$4\mathrm{.}67$ The prismatic bar shown is made of a steel that is assumed to be

elastoplastic with ${}_Y=300$MPa and is subjected to a couple $M$ paral$-$

lel to the $x$ axis. Determine the moment $M$ of the couple for which

$($a$)$ yield first occurs, $($b$)$ the elastic core of the bar is $4$ mm thick.

Fig. P$4\mathrm{.}67$

$4\mathrm{.}68$ Solve Prob. $4\mathrm{.}67,$ assuming that the couple $M$ is parallel to the $z$ axis.

Can you so $4\mathrm{.}68$ please! Answer is a$)57\mathrm{.}6$ b$)83\mathrm{.}2$