Thin-Walled Curved Beam Finite Element

The generalized displacements and forces at the two nodes of the beam elements are: three translations and their corresponding forces, three rotations and their corresponding moments, the out-of-plane warping of the end cross section and its corresponding bi-moment. The solutions to the homogeneous differential equations governing the static deformation of curved beams along with kinematical boundary conditions yield the required displacement functions of the element. The stiffness matrix is formed by evaluating the stress resultants at the two ends of the element corresponding to each unit generalized displacement. The method using the principle of virtual work to obtain the equivalent nodal forces due to external loading and the consistent mass matrix is outlined. Several examples are presented and comparisons made to demonstrate the accuracy and the usefulness of the element. This element has been successfully used in the finite element discretization of curved girders of horizontally curved highway bridges in studying the response of the bridges subjected to moving loads.