Consider an isotropic linear elastic pipe of inner radius a and outer radius b embedded in rigid (i.e., non-deforming) material and holding a fluid at pressure pa. Ignore the effects of gravity. This may be a good model for a PVC pipe embedded in rock or concrete. Assume the problem is symmetric and that strains out of the plane shown in Fig. are zero. (a) What state of strain exists in the pipe, plane strain or plane stress? (b) Determine the stress components, orr and 000, and displacements, ur, in the pipe. (c) Is the stress difference orr-000 greatest at r = a or r = b? Note: the location of the greatest stress difference is where plasticity will occur first (to be covered later in class).

Consider an isotropic linear elastic pipe of inner radius a and outer radius b embedded in rigid (i.e., non-deforming) material and holding a fluid at pressure pa. Ignore the effects of gravity. This may be a good model for a PVC pipe embedded in rock or concrete. Assume the problem is symmetric and that strains out of the plane shown in Fig. are zero. (a) What state of strain exists in the pipe, plane strain or plane stress? (b) Determine the stress components, orr and 000, and displacements, ur, in the pipe. (c) Is the stress difference orr-000 greatest at r = a or r = b? Note: the location of the greatest stress difference is where plasticity will occur first (to be covered later in class).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities that influence the thermal property of the materials are mass, density, temperature, and many others.

Question

Pipe
Pa
Fluid
Rigid rock
Figure 1: A pipe embedded in rigid rock.
Consider an isotropic linear elastic pipe of inner radius a and outer radius b embedded in
rigid (i.e., non-deforming) material and holding a fluid at pressure Pa. Ignore the effects of
gravity. This may be a good model for a PVC pipe embedded in rock or concrete. Assume
the problem is symmetric and that strains out of the plane shown in Fig. 1are zero.
(a) What state of strain exists in the pipe, plane strain or plane stress?
(b) Determine the stress components, orr and σ00, and displacements, ur, in the pipe.
(c) Is the stress difference orr - 000| greatest at r=a or r = b? Note: the location of the
greatest stress difference is where plasticity will occur first (to be covered later in class).

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