Discussion
A thin cylindrical pressure vessel with closed ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is:
Answer: D
The ratio of hoop stress to longitudinal stress is 2 : 1.
\[ \begin{aligned} \sigma_{h} &= \frac{pd}{2t}, \quad \sigma_{l} = \frac{pd}{4t} \\ \frac{\sigma_{h}}{\sigma_{l}} &= 2 \end{aligned} \]
The hoop stress resists the pressure across a length of the cylinder, while the longitudinal stress resists it only over the circular end, which halves the ratio of force to wall area. 1:1 would hold only for a sphere, where both stresses equal \(\frac{pd}{4t}\).
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