ASME VIII UG-27 & UG-32 Thickness, Explained With a Full Worked Example

1. Two Stress Directions in a Cylinder

Internal pressure pushes the cylinder wall outward in two ways at once. Around the circumference, the pressure tries to split the shell lengthwise — this hoop stress is the larger of the two, and on elementary theory it equals P·R/t. Along the axis, the pressure on the heads pushes the shell apart like a piston — the axial (longitudinal) stress is half the hoop value, P·R/(2t).

Elementary theory, though, is a thin-wall approximation. It assumes stress is uniform through the wall, which is only acceptable when the wall is thin relative to the radius. Real vessels — especially at higher pressures — have a pronounced stress gradient: the inside surface carries more than the average. ASME's answer is not a fudge factor but the exact thick-wall (Lamé) solution, rearranged so that the unknown thickness sits alone in the numerator.

The design allowable stress S comes from ASME Section II Part D at the design temperature, and E is the weld joint efficiency from UW-12 — a quality factor for the seam, not the material. Those two lookups, plus P and R, are the entire input set.

2. UG-27, Line by Line — and the Origin of 0.6P

Take the Lamé hoop-stress equation at the inside surface of a cylinder and solve for thickness. After collecting terms, the result is exactly t = P·R/(S·E − 0.6P). The 0.6 multiplying P is the inside-surface Lamé coefficient — not a safety margin and not a thin-wall correction, but the precise consequence of the stress concentration at the bore. The longitudinal formula gets +0.4P in the denominator from the same derivation, one dimension down.

Two consequences follow. First, the formula stays accurate far beyond thin-wall territory: the code sanctions it up to t = R/2, equivalently P = 0.385·S·E. Second, the denominator shrinking as P rises means thickness grows faster than linearly with pressure — a behavior thin-wall intuition gets wrong, and one reason quick spreadsheet formulas that ignore it under-thicken mid-pressure vessels.

You must check both formulas because the efficiencies can differ. The circumferential formula divides by the efficiency of the longitudinal seam (Category A), the axial formula by the circumferentialseam (Category B). With a fully radiographed longitudinal seam both usually point the same way; with spot RT on one and full RT on the other, run the numbers — thecalculator reports both and names the governing one.

3. UG-32: The Four Head Formulas

Formed heads each get their own closed form in UG-32, reflecting how curvature is distributed:

• →2:1 semi-ellipsoidal (UG-32(d)): t = P·D·K/(2SE − 0.2P). For a 2:1 head the shape factor K = (1/6)[2 + (D/2h)²] equals 1, and the head may equivalently be treated as a hemisphere of radius L = 0.9D. This is the industry default head.
• →Torispherical / flanged-and-dished (UG-32(e)): t = 0.885·P·L·M/(SE − 0.1P), with M = ¼(3 + √(L/r)). The small standard knuckle (r ≈ 6% of L) drives M to about 1.77 — which is why F&D heads run several times thicker than 2:1 ellipsoids for the same duty.
• →Hemispherical (UG-32(f)): t = P·R/(2SE − 0.2P) — the material-optimal shape, half the wall of the cylinder it closes, at the price of depth and forming cost.
• →Conical (UG-32(g)): t = P·D/(2cos α·(SE − 0.6P)) for transition sections; the knuckle region gets its own check.

A useful cross-check falls out of the ellipsoidal formula: with equal E, a 2:1 head thickness lands within a few percent of the shell thickness it closes. If your head comes out wildly different from your shell, check units before checking anything else.

4. Worked Example: 1,200 mm Separator Vessel

A horizontal three-phase separator, carbon steel, non-lethal service:

Shell, circumferential:t = 1.0 × 600 / (138 × 0.85 − 0.6 × 1.0) = 600 / 116.7 = 5.14 mm.Shell, axial:t = 600 / (2 × 117.3 + 0.4) = 600 / 235.0 = 2.55 mm. The longitudinal-seam formula governs, as expected.

Add CA: 5.14 + 2.0 = 7.14 mm, round up the standard plate series to 8 mm nominal. The 2:1 ellipsoidal heads: t = 1.0 × 1200 / (2 × 117.3 − 0.2) = 1200 / 234.4 = 5.12 mm; + CA = 7.12 mm — again an 8 mm head, matching the shell as the cross-check predicted.

MAWP back-calculation on the corroded wall (8 − 2 = 6 mm): P = S·E·t / (R + 0.6t) = 117.3 × 6 / (600 + 3.6) = 1.17 MPa. The corroded vessel at design temperature still carries 17% above design pressure — the margin your relief valve set point and hydrotest pressure (1.3× MAWP for the standard case) will consume by design.

UG-16(b) closes the loop: the 6 mm corroded wall far exceeds the 1.6 mm minimum formed thickness, so the 8 mm plate stands. That entire chain — both seam directions, head, CA rounding, MAWP, min-thickness check — is exactly what thepressure vessel thickness calculatorexecutes in real time, in either unit system, with the II-D stress look-up built in.

5. What These Formulas Do Not Cover

UG-27/UG-32 size the basic geometry of the pressure boundary — nothing more. A complete VIII-1 design still needs nozzle reinforcement (UG-37), external-pressure screening (UG-28) if vacuum or jacket pressure exists, MDMT impact rules (UCS-66), the actual joint design and radiography plan (UW-3/UW-11/UW-12), wind and seismic per UG-22, and — for cyclic service — a fatigue screening. Code-stamped work belongs with an ASME-certified shop and an Authorized Inspector; the formulas here are how you check their work, scope a budget, and write a smarter RFQ.

For pipe-rack and package work, pair this with thepipe weight calculator and thepipe schedule chart; flange weights for the nozzle BOM come from the flange weight calculator.

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