The Theory of Static Loads in Bins

The classical formula for the pressure in deep bins containing granular material is derived here employing considerably weaker assumptions than previous derivations. Three important points are established in this rigorous derivation. First, it is shown that the classical formula due to Janssen is a lower bound on the average pressure the granular material can exert on a bin wall rather than necessarily the actual stress. Second, it is shown that Janssen’s assumption of constant vertical stress over the bin’s horizontal cross section is not necessary to obtain his classical formula. Third, it is shown that the coefficient introduced by Janssen should be interpreted as the ratio of the horizontal stress averaged over the lateral boundary perimeter to the vertical stress averaged over the horizontal cross-sectional area of the bin.