Question $5$: A stepped shaft is subjected to three torques acting as shown below. Part of the shaft $($BC$)$ is hollow and the entire shaft is made of steet with G $=80$ GPa and a yield stress of $150$ MPa Dimensions fothameter and iength$)$ gond magnitude of the torques are given in the diagran:

$[12$ marks$]($a$)$ determine the maximum shear stress in the stepped shaft and sketch the corresponding variation of shear stress along the shaft radius at this point.

$[8$ marks$]($b$)$ find the angle of twist at the free end of the shaft and give your answer in degrees.

$[2$ marks$]($c$)$ A shoulder fillet is used at the steps in the shaf $($points B and C$)$ to reduce the stress concentration factor $K$ to a value of $1\mathrm{.}4$ Is this sufficient to avond failure in the shaft?

$($ provide the answer with detailed steps and these are previous years past papers$)$