Analysis Of Shear Lag Effect In Thin Walled Curved Box Girder

With the large-scale construction of expressways, large interchange projects and urban viaducts, there have been a lot of curved girder bridges. More complex curved bridges were adopted to gain a smooth traffic, meet the needs of line shapes or eliminate the restriction of surrounding environment, which promoted the application of thin-walled curved box girder in bridge projects extensively. Shear deformation in the flange plate occurs when the wide beams of curved-box structure bear the symmetrical bending load, which results in the nonuniform distribution of the normal stress along the width direction, and arises the shear lag effect and the coupling effect from bending, twisting and shear lag. Therefore, the mechanical analysis of curved box girder is much more complex than that of the straight box girders. In order to simplify the analysis, scholars in curved box girder often neglected the shear lag effect many years ago, which led to transverse cracks of wide box girders in overpasses and viaduct. Even if the shear lag effect based on the thin-walled bar theory was considered later, the mechanical properties of curved box girder have still been difficult to reflect objectively, if the warping displacement effect from the second shear deformation in constraint torsion would have be omitted, that is to say, the general displacement resulting from the constrained torsion and warping was taken as the first derivative of the torsional angle.To understand the overall mechanical properties of the thin-walled curved-box girders, an improved method is put forward in the paper. The method is based on the assumption of rigid peripheral rims, shear lag deformation is added to the basic deformation, and the shear lag effect of curved box girders is considered and merges into the effect of the second shear deformation on torsion warping displacement from the constraint wrap. According to the representative single-cell single trapezoidal box girder, the general formula of the geometrical properties on shear-lag-warping cross section is put forward in the article. In the formula, the self-balancing conditions of the shear lag and warping stress are considered, the shear lag and warping displacement model is selected. Energy variational method is adopted to establish the differential equations and the corresponding boundary conditions in controlling the flex and torsion of thin-walled curved box girder. The results show that:1. If the warping torsion general displacement is substituted for the first derivative of torsional angle in the deduced basic differential equations, then the equations are transformed into the differential equations of second shear deformation in the references. Furthermore, if the shear lag deformation is also neglected, the equations are transformed into Vlasov equation. Therefore, the established differential equations extend the Vlasov equation, and reflect the mechanical properties of thin-wall curved box girder objectively.2. Galerkin method and difference method are used to solve a plexiglass model of curved box girder, respectively. The result shows that the theoretical values are consistent with the measured values, which verifies the calculation method and the basic equation established in the article.3. The shear lag of curve bending beam only affects on the bending normal stress to some degree, while it has little effect on the warping stress. Meanwhile, the warping torsion deformation has a little effect on bending shear lag effect. The result indicates that shear lag warping deformation and warping torsion deformation are mutually independent on the whole basically.4. Usually, the restrained torsion second shear deformation has little effect on the simply-supported curved box girders. However, it has evident effect on the fixed end and the neighbouring sections of the fixed-end constraint box girder, such as cantilever-box beam.