$3\mathrm{.}139$ A $5-$kip$-$ft torque is applied to a hollow aluminum shaft having the cross section shown. Neglecting the effect of stress concentrations, determine the shearing stress at points a and $b.$

Answer

$($a$)5\mathrm{.}82$ ksi $.($b$)2\mathrm{.}91$ ksi $.$

$3\mathrm{.}138$ An $8-$ft$-$long steel member with a $W831$ 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. $3\mathrm{.}137.)$

Answer $($a$)4\mathrm{.}55$ ksi $.($b$)2\mathrm{.}98$ ksi. $($c$)\frac{5\mathrm{.}08}{2\mathrm{.}56}.$

Appendix E

Appendix E Properties of Rolled$-$Steel Shapes

$($U$.$S$.$ Customary Units$)$

W Shapes

$($Wide$-$Flange Shapes$)$

$\backslash$table$[[$Designation ${?}^{},$Area

$A,i{n}^2,$Depth d$,$ in$.,$Flange,$\backslash$table$[[$Web$],[$Thick$-],[$ness$],[t_w,$ in$.]],$Axis $x-x,$Axis $Y-Y$