ASME VIII-1 pressure vessel

Shells

Division 1 sizes a cylindrical shell twice and makes you take the thicker answer. Hoop stress governs the longitudinal seam, UG-27(c)(1):

t = P·R / (S·E − 0.6·P)

Longitudinal stress governs the circumferential seam, UG-27(c)(2):

t = P·R / (2·S·E + 0.4·P)

The hoop equation almost always wins — roughly a factor of two — which is why a vessel that fails from over-pressure splits along its length rather than parting at a girth weld. The second equation still matters when the circumferential seam has a lower joint efficiency than the longitudinal one, which happens more often than people expect.

Heads

Three head forms, three clauses:

• 2:1 ellipsoidal, UG-32(d): t = P·D / (2SE − 0.2P)
• Hemispherical, UG-32(f): t = P·R / (2SE − 0.2P)
• Torispherical with L = D and r = 0.06D, UG-32(e): t = 0.885·P·L / (SE − 0.1P)

A hemispherical head needs about half the wall of the shell it closes. It is also the most expensive thing on the drawing to form, and it eats length. The 2:1 ellipsoidal head is the usual compromise and is what this tool defaults to.

MAWP

Run the shell equation backwards on the corroded wall and you get the maximum allowable working pressure:

P = S·E·t / (R + 0.6·t)

The vessel's MAWP is the lowest MAWP of any of its pressure parts, so the tool reports which one governs. In practice a nozzle reinforcement or a flange rating usually governs before the shell does — this calculator does not evaluate those, and a real MAWP stamp has to.

A note on the RPV steels

SA-533 Gr. B Cl. 1 (plate) and SA-508 Gr. 3 Cl. 1 (forging) are the Mn-Mo-Ni low-alloy steels reactor pressure vessels are actually made from, so they are in the list. Both are quoted here with their Division 1 allowable — the lesser of UTS/3.5 and two-thirds of yield, which lands near 157 MPa at ambient for the specified minimum properties.

In real service these are almost always Section III materials, and Section III does not work this way. It designs against a design stress intensity S_m, with separate limits on primary membrane, primary bending and secondary stress, and it requires fracture toughness qualification against RT_NDT and irradiation shift that no thickness equation captures. Treat a Division 1 number on these materials as a sizing sketch, never as a Section III result.

Where this stops being valid

UG-27 is a thin-wall formulation. It applies while t ≤ 0.5R and P ≤ 0.385·S·E. Past either limit the stress distribution through the wall is no longer close enough to linear and you move to the thick-wall treatment in Appendix 1-2. The tool refuses to give you a comfortable answer outside that range, on purpose.