Procedure to calculate deflections of curved beams

In the study presented here, the problem of calculating deflections of curved beams is addressed. The curved beams are subjected to both bending and torsion at the same time. The Castigliano theorem, taught in many standard courses in Strength of Materials, Mechanics of Solids, and Mechanics of Materials, is used to determine the beam deflections. Using the methodology presented here, beam deflections that cannot be found in handbooks or textbooks can be calculated without too much effort. The Castigliano theorem and a numerical integration algorithm from the MATLAB package have been used. The examples investigated in this paper deal with elliptically curved beams. The beams are either statically determinate or statically indeterminate. Limiting cases of the elliptical beam are bending of straight beams and bending and torsion of a circular beam. Beam deflections obtained in the limiting cases are compared with handbook formulae.