The steel pipe $($E $=200$ GPa, $=0\mathrm{.}3$ and $=10^(-5)1/$oC$)$ has an inner diameter $12$ mm and $3$ mm wall thickness. The pipe was fitted between walls when$=20$ oC If the gas flowing through it changes the temperature of the pipe uniformly from$=1000$C to$=500$C at B$,$ determine:

a$)$ The axial force it exerts on the wall, and

b$)$ Maximum shear and normal stresses in the pipe

Disregard possible buckling of the pipe. Hint: use the principle of superposition.