Calculation
τ = 16·T/(π·d³); S = τzul/τ
Torsional stress grows linearly with torque and falls with the cube of diameter, so small diameter changes have an outsized effect.
Dubbel Festigkeitslehre C 2.5.1, Gl. (46): τmax = Mt/Wp mit Wp = π·d³/16; S = τzul/τmax
Solid-shaft torsion safety factor
Torsional stress grows linearly with torque and falls with the cube of diameter, so small diameter changes have an outsized effect.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Safety factor S — Ratio of allowable to actual torsional stress.
- Torque T — Torque to be transmitted at the considered shaft cross-section.
- Shaft diameter d — Diameter of the solid shaft at the considered cross-section.
- Allowable torsional stress τzul — Material- and application-dependent limit, e.g. from Roloff/Matek guideline values or a given design specification.
Example
T=200 N·m, d=30 mm and τzul=100 MPa give τ=16·200/(π·0.03³)≈37.7 MPa and S=100/37.7≈2.65.
Assumptions and limits
Pure torsion of a solid circular shaft with no notches, bending or fatigue check; not a substitute for a complete verification under DIN 743.
Understand Solid-shaft torsion safety factor
This calculator determines torsional stress and safety factor of a solid circular shaft under pure torsion, a quick preliminary check alongside the full verification under DIN 743.
What does this quantity describe?
For pure torsion of a solid shaft, τ=16·T/(π·d³). Safety factor S=τzul/τ compares this stress against an allowable limit.
Formula and variables
τ = 16·T/(π·d³); S = τzul/τ
τ = 16·T/(π·d³)S = τzul/τ
| Symbol / input | Meaning |
|---|---|
| Safety factor S | Ratio of allowable to actual torsional stress. |
| Torque T | Torque to be transmitted at the considered shaft cross-section. |
| Shaft diameter d | Diameter of the solid shaft at the considered cross-section. |
| Allowable torsional stress τzul | Material- and application-dependent limit, e.g. from Roloff/Matek guideline values or a given design specification. |
Choose the inputs correctly
T is the torque to be transmitted, d the shaft diameter at the considered cross-section, and τzul the material's allowable torsional stress.
How to use the calculator
Take T from drive sizing, d from the design drawing, and τzul from material properties or a design guideline.
Worked example
T=200 N·m, d=30 mm and τzul=100 MPa give τ≈37.7 MPa and S≈2.65.
Understand the result and units
S<1 means calculated failure; S well above 1 shows margin but may also indicate an oversized diameter.
T is a torque, d a length and τzul a stress. S is dimensionless.
Typical applications
Initial rough sizing of a shaft before a full fatigue calculation is performed.
Assumptions, limits and common mistakes
Pure torsion with no simultaneous bending, no notch effect and no fatigue check; not a substitute for a complete calculation under DIN 743.
Common mistake: Do not confuse shaft diameter with the root diameter at a keyway or spline, where actual stress is higher.
Frequently asked questions
What is “Solid-shaft torsion safety factor” used for?
Initial rough sizing of a shaft before a full fatigue calculation is performed.
Where do the input values come from?
T is the torque to be transmitted, d the shaft diameter at the considered cross-section, and τzul the material's allowable torsional stress.
What does the result not cover?
Pure torsion with no simultaneous bending, no notch effect and no fatigue check; not a substitute for a complete calculation under DIN 743.