$4\mathrm{.}22$ A $30$ mm diameter steel rod passes centrally through a brass tube of external and internal

diameters of $36$ and $32$ mm $,$ respectively. The tube is closed at each end by rigid plates of

negligible thickness as shown in Figure $4\mathrm{.}22.$ The nuts on the rod are tightened until a stress

of $12$ MPa is developed in the rod. Determine the stresses induced in the rod and tube when

the temperature of the assembly is raised to $60C.$ The modulus of elasticity and coefficient

of thermal expansion for steel and brass are:

$E_s=210$GPa,${}_s=11\mathrm{.}5{10}^{-6}$ per $C$

$E_b=80$GPa,${}_b=19{10}^{-6}$per$C$

rigure $4\mathrm{.}22$ Msselility UI sieEl ivu allu viaso tune.