KEVOS® 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. | |
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.
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