Exact Buckling Analysis of Constrained Stepped Columns

An analytical technique, called the Effective Stiffness Method (ESM), is developed for static buckling analysis of one-dimensional continua. Based on a distributed transfer function formulation, the ESM delivers exact buckling solutions for constrained stepped columns, eccentrically loaded columns, and columns with initial deflection. The method also obtains highly accurate buckling solutions for columns with arbitrary non-uniform cross-section. The ESM treats different column configurations in a systematic manner, and is numerically efficient. Unlike conventional analytical methods, the proposed method does not use series of continuous functions. The capabilities and advantages of the ESM are demonstrated in numerical examples.