Stress distribution in hoppers

Abstract

The method of characteristics, used in a previous paper [1] to calculate limiting stress distributions is granular material in two-dimensional vertical-sided bins, is extended to similar problems in two-dimensional hoppers. Under normal conditions, a continuous solution arises in the active case and a discontinuous one in the passive case. The existence of Jenike's radial stress field at the apex [2] is considered and comparisons are made with the exact solution developed here to investigate the distance over which the radial stress field is valid. It is found that in the active state the exact solution approaches the radial stress field very slowly, so that the latter is valid only in the immediate vicinity of the apex. In the passive case a saw-tooth stress distribution is found, unlike the continuous distribution predicted by the radial stress field. The latter does, however, give a good average value. Wall stresses given by the present method are compared with those predicted by the approximate methods of Walker [3], Walters [10] and Enstad [11]. Substantial agreement is found in the active state, but the discontinuous solutions found in the passive state differ markedly from the continuous solution predicted by the approximate methods.