In the system shown, the $2014-$T$6$ aluminum rod has a diameter of $0\mathrm{.}5$ in $.$ It is lightly attached to the rigid supports at A and $B$ when $T=70F.$

$($a$)$ If the temperature is decreased to $10$F what is the load applied to the supports at A and $B.($For this part assume that the load $P=0).$ Write the equations and explain your method but you do not need to solve.

$($b$)$ If a load $P=16lb$ is now applied to the central disk write the expressions that would allow you to find the new forces at A and B$.$ Set up the equations such that you have the same number of equations as unknowns and explain your method but do not solve.