Circularly Curved Beams under Plane Loads

The exact 6 × 6 stiffness matrix for a circularly curved beam subjected to loading in its own plane, derived from the governing differential equations and from the finite element procedure, is presented, the elements of the stiffness matrix being obtained explicitly, thus eliminating the need for any numerical matrix inversion procedures in the formulation of the matrix. The displacement transformation matrix, which allows the beam element to be incorporated into a general frameworks program is then formulated, after which the treatment of distributed loading is described. The accuracy and correctness of the stiffness and transformation matrices are verified by comparison with a range of convergent solutions obtained from subdivision of the curved members into a number of straight segments.