The theory of static stresses in bins and hoppers
Description
A study on the static stresses developed by granular materials in storage containers is presented here in two parts. The first part of this work was initiated by the improvements provided by Cowin on the classical Janssen's formulas for bin static stresses. Janssen assumed that the horizontal and vertical stresses inside the bin at a particular depth were uniform. He also assumed that full frictional force is mobilized at the bin wall. Cowin replaced these stronger assumptions with less restrictive assumptions and rederived the essence of Janssen's results. In his improved formulas Cowin also included the effect of material consolidation upon the bin stresses, an aspect, which was not considered in the original Janssen's formulas. In the first part of this dissertation, a reassessment of most of the experimental investigation, based on Cowin's improved formulas is presented. Also, an experimental investigation on the granular material consolidation is reported and the results of this investigation show that the improved formulas are reasonable and practical In the second part, a concept from classical Janssen's theory is incorporated into an equilibrium continuum theory and applied to two dimensional bin and hopper problems. The method of characteristics is used to obtain the bin and hopper static stress solutions and the results are compared with solutions obtained from limiting static equilibrium (LSE) theory. The LSE theory also uses the method of characteristics and the solutions involve cumbersome numerical procedures. But, the method based on equilibrium continuum theory presents analytical solutions and gives bounds on bin and hopper static stresses