The figure shows the front view and the cross section view of a brass link which is labeled 1. A steel rod labeled 2 is shown below. The inside length of the brass link is 250 millimeters. The width and the thickness of the brass link are 20 millimeters and 10 millimeters respectively. A 30 millimeters diameter steel rod is shown below. The length of the steel rod is 0.2 millimeters longer than the inside length of the brass link.

Material properties

Brass link

E = 105 GPa
α = 20.9 × 10-6/°C

Steel rod

E = 200 GPa
α = 11.7 × 10-6/°C

A brass link and a steel rod have the dimensions shown at a temperature of 20°C. The steel rod is cooled until it fits freely into the link. The temperature of the entire link-and-rod assembly is then warmed to 40°C.

Determine:
a) the final normal stress in the steel rod
b) the deformation of the steel rod