Determine the stress in the meridional direction:
A doubly curved shell of thickness 8 mm is filled through a liquid under an internal pressure of 2.0 N/mm^{2}. At a specific point on the shell having radii of curvature 800 mm and 500 mm, the stress along with the circumferential direction is found to be 40 N/mm^{2}. Determine the stress in the meridional direction.
Solution
Thickness, t = 8 mm.
Internal pressure, p = 2 N/mm^{2}.
Circumferential stress, f_{1} = 40 N/mm^{2}.
Radius, r_{1} = 800 mm.
Meridional radius, r_{2 }= 500 mm.
Using the relationship,
f_{1 } / r_{1} + f_{2} / r_{2} = p/ t
40/ 800 + f_{2} /500 = 2/8
f_{2} = ((2 /8 )- (40 /800)) × 500 = 100 N/mm^{2}