Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. I: Stability formulation and closed-form solutions

For spatial stability analysis of shear deformable thin-walled curved beams with non-symmetric cross-sections, an improved analytical formulation is proposed. Firstly the displacement field is introduced considering the second order terms of semi-tangential rotations. Next an elastic strain energy is derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. And then the potential energy due to initial stress resultants is consistently derived with accurate calculation of Wagner effect. In addition, closed-form solutions for in-plane and lateral-torsional buckling loads of curved beams subjected to uniform compression and pure bending are newly derived. In the companion paper, FE procedures are developed by using curved and straight beam elements with arbitrary thin-walled sections. In numerical examples, to illustrate accuracy and validity of this study, closed-form solutions for in-plane and out-of-plane buckling loads are presented and compared with those obtained from analytical solutions by other researchers.