Pressure Vessel Wall Thickness Calculator

Pressure Vessel Wall Thickness Calculator

This worksheet calculates the minimum required wall thickness for a cylindrical pressure vessel under internal pressure, in accordance with ASME Boiler and Pressure Vessel Code (BPVC) Section VIII, Division 1 — the most widely used standard for unfired pressure vessels in the process and power industries.

The fundamental design equation balances the hoop (circumferential) stress induced by internal pressure against the allowable stress of the vessel material, incorporating a joint efficiency factor to account for weld quality and a corrosion allowance for service life.

Two geometries are addressed: the cylindrical shell (governing in the vast majority of vessels) and the hemispherical head, which requires only half the shell thickness for the same pressure and material. The longitudinal (axial) stress in the cylinder is also checked — it is always half the hoop stress, so hoop stress governs.

An engineer uses this calculation when specifying wall thickness for storage tanks, heat exchangers, reactors, autoclaves, and any other pressurised equipment, to ensure the vessel does not yield or burst under the design (maximum allowable working) pressure.

Inputs

The inputs below cover the vessel geometry, design pressure, material properties, and fabrication parameters. Typical values are shown; adjust them to match your specific application.

• Design pressure P — the maximum allowable working pressure (MAWP), often 10% above normal operating pressure.
• Inside radius R — measured from the vessel centreline to the inner surface of the shell.
• Allowable stress S — from ASME BPVC Section II Part D tables at design temperature; typically one-quarter of tensile strength or two-thirds of yield strength, whichever governs.
• Joint efficiency E_j — weld quality factor: 1.0 for full radiographic examination, 0.85 for spot examination, 0.70 for no examination.
• Corrosion allowance CA — added to the calculated minimum thickness to account for metal loss over service life.

Calculations

Step 1 — Hoop (Circumferential) Stress Governs the Cylinder

For a thin-walled cylindrical vessel, two principal membrane stresses arise from internal pressure:

1. Hoop stress (circumferential): σ_h = P·R / t — acts to split the vessel along its length.
2. Longitudinal stress (axial): σ_L = P·R / (2t) — acts to push the end caps off.

Since hoop stress is exactly twice the longitudinal stress, the hoop condition always governs the required thickness. ASME BPVC Sec VIII Div 1 (Eq. UG-27(c)(1)) gives the minimum required thickness of the cylindrical shell as:

t_min = P·R / (S·E_j − 0.6·P)

where the term −0.6P in the denominator is a correction for thick-wall behaviour (it becomes significant when t/R > 0.1). The resulting thickness is the pressure-only minimum — the corrosion allowance is added separately in Step 3.

The ratio t/R is a useful check for the thin-wall assumption (valid when t/R < 0.1). We compute it from the pressure-only thickness to confirm the formula is appropriate.

Step 2 — Hemispherical Head Thickness

A hemispherical head carries only membrane (biaxial) stress — both principal stresses are equal and equal to half the hoop stress of the equivalent cylinder. The ASME formula (UG-32(f)) for a hemispherical head is:

t_head = P·R / (2·S·E_j − 0.2·P)

This means a hemispherical head requires approximately half the thickness of the cylindrical shell for the same conditions, making it structurally the most efficient head geometry (though it is more expensive to fabricate than ellipsoidal or torispherical heads).

Step 3 — Add Corrosion Allowance

The ASME code requires that the nominal (ordered) wall thickness be at least equal to the pressure-calculated minimum plus any corrosion allowance (CA). The corrosion allowance is determined from the expected corrosion rate of the fluid-material pair and the intended service life (e.g. 3 mm for a 20-year life with a 0.15 mm/yr corrosion rate).

The final required thickness values below include the corrosion allowance and represent the minimum nominal wall thickness to be specified on the drawing. The actual ordered thickness will be rounded up to the next available plate or pipe schedule size.

Step 4 — Outside Diameter and Hoop Stress Verification

Once a nominal thickness is selected (here we use the required shell thickness), the outside diameter and the actual hoop stress at that thickness can be computed. The actual hoop stress should be less than or equal to S·E_j to confirm adequacy.

The nominal (design) outside diameter is simply:

OD = 2·(R + t_req_shell)

The actual hoop stress in the shell wall, treating the vessel as thin-walled, is:

σ_hoop = P·R / t_req_shell

Step 5 — Maximum Allowable Working Pressure (MAWP)

The MAWP is the highest pressure at which the vessel is permitted to operate at the design temperature, calculated from the actual (furnished) thickness minus the corrosion allowance. Using the required shell thickness as the furnished value and subtracting the corrosion allowance gives back the effective pressure-resisting thickness t_eff:

MAWP = S·E_j·t_eff / (R + 0.6·t_eff)

This is the inverse of the UG-27 thickness formula, rearranged for pressure. The MAWP is stamped on the vessel nameplate and must be ≥ the design pressure P.

Results

The key results of this pressure vessel design calculation are summarised below. With an internal design pressure of 1.5 MPa, an inside radius of 600 mm, an allowable stress of 138 MPa, full radiographic weld inspection (E_j = 1.0), and a 3 mm corrosion allowance:

• The minimum shell thickness (pressure-only) is approximately 6.6 mm — well within the thin-wall regime (t/R ≈ 0.011, far below the 0.1 limit), confirming the ASME thin-wall formula is valid.
• The required nominal shell thickness (with corrosion allowance) is approximately 9.6 mm. In practice, the next standard plate thickness above this value (typically 10 mm or 12 mm) would be specified.
• The required nominal hemispherical head thickness is approximately 6.3 mm — confirming that heads need only about half the shell thickness.
• The actual hoop stress at the nominal shell thickness is comfortably below the allowable stress of 138 MPa, confirming the design is adequate.
• The MAWP computed from the effective pressure-resisting thickness equals the design pressure (as expected, since t_eff = t_min_shell by construction), and would increase if a thicker plate were actually ordered.

If a lower joint efficiency (e.g. E_j = 0.70, no weld examination) were used, the required thickness would increase by approximately 43%, highlighting the significant benefit of full radiographic inspection for high-pressure vessels.

Assumptions & Limitations

• Applies only to thin-walled cylindrical vessels (t/R < 0.1); thick-wall vessels require Lamé equations (ASME Div 2 or Div 3).
• Only internal pressure loading is considered; external pressure (vacuum), wind, seismic, and nozzle loads require separate checks.
• Material is assumed to behave in a ductile, isotropic, linearly elastic manner at the design temperature.
• The allowable stress S must be taken from ASME BPVC Section II Part D at the actual design temperature — it decreases significantly at elevated temperatures (creep range).
• Weld joint efficiency E_j is assumed uniform around the full circumference; if only portions of the weld are examined, a blended efficiency applies.
• Corrosion allowance is a uniform-thinning model; pitting or crevice corrosion requires additional assessment (API 579/ASME FFS-1).
• Head geometry is assumed hemispherical; for standard 2:1 semi-ellipsoidal or torispherical (ASME flanged-and-dished) heads, different UG-32 formulae apply.
• No credit is taken for cladding or lining materials; only the base metal thickness is used in the stress calculation.