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Pressure · guide

ASME VIII-1 shell thickness (UG-27)

Sizing a cylindrical shell for internal pressure is the most common pressure-vessel calculation there is. ASME Section VIII Division 1, paragraph UG-27, gives the formulas. Here is what each term means and which case governs.

Circumferential stress (longitudinal joints)

Internal pressure puts the cylinder wall into a hoop stress that the longitudinal welds must carry. The required thickness for the circumferential-stress case is:

t = P·R / ( S·E − 0.6·P )

with P the internal design pressure, R the inside radius (in the corroded condition), S the allowable stress at design temperature, and E the joint efficiency. The 0.6P term is the thick-wall correction that keeps the formula valid as thickness grows.

Longitudinal stress (circumferential joints)

The axial stress is half the hoop stress, so the circumferential-joint case needs less thickness:

t = P·R / ( 2·S·E + 0.4·P )
Both formulas apply when t < R/2 (or P ≤ 0.385·S·E). Thicker walls fall outside their range and require the Appendix 1 thick-wall equations instead.

From thickness to MAWP

For an existing vessel you usually want the reverse: the maximum allowable working pressure for the thickness you actually have. Invert the circumferential formula:

P = S·E·t / ( R + 0.6·t )

Evaluate it on the corroded thickness and add the static head where the liquid contributes, then take the lowest MAWP across all components as the vessel's rating.

Open the calculatorPressure-vessel shell calculator →Compute required shell thickness and MAWP for both stress cases, with allowable stress, joint efficiency and corrosion allowance handled.

What the formula does not include

UG-27 covers the shell under pressure only. A real design must add the corrosion allowance, check heads, nozzles and reinforcement, account for external pressure and other loads (wind, weight, nozzle loads), and confirm the allowable stress at the actual metal temperature. Treat the shell thickness as the starting point, not the finished vessel.

Frequently asked

Which governs — circumferential or longitudinal stress?
For a cylinder under internal pressure the circumferential (hoop) stress is twice the longitudinal stress, so the circumferential-stress formula normally governs and gives the larger required thickness. You still check both, because joint efficiency can differ between the longitudinal and circumferential seams.
What is joint efficiency E?
E accounts for the reliability of welded joints and the extent of radiographic examination. Fully radiographed double-welded butt joints approach E = 1.0; lesser examination or joint types reduce E, which increases the required thickness.
What is MAWP?
The Maximum Allowable Working Pressure is the highest pressure the weakest component can sustain at the design temperature in its operating position, given the actual (corroded) thickness. It is found by inverting the thickness formula for pressure.

References

  1. ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, paragraph UG-27 ("Thickness of Shells under Internal Pressure").
  2. ASME Section II, Part D — allowable stresses.
  3. E.O. Bergman, "The Design of Vertical Pressure Vessels," ASME.
  4. D.R. Moss, M. Basic, "Pressure Vessel Design Manual," Elsevier.

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