Pressure vessel shell
The cylindrical shell thickness for internal pressure, with the corrosion allowance, the joint efficiency and the reverse check — what working pressure a plate of the thickness you have will actually carry.
| Quantity | Value | Unit |
|---|---|---|
| Circumferential thickness | 3.64 | mm |
| Longitudinal thickness | 1.81 | mm |
| Governing thickness | 3.64 | mm |
| With corrosion allowance | 6.64 | mm |
| MAWP at supplied thickness | 1.372 | MPa |
| Hoop stress at design pressure | 100.6 | MPa |
ASME VIII Div. 1 UG-27(c)(1): thin-wall cylindrical shell under internal pressure.
t = P·R / (S·E − 0.6P) · ASME VIII Div. 1 UG-27(c)(1).
t = P·R / (2SE + 0.4P) · Half the hoop requirement.
P = S·E·t / (R + 0.6t) · Rearranged for a supplied thickness.
A clear path from inputs to results.
The cylindrical shell is the first calculation on any pressure vessel: how thick the plate has to be for the design pressure, and what pressure the plate you already have will carry. UG-27 governs the circumferential seam; the longitudinal seam needs half.
How to use
- Enter the design pressure and the inside radius.
- Set the allowable stress and joint efficiency for the material and weld.
- Read the required thickness with allowance, then the MAWP of the supplied plate.
The formula
Reference: ASME Boiler and Pressure Vessel Code, Section VIII Division 1, UG-27(c)(1).
Worked example
1 MPa at 1,000 mm inside diameter
- R 500 mm, S 138 MPa, E 1.0, 3 mm allowance.
- 1
t = 1 × 500 / (138 − 0.6) = 3.64 mm. Add 3 mm → 6.64 mm. An 8 mm plate gives MAWP = 138 × 5/(500 + 3) = 1.37 MPa.
6.6 mm required; 8 mm carries 1.37 MPa.
Interpreting the result
Hoop stress is twice the longitudinal stress, so the circumferential seam always governs a cylinder. That is why a longitudinal crack in a pressured cylinder runs along its length.
Assumptions & limitations
- Thin-wall cylinder (t < R/2).
- Internal pressure only; external pressure is a different check.
- Allowable stress already includes the temperature derating.
- Heads, openings and nozzle reinforcement are separate calculations.
Frequently asked questions
Why does joint efficiency matter so much?
It is the derating for the weld quality: E = 0.7 nearly halves the capacity of the same plate compared with a fully radiographed seam.
Can I use this for a pipe?
Yes, with the pipe code: ASME B31.3 uses the same form with the coefficient 0.6 for the longitudinal joint.
Where does the 0.6 come from?
It accounts for the triaxial stress state at the inner surface; without it the thin-wall formula overestimates the allowable pressure.
What about corrosion?
It is added to the calculated thickness, not multiplied into it — which is why the MAWP check uses the thickness after allowance.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.