In a compound cylinder, hoop stress throughout the metal is-

Explanation:

• The compound cylinder is formed by shrinking a cylindrical jacket, also called tube or tyre, onto another cylinder/tube which initially introduces hoop compressive stresses in the inner tube and hoop tensile stresses in the outer tube.
• In the case of two cylinders, the outside cylinder has an internal diameter slightly less than the external diameter of the inside cylinder, so that when the cylinder is shrunk on, the required radial pressure is developed at the interface.
• The outside cylinder is expanded by heating and the two cylinders are assembled together .
• When the compound cylinder is subjected to internal pressure, both the inner and outer tubes are subjected to hoop tensile stress due to internal pressure alone.
• The final hoop stresses in both the tubes are determined by adding the stresses induced during shrinking and the stresses developed due to the internal pressure alone.
• Thus this arrangement can be used to make the hoop stresses more or less uniform throughout the metal.