Stress Analysis and Deflection of Longitudinal Beam and Validate by using ANSYS

Abstract

This study investigates the deflection and stress distribution in a long, slender longitudinal beam of uniform rectangular cross section made of linear elastic material properties that are homogeneous and isotropic. The deflection of a longitudinal beam is essentially a three dimensional problem. An elastic stretching in one direction is accompanied by a compression in perpendicular directions. The beam is modeled under the action of three different loading conditions: vertical concentrated load applied at the free end, uniformly distributed load and uniformly varying load which runs over the whole span. The weight of the beam is assumed to be negligible. It is also assumed that the beam is inextensible and so the strains are also negligible. Considering this assumptions at first using the Bernoulli-Euler’s bending- moment curvature relationship, the approximate solutions of the longitudinal beam was obtained from the general set of equations. Then assuming a particular set of dimensions, the deflection and stress values of the beam are calculated analytically. Finite element analysis of the beam was done considering various types of elements under different loading conditions in ANSYS 14.5. The various numerical results were generated at different nodal points by taking the origin of the Cartesian coordinate system at the fixed end of the beam. The nodal solutions were analyzed and compared. On comparing the computational and analytical solutions it was found that for stresses the 8 node brick element gives the most consistent results and the variation with the analytical results is minimum.