Curvature and the Solution of Eccentrically Loaded Columns

The eccentrically loaded column of perfectly plastic material has been studied analytically in considerable detail, but the approach to date always begins by solving the basic differential equations for the deflection curve. Simple illustrations demonstrate that the curvature curve of the column plays exactly the same role as deflection did; while the necessary steps in obtaining the solutions are reduced considerably. Using this concept, expressions for the curvature curve of an eccentrically loaded column of rectangular cross-section at all stages of plasticity are derived. It is shown how solutions for the critical loads of the column may be obtained directly from this approach. The analytically obtained results of column curves are compared with the existing solutions and good agreement is observed.