Exact expressions for stability functions of a general non-prismatic beam–column member

Abstract Exact elastic stability functions for any general non-prismatic beam–column member under uniform tensile or compressive axial force have been obtained for the first time. A power series approach has been used in solving the fourth-order ordinary differential equation with variable coefficients. Examples are presented to check the accuracy, validity and effectiveness of the present method and to compare the results with the available analytical and numerical solutions. The results obtained using the exact analysis presented herein have shown excellent agreement with previous available results. The exact derived elastic stability functions can be used in formulating an exact tangent-stiffness matrix for a non-prismatic beam–column member and thus one can generate an accurate non-linear second-order analysis of rigid and semi-rigid plane frames with non-prismatic members.

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