In order to reduce the hoop stresses developed in thick cylinders subjected to large internal pressure, compound cylinders with one thick cylinder shrunk over the other are used.
- With calculated junction pressure between the two cylinders, it is possible to reduce the hoop stress and to make it more or less uniform over the thickness. Lame’s expressions are applied to both the inner and outer cylinders before and after the introduction of the internal fluid pressure, and the stresses in the two stages are superposed to obtain the final values.
- When the outer cylinder is shrunk over the inner cylinder, the difference between the inner diameter of the outer cylinder and the outer diameter of the inner cylinder determine the shrinkages pressure developed at the junction. This difference can be worked out as given in subsequent paragraphs.
Let rj be the common radius at the junction after shringing on.
Let Sr1 be the difference between the outer radius of inner cylinder and rj and Sr2 be the difference between rj and inner radius of the outer cylinder.
If Sr be the difference in the radii before shrinking on, then we have
i.e. the original difference of radii at the junction will be given by the algebraic difference between the hoop stresses for the tubes at the junction multiplied by the junction radius divided by E.