Determination of Elastic Buckling Load of Tapered Columns Using a Novel Analytical Method Based on Maclaurin Expansion

Abstract

Elastic tapered columns are a class of important structural components, which have wide applications in civil structures. This is because their ability to increase both strength and stability, reduce the whole weight of structure and consequently reducing earthquake forces. In this study, it is assumed that flexural rigidity of the considered columns with desired end conditions varies smoothly along the beam axis by power-law formulations and or exponential ones. For accurate estimation of the stability characteristics, the equilibrium equation should be solved. In the presence of arbitrary variation in geometrical properties, the governing equation becomes a differential equation with variable coefficients in which the classical methods adopted in stability analysis of uniform columns are not efficient and no longer valid. It is noteworthy that exponential variation of mechanical properties is one of the most special states of non-prismatic columns that few methods are able to solve its governing differential equation. For such complicated problem, numerical, analytical and mathematical methodologies are usually employed by researchers to solve the equilibrium equation and evaluate exact buckling loads. In the current paper, a novel semi-analytical technique based on combination of polynomial approximation and the Maclaurin series is proposed to solve the governing differential equation. The critical buckling loads of the beam are finally obtained by imposing the natural and initial boundary conditions and solving the eigenvalue problem. The obtained outcomes are compared to the results of other available benchmarks. The competency and efficiency of the method is then remarked.