A triple$-$threaded power screw, used in a screw jack, has a nominal diameter of $50$ mm and a pitch of $8$ mm $.$ The threads are square and the length of the nut is $48$ mm $.$ The screw jack is used to lift a load of $7\mathrm{.}5$ kN $.$ The coefficient of friction at the threads is $0\mathrm{.}12$ and the collar friction is negligible. Calculate:

$($i$)$ the principal shear stress in the screw body;

$($ii$)$ the transverse shear stresses in the screw and the nut; and

$($iii$)$ the unit bearing pressure.

State whether the screw is self$-$locking.

$[($i$)4\mathrm{.}39,($ii$)2\mathrm{.}37$ and $1\mathrm{.}99,($iii$)\backslash (2\mathrm{.}16\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )]$