FieldEngineersKitEngineering Reference & ASME Code Basis
1. Core Formula & Variable Definitions
ASME BPVC Section VIII Division 1 UG-32 · ASME BPVC Section VIII Division 1 Mandatory Appendix 1 · ASME BPVC Section II Part D Table 1A
treq = P · D2 S E − 0.2 P (2:1 ellipsoidal · UG-32(d))
treq = 0.885 P · LS E − 0.1 P (torispherical · L = D · UG-32(e))
treq = P · R2 S E − 0.2 P (hemispherical · R = 0.5 D · UG-32(f))
treq = P · D2 cos(α) (S E − 0.6 P) (conical · α ≤ 30° · UG-32(g))
tnom = treq + C.A.
ASME Section VIII Division 1 Paragraph UG-32 sizes formed heads for internal pressure on the concave side. Symbols use t_req for the pressure-resisting minimum and t_nom = t_req + corrosion allowance for nominal design thickness — distinct from B31.3 pipe t_nom_req (mill under-tolerance). Confirm allowable stress S from the project edition of Section II Part D Table 1A.
- t_req (Minimum required thickness) — Pressure-resisting head thickness from UG-32 before corrosion allowance (mm or in).
- t_nom (Nominal design thickness) — t_nom = t_req + C.A. — ordered plate / formed-head design thickness screen.
- P (Internal design pressure) — Internal design gauge pressure (MPa or psi).
- D (Inside diameter) — Head inside diameter at the skirt / attachment plane (mm or in).
- L (Inside crown radius) — Torispherical crown radius. This calculator uses L = D for standard 6% knuckle F&D screening.
- R (Inside radius) — Hemispherical inside radius R = 0.5 D.
- α (Half-apex angle) — Conical half-apex angle (degrees). UG-32(g) without knuckle limited to α ≤ 30°.
- S (Allowable stress) — Maximum allowable tensile stress from ASME Section II Part D Table 1A at design metal temperature (MPa or psi).
- E (Joint efficiency) — Weld joint efficiency (0.70 / 0.85 / 1.00) per radiography extent.
- C.A. (Corrosion allowance) — Specified corrosion / erosion allowance added to t_req (mm or in).
2. Design Allowances & UG-32 Scope
Default screening duty is Metric 2:1 semi-ellipsoidal, ID 1500 mm, P 1.5 MPa, T 150 °C, SA-516 Gr.70, E = 1.00, C.A. = 3.0 mm. Results size concave-side internal pressure only.
Added after UG-32 pressure thickness: t_nom = t_req + C.A. Typical carbon-steel PV service uses 1.5–3.0 mm.
Radiography category per Section VIII joint type. Full radiography uses E = 1.00; spot radiography often E = 0.85.
Standard ASME flanged-and-dished (≈6% knuckle) screening sets inside crown radius L equal to inside diameter D.
Wind, seismic, and nozzle local loads (UG-22), external pressure / vacuum (UG-28), and forming thinning / mill under-tolerance are not included. Complete a stamped vessel calculation package for fabrication.
Quick Reference Lookup Table
| Inside D (mm) | S (MPa) | t_req (mm) | t_nom (mm) |
|---|---|---|---|
| 1000 | 137.9 | 5.44 | 8.44 |
| 1500 | 137.9 | 8.17 | 11.17 |
| 2000 | 137.9 | 10.89 | 13.89 |
| 2500 | 137.9 | 13.61 | 16.61 |
| 3000 | 137.9 | 16.33 | 19.33 |
At the same P/D/S/E/C.A. duty (ID 1500 mm), engine screens give torispherical t_nom ≈ 17.46 mm, hemispherical ≈ 7.08 mm, and conical (α = 30°) ≈ 12.48 mm — torispherical is thicker than 2:1 SE; hemispherical is thinnest.
3. Material Specifications & Temperature Limits
Allowable stress S is interpolated from ASME Section II Part D Table 1A screening curves bound in this calculator. Confirm the project code edition before stamped design.
| Material Group | Temperature Range | Allowable Stress / Limit | Engineering Notes |
|---|---|---|---|
| SA-516 Gr.70 (Carbon Steel Plate) | −29 °C to 482 °C (−20 °F to 900 °F) screening | 20.0 ksi (137.9 MPa) through ≈400 °F; derates above 500 °F | Primary PV carbon plate. Long-term graphitization risk rises above ≈427 °C — follow project metallurgy limits. |
| SA-240 304L (Austenitic SS) | Cryogenic to ≈816 °C (1500 °F) stress table screen | 16.7 ksi (115 MPa) near ambient; derates with temperature | Low-carbon austenitic plate for corrosive / clean services. |
| SA-240 316L (Austenitic SS) | Cryogenic to ≈816 °C (1500 °F) stress table screen | 16.7 ksi (115 MPa) near ambient; Mo grade for chloride service | Molybdenum addition improves pitting resistance versus 304L. |
| SA-387 Gr.11 Cl.2 (1¼Cr–½Mo) | Up to ≈593 °C (1100 °F) screening | 17.1 ksi (≈118 MPa) through mid-range temperatures | Cr-Mo alloy plate for elevated-temperature hydrocarbon services. |
Code Applicability & Safety Boundaries
- UG-32 formulas apply to internal pressure on the concave side only. External pressure / vacuum requires UG-28.
- Conical heads without a knuckle are limited to half-apex angle α ≤ 30° under UG-32(g) as implemented here.
- P/(S·E) > 0.385 triggers a thin-wall applicability REVIEW flag — confirm Appendix-1 / thick-wall rules for that duty.
4. Step-by-Step Worked Example
Field VerificationShowHide
Step-by-Step Worked Example: 2:1 Semi-Ellipsoidal Head
Size the required and nominal thickness for a 2:1 semi-ellipsoidal pressure vessel head at 1.5 MPa and 150 °C using SA-516 Gr.70 plate with full radiography and 3.0 mm corrosion allowance.
Resolve allowable stress S at design temperature
Apply UG-32(d) for 2:1 ellipsoidal head
Add corrosion allowance for nominal design thickness
Back-calculate MAWP from t_req
5. How to calculate ASME VIII-1 UG-32 head thickness
- 1
Select head geometry
Choose 2:1 ellipsoidal, torispherical (L = D), hemispherical, or conical (α ≤ 30°) to match the vessel drawing.
- 2
Enter D, P, T, material, E, and C.A.
Use inside diameter and internal design pressure. Material sets S(T) from the II-D screening curve; radiography sets E.
- 3
Read t_nom and t_req
Hero value is t_nom (with C.A.). Badge shows t_req without C.A. Review MAWP and UG-32 Pass/Fail status.
- 4
Export and carry related tools
Export JSON/CSV/PDF, then open Pipe Wall Thickness or Tank & Vessel Volume with the same D / P / T duty.
6. Frequently Asked Questions & Technical References
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No. UG-32 sizes formed pressure vessel heads. ASME B31.3 Para. 304.1.2 sizes straight pipe and uses different symbols (including mill under-tolerance t_nom_req). Do not interchange the formulas.
For the same P, D, S, and E, UG-32(e) with L = D applies the 0.885 crown factor and yields a larger t_req than UG-32(d). A hemispherical head (UG-32(f)) is typically the thinnest.
No. This tool covers internal pressure on the concave side only. External pressure and vacuum are governed by UG-28 charts and rules.
Use the project vessel specification. Typical carbon-steel process vessels use 1.5–3.0 mm; stainless often uses 0 mm when corrosion is negligible. The calculator adds C.A. after UG-32: t_nom = t_req + C.A.