LAUSR

Abstract The second-order analysis of a prismatic beam-column on elastic foundation with initial transverse deflections and semi-rigid end-connections subject to transverse load is presented. The simultaneous effects of bending and shear deformations, and concentric axial forces at both ends are also included. The transverse loads and the initial deflections are expressed using Fourier series allowing the modeling of any type of applied loads and initial imperfections. The proposed structural method is also capable of capturing the phenomenon of snap-through, snap-back (i.e, buckling reversals) as well as the values of the beam elastic critical loads and corresponding buckling shapes and the post-buckling behavior. Three comprehensive examples are presented in detail that shows the accuracy and simplicity of the proposed method. From this study it is concluded that: 1) unconnected deflection trajectories are separated by the critical loads; 2) there is a minimum stiffness of the elastic horizontal spring located at one of the ends of the beam-column that guarantees its lateral stability; and 3). there is also a minimum value for the geometric parameter m that guarantees the beam-column lateral stability.