Fourier Series solutions for deflection analysis on simply supported beams subjected to distributed loads

Abstract

This article presents a study of the Fourier Series Method in the one-dimensional analysis of the elastic line and bending moment of a simply supported beam submitted to a distributed load. The analysis of deformation is an important procedure in Structural Engineering. The method was applied to three different types of distributed loads: one uniform and two triangular. The results were obtained from the representation of the elastic line of a beam simply supported through a Fourier Series. From the manipulation of beam equations and Fourier Series, graphs with different amounts of terms were plotted in the Series for deflection, bending moment and loading. These graphs were more clearly represented through tables. Evaluating the method, by comparing with the analytical method of successive integrations, it was concluded that the Fourier Series method provides very satisfactory results in the deflection analysis of this type of beams.