Study of Effects of Weight Force on the Deflection of Simply Supported Beam Under Uniform Distributed Load

In the present study, the long slender simply supported beam having uniform square cross section made of linear elastic material properties that are homogeneous and isotropic is taken, and the deflection of the beam is investigated. The deflection of a beam is essentially a three-dimensional problem. A compression accompanies an elastic stretching in one direction in perpendicular directions. The model of a beam is studied under two different conditions [1]. Under both, the condition some boundary conditions are the same as uniformly distributed load, with one end fixed and on the other end with a directional constraint. The difference in the two conditions is that in one condition, the weight of the beam is assumed to be negligible, and in the second case, the weight of the beam is considered. It is also assumed that the beam is inextensible and thus strains are also negligible. Considering this assumption first using the Bernoulli-Euler bending moment-curvature relationship, approximate solutions of the beam are obtained from the general set of equations. Then assuming a set of dimensions, deflection values of the beam are calculated analytically. A finite element analysis of the beam when the weight force is considered is conducted in ANSYS 14.5. Numerical results are generated by taking the origin of the Cartesian coordinate system at the fixed end of the beam. The deflection of the beam from its weight is 2.9%.