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A typical example of plane strain is the pressurisation of long cylinders where the above equations given accurate results, particularly in the middle portion of the cylinder, whether the end conditions are free, partially fixed or rigidly fixed.

An example of the transfer of a plane stress to a corresponding plane strain solution is given when the relevant equations for the hoop and radial stresses present in rotating thick cylinders are readily obtained from those of rotating thin discs by use of the substitution v/(l — v) in place of v (see §4.4).

8.23. The stress-strain relations

The following formulae form a useful summary of the relationships which exist between the stresses and strains in a general three-dimensional stress system.

(a) Strains in terms of stress

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