Hoop stress (circumferential stress) σh = PD/(2t) acts around the circumference of a cylindrical pressure vessel. It is twice the longitudinal stress and is the primary design stress for thin-wall vessels.

What is the thin-wall assumption?

The thin-wall assumption applies when D/t > 20 (or t < D/20). In this case, stress is approximately uniform through the wall thickness. For thick-wall vessels (D/t < 20), use Lamé equations.

Why is hoop stress twice longitudinal stress?

Due to geometry: the circumferential direction has twice the effective area ratio compared to the longitudinal direction. This is why cylindrical vessels typically fail along a longitudinal seam (perpendicular to hoop stress).

What is von Mises stress in a pressure vessel?

For a biaxial stress state (σh, σl), von Mises stress σ_vm = √(σh² - σh·σl + σl²). For thin-wall vessels, σ_vm = σh·√(3)/2 ≈ 0.866·σh. This is used with yield criteria.

What codes govern pressure vessel design?

ASME BPVC Section VIII (USA), EN 13445 (Europe), PD 5500 (UK), AS 1210 (Australia). These codes include safety factors, weld efficiency, corrosion allowance, and material-specific rules beyond simple thin-wall formulas.

Free Engineering Tool

Pressure Vessel Calculator

Calculate hoop stress σ_h = PD/(2t) and longitudinal stress σ_l = PD/(4t) for thin-wall cylindrical pressure vessels.

Thin-Wallσh = PD/(2t)#172

Results

Hoop Stress σh

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Longitudinal Stress σl

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Von Mises Stress σvm

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D/t Ratio

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Thin-Wall Check

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Vessel Cross-Section & Stress Directions

Thin-Wall Pressure Vessel Formulas

⚠️ Note: Thin-wall assumption valid when D/t > 20. For thick-wall vessels use Lamé equations. Always follow ASME BPVC or EN 13445 for actual design.

Pressure Vessel Calculator | Thin-Wall Hoop & Longitudinal Stress | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Thin-Wall Pressure Vessel Formulas