The solid cylindrical rod BC with length $L=24$ in is attached to the rigid lever AB of length $a=15$ in and to the fixed support at $C.$ It is required that when a $P=100lbf$ load is applied at $A,$ point A cannot be displaced by more than $1-$in $($downward$).$ Rod $BC$ is made of aluminum with an allowable stress of $10$ ksi and a modulus of rigidity of $G=3900$ksi. Under these conditions $($A$)$ determine the smallest diameter that can be used, and $($B$)$ determine the maximum stress and the displacement of A using the diameter in part $A.$ Ans. Part $A=1\mathrm{.}09$ in