A spherical container made of steel has 20 ft outer diameter and wal thickness of 1/2 inch. Knowing the internal pressure is 50 psi, estimate the maximum normal stress and the maximum shearing stress in the container

maximum normal stress = 5975 psi

maximum shear stress = 2987.50 psi

Explanation:

Given data

dia = 20 ft

wall thickness = 1/2 inch

internal pressure = 50 psi

To find out

the maximum normal stress and the maximum shearing stress

Solution

By the Mohr's circle we will find out shear stress

first we calculate inner radius

i. e. r = (diameter/2) - t

r = (20 * 12 in) / 2 - (1/2)

r = 120 - 0.5 = 119.5 inch

Now we find out maximum normal stress by given formula

normal stress = (internal pressure * r) / 2 t

normal stress = (50*119.5) / 2 * 0.5

maximum normal stress = 5975 psi

and minimum normal stress is 0, due to very small radius

and maximum shear stress will be

shear stress = (maximum normal stress - minimum normal stress) / 2

shear stress = (5975 - 0) / 2

maximum shear stress = 2987.50 psi