BIZOMAT MAKEOS · Strength
Tube Collapse under External Pressure
At what external pressure will this long tube collapse, and is the margin enough?
Elastic buckling (collapse) pressure and yield-limited pressure of a long thin round tube under external pressure, with the safety factor against an applied pressure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Outside diameter of the tube or shell. |
| Wall thickness | mm | Minimum wall thickness. |
| Elastic modulus | GPa | Elastic modulus from the material data sheet (steel is typically about 200 GPa). |
| Poisson’s ratio | Poisson’s ratio (about 0.3 for steel). | |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification. |
| External pressure (net) | MPa | Net external pressure (outside minus inside); full vacuum is about 0.1 MPa. |
| Required safety factor | Factor required by your code (external pressure codes commonly use about 3). |
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: Outside diameter
- What it is
- The outside diameter of the round tube or shell that carries the external pressure; the tool uses the mean diameter, outside diameter minus wall thickness.
- 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 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the outside diameter, not the bore or the mean diameter.
What this means: Wall thickness
- What it is
- The wall thickness of the tube, ideally the minimum after manufacturing tolerance and any corrosion allowance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Elastic collapse pressure rises with the cube of the thickness-to-diameter ratio; the yield limit rises in direct proportion.
- Get it right
- Use the minimum thickness: elastic collapse pressure varies with the cube of thickness, so a thinner wall matters a lot.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the tube material, which sets its resistance to elastic buckling.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Elastic collapse pressure is proportional to the modulus; the yield limit does not depend on it.
- Get it right
- Enter gigapascals; take the value at the operating temperature from the data sheet.
What this means: Poisson’s ratio
- What it is
- Poisson’s ratio of the tube material: the sideways contraction divided by the lengthwise stretch under load, used in the elastic buckling term.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is a ratio, not a percentage; take it from the material data sheet.
What this means: Yield strength
- What it is
- The minimum yield strength of the tube material, which limits collapse when the wall yields before it buckles.
- 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 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yield-limited pressure rises in direct proportion; it matters only for thicker tubes where yield governs.
- Get it right
- Use the specified minimum or certificate value at the operating temperature, not a typical value.
What this means: External pressure (net)
- What it is
- The net pressure pushing in on the tube: pressure outside minus pressure inside, as in a vacuum vessel or a pipe buried in fluid.
- 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 0.5 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The safety factor falls in inverse proportion to this pressure.
- Get it right
- Use the difference across the wall, not an absolute or gauge reading on one side only.
What this means: Required safety factor
- What it is
- The minimum ratio of governing collapse pressure to applied pressure that your code or specification demands; the calculated safety factor is checked against it.
- 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 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the applicable pressure vessel code or customer specification, not from the example.
Method and formulas
- Mean diameter Dm = D − t.
- Elastic collapse (long tube): p_cr = 2E ÷ (1 − ν²) × (t ÷ Dm)³.
- Yield limit: p_y = 2 S_y t ÷ Dm; the lower governs.
- Example: a 100 × 2 mm steel tube collapses at about 3.7362 MPa; the factor at 0.5 MPa is 7.4724.
Limitations
- Long, perfectly round tubes; out-of-roundness and short lengths between stiffeners change the result substantially.
- Pressure vessels under external pressure must be designed to their code charts (e.g. AS 1210, ASME VIII).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check tubes and shells under vacuum
- Check heat exchanger tubes with shell-side pressure
- Screen a jacketed vessel inner shell
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Elastic collapse pressure
- Yield-limited pressure
- Governing collapse pressure and safety factor
Interpreting the result
- Stiffening rings shorten the effective length and greatly raise the collapse pressure.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 293–294. 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.
Useful alongside · BIZOMAT original book
Column separation and the pipeline profile
In Water Hammer by the Numbers
What it covers: Draw the minimum head envelope after a pump trip against the pipe's profile, find where pressure goes sub-atmospheric or boils, and see why the rejoining columns are so dangerous.
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