A review of simple formulae for elastic hoop stresses in cylindrical and spherical pressure vessels: What can be used when

• Consistent derivation of lower and upper bounds for hoop stresses.
• Justifies ranges of application for hoop stress formulae.
• Furnishes the cylindrical analogue of the improved formula for spheres in Roark.
• Provides correct formulae for external pressure, with applicable upper limits.

Classical simple formulae for elastic hoop stresses in cylindrical and spherical pressure vessels continue to be used in structural analysis today because they facilitate design procedures. Traditionally such formulae are only applied to thin-walled pressure vessels under internal pressure. There do exist, however, some variations of these formulae that remain simple yet permit wider use. Here, by reviewing various underlying rationales for simple hoop stress formulae, we make a determination of when and how well different formulae apply. For the formulae that do apply to thicker vessels than usually recognized, we give companion results for external pressure.