# Shear Lag Effect on Box Steel Beams with Wide Curved Flanges
## 3 Review of Previous Research on Shear Lag Effect  
Many authors have investigated the phenomenon of shear lag, and with the development of numerical methods, numerous studies have been conducted to compare results with those obtained by analytical and experimental methods. The result was a certain discrepancy in the output data due to certain peculiarities of the individual methods. Experimental methods provide empirical data that reflect the actual behavior of a specific structure. Although it is the most realistic method, it requires significant resources including structural material, human labor, and time. Physical models also often have to be scaled down (especially in structural engineering) which leads to the uncertainty of full-scale behavior replication. If structural models are examined under a high load rate, several \"identical\" models may lead to different behavior under the same load rate due to non-linear behavior because of geometric and/or material model uncertainties--local and global imperfections, yield strength, hardening rate, etc. Experimental methods are also limited by the (im)possibility of producing physically and mathematically \"ideal\" boundary and loading conditions. Analytical (exact or approximate--e.g., Fourier series) methods are precise and simple as they provide exact solutions under specific conditions which are often the result of several simplifications including material and geometry properties, as well as loading and boundary conditions. The less simplified problem leads to more complex equations which are difficult or impossible to solve analytically which leads us to a more versatile method--a numerical one. Numerical methods are adaptable to complex and arbitrary geometry and loading conditions which would be impractical to replicate experimentally, but they are, with certain generalizations compared to analytics, often sensitive to the element mesh and type, as well as to the specifics of the results (stress concentrations--singular points). The beginnings of research dates back to the first half of the twentieth century when, in [3; 9], the phenomenon of shear lag was solved by various analytical methods and described by equations suitable for practical engineering use. In addition to increased stress in the fiber at the web-flange junction, slightly increased deflection of the beam due to shear lag was quantified. In [10], [PERSON] further analytically divided the (longitudinal) stress state of the cross-section into the first part caused by bending, and the other part caused by the cross-section warping. In [11], an analytical derivation of the expression for the effective width of the cross-section (taking into account the effect of shear lag) was presented, which is today an integral part of European standards for the design of steel continuous beams. [PERSON] et al. [12], considered a box beam as a set of interconnected shells  
Figure 3: Box-shaped cross-section with curved flange. loaded with membrane forces. Analytical solutions for different b/L and b/H ratios, as well as different loading cases, analyzed the occurrence of transverse normal stress due to the prevention of transverse movement of the beam's midpoint due to symmetry of the beam geometry, loading, and boundary conditions. In [13], at the end of the last century, a parametric study was conducted using the finite element method with variations in loading conditions, as well as boundary conditions, the ratio of flange width to beam span b/L, and the ratios of the modulus of elasticity to shear modulus E/G in order to consider the orthotropy of the cross-section. Furthermore, the effects of the dimensions of the web (H, \(\mathrm{t_{w}}\)) and the thickness of the flange \(\mathrm{t_{f}}\) were examined.