Find the radial pressure between the rod and the casing,

Question

A steel rod of diameter 50mm is forced into a bronze casing of outside diameter 90mm, producing a tensile hoop stress of 30 MPa at the outside diameter of the casing. Find:

(i)   the radial pressure between the rod and the casing,

(ii) the shrinkage allowance and

(iii) the rise in temperature which would just eliminate the force fit.

Assume the following material properties:

E_s = 2$\times$10⁵ MPa, m_s = 0.25, a_s =1.2$\times$10^–5/ °C and  E_b = 1$\times$10⁵ MPa, m_b= 0.3,

a_b= 1.9$\times$10^–5/°C.