$2\mathrm{.}58$ Knowing that a $0\mathrm{.}02-$in$.$ gap exists when the temperature is $75$@$F,$ determine $(a)$ the temperature at which the normal stress in the

aluminum bar will be equal to $-11$ksi,$(b)$ the corresponding exact length of the aluminum bar.

$E=1010,E=10\mathrm{.}610$

$=12\frac{{10}^{-6}}{}F,=12\mathrm{.}9\frac{{10}^{-6}}{}F$

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

$2\mathrm{.}59$ Determine $($a$)$ the compressive force in the bars shown after a temperature rise of $180$@$F,($b$)$ the corresponding change in length

of the bronze bar.