$2\mathrm{.}58$ Knowing that a $0\mathrm{.}5-mm$ gap exists when the temperature is $24C,$

determine $($a$)$ the temperature at which the normal stress in the alumi$-$

num bar will be equal to $-75$MPa,$(b)$ the corresponding exact

length of the aluminum bar.

Bronze

$A=1500m{m}^2$

$E=105$GPa

Aluminum

$A=1800m{m}^2$

$=21\mathrm{.}6{10}^{-6}C$

$E=73$GPa

$=23\mathrm{.}2{10}^{-6}C$

Fig. P$2\mathrm{.}58$ and P$2\mathrm{.}59$