An Application of Finite Element Method to the Simple Beam Problem

Abstract

Deflection is often the dominant design criterion of a flexural member. The theoretical methods commonly used to determine beam deflections become extremely complex for irregular and combined loading conditions. A finite element method is developed for determining the deflection of a simple beam for a variety of loading conditions. The results which are obtained by the method developed are compared with results determined by theoretical methods, and high accuracy is revealed. With relatively minor modification, the numerical method developed could be expanded to consider other structural members, such as cantilevers and beam-columns, or even simple frames and trusses. This potential for development, along with the present capability to consider successive beam cross sections quickly and accurately provide this method with flexibility and efficiency unmatched by standard theoretical methods.