Statics, stability and vibration of non-prismatic linear beam-columns with semirigid connections on elastic foundation

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.