An outer cylinder (jacket) with the internal diameter slightly smaller than the outer diameter of the main cylinder is heated and fitted onto the main cylinder. When the assembly cools down to room temperature a composite cylinder is obtained.
- In this process the main cylinder is subjected to an external pressure leading to a compressive radial stress at the interface.
- The outer cylinder or the jacket is subjected to an internal pressure leading to a tensile circumferential stress at the inner wall.
- Under this condition as the internal pressure increases the compression in the inner cylinder is first released and then only the cylinder begins to act in tension.
- Gun barrels are normally pre-stressed by hooping since very large internal pressures are generated.
Here the main problem is to determine the contact pressure ps. At the contact surface the outer radius rsi of the inner cylinder is slightly larger than the inside diameter rso of the outer cylinder. However for stress calculations we assume that . The inner and outer cylinders are shown in figure below.
For the outer cylinder the radial and circumferential stresses at the contact surface may be given by
In order to find the radial displacements of the cylinder walls at the contact we consider that .
This gives the radial displacement of the inner wall of the outer cylinder as
Similarly for the inner cylinder the radial and circumferential stresses at the outer wall can be given by