Q$.3$ A copper rod $36$ mm diameter passes centrally through a steel tube of internal

diameter $40$ mm and external diameter $50$ mm $.$ The composite section is

rigidly fixed together with nuts and washers of negligible thickness. The bar

is then heated through $30C.$ Find the stresses in copper rod and steel tube.

Take $E_{\text{s}\text{t}\text{e}\text{e}\text{l}}=0\mathrm{.}200M\frac{N}{m}{m}^2$;$E_{\text{c}\text{o}\text{p}\text{p}\text{e}\text{r}}=0\mathrm{.}110M\frac{N}{m}{m}^2$

${}_{\text{s}\text{t}\text{e}\text{e}\text{l}}=\frac{0\mathrm{.}000012}{}C$;${}_{\text{c}\text{o}\text{p}\text{p}\text{e}\text{r}}=\frac{0\mathrm{.}000016}{}C$

$[4][$CO$1]$