BIZOMAT MAKEOS · Strength
Pressure Cylinder Wall Stress
What stresses does internal pressure cause in this tube or cylinder wall?
Hoop, radial and longitudinal stresses in a cylinder under internal pressure by Lamé’s thick-wall equations, with the thin-wall estimate and a von Mises safety factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Inside diameter | mm | Bore of the tube or cylinder. |
| Wall thickness | mm | Minimum wall thickness after tolerances, corrosion and machining allowances. |
| Internal pressure (gauge) | MPa | Maximum working (or test) gauge pressure; 1 MPa = 10 bar. |
| Ends | choice | Closed if the pressure on the end caps is carried by this wall (e.g. a capped cylinder). |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification, not a typical value. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Inside diameter
- What it is
- The bore of the tube, pipe or cylinder: the diameter of the inside surface that the pressure acts on.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the inside diameter, not the outside diameter or nominal pipe size.
What this means: Wall thickness
- What it is
- The wall thickness between the bore and the outside surface that carries the pressure.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker wall lowers the hoop stress and raises the safety factor.
- Get it right
- Use the minimum thickness after manufacturing tolerance, corrosion allowance and machining, not the nominal thickness.
What this means: Internal pressure (gauge)
- What it is
- The internal pressure above the outside (atmospheric) pressure, at the maximum working or test condition.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All stresses rise in proportion to the pressure, so the safety factor falls in proportion.
- Get it right
- Enter gauge pressure in MPa: 1 MPa is 10 bar. Do not add atmospheric pressure.
What this means: Ends
- What it is
- Whether the pressure force on the end caps is carried by this wall (closed ends) or by something else such as tie rods or an external frame (open).
- Units and format
- Choose one of 2 options from the list: Closed (end load carried by the wall); Open or end load carried elsewhere.
- Example
- The form opens with “Closed (end load carried by the wall)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Closed ends add a longitudinal stress to the wall, which changes the von Mises result.
What this means: Yield strength
- What it is
- The minimum yield strength of the cylinder wall material, from the material certificate or specification. The von Mises stress at the bore is compared with it.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 355 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the specified minimum at the operating temperature, not a typical value.
What this means: Required safety factor
- What it is
- The minimum ratio of yield strength to von Mises stress the wall must achieve, from your design code, customer specification or company standard.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Pressure equipment must follow its design code, which sets its own allowable stresses.
Method and formulas
- ro = ri + t. Hoop at bore σθ = p(ro² + ri²) ÷ (ro² − ri²); radial σr = −p.
- Longitudinal (closed ends) σz = p ri² ÷ (ro² − ri²).
- Thin wall σθ ≈ p d_mean ÷ 2t; von Mises from the three principal stresses at the bore.
- Example: 80 mm bore, 10 mm wall at 25 MPa gives a bore hoop stress of 113.89 MPa and a factor of 2.9514.
Limitations
- Elastic stresses away from ends, ports and welds; these features raise local stress.
- Pressure equipment must be designed to its code (e.g. AS 1210 or ASME VIII), which sets allowable stresses and thicknesses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check hydraulic cylinder barrels, tubes and pipes
- Compare thin-wall and thick-wall results
- Screen a wall thickness before code design
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Hoop stress at the bore (Lamé)
- Longitudinal and radial stress
- Thin-wall hoop stress
- von Mises stress and safety factor
Interpreting the result
- If the thin-wall result is much lower than Lamé, the wall is thick and the Lamé result governs.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · Library collection
Pressure vessels and thin-walled cylinders: stresses, design codes, relief valves and inspection
In Machine Elements and Mechanical Design
What it covers: Why pressurised cylinders split lengthwise, how hoop and longitudinal stresses are calculated, how vessels are designed to codes, and how relief valves and inspection keep them safe.
Method explained here · BIZOMAT original book
Thick walls
In Stress Transformation by the Numbers
What it covers: How stress varies through a thick cylinder wall under pressure by Lamé's equations, how the thin-wall formula compares, why extra wall stops helping, and the pressure cylinder tool.
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