Statics, stability and vibration of non-prismatic linear beam-columns with semirigid connections on elastic foundation. (15th February 2019) - Palacio-Betancur, Alejandro; Aristizabal-Ochoa, J. Darío
Highlights: The static, stability and vibration of non-prismatic straight beam-columns with generalized end conditions and resting on elastic foundation are presented. The effects of a variable two-parameter elastic foundation are discussed. Based on the conjugate beam principle, the bending flexibility coefficients and the shape functions of the element are obtained. The proposed method only requires a simple numerical integration method to solve problems of non-prismatic elements. The concept of fixity factor at each end for non-prismatic elements is introduced as a useful tool in their structural analysis. Three comprehensive examples were presented that show the effectiveness and simplicity of the proposed method. Abstract: A method that evaluates the static, stability and vibration behavior of non-prismatic Euler-Bernoulli straight beam-columns resting on a two-parameter elastic foundation with generalized end conditions is presented. The static stiffness matrix and shape functions of the element are derived including the combined effects of semi-rigid connections and lateral springs at both ends using the conjugate beam principle. The fixity factors of a non-prismatic element are defined and used in the definition of its characteristic matrices according to the consistent method. It is shown that static, stability and vibration analysis of non-prismatic beam-columns under any transverse loading and axial end loads with generalized end conditions can be carried out once the main flexibility coefficients of the member are determined. Three comprehensive examples are presented that show the simplicity and accuracy of the proposed method. The calculated results using the proposed approach are compared to those available in the technical literature.