Question

A brass hoop of an inside diameter of 40 cm and a thickness of 1 cm fits snugly at 180°C over a steel hoop which is 1.5 cm thick. Both the hoops are 5 cm wide. If the temperature drops to 20°C, determine the circumferential stress in each hoop and the radial pressure at common radius. For steel

E = 200GPa α = 12 x 10-6/ °C and for brass E = 100GPa α = 20 x 10-6 /°C ( Fig 5.15).

Answer 1

Brass hoop initial temperature = 180°C

Final temperature = 20°C

Reduction in temperature = 160°C

As the brass hoop cools down, brass will try to contract, exerting pressure on steel hoop, say the radial pressure developed at common radius of 200 mm is p′ as shown. Due to p′, compressive hoop stress in steel hoop will be developed.

At the same time steel hoop exerts outer pressure p′ on brass hoop and tensile hoop stress will be developed in brass hoop. In brass