Q $1.$

$($a$)$ Determine the required outside diameter for a hollow shaft if inside diameter is $50$ mm ;

to carry a torque of $1000N-m$ with a maximum torsional shear stress of $50$ MPa $.(6)$

Hint: Outside diameter must be computed using the trial and error method. You need to

balance both sides of the equation by taking trial values. You can start it with $Do=$

$55$ mm $.$

$($b$)$ Compute shear stress at inside diameter and draw stress distribution diagram

$($c$)$ If this hollow shaft is replaced by solid shaft $($same stress$/$torque$/$length$),$ compute the

diameter of the solid shaft.

$($d$)$ The permissible angle of twist is $0\mathrm{.}00064ra\frac{d}{m}$ for the solid shaft. Is this shaft safe?

Assume the shear modulus for steel as $80$ GPa $.$ If unsafe then redesign.

$(6)$