An Analytic Approach for Exactly Determining Critical Loads of Buckling of Nonuniform Columns

This paper studies buckling instability of columns with variable bending stiffness subjected to an axially compressive load. An analytic approach has been presented to determine critical buckling loads of a nonuniform column with or without continuous elastic restraint along its length. We transform this problem into a Fredholm equation, and then to a system of linear equations. The desired buckling loads can be easily obtained by solving the least positive eigenvalue of the resulting system. The validity and efficiency of the method is confirmed by comparing our numerical results with those available. The influences of variable cross-section or elastic restraint stiffness on the buckling loads of a simply-supported column are analyzed. A suboptimal design of a tapered cylindrical bar with fixed weight is given. The present results are of benefit to the optimal design of beam/column structures.