THEORETICAL METHOD FOR DETERMINING THE VIBRATING FREQUENCY OF SKEWED GIRDER BRIDGES INCLUDING SHEAR DEFORMATION EFFECT

There were no explicit solutions to the vibrating frequencies of skewed girder bridges, and it was difficult to calculate the impact factors by using the empirical method recommended by Chinese general code for the design of highway bridges and culverts. Considering the coupling effect of flexure-torsion vibrating for skewed girder bridges, the modified Timoshenko beam theory was adopted to establish the dynamic flexural stiffness matrix, and Saint-Venant free torsion theory to establish the dynamic torsion stiffness matrix. Incorporating the skewed supporting boundary conditions, the dynamic stiffness matrix of a skewed beam element was derived based on the skewed coordinate. Using the moment-slope finite element stiffness matrix and its singularity, the transcendental equation to determine the free vibration frequency for skewed girder bridges was presented. Using the bisection method, the vibrating frequencies of A-type skewed girder bridges were analyzed. The changing tendencies of the first five orders frequencies for different skew angles were obtained, and the first five orders frequencies of a simply-supported Bernoulli-Euler beam, a simply-supported Timoshenko beam, a skewed-supported Bernoulli-Euler beam and a skewed-supported Timoshenko beam were compared. Some conclusions are summarized that the fundamental frequency augments and the second order frequency decreases with the skewed angles enlarged, Timoshenko beam theory should be adopted in calculating the vibrating frequencies of skewed bridges to include the shear deformation effect.