Analysing shear‐lag warping displacement functions and mechanical characteristics of rectangular concrete box‐girder bridges

Abstract A theoretical foundation for the accurate analysis of the shear‐lag effect in rectangular box‐girder flange slabs is established in this study through the selection of appropriate warping displacement functions. Initially, a series of warping displacement functions that fulfil the basic warping mode of the box‐girder flange slabs is proposed based on the principle of longitudinal warping displacement function setting. Subsequently, the shear‐lag effect, self‐equilibrium condition for shear‐lag warping stress and Timosheko shear deformation are comprehensively considered. The governing differential equations and corresponding natural boundary conditions of the box girder are determined by applying the energy variation principle. The box girder's natural frequency is calculated by solving the governing differential equations under the given warping displacement functions and boundary type. The accuracy of the various warping displacement functions is subsequently evaluated based on the natural frequency values of box girders. A high‐precision longitudinal warping displacement function for box‐girder flange slabs is selected, thus enhancing the analysis precision of the box girders' mechanical properties. Additionally, the necessity of selecting appropriate warping displacement functions is verified through static and dynamic analyses of the box girders. Furthermore, comparisons are made between the finite element solutions and the corresponding analytical solutions utilizing the proposed warping displacement functions, demonstrating the validity of this approach for analysing the box‐girder response. Consequently, the proposed method provides a robust basis for understanding the mechanical properties of rectangular box girders and enriches the existing analytical theory of box structures, guiding the design of rectangular concrete box‐girder bridges.