KEVOS® MAKEOS · Strength
Round Shaft under Axial Load, Bending and Torsion
What are the combined stresses in this round shaft or bar, and is it safe against yield?
Direct, bending and torsional stresses in a solid or hollow round shaft carrying axial load, bending moment and torque together, with principal stresses, von Mises and Tresca safety factors.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Outside diameter at the section. |
| Bore (0 = solid) | mm | Bore of a hollow shaft (0 if solid). |
| Axial force (+ tension, − compression) | N | Axial force at the section. |
| Bending moment | N·m | Resultant bending moment at the section. |
| Torque | N·m | Torque at the section. |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification. |
| Required safety factor | Factor of safety required by your design code, customer specification or company standard. |
Method and formulas
- A = π(d² − dᵢ²)/4; Z = π(d⁴ − dᵢ⁴)/32d; Zp = 2Z.
- σ = P/A + M/Z (at the outer fibre where they add); τ = T/Zp.
- σ₁,₂ = σ/2 ± √((σ/2)² + τ²); von Mises √(σ² + 3τ²); Tresca √(σ² + 4τ²).
- Example: the default shaft has σ = 63.662 MPa, τ = 39.789 MPa and a von Mises stress of 93.82 MPa.
Limitations
- Static strength; stress concentrations and fatigue need separate checks (see the Goodman tool).
- Slender compressed shafts must also be checked for buckling.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a shaft with thrust, bending and torque
- Check a bolt or rod in tension and torsion
- Check a propeller or screw shaft
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Direct, bending and shear stresses
- Principal stresses
- von Mises and Tresca equivalent stresses and safety factors
Interpreting the result
- Use von Mises for ductile shafts; Tresca is slightly more conservative.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218, 295–303. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Round Shaft under Axial Load, Bending and Torsion calculator
