Análise de deflexões de vigas via equação diferencial ordinária linear e não linear

Abstract

Beams are structural elements present in almost all buildings, their function is basically to overcome gaps and transmit the actions on them to the supports, such as the pillars. Thus, in projects, it is sought that the structures meet the acceptable parameters, such as avoiding excessive displacements. Based on the study of beam deflections, this paper presents the mathematical deduction of the nonlinear and linear ordinary differential equations (ODEs) that control this phenomenon. Inaddition, two case studies were performed, one balance beam and one two-beam, where, for them,were found the respective nonlinear and linear ODEs that govern their deflections.Two experimental tests were performed in order to compare their results with the respective ODE solutions, numerical based on the Finite Difference Method (MDF) for the nonlinear and analytical via integration for the linear ones, in which the most appropriate ODE was found for each of the case studies.