BIZOMAT MAKEOS · Strength
Tube or Shell under External Pressure (Collapse Thickness and Factor)
How thick must this long tube or vacuum shell be to resist collapse under the outside pressure, and what safety factor does the chosen wall give after corrosion?
Design of a long round tube or cylindrical shell under external pressure or vacuum: elastic collapse pressure and the yield-limited pressure for the wall left after corrosion allowance, the governing mode and safety factor (as the tube collapse tool), the least wall that gives your required factor (found by search) plus allowance, the diameter-to-thickness ratio and the mass per metre.
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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 | Nominal wall thickness. |
| Corrosion allowance | mm | Corrosion allowance removed before the check. |
| Elastic modulus | GPa | Elastic modulus at temperature. |
| Poisson’s ratio | Poisson’s ratio. | |
| Yield strength | MPa | Yield strength at temperature. |
| External pressure (net) | MPa | Net external pressure (0.1 MPa for full vacuum with atmosphere outside). |
| Safety factor required | Safety factor on collapse you require (often 3 or more for buckling; follow your code). | |
| Density | kg/m³ | Density for the mass per metre. |
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 tube or cylindrical shell. The collapse formulas use the mean diameter, which is this diameter less the wall.
- 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 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Wall thickness
- What it is
- The nominal wall thickness as made, before the corrosion allowance is taken off for the check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 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 remaining wall.
What this means: Corrosion allowance
- What it is
- The wall thickness expected to be lost to corrosion or erosion over the service life. It is removed before the collapse check and added back to the wall needed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Elastic modulus
- What it is
- Young’s modulus of the shell material at the design temperature, from the material data or your design code.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 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 directly proportional to it.
- Get it right
- Enter it in GPa, not MPa: 1 GPa = 1000 MPa, so divide a data-sheet value given in MPa by 1000.
What this means: Poisson’s ratio
- What it is
- Poisson’s ratio of the shell material, from the material data; it enters the elastic collapse formula.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 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.
What this means: Yield strength
- What it is
- The yield strength of the shell material at the design temperature, which sets the yield-limited collapse pressure for thicker walls.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 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.
What this means: External pressure (net)
- What it is
- The net pressure pushing inward on the wall: outside pressure minus inside pressure. Full vacuum inside with atmosphere outside is one atmosphere net.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100 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 is inversely proportional to this pressure.
- Get it right
- MPa, not bar: 1 bar = 0.1 MPa.
What this means: Safety factor required
- What it is
- The safety factor on collapse you require (governing collapse pressure ÷ applied pressure), from your pressure equipment code.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. 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.
What this means: Density
- What it is
- The density of the tube material, used only to work out the mass per metre.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Long tube elastic collapse p_cr = 2E ÷ (1 − ν²) × (t ÷ D_m)³; yield limit p_y = 2 S_y t ÷ D_m, with D_m = D − t and t after corrosion (as the tube collapse tool).
- Safety factor = smaller collapse pressure ÷ applied pressure.
- Least wall found by bisection on t for the required factor, plus corrosion allowance.
- Example: 2 mm (1.5 mm corroded) collapses elastically at 1.5523 MPa, a factor of 3.1047; 1.9832 mm is needed.
Limitations
- Long tube without stiffening rings; short shells between stiffeners are stronger.
- Out-of-roundness lowers the collapse pressure sharply: keep it within the code limit.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a vacuum pipe or vessel shell
- Check a heat-exchanger tube for shell-side pressure
- Check a submerged pipe
Who it is for
- Mechanical engineers
- Design engineers
- Inspection engineers
What you get
- Elastic and yield collapse pressures, governing mode and factor
- Least wall for the required factor
- D/t and mass per metre
Interpreting the result
- Collapse pressure rises with the cube of the wall ratio: a little more wall or a stiffening ring helps greatly.
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.
Method explained here · BIZOMAT original book
Thin walls and shells under vacuum
What it covers: How thin walls buckle locally and how tanks and tubes collapse under external pressure: long and short shells, why a tank can be sucked in by a small vacuum, and how a blocked vent nearly did it.
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Open the Tube or Shell under External Pressure (Collapse Thickness and Factor) calculator