The solid $0\mathrm{.}75-in.-$diameter rod is subjected to a uniform axial distributed loading along its length of $w=625l\frac{b}{f}t.$ Two concentrated loads also act on the rod: $P=2000lb$ and $Q=1100lb.$ Assume $a=19in.$ and $b=38in.$ Determine the normal stress in the rod at the following locations:

$($a$)x=12$ in$.$

$($b$)x=36$ in$.$

Part $1$

Cut a cross$-$section at $x=12$ in$.$ and draw a free body diagram. Solve for the internal normal force.

Answer:

$F=$

lb