$($adapted from Hibbeler ${10}^{th}$ ed$.$ probs. $5-84$ & $5-85)$

The shaft shown has an A$36$ steel core, with an Am$1004-$T$61$

magnesium sleeve firmly bonded to it down the entire length. The

allowable stress for the steel is $75$ MPa $,$ and for the magnesium it is $45$

MPa. Find:

a$.$ The maximum allowable torque $(T)$ that can be applied.

b$.$ The angle of twist of the shaft under this applied torque.

Answers: $($a$.)T_{\text{m}\text{a}\text{x}}=4335\mathrm{.}4N^{**}m($steel part controls$)$; $($b$.)2\mathrm{.}578$