ASME UG-32 Formed-Head Thickness (Ellipsoidal, Hemispherical, Torispherical)
The ASME Section VIII head thickness, for ellipsoidal, hemispherical, and torispherical heads.
Example
You enter
- Design pressure (psig) 150
- Inside diameter, corroded (in) 48
- Allowable stress at design temp (psi) 17500
- Joint efficiency E (1.00 full RT, 0.85 spot, 0.70 none) 0.85
- Corrosion allowance (in) 0.0625
- Head type ellipsoidal
You get
- Allowable stress x joint efficiency S·E (psi) 14875
- Required thickness 0.242261
- T with allowance (in) 0.304761
- MAWP at the required thickness 150
Checked against published worked examples from: ASME BPVC VIII-1 UG-32 (CASTI Example 8.1 cross-check).
Details, formula, and sources
ScopeASME BPVC Section VIII Div 1 UG-32 internal-pressure heads: a 2:1 ellipsoidal head t = PD/(2SE - 0.2P), a hemispherical head t = PR/(2SE - 0.2P) with R = D/2, and a standard flanged-and-dished (torispherical) head t = 0.885PL/(SE - 0.1P) with crown radius L = D and a 6% knuckle. D is the INSIDE diameter in the corroded condition; the allowance is added after. For a 48-in vessel at 150 psi, 17,500 psi allowable, E 0.85: hemispherical 0.121 in (thinnest, the strongest shape), ellipsoidal 0.242 in, torispherical 0.429 in (thickest) - the cheap dished head trades wall for a shallow profile. Reports the thickness and the MAWP. Non-2:1 (K factor) and non-standard torispherical (M factor) are separate. Coefficients verified vs the CASTI Guidebook and ASME UG-32. A check; the vessel engineer governs.
Formula or table2:1 ellipsoidal: t = P D / (2 S E - 0.2 P). Hemispherical: t = P R / (2 S E - 0.2 P), R = D/2. Standard flanged-and-dished torispherical (L = D, r = 0.06 L): t = 0.885 P L / (S E - 0.1 P). D is the inside diameter; the corrosion allowance is added after.
Source and editionASME BPVC Section VIII Division 1, UG-32, formed-head thickness under internal pressure, by section number; no allowable-stress or joint-efficiency table is reproduced - both are entered.
Free accessThe UG-32 head equations are reproduced across published engineering references; both the equations and the 0.885 standard-F&D coefficient were confirmed against the CASTI Guidebook to ASME Section VIII Div 1 (Eq 8.1 and worked Example 8.1) and a second independent source. The BPVC itself is available through ASME.
What governsEstimate. AHJ and licensed professional govern.
API field namesdesign_pressure_psi, inside_diameter_in, allowable_stress_psi, joint_efficiency, corrosion_allowance_in, head_type, se, t_required_in, t_with_allowance_in, mawp_psi
- Inside diameter, corroded D is the inside diameter in the corroded condition; the allowance is added to the computed thicknessASME BPVC VIII-1 UG-32
- Standard heads 2:1 ellipsoidal (K = 1) and standard F&D torispherical (L = D, r = 0.06 L, M = 1.77); other ratios use the K / M factors of Appendix 1-4ASME BPVC VIII-1 UG-32 / Appendix 1-4
- Coefficients verified all three forms and the 0.885 coefficient confirmed vs CASTI Guidebook Eq 8.1 / Example 8.1 and a second sourceCASTI Guidebook to ASME Section VIII Div 1