-
A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is
-
- 0
- 1
- 1.08
- 2.02
- 0
Correct Option: D
Hoop stress for a thin spherical shell
| σh = | ||
| 2t |
Applying logarithm on both sides, we get
| log(σh) = log |  |  | + log(r) - log(t) | |
| 2 |
Differentiating above equation,
| = 0 + | - | ||||
| σh | r | t |
| Given : | = 0.01 and | = -0.01 | ||
| r | t |
Substituting, we get
| = 0.02 | ||
| σh |
Hence percentage increase will be 2%.
