A $30-$inch$-$long rod having a $4-$inch diameter is mounted to a floor, as shown in the elevation

view shown below. The rod is made of a $12-$inch$-$long composite section $($Section AB $)$

consisting of a $2-$inch$-$diameter copper core rigidly bonded to an outer aluminum shell, as well

as a $18-$inch$-$long all steel section $($Section BC$)$ that is $4$ inches in diameter. The entire $30-$inch

rod is subjected to a temperature increase of $75F(30PTS)$ :

a$)$ Calculate the magnitude of the force developed in the composite section $($Section AB $)$ due

to the temperature increase. $[10$ PTS$]$

b$)$ Calculate the normal stress that develops in the copper core at point $x$ due to the

temperature increase and state whether it is tensile or compressive. $[5+2=7$ PTS$]$

c$)$ Calculate the magnitude and direction of the movement $($deflection$)$ of free end $A$ of the

rod due to the temperature change. Show the direction using an arrow. $8+2=10PTS$

d$)$ Calculate the normal stress that develops in the steel rod at point $Y$ due to the temperature

increase. $[3$ PTS$]$

Notes:

The copper core and aluminum shell in section AB are rigidly bonded to each other

and therefore must move together.

Material properties

$E_{al}=10\mathrm{.}1{10}^6,{}_{al}=13\mathrm{.}1\frac{{10}^{-6}}{}F,$

$E_{\text{c}\text{o}\text{p}}=17\mathrm{.}0{10}^6,{}_{\text{c}\text{o}\text{p}}=9\mathrm{.}4\frac{{10}^{-6}}{}F,$

$E_{st}=30{10}^6,{}_{st}=6\mathrm{.}5\frac{{10}^{-6}}{}F$