$2\mathrm{.}7-7$ The truss ABC shown in the figure supports a hor$-$

izontal load $P_1=300lb$ and a vertical load $P_2=900lb.$

Both bars have a cross$-$sectional area $A=2\mathrm{.}4$ in ${?}^2$ and

are made of steel with $E=30{10}^6.$

$($a$)$ Determine the strain energy $U_1$ of the truss when

the load $P_1$ acts alone $(P_2=0).$

$($b$)$ Determine the strain energy $U_2$ when the load $P_2$

acts alone $(P_1=0)$

$($c$)$ Determine the strain energy $U_3$ when both loads

act simultaneously.