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

Wen-Jie Niu

《Research Journal of Applied Sciences, Engineering and Technology》 4卷22期 (2012/11) Pp. 4830-4834

並列摘要

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 σ_x 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 σ_x is no more than 12%. Material mechanics solution τ_(xy) is always correct for the problem of simply supported beam under uniform load. Material mechanics solution σ_y is not applicable for the problem of simply supported beam under uniform load.

並列關鍵字

Beam cross section coordinate in x direction ； material mechanics solution ； plane stress theory of theory of elasticity ； ratio of beam height to beam length ； relative error