a$)$ Find out the maximum safe load and maximum efficiency among the following riveted joints having thickness of $10$ mm plates with $20$ mm diameter of the rivets having a pitch of $60$ mm:

$($i$)$ Single riveted lap joint

$($ii$)$ Double riveted, single cover butt joint.

$($iii$)$ Double riveted, double cover butt joint.

$($iv$)$ Triple riveted, double cover butt joint

Assume

Permissible tensile stress in plate $120$ MPa

Permissible shear stress in rivets $=90$ MPa

Permissible crushing stress in rivets $=180$ MPa