BIZOMAT MAKEOS · Strength
Pressurised Tube Under Torsion Check (Hoop, Axial and Shear Stress, Principal Stresses, Yield)
For a thin-walled tube under internal pressure that also carries torque and an axial load, what are the principal stresses, and is the safety factor against yield enough?
Check of a thin-walled tube or shaft under internal pressure, end thrust and torque: the hoop and axial stresses from pressure (closed ends) plus the axial load, the shear stress from torque in the thin wall, then the principal stresses, their direction, the maximum shear and the von Mises equivalent stress with the safety factor against yield (as the principal stress tool), against your required factor.
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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. |
| Wall thickness | mm | Wall thickness. |
| Internal pressure | MPa | Internal gauge pressure; ends are taken as closed, so pressure also loads the tube axially. |
| Axial load (tension positive) | kN | Extra axial load (tension positive, compression negative). |
| Torque | N·m | Torque carried by the tube. |
| Material | ||
| Yield strength | MPa | Yield strength of the tube material. |
| Required safety factor | Safety factor on yield you need. | |
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 hollow shaft. The tool works the stresses from the mean diameter, outside diameter minus wall thickness.
- 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.
- Effect on the result
- A larger diameter raises the hoop and axial stress from pressure and lowers the shear stress from torque.
- Get it right
- Use the outside diameter, not the bore.
What this means: Wall thickness
- What it is
- The wall thickness of the tube. Hoop, axial and shear stresses are all taken as spread evenly across it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All stresses fall roughly in inverse proportion to the wall thickness.
- Get it right
- Use the minimum wall after mill tolerance and any corrosion; the tool warns when the wall is too thick for thin-wall formulas.
What this means: Internal pressure
- What it is
- The internal pressure in the tube above the outside pressure. The ends are taken as closed, so the pressure also pulls the tube lengthways.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Hoop and axial stresses rise in direct proportion to the pressure.
- Get it right
- Use gauge pressure in MPa (1 MPa = 10 bar), not absolute.
What this means: Axial load (tension positive)
- What it is
- Any end load along the tube axis in addition to the pressure thrust, such as from supports or connected equipment. Tension is positive, compression negative.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts -1000000 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It raises or lowers the axial stress in proportion to its size.
- Get it right
- Enter it in kN and do not include the pressure end thrust, which the tool already adds.
What this means: Torque
- What it is
- The twisting moment carried by the tube about its axis. It sets the shear stress in the thin wall.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -100000000 N·m to 100000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The shear stress from torque rises in direct proportion to it.
- Get it right
- Enter it in N·m; a torque in kN·m must be multiplied by 1000.
Material
What this means: Yield strength
- What it is
- The yield strength of the tube material at its working temperature, from the material specification or test certificate. The von Mises stress 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 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 safety factor rises in direct proportion to the yield strength.
- Get it right
- Use yield strength, not tensile strength, and take the value at the working temperature.
What this means: Required safety factor
- What it is
- The safety factor on yield that your design code, client or engineer requires. The calculated factor must be at least this.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the factor your code or engineer sets for this service; the tool does not choose one.
Method and formulas
- Mean diameter D_m = OD − t; hoop σ_h = p D_m ÷ 2t; axial σ_a = p D_m ÷ 4t + N ÷ (π D_m t); shear τ = 2T ÷ (π D_m² t).
- σ₁,₂ = (σ_a + σ_h) ÷ 2 ± √(((σ_a − σ_h) ÷ 2)² + τ²) (as the principal stress tool, with σx axial and σy hoop).
- von Mises √(σ₁² − σ₁σ₂ + σ₂²); safety factor = yield ÷ von Mises.
- Example: hoop 120 MPa, axial 60 MPa and shear 34.539 MPa give 119.91 MPa von Mises, a factor of 2.0849.
Limitations
- Thin wall (thickness up to about a tenth of the diameter); thick tubes need the Lamé equations.
- Away from ends, ports and welds, where local stresses are higher.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a hydraulic swivel or rotary union tube
- Check a pressurised drive tube
- Check a pipe under torque from misalignment
Who it is for
- Design engineers
- Hydraulic engineers
- Stress analysts
What you get
- Hoop, axial and shear stress
- Principal stresses and direction
- von Mises stress and safety factor
Interpreting the result
- Torque adds less than you might expect when hoop stress dominates, because the stresses combine as a vector, not a sum.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218, 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 · BIZOMAT original book
Tubes under pressure, thrust and torque
In Stress Transformation by the Numbers
What it covers: How to check a thin-walled tube or hollow shaft under pressure, axial load and torque together, what the pressurised tube tool leaves out, and how to add bending and exact torsion.
Method explained here · BIZOMAT original book
First yield, collapse and proof tests
In Yield and Plastic Flow by the Numbers
What it covers: How a thick tube goes from first yield at its bore to plastic collapse, what a proof test proves, and how to judge a barrel after a test bench overpressure.
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