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

-- 2. Active and Passive States of Stress --

These states of stress are also called Rankine states and were first defined in soil mechanics [Nedderman, 1992]. A simplistic but picturesque description of the two states of stress can be obtained by viewing the gymnast who tries to sustain himself on two vertical, parallel walls as shown in Fig. 2.


Fig. 2 - Gymnast in the a) passive (left) and b) active (right) states of stress

In both positions, the gymnast is in equilibrium and supports his own weight by friction of his hands on the wall. In the upper position (Fig. 2a) the gymnast feels as if the walls were being pushed inwards; the maximum stresses in his hands and upper body are mostly horizontal. This is the so-called passive state. In the lower, hanging position (Fig. 2b) he feels as if the walls were being pulled apart; the maximum stresses in his body are mostly vertical. This is the active state. Larger stresses are usually generated in the active state (lower position) as compared with the passive state (upper position).

Similar states are achieved in storage silos (in the bin / hopper geometry) and are associated with filling and discharging the bulk material from the silo. During filling (left side of Fig. 1) bulk powder is loaded into the silo from above. The material arranges itself in a heap and is sustained by the walls of the bin in somewhat similar fashion as the gymnast in Fig. 2b, generating the active state of stress.

During discharge, material is withdrawn from the open, lower end of the hopper and the powder arches on the wall and generates the passive state of stress. This situation is depicted schematically in Fig. 3 (only the hopper is presented and not the entire silo) where the active state of stress is associated with filling and storage while emptying is associated with the passive state.


Fig. 3 - Trajectories of major principal stress in a hopper during filling and discharge

The stress 1 in Fig. 3, denoted as the maximum or so called major principal stress, occurs on a plane with no shear stresses present. In most practical situations both the active and the passive state coexist as shown in Fig. 3c, with the switching point usually situated at the joint between the bin and the hopper.
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