## Dnr

Ea

V2

— = - and T = a + bloger dr r and the equations become

B EaT

In practical applications where the temperature is higher on the inside of the disc or thick cylinder than the outside, the thermal stresses are tensile on the outside surface and compressive on the inside. They may thus be considered as favourable in pressurised thick cylinder applications where they will tend to reduce the high tensile stresses on the inside surface due to pressure. However, in the chemical industry, where endothermic reactions may be contained within the walls of a thick cylinder, the reverse situation applies and the two stress systems add to provide a potentially more severe stress condition.

Examples

### Example 4.1

A steel ring of outer diameter 300 mm and internal diameter 200 mm is shrunk onto a solid steel shaft. The interference is arranged such that the radial pressure between the mating surfaces will not fall below 30 MN/m2 whilst the assembly rotates in service. If the maximum circumferential stress on the inside surface of the ring is limited to 240 MN/m2, determine the maximum speed at which the assembly can be rotated. It may be assumed that no relative slip occurs between the shaft and the ring. For steel, p = 7470 kg/m3, v = 0.3, E = 208 GN/m2.

Solution

r1 8

0 0