Thin Cylinder Calculator
Hoop stress in a thin cylinder is pd/2t, twice the longitudinal stress: 2 MPa in a 1 m cylinder with 10 mm walls gives σh = 100 MPa.
100 MPa
- Longitudinal stress σl = pd/4t
- 50 MPa
- Maximum in-plane shear (σh − σl)/2
- 25 MPa
- Hoop strain εh
- 0.000425
- Longitudinal strain εl
- 0.0001
- Volumetric strain εv = 2εh + εl
- 0.00095
- Thin-wall assumption valid
- yes (d/t ≥ 20)
Step-by-step solution
- σh = pd/2t = 2 × 1000 ÷ (2 × 10) = 100 MPa
- σl = pd/4t = 50 MPa
- εv = (pd/4tE)(5 − 4ν) = 0.00095
Thin Cylinder Formula
σh = pd/2t, σl = pd/4t
p internal pressure, d internal diameter, t wall thickness; sphere σ = pd/4t
Worked Example
A 1 m diameter cylinder with 10 mm walls at 2 MPa:
- σh = pd/2t = 2 × 1000 ÷ (2 × 10) = 100 MPa
- σl = pd/4t = 50 MPa
- εv = (pd/4tE)(5 − 4ν) = 0.00095
Maximum in-plane shear (σh − σl)/2: 25 MPa · Hoop strain εh: 0.000425 · Longitudinal strain εl: 0.0001 · Volumetric strain εv = 2εh + εl: 0.00095 · Thin-wall assumption valid: yes (d/t ≥ 20)
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Frequently asked questions
Why do thin cylinders split lengthwise?
The hoop stress pd/2t is twice the longitudinal stress, so the critical crack runs along the length.
What is the volumetric strain of a thin cylinder?
εv = 2εh + εl = (pd/4tE)(5 − 4ν). For a sphere it is 3(pd/4tE)(1 − ν).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Thin Cylinder Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/thin-cylinder-calculator/
IEEE
Scientific Converters, "Thin Cylinder Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/thin-cylinder-calculator/