By R. M. Nedderman
This e-book outlines the elemental technological know-how underlying the prediction of pressure and speed distributions in granular fabrics. the character of a rigid-plastic fabric is mentioned and a comparability is made among the Coulomb and conical (extended Von Mises) versions. The equipment of measuring fabric houses are defined and an interpretation of the experimental effects is taken into account within the context of the severe country thought. workouts and options are only if may be rather helpful for the reader.
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Additional info for Statics and Kinematics of Granular Materials
We therefore conclude that the Coulomb line cannot cut Mohr's circle. Thus, the Mohr-Coulomb analysis is based on the concept that slip will only occur if the Coulomb line touches Mohr's circle and that under no circumstances can the Coulomb line cut the circle. In fact, Coulomb's yield criterion is not concerned with the direction of slip but merely imposes an upper limit on the magnitude of the shear stress that can occur on a plane. 3. We can therefore see that at critical stability there are two incipient slip planes represented on the diagram by the points S and S' and therefore that incipient slip planes always occur in pairs.
Let us consider a vertical plane through the material such as that indicated by the line AA. Considerations of symmetry show that the shear stress on this plane must be zero. bgy = yy where pb is the bulk density of the material and g is the acceleration due to gravity. It is common in this subject to denote the product pbg by 7 which is known as the weight density of the material and should not be confused with the shear strain rate 7^. Thus the compressive normal stress in the vertical direction increases linearly with depth.
9 Mohr's circle for the stresses in the active Rankine state. The force PA required to prevent the block slipping down the plane is Mg sin a - |xMg cos a whereas the force PP required to pull the block up the plane is Mg sin a + \xMg cos a. 3) will be stable. 9. 7) v } (3A8) where KA is defined by The constant KA, which represents the ratio of horizontal and vertical stresses in a cohesionless material, is known as Rankine's coefficient of active earth pressure. 10) are typical examples. It is fashionable to combine such pairs into a single equation by introducing the quantity K which has the value - 1 in the active case and the value +1 in the passive case.