Discussion
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
Answer: D
The hoop stress rises by about 2.02 %.
For a thin spherical shell the stress is the same in every direction in the wall:
\[ \sigma = \frac{pr}{2t} \]
With the pressure unchanged, the stress scales as r/t:
\[ \frac{\sigma_{new}}{\sigma} = \frac{1.01}{0.99} = 1.0202 \]
So the stress increases by 2.02 %. Adding the two 1 % changes gives 2 %, close but not exact; 1 % counts only one of the two changes; and 0 would need the changes to cancel, but a larger radius and a thinner wall both raise the stress.
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