Question $1$

A compound bar $2\mathrm{.}2$ m long is made up of two pieces of metal; one of low alloy steel

$\{$:$213$GPa,$=14\mathrm{.}9{10}^{-6}\frac{m}{}C)$ and the other of copper $(E=110$GPa,$=16\mathrm{.}4{10}^{-6}\frac{m}{}C).$

The cross$-$sectional area of the steel is $25c{m}^2,$ while that of the copper is $20c{m}^2.$ Both pieces

are $2\mathrm{.}2$ m long and are rigidly connected together at both ends at an ambient temperature of

$25C.$ The bar is restrained against bending.

a$)$ Calculate the stresses in the two materials if the temperature is raised to

$(10$ marks$)$

$150C.$

b$)$ Calculate the stresses in the materials if a tensile load of $10$ kN is applied $(10$ marks$)$

to the bar at the elevated temperature.