closed) that prevent buckling, and their longitudinal stiffness is taken into account when determining effective width by calculating the orthotropy coefficient of the web \(\alpha_{0}\). Longitudinal stiffeners only increase the longitudinal stiffness of the web and not the shear stiffness, thereby increasing the effect of shear lag in such beams.