$8\mathrm{.}11$ A rectangular beam made of ABS plastic is $b=20mm$ deep and $t=10mm$ thick. As shown in Fig. $8\mathrm{.}13($a$),$ a bending moment $M$ is applied, and a through$-$thickness edge crack may be present. For a safety factor against brittle fracture of $2\mathrm{.}5$ in stress, what is the largest crack length a that can be allowed if $($a$)M=10N*m,$ and $($b$)M=3\mathrm{.}0N*m?$ Finally, $($c$)$ what are the safety factors against fully plastic yielding for case $($a$)$ and for case $($b$)?$