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An exact free vibration and buckling analysis of a tapered beam-column with general connections is calculated. All structural elements are made of functionally graded material. In this study, a power function is assumed for the variation of the elastic modulus along the cross-section’s height. Extensional-coupling effects are considered in the proposed formulation. By solving the related fourth-order differential equation, the exact answers are obtained. The Bessel functions are utilized in this solution. In addition, the effect of connection flexibility is assessed by considering rotational and transitional springs at the two ends of the element. The suggested stiffness matrix can analyze the free vibration and buckling of a frame made of functionally graded material tapered beam-columns with semi-rigid connections and supports. To validate the proposed formulation, several benchmarks and novel examples are separately analyzed. All numerical findings clearly demonstrate the usefulness of the authors’ scheme.

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