Pressure vessel

Required wall thickness and MAWP of the shell and the heads under internal pressure, nozzle reinforcement by the area-replacement rule, vacuum and external pressure, and the hydrostatic or pneumatic test pressure — with every formula and substitution shown.

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INPUT

1 · Design conditions

Design pressure [MPa] internal, at the top Design temperature [°C] for the record

Liquid head [m] added to every part Specific gravity

2 · Material allowable stress S

S at design temperature [MPa] Section II-D, your edition S at test temperature [MPa] for the test pressure

Corrosion allowance [mm] Plate undertolerance [mm] UG-16(c)

3 · Shell cylinder

Diameter [mm] Measured on the

Length tangent to tangent [mm]

Nominal thickness [mm] E, longitudinal seam carries the hoop stress

E, circumferential seams 1.00 full RT · 0.85 spot RT · 0.70 none (type 1 butt joints)

4 · Heads both ends

Type Joint efficiency 1.00 for a seamless head

D/2h 1.0 to 3.0

Crown radius L [mm] inside Knuckle radius r [mm] inside

Nominal thickness [mm] Minimum after forming [mm] thinning in the knuckle

5 · Nozzles Pro+ · UG-37

Set-in nozzles normal to the wall. A pipe wall is taken 12.5 percent thinner (mill undertolerance) when the box is ticked.

6 · External pressure Pro+ · Code Case 2286

External pressure [MPa] full vacuum 0.101 MPa · 14.7 psi; 0 = none Unsupported length [mm] 0 = T–T + ⅓ of each head

Yield strength at design temp. [MPa] Elastic modulus at design temp. [GPa]

7 · Test

Test Basis

Example values, not a real vessel. The allowable stress is yours to enter from the code edition you build to; the page does not reproduce the Section II-D tables.

MAWP · VESSEL1.007 MPa

HYDROTEST1.31 MPa

VESSEL · ELEVATION

HEADS · SAME DIAMETER, SAME PRESSUREt incl. CA · inside depth · click to use

NOZZLE · AREA REPLACEMENT · UG-37

No plate undertolerance entered. UG-16(c) lets you ignore up to 0.01 in (0.3 mm) or 6 percent of the ordered thickness, whichever is smaller; anything more must be deducted.

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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References: ASME BPVC Section VIII, Division 1 — UG-27, UG-32, Appendices 1-1 and 1-4, UG-37, UG-45, UG-99, UG-100; Division 2, 4.4 (Code Case 2286) for external pressure; Moss & Basic, Pressure Vessel Design Manual (4th ed., 2013); DIN 28011 and DIN 28013 head proportions. Checked against published COMPRESS and Advanced Pressure Vessel reports.

ASSUMPTIONS & LIMITS

ASME Section VIII, Division 1, internal pressure, in the corroded condition, on the inside or the outside dimensions as chosen. Heads and shell share the inside (or the outside) diameter.
The allowable stress S is yours, from Section II, Part D for your material, temperature and code edition.
Both heads are the same; the cylinder is one course. Cones, flat heads and jackets are not covered.
Klöpper and Korbbogen heads use the standard crown and knuckle radii of DIN 28011 and DIN 28013 and are designed as torispherical heads by Appendix 1-4(d).
Ellipsoidal and torispherical heads of a material with a tensile strength over 80 ksi (552 MPa) are designed with S = 20 ksi (138 MPa) at ambient temperature, reduced in proportion at the design temperature (Appendix 1-4(b)).
Nozzles are normal to the wall, set in, with F = 1, one at a time (no overlapping reinforcement).
External pressure (when entered) by Code Case 2286, the rules of VIII-2 4.4, for carbon and low-alloy steel. Wind, seismic, support and piping loads are not part of this check.

DISCLAIMER · For education and preliminary sizing only. Results must be reviewed by a qualified engineer before use in design.

BEYOND THE FORMULAS

Nozzle loads from piping, saddles and lugs, thermal transients and fatigue — we analyse the vessel by FEA, design by analysis to Division 2 Part 5 or EN 13445-3.

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