Force Deformation Equations for Initially Curved Laterally Loaded Beam Columns

Abstract

The analytical inclusion of the effects of initial curvature and lateral load in the force deformation equations of a two‐noded beam‐column element is considered. Current position‐(Eulerian) based equations are developed that give both the end‐shortening and nodal forces for a deformed element under the action of a significant axial compression. Consideration is restricted to an initial curvature in the form of a single sinusoidal half‐wave, and to a sinusoidal approximation of a symmetric triangular lateral load. The equations developed are compatible with the existing Eulerian force deformation equations presented by Oran for straight axially loaded beam columns. A tangent stiffness matrix compatible with the new force deformation equations is not presented. The correctness of the new formulation is demonstrated by various analytical comparisons with the results of some standard beam‐column problems, and by a number of numerical comparisons between results obtained using the new formulation and those predicted by conventional nonlinear analyses, which employ a number of standard beam‐column elements to model each structural member. The use of the new equations can lead to a significant savings in the core storage required for the analysis of full‐size lattice domes.