Educ. Reso. for Part. Techn. 992Q-Tardos
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Copyright © 1999 ERC at the Univ. of Florida

Stresses in Bins and Hoppers, by Gabriel I. Tardos

-- 1. Introduction --

The purpose of this section is to calculate stresses present in a static, nonmoving mass of powder. Since the most important device used in industry to store and feed powders is the silo, the applications given in this section are restricted to this geometry. The results are subsequently used for silo design.

A silo for powder storage is usually a tall structure consisting of a rectangular or cylindrical body of constant cross section called a bin connected at the lower end to a prismatic or conical section called the hopper, as shown schematically in Fig. 1.


Fig. 1 - Silo Geometries: 2D plane, 3D square, 3D circular

The hopper terminates at its lower end in a relatively small outlet that is further connected to a vertical pipe usually called a standpipe or to a powder feeding device. Silos come in different shapes and sizes, but for the present considerations only the geometries shown in Fig. 1 are analyzed. These are
the 2D or "plane" silos (Fig. 1a) where the dimension perpendicular to the plane of the figure is large compared with the width 2 b

the 3D square silos (Fig. 1b) with the characteristic width 2 b

the 3D circular silos (Fig. 1c) with the characteristic diameter 2 b

The hopper has two additional geometric characteristics namely the half-angle, , measured from the vertical as shown and the outlet dimension or span, B.

The powder material stored in the silo is characterized by its bulk density

[1]      B = S (1 - ) = S v = / g

where S is the material density, is the porosity or void fraction, v = 1 - is the solid fraction and = B g is the specific bulk gravity.

These powder properties are supplemented by a powder-silo-wall characteristic called the wall-powder friction angle, W. Both and W have to be measured experimentally and are intrinsic properties of the bulk material and the wall of the silo.

The method to determine stresses in the bin was originally developed by Janssen [1895] to calculate wall stresses but can also be used to find average stresses in the bulk material. The method was generalized later and applied to calculate stresses in converging hoppers. A full account of these methods can be found in the authoritative text of Drescher [1991] where several different methods to calculate stresses in powders are given in detail. Here we restrict our attention to the more simple approach of the method of slices and use the results to design hoppers.

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