Discussion
A thin cylinder (thickness, t and diameter, d) with closed ends is subjected to an internal pressure, p. The ratio of hoop stress to longitudinal stress developed in the wall of the cylinder is
Answer: D
The ratio is 2:1.
For a thin cylinder with closed ends, a force balance on a longitudinal section gives the hoop stress, and one on a transverse section gives the longitudinal stress:
\[ \begin{aligned} \sigma_{h} &= \frac{pd}{2t} \\ \sigma_{l} &= \frac{pd}{4t} \end{aligned} \]
so \(\sigma_{h}/\sigma_{l} = 2\). The hoop stress is the larger, which is why thin pipes split along their length. 1:2 inverts the ratio, and 1:1 would hold only for a thin sphere, where the stress is \(pd/4t\) in every direction.
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