Relative Error of the Mechanics of Material Solution on Simply Supported Beam under Uniform Load

摘要

The mechanics of material solution is a coarse analytical solution on the problem of simply supported beam under uniform load. This paper intends to determine the relative error of the mechanics of material solution. Solutions according to plane stress theory of elasticity theory are believed to be the true solution. Results indicate that material mechanics solution σx seems applicable only when the ratio of beam height to beam length is less than 0.1 and the ratio of distance between beam studied cross section and midpoint in x direction to beam length is less than 0.49. When the ratio of beam height to beam length is less than 0.1 and the ratio of distance between beam studied cross section and midpoint in x direction to beam length is less than 0.49, maximum value of relative error for material mechanics solution σx is no more than 12%. Material mechanics solution τxy is always correct for the problem of simply supported beam under uniform load. Material mechanics solution σ_x is not applicable for the problem of simply supported beam under uniform load.