$3\mathrm{.}138$ An $8-$ft$-$long steel member with a W$831$ cross section is subjected to a $5-$kip$-$in$.$ torque. The properties of the rolled$-$steel section are given in Appendix E$.$ Knowing that $G=11\mathrm{.}2{10}^6,$ determine $(a)$ the maximum shearing stress along line $a-a,($b$)$ the maximum shearing stress along line $b-b,(c)$ the angle of twist. $($See hint of Prob. $3\mathrm{.}137.)$

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