Improved finite beam element method for analyzing the flexural natural vibration of thin-walled box girders

Abstract

This study establishes the improved element stiffness and mass matrices of the thin-walled box girder, using a cubic Hermite polynomial shape function and based on an improved displacement function for shear-lag warping meeting the axial equilibrium condition of shear-lag warping stress and the consistency requirements of the displacement function. The improved thin-walled box girder element comprehensively considers multiple influencing factors, such as the thin-walled box girder shear-lag effect, shear deformation, and rotational inertia. The element shape function has first-order continuity at the element interface and satisfies the calculation precision with relatively few degrees of freedom. A finite beam element method program that can be used to calculate the natural vibration frequencies of thin-walled box girders was compiled based on the improved thin-walled box girder element. This program was used to calculate the natural vibration frequencies of many thin-walled box girder samples with different span-width ratios, span-height ratios, and boundary conditions. After comprehensively considering the influencing factors, the calculation results obtained from finite beam element method are in good agreement with those obtained from an ANSYS finite element calculation, thus demonstrating the rationality and validity of the improved thin-walled box girder element stiffness matrix and mass matrix proposed in this study. Finally, factors influencing the thin-walled box girder shear-lag effect and shear deformation were analyzed, providing relevant reference for project designers.