Problem $10$

The cylindrical rodAB has a length $L=5ft$ and a $0\mathrm{.}75-$in$.$ diameter;

it is made of a mild steel that is assumed to be elastoplastic

with $E=29{10}^6$ and ${}_y=36$ksi. A force $P$ is applied to the

bar and then removed to give it a permanent set ${}_p.$ Determine

the maximum value of the force $P$ and the maximum amount ${}_m$

by which the bar should be stretched if the desired value of ${}_p$ is

$($a$)0\mathrm{.}1$ in$.,($b$)0\mathrm{.}2$ in$.$