Thin-Cylinder Hoop Stress
Estimate tensile membrane stress from internal pressure in a thin cylinder.
Try this formula
Calculate tensile membrane stress magnitude or choose another supported quantity.
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Try this formula
Calculate tensile membrane stress magnitude or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Tensile membrane stress magnitude
Enter the known values to see the result.
Use a thin wall with t/r ≤ 0.1 and positive internal-to-external pressure difference. The wall is uniform; radial stress is small relative to membrane stress. Use a membrane region away from joints, supports, and openings. This simplified membrane model does not assess external-pressure buckling or local stresses.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
raymond212 — MECH 260 — Mechanics of MaterialsReference equation: Thin-Walled Vessels. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Pressure acts over a large projected surface while the wall carries the load through a small resisting area. Stress grows with pressure and radius and falls as the wall becomes thicker.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Tensile membrane stress magnitude | ||
| Internal minus external pressure | ||
| Mean vessel radius | ||
| Wall thickness |
Real-World Applications
Vessel stress
Estimate nominal membrane demand under internal pressure.
Geometry comparison
Compare pressure-induced stress for different wall dimensions.
Worked Example
Problem
A thin cylinder has pressure difference 2 MPa, mean radius 0.25 m, and wall thickness 0.005 m. Find the membrane stress.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Thin-Walled Vessels. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use a thin wall with t/r ≤ 0.1 and positive internal-to-external pressure difference.
- • The wall is uniform; radial stress is small relative to membrane stress.
- • Use a membrane region away from joints, supports, and openings.
- • This simplified membrane model does not assess external-pressure buckling or local stresses.
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