Quantification of Saint-Venant's principle for a general prismatic member

Abstract

A method to quantify Saint-Venant's principle for general prismatic members is described. Finite elements are used to model the member cross-section to allow the analysis of arbitrary geometries, material properties, and nonhomogeneities. The variation in the structural response along the member's length, away from the loaded end, is modelled with an exponential decay which has been established in the literature to be the correct form. Many analytic results exist in the literature for special cases. Because of its ability to handle arbitrary cross sectional geometries, this semi-analytic finite element method can provide a firm footing for the utilization of Saint-Venant's principle for whole new classes of problems. Results for several typical problems are given.