Pressure vessel shell: wall stresses and thickness
Hoop and longitudinal stresses in the cylindrical shell of a vessel or pipe under internal pressure, the required wall thickness and the allowable pressure per GOST 34233.2 with the weld joint efficiency and allowances.
σ_t = p · (D + s − c) / (2 · (s − c))σ_x = p · D² / (4 · (s − c) · (D + s − c))s_R = p · D / (2 · φ · [σ] − p), s ≥ s_R + c[p] = 2 · φ · [σ] · (s − c) / (D + s − c)The GOST 34233.2 formulas for cylindrical shells apply for (s − c) / D ≤ 0.1 (up to 0.3 for pipes below 200 mm). The stresses are membrane stresses in the wall without allowances; the longitudinal stress comes from the pressure on the heads, without bending, weight or support loads. ASME VIII-1 (UG-27) gives practically the same thickness: t = P · R / (S · E − 0.6 · P). Heads, nozzles and supports are checked separately.
Source: GOST 34233.2-2017 (formerly GOST 14249-89) — cylindrical shells; ASME BPVC Section VIII Div. 1, UG-27
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Not below the operating pressure and the relief valve set pressure.
Corrosion allowance (corrosion rate × design life, usually 1–3 mm) plus the mill under-tolerance and forming thinning.
GOST 34233.1 at 20 °C: 09G2S 196 MPa, steel 20 147, St3sp 154, 12Kh18N10T 184; ASME SA-516 Gr. 70 138 MPa. At higher temperatures use the tables of the code.
1.0 for a double-welded full-penetration butt joint with 100 % inspection or a seamless pipe; ASME VIII-1: 1.0 / 0.85 / 0.70 with full, spot and no radiography.
Unit converter for this formulaPressure · Length · Fraction and percent
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- σ_x — Longitudinal stress–
- s_R — Required thickness without allowances–
- s_min — Required thickness with allowances–
- [p] — Allowable pressure at thickness s–
- σ_t / (φ · [σ]) — Stress utilisation–
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Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.