Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames

The potential energy expression and the (14 by 14) stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived. The transformation matrix relating the forces and displacements (including bimoment and warping parameter) at the adjacent end cross section of two elements meeting at an angle is deduced as the limiting case of a transfer matrix of a curved beam. To cope with asymmetric cross sections, some element displacements and forces are referred to the shear center and others to the cross-sectional centroid and the matrix for transformation from shear center to centroid is set up. The incremental larger-displacement analysis is formulated using the Eulerian coordinate approach with updating of the local coordinate systems at each load increment. The deformed beams are imagined to be composed of straight elements. Results of lateral post-buckling analysis of various beams are presented.