Q$2$ In Fig. P$3\mathrm{.}15,$ rigid bar ABC is supported by axial member $(1),$ which has a cross$-$sectional area of $400m{m}^2,$ an elastic modulus of $E=70$GPa, and a coefficient of thermal expansion of $=22\mathrm{.}5\frac{{10}^{-6}}{}C.$ After load $P$ is applied to the rigid bar and the temperature rises $40C,$ a strain gage affixed to member $(1)$ measures a strain increase of $2,150.$ Determine:

$($a$)$ the normal stress in member $(1).$

$($b$)$ the magnitude of applied load $P.$

$($c$)$ the deflection of the rigid bar at $C.$

Fig. P$3\mathrm{.}15$