Atwo-node element is suggested for analyzing the stability and free vibration of Timoshenko beam.Cubic displacement polynomial\r\nand quadratic rotational fields are selected for this element.Moreover, it is assumed that shear strain of the element has the constant\r\nvalue. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy\r\nand its stationing to shear strain. By exploiting these interpolation functions, beam elements� stiffness matrix is also examined.\r\nFurthermore, geometric stiffnessmatrix andmassmatrix of the proposed element are calculated by writing governing equation on\r\nstability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These\r\ntests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.
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