$4\mathrm{.}89$ and $4\mathrm{.}90$ For the beam indicated, a couple of moment equal to the full plastic moment $M_p$ is applied and then removed. Using a yield strength of $42$ ksi $,$ determine the residual stress at $($a$)y=1in.,($b$)y=2$ in$.$

$4\mathrm{.}89$ Beam of Prob. $4\mathrm{.}75.$Fig. P$4\mathrm{.}75$