Buckling of Inelastic, Tapped, Pin-Ended Columns

A numerical method for finding buckling loads of pin-ended tapered columns which are elastic, elastic-plastic, or completely plastic is presented. An enclosure theorem is used to find upper and lower bounds on the first eigenvalue, which is a measure of the lowest buckling load of the mathematical model of the column. A numerical method is used to systematically determine the least upper bound and the greatest lower bound. By using an effective modulus of elasticity, upper and lower bounds on the first eigenvalue are found for inelastic as well as elastic material behavior. A three-parameter stress-strain relationship is used to describe the behavior of the material. In order to assess the adequacy in the elastic-plastic and plastic ranges of the effective modulus description used in the mathematical model, the computed bounds are compared to the results of tests on 44 aluminum columns having various tapers and slenderness ratios. The experimental data are in good agreement with the lower bound of the analysis of the mathematical model.