ASME Required Wall Thickness (t = PR/(SE − 0.6P))

This is the equation a pressure vessel is actually built to. ASME Section VIII Division 1, paragraph UG-27(c)(1), gives the required thickness of a cylindrical shell for circumferential stress as $t = \frac{PR}{SE - 0.6P}$, with $R$ the inside radius in the corroded condition, $S$ the maximum allowable stress from the Section II Part D table for that material at that temperature, and $E$ the joint efficiency from UW-12. A vessel at 300 psi with a 24 in inside radius in a material good for 17 500 psi, fully radiographed so $E = 1.0$, needs $7200/17\,320 = 0.416$ in.

Two features distinguish it from the textbook $pr/t$. The $E$ is a penalty for not knowing whether the weld is sound: 1.0 for a fully radiographed double-butt joint, 0.85 for spot examination, 0.70 for none. It is a tabulated choice, not a dial — if the arithmetic asks for 0.91 you buy 1.0 and pay for the radiography. And the $0.6P$ in the denominator is a thick-wall correction, which effectively evaluates the stress a little way in from the bore rather than at the mean radius. It is what lets a formula derived for thin shells stay honest up to $t = 0.5R$, equivalently $P \le 0.385SE$. Past that limit the paragraph does not apply and Appendix 1-2 or the Lamé solution takes over.

The number that comes out is the pressure-design thickness and nothing else. Corrosion allowance is added on top, mill under-tolerance on top of that, and then it is rounded up to a plate thickness that is actually rolled. External pressure, wind and seismic, the weight of the contents, nozzle reinforcement and any local loads are separate calculations that can each govern instead. The formula is imperial-native in practice rather than in algebra — every term is dimensionally consistent, so it works unchanged in MPa and millimetres, but the allowable stresses that feed it are published in ksi and the trade thinks in inches.