Abstract
The aim of this paper is to present the governing equations of motion of an elastic and uniform thin-walled open section which the axial curve is a space curve. The rigorous governing equations are formulated by reducing the three-dimensional continuum to the one-dimensional one. In this process, the modified Hellinger-Reissner's variational theorem is employed and the warping is expressed by the warping function considered the effects of the curvature and torsion of the axial curve. The derived equations are applicable to the problems including the large displacements and large angles of rotations and subjecting the deformations of the cross section and they are expressed in the lagrangian representations. Also, considering the practical use, the general equations are approximated and furthermore the linear theory is stated. The derived equations of a thin-walled open section are indepedent of the engineer's torsion-bending theory and are the treatments of the three-dimensional analysis. As the result, the presented general equations have the same forms as the theory of rods. Hence, it is shown that the theory of a thin-walled open section can be treated as the problem of rods. The resultants are the brief forms than the expressions of the engineer's torsion-bending theory and do not contain the contradictions on theory.
