The Element Stiffness Matrix of a Tapered Beam with Effects of Shear Deformation and its Stability Application

Abstract

Starting from second-order effect, the governing differential equation of a tapered beam considering effects of axial force and shear deformation is established, the exact element stiffness matrix of a tapered beam with effects of shear deformation is proposed, and whose inertia moment is quadratic along the longitudinal axis. When the effect of shear deformation is ignored, the proposed stiffness matrix will degenerate into the Bernoulli-Euler ones. By using of the presented stiffness matrix, the stability and nonlinear of structures which contain tapered elements can be analyzed. Finally, the stability of some typical structures are analyzed in the numerical examples, the results prove that when the slenderness ratio is small, the effect of shear deformation can’t be neglected; As increasing, the results of beam considering shear-deflection are close to Bernoulli-Euler ones’.