Large-deflection and post-buckling behavior of slender beam-columns with non-linear end-restraints

The large-deflection analysis and post-buckling behavior of laterally braced or unbraced slender beam-columns of symmetrical cross section subjected to end loads (forces and moments) with both ends partially restrained against rotation, including the effects of out-of-plumbness, are developed in a classical manner. The classical theory of the “Elastica” and the corresponding elliptical functions utilized herein are those presented previously by Aristizabal-Ochoa [1]. The proposed method can be used in the large-deflection analysis and post-buckling behavior of elastic slender beam-columns with rigid, semi-rigid, and simple flexural connections at both ends including linear and non-linear inelastic connections like those that suffer from flexural degradation (such as flexural cracking and elasto-plastic connections) or flexural stiffening. Only bending strains are considered in the proposed analysis. Results from the proposed method are theoretically exact from small to very large curvatures and transverse and longitudinal displacements for laterally braced or unbraced slender beam-columns under bending caused by end loads. The large-deflection analysis and post-buckling behavior of slender beam-columns with both supports partially restrained against rotation and with sway inhibited or uninhibited are complex problems requiring the simultaneous solution of two coupled non-linear equations with elliptical integrals whose unknowns are the limits of the integrals. The validity of the proposed method and equations are verified against solutions available in the technical literature. Three comprehensive examples are included that show the effects of linear and non-linear connections at both ends on the large-deflection analysis and post-buckling behavior of slender beam-columns.