Question

A thin spherical shell of internal diameter d is subjected to an internal pressure p. if σ is the tensile stress for the shell material, then the thickness of the shell (t) is equal to
1. \(\frac{pd}{2\sigma}\)
2. \(\frac{pd}{4\sigma}\)
3. \(\frac{pd}{\sigma}\)
4. \(\frac{4pd}{\sigma}\)

Answer 1

Correct Answer - Option 2 : \(\frac{pd}{4\sigma}\)

Explanation:

Thin spherical shell:

The hoop stress/longitudinal stress of a spherical shell is given by

\({\sigma _L} = {\sigma _H} = \frac{{pd}}{{4t}}=\sigma\)

where p = pressure applied, d = diameter of shell and t = thickness of the shell

After re-arranging the above equation, we get

\(t=\frac{pd}{4\sigma}\)