Engineering guide
UG-27 is the basic equation of ASME BPVC Section VIII Division 1 for pressure-retaining shells: the paragraph delivers the required wall thickness of cylindrical and spherical shells under internal pressure — and, conversely, the maximum allowable working pressure (MAWP) for an existing wall thickness. This module calculates both directions and adds the alternative formulas of Mandatory Appendix 1, which apply to thick-walled shells beyond the validity limits of UG-27.
For the cylindrical shell, the circumferential (hoop) stress (longitudinal joint) is verified with t = P·R/(S·E − 0.6·P) and the longitudinal stress (circumferential joint) with its own equation; for spherical shells, t = P·R/(2·S·E − 0.2·P) applies. Inputs are the inside radius, the design pressure, the allowable stress S of the material at design temperature and the joint efficiency E from the examination scope per UW-11/UW-12. In addition, the module reports the required wall thickness at 100 % utilization — the reference value tr needed by the opening reinforcement calculation per UG-37.
Calculating the wall thickness of a cylindrical shell to ASME is the starting point of practically every vessel design to VIII-1: from the preliminary sizing at the proposal stage, through the component verification, to the MAWP determination for the nameplate and the test pressure.
Scope
- Thickness of cylindrical shells under internal pressure
- Thickness of spherical shells under internal pressure
Typical workflow
Define the design data
Inputs are the design pressure, the inside radius (in the corroded condition, i.e. plus corrosion loss), the material with its allowable stress S at design temperature and the joint efficiency E, which follows from the joint type and the radiographic examination scope per UW-11/UW-12.
Calculate the required wall thickness
For the cylindrical shell, the wall thickness is determined from the circumferential stress equation t = P·R/(S·E − 0.6·P); in addition, the longitudinal stress equation is checked, which becomes governing only with additional axial loads or a small circumferential joint efficiency. For spherical shells, t = P·R/(2·S·E − 0.2·P) applies.
Check the validity limits
The UG-27 formulas apply for t ≤ 0.5·R and P ≤ 0.385·S·E (cylinder). For thick-walled shells or higher pressures, the module switches to the equations of Mandatory Appendix 1, which are based on the thick-wall solution.
Allowances and as-built thickness
The corrosion allowance and, where applicable, the undertolerance of plate or pipe are added to the calculated thickness; this yields the ordering or as-built thickness. The minimum thickness per UG-16 (1.6 mm) must be observed.
Report the allowable pressure and tr
Conversely, the module calculates the MAWP of the shell from the existing wall thickness (minus allowances). Additionally, the required wall thickness at 100 % utilization (E = 1.0) is output — the value tr that the opening reinforcement per UG-37 uses as its reference.
Frequently asked questions
Why does the term 0.6·P appear in the denominator of the cylinder formula?
The boiler formula t = P·R/(S·E) strictly applies only to the membrane surface of thin-walled shells. The term −0.6·P corrects the equation so that it approximately captures the higher stress at the inner fiber of thicker walls — it thereby remains usable up to t = 0.5·R and P = 0.385·S·E. For the sphere, the correction term is −0.2·P, since the sphere carries only half the hoop stress.
Which radius is used in the calculation — new or corroded?
Always the corroded condition: the inside radius grows by the corrosion allowance, and the load-bearing wall thickness is the as-built thickness minus the allowance. Calculating with as-new dimensions overestimates the MAWP over the service life. Also when re-rating existing vessels, the measured actual condition (remaining wall thickness, expanded radius) must be used.
What does the joint efficiency E mean and what does it depend on?
E rates the longitudinal joint of the shell according to the non-destructive examination scope per UW-11/UW-12: E = 1.0 for full radiography, 0.85 for spot radiography (spot RT), 0.70 without radiography. For the circumferential stress equation the longitudinal joint counts; for the longitudinal stress equation the circumferential joint. A lower examination scope is thus directly paid for with more wall thickness — an economic trade-off between examination cost and material use.
Why does UG-37 need the wall thickness at 100 % utilization?
The opening reinforcement per UG-37 compares available excess thicknesses with the required thickness tr, which by definition is calculated with E = 1.0 — the weld quality is captured there by its own rules. That is why the module outputs, alongside the actual required thickness, also tr at full utilization; confusing the two values is a typical error source in nozzle verifications.
Worked example
For a cylindrical shell per ASME VIII-1 UG-27, the required wall thickness and the MAWP of the selected design are to be determined.
Given
| Design pressure P | 1.6 MPa (16 bar) |
|---|---|
| Inside radius R (corroded) | 500 mm |
| Material SA-516 Gr. 70, allowable stress S | 138 MPa |
| Joint efficiency E (full radiography) | 1.0 |
| Corrosion allowance c | 1.0 mm |
Solution
Applicability of the UG-27 equation
P = 1.6 MPa ≤ 0.385·S·E = 0.385 · 138 · 1.0 = 53.1 MPa — thin-wall equation permissible.
Required wall thickness (circumferential stress)
t = P·R / (S·E − 0.6·P) = 1.6 · 500 / (138 · 1.0 − 0.6 · 1.6)
t = 800 / 137.04 = 5.84 mm
With corrosion allowance: t + c = 5.84 + 1.0 = 6.84 mm → selected 8.0 mm plate.
MAWP of the selected design
Load-bearing wall thickness: teff = 8.0 − 1.0 = 7.0 mm
MAWP = S·E·teff / (R + 0.6·teff) = 138 · 1.0 · 7.0 / (500 + 0.6 · 7.0)
MAWP = 966 / 504.2 = 1.92 MPa (19.2 bar)
Result
| Required wall thickness (without allowance) | 5.84 mm |
|---|---|
| Selected plate thickness | 8.0 mm |
| MAWP (corroded) | 1.92 MPa ≈ 19.2 bar |
Technical content source: LV-Solved-Problems-Content 628d313247e7