Exact Stiffnesses for Tapered Members

Abstract

A simple method for deriving closed-form expressions for the components of the stiffness matrix and fixed-end forces and moments for tapered members is presented. The governing differential equations and the boundary integral method are used to obtain exact expressions for axial, torsional, and flexural stiffnesses. The necessary fixed-end forces and moments are also derived. The procedure of the proposed method is explained through a practical class of tapered members. The procedure, however, can be extended to other axial, torsional, and flexural stiffness variations. The correctness of the obtained stiffness expressions is verified through numerical examples.