Natural Frequencies of Curved Girders

A general finite element displacement formulation is presented to determine the natural frequencies of spatial thin-walled curved girders including the warping contribution. Also included are the rotatory inertia effects with respect to flexure and torsion, and the effects of antisymmetry of cross section (found to be significant). The stiffness and inertia properties of the finite element are obtained using the solutions of homogeneous differential equations governing the static problem as deformation modes. The obtained element relationships were programmed for use in digital computers, and a few example problems were analyzed. Some charts are given to expedite the determination of natural frequencies of horizontally curved girders.