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/mm². 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/mm². Determine the stress in the meridional direction.

Solution

Thickness, t = 8 mm.

Internal pressure, p = 2 N/mm².

Circumferential stress, f₁ = 40 N/mm².

Radius, r₁ = 800 mm.

Meridional radius, r₂ = 500 mm.

Using the relationship,

f₁  / r₁ +  f₂ / r₂ =  p/ t             

40/ 800   +   f₂ /500  = 2/8

f₂   = ((2 /8 )- (40 /800)) × 500 = 100 N/mm²