A new practical method for the flexural analysis of thin-walled symmetric cross-section box girders considering shear effect

Abstract

This study proposes a new analytical flexure theory that considers the shear deformation of the web and flange of a thin-walled box girder. Starting with the relationship between the strain and displacement of each slab, the flexural displacement function of thin-walled box girders considering the shear deformation effect is derived by using the deformation continuity condition. Compared with the traditional flexural displacement model, this function obtained by the theoretical analysis is more rigorous and can be transformed into the flexural displacement function of the traditional shear lag or Timoshenko beam by eliminating some parameters. Then, according to the balance conditions of axial force and bending moment, the shear deflection deformation state and Euler–Bernoulli beam deflection deformation state are decoupled. On this basis, a new convenient method for calculating the warping stress and shear deflection of thin-walled girders is proposed. Furthermore, a simplified analysis method for converting continuous box girders into simply supported beams is proposed on the basis of continuity condition of shear deflection at middle supports. Taking into account the shear deflection deformation state, a beam-type finite element model considering the shear deformations of each box wall is developed by using Hermite polynomials to analyze the complex variable cross-section box girder. Finally, numerical examples are used to verify the effectiveness of the simplified method and the beam-type finite element model. Numerical examples show that the flexural stress and deflection calculated by the proposed method agree well with the three-dimensional finite element model analysis results. The shear warping normal stress has a larger value at the shear force discontinuity point. In the control cross-section, the normal warping stress and shear deflection caused by shear deformation both exceed 75% and 38% of stress and deflection of the Euler–Bernoulli beam, respectively.