An analytical model for predicting stresses in grain storage bins

A grain pressure theory has been developed from analysis of nonuniformly distributed stresses on a differential element of grain in a planar bin. The theory assumes that (1) grain is a cohesionless continuum whose yielding behavior is governed by the Mohr-Coulomb criterion, and (2) the shear stress varies linearly across the bin width. The theory predicts a parabolic distribution of horizontal and vertical stresses across the bin. The horizontal to vertical stress ratio, which is assumed to be a constant in the Janssen equation, is calculated as a function of the angle of internal friction, the coefficient of wall friction, and the bin size. The predicted stress ratio varies in both the horizontal and vertical directions, with a lower bound equal to the Rankine stress ratio. The horizontal stress predicted by the present theory is generally higher than that of Janssen. The vertical stress predicted by the present model is lower than that of Janssen at the wall and higher that that of Janssen at the bin center. Model predictions of stresses are in reasonable agreement with available data in the literature.