Theoretical research on naturally curved and twisted beams under complicated loads

This paper presents an analytical method for the study of naturally curved and twisted beams under complicated loads, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. The solutions derived in this paper can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. A generalized warping coordinate for a curved coplanar beam subjected to the action of vertical distributed loads is given for verification.