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Pressure Vessel Head Design

Calculate head thickness per ASME Section VIII, Division 1

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Disclaimer: This tool is provided for preliminary sizing and educational reference only. Results must be independently verified by a qualified engineer against the code edition, addenda and project specifications that apply to your design. It is not a substitute for a stamped design calculation.

How the pressure vessel head thickness calculation works

This tool calculates the minimum required thickness of formed heads under internal pressure (pressure on the concave side) using the formulas of ASME BPVC Section VIII, Division 1, paragraph UG-32.

The allowable stress is looked up from the material database at the design temperature. Corrosion allowance is added, and SI or US customary units can be used throughout.

Formulas

2:1 ellipsoidal head, UG-32(d)
t = P·D / (2·S·E − 0.2·P)
Torispherical (F&D) head, UG-32(e)
t = 0.885·P·L / (S·E − 0.1·P)
Hemispherical head, UG-32(f)
t = P·L / (2·S·E − 0.2·P)
Design thickness
t_design = t + C
tMinimum required thickness after forming, excluding corrosion allowance
PInternal design pressure
DInside diameter of the head skirt
LInside crown radius of an F&D head, or inside spherical radius (D/2) of a hemispherical head
SMaximum allowable stress at design temperature (Section II Part D)
ELowest efficiency of any joint in the head (UW-12)
CCorrosion allowance

Worked example: 2:1 ellipsoidal head (imperial units)

  1. Design pressure P = 150 psi, inside diameter D = 36 in.
  2. Allowable stress S = 20,000 psi (confirm against your code edition), seamless head E = 1.0, corrosion allowance C = 0.125 in.
  3. t = (150 × 36) / (2 × 20,000 × 1.0 − 0.2 × 150) = 5,400 / 39,970 = 0.135 in.
  4. Minimum thickness after forming = 0.135 + 0.125 = 0.260 in.
  5. For comparison, a standard F&D head with L = 36 in needs t = (0.885 × 150 × 36) / (20,000 × 1.0 − 0.1 × 150) = 0.239 in, while a hemispherical head needs about half the ellipsoidal thickness: (150 × 18) / 39,970 = 0.068 in.

Limitations and design notes

  • The calculated value is the minimum thickness after forming. Order plate thick enough to cover thinning in the knuckle and crown during forming; head manufacturers typically publish their thinning allowance.
  • The F&D formula assumes a knuckle radius of 6% of the crown radius, with L no greater than the outside diameter of the skirt. Heads outside the proportions covered by UG-32 are designed to Mandatory Appendix 1-4.
  • Heads under external pressure (pressure on the convex side) are designed to UG-33 and are not covered here.

References

  • ASME BPVC Section VIII, Division 1: UG-32, UW-12, Appendix 1-4
  • ASME BPVC Section II, Part D: Table 1A