Deflections of postbuckled unloaded elasto-plastic thin vertical columns

Abstract

Thin vertical columns form a curve with large deflections and slopes when loaded axially by larger than the critical buckling load. For thin columns of elasto-plastic properties, these loads could induce either an elastic state throughout the length of the bar, or an elasto-plastic state with a moment at the base of the bar larger than the yield moment but smaller than the plastic moment. As the load increases, deflections and slopes of the median line of the column increase and yielding progresses from the base towards the free end. However, it is possible that the moments along the median line of the column may decrease, i.e. the column unloads. Due to the large curvatures of the column, the exact expression for the curvature of the median line is used in the Bernoulli-Euler equation (Theory of the Elastica). The boundary-value problem that results contains nonlinear ordinary differential equations. The Euler-Gauss predictor-corrector method has been used to solve the nonlinear differential equations numerically. Deflections of unloaded elasto-plastic thin columns are presented in a graphical form and compared with those of a linearly elastic material.