Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. I: Theoretical Considerations Based on Semitangential Property

To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguezʹ rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the thin-walled space frame element are derived using Hermitian polynomials considering shear deformation effects, and a new scheme to evaluate incremental member forces and load correction stiffness matrices due to off-axis loads is presented and its physical meaning is addressed. Furthermore, finite-element solutions displaying spatial postbuckling behaviors are evaluated and compared with available solutions.