A thin-walled closed cylindrical pressure vessel of internal radius \(r\), wall thickness \(t\), and internal pressure \(p\) has hoop (circumferential) stress \(\sigma_h\) and longitudinal stress \(\sigma_L\). Which relationship is correct?

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Civil Engineering QUESTION #2118

Question 1

\(\sigma_h = \sigma_L = \dfrac{pr}{t}\)
\(\sigma_h = \dfrac{pr}{t}\) and \(\sigma_L = \dfrac{pr}{2t}\)✔️
\(\sigma_h = \dfrac{pr}{2t}\) and \(\sigma_L = \dfrac{pr}{t}\)
\(\sigma_h = \sigma_L = \dfrac{pr}{2t}\)

Correct Answer Explanation

Hoop stress (resists diametral bursting): \(\sigma_h = \dfrac{pr}{t}\). Longitudinal stress (resists end cap force): \(\sigma_L = \dfrac{pr}{2t}\). Therefore hoop stress is exactly twice the longitudinal stress. This is why cylindrical pressure vessels fail by splitting longitudinally (hoop stress governs design), and why pipes are wound with more fibers circumferentially in filament-wound construction.

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