# Shear Lag Effect on Box Steel Beams with Wide Curved Flanges
## 3 Review of Previous Research on Shear Lag Effect
Since previous research did not achieve a uniform standpoint of all the authors, this numerical research concluded that in slender, thin-walled beams, varying the mentioned parameters (satisfying the conditions H < 0.5 \(\times\) L and H > 10 \(\times\) t\({}_{\mathrm{f}}\)) does not have a pronounced effect. Also, varying the thickness of the flange and web while maintaining a constant ratio (\(\mathrm{t_{f}}/\mathrm{t_{w}}\) = const.) does not affect the shear lag effect. The paper confirmed expressions obtained earlier by analytical methods (including those in [3]) and obtained empirical formulas for quantifying the shear lag coefficient, which excludes part of the cross-section to consider the increase in longitudinal stress at the junction of the flange with the web--a principle adopted by Eurocode. The principle was further applied to beams with longitudinal stiffeners by modifying (increasing) the E/G ratio, where the shear lag effect is even more pronounced. In recent research over the past twenty years, extensive numerical parametric analyses of single-span beams [14] and multi-span beams [15; 16] have been conducted, and box beams were analyzed, while the effect of shear lag was described as a \"stress concentration factor\", which is a product of stress at the joint with the web and theoretical stress that would have been obtained by the beam theory with [PERSON]'s hypothesis of plane sections. In these studies, the effects of all the relevant factors on the shear lag of beams were examined: the height of the cross-section h; the thickness of flanges \(\mathrm{t_{f}}\) and web \(\mathrm{t_{w}}\) (and their ratio); the form of load application (concentrated or distributed loads); the density of the element mesh; and the ratio of flange width to span (b/L). The problem associated with the finite element method, related to the type and density of the element mesh, was solved by the \"multi-mesh extrapolation\" method [17], where the size of the finite element was gradually reduced towards a \"finer\" mesh, and ultimately the stress concentration value was extrapolated to the size of the finite element tending towards zero. In recent years, several authors extensively elaborated the shear lag effect in composite concrete-steel beams, which are highly cost-effective due to the favorable composite combination of steel and concrete in tension and compression, respectively. In [18], the authors proposed a simplified analysis method considering shear lag effect of steel-concrete composite decks, including the experimental static load test of composite twin I-girder deck and box girder deck, subjecting it to vertical bending and compressive axial loads. [PERSON] et al. [19] investigated stress and deflection behavior in double-box cross-section composite beams through simultaneous analytical and experimental studies. Comparative analysis of the results from both studies showed good agreement within the linear phase, but the ignored influence of relative concrete-steel slips and material nonlinearity needs to be further analyzed. [PERSON] et al. [20] proposed a beam finite element model considering the slip, shear lag, and time-dependent effects of steel-concrete composite box beams. The results show that concrete rheology including shrinkage and creep significantly influences the structural responses of the composite box beams, affecting (increasing) relative slippage and vertical beam deflection. [PERSON] et al. [21] assembled a finite beam element with 26 degrees of freedom for curved (in plan layout) considering various effects such as constrained torsion, distortion, shear lag, and biaxial slip. That method represents a significant step forward in comparison to standard FEM models which imply high computational costs for modeling such a complex task.