Problem$-3$: A cylindrical pressure vessel with $1$ m inner diameter is subjected to internal steam pressure of $1\mathrm{.}0$ MPa $.$ The permissible stresses for the cylinder plate and the rivets in tension, shear and compression are $80,60$ and $120\frac{N}{m}{m}^2$ respectively. The efficiency of longitudinal joint can be taken as $75\%$ for the purpose of calculating the plate thickness. The efficiency of circumferential lap joint should be at least $62\%.$ Design the circumferential lap joint and calculate:

i$.$ Thickness of the plate;

ii$.$ Diameter of the rivets;

iii. Number of rivets;

iv$.$ Pitch of rivets;

v$.$ Number of rows of rivets; and

vi$.$ Overlap of the plates.

Make a neat sketch of the joint showing all calculated values of dimensions.