BIZOMAT MAKEOS · Power Transmission
Circular Shaft Torsion
What torsional stress and twist does this circular shaft develop?
Calculate elastic torsion of a uniform solid or hollow circular shaft with a supplied shear modulus.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outside diameter | mm | Actual uniform shaft outside diameter. |
| Inside diameter | mm | Bore diameter; enter zero for a solid shaft. |
| Loaded length | mm | Length over which the stated torque acts. |
| Torque | N·m | Transmitted torque for the chosen load case. |
| Shear modulus | MPa | Material shear modulus at the operating temperature. |
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 uniform round shaft along the loaded length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For a solid shaft, shear stress falls with the cube of diameter and twist with the fourth power.
- Get it right
- Use the smallest diameter in the loaded length; shoulders and keyways need separate checks.
What this means: Inside diameter
- What it is
- The diameter of the central bore of a hollow shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 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 bore reduces the polar moment, raising stress and twist.
- Get it right
- Enter 0 for a solid shaft; the bore must be smaller than the outside diameter.
What this means: Loaded length
- What it is
- The length of shaft between the points where the torque is applied and reacted, over which the twist is measured.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Twist is directly proportional to length; stress does not change.
- Get it right
- Use the distance between the driving and driven members, not the total shaft length.
What this means: Torque
- What it is
- The twisting moment carried by the shaft for the load case you are checking.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shear stress and twist are directly proportional to torque.
- Get it right
- The Torque, Power and Speed tool converts kW and rpm to N·m; include any peak or start-up torque you need to check.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the shaft material, its stiffness in twisting, from material data at the operating temperature.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.001 MPa to 10000000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Twist is inversely proportional to shear modulus; stress does not change.
- Get it right
- Do not enter Young’s modulus E; the shear modulus G is a different, smaller value. Use MPa.
Method and formulas
- Polar area moment J = π × (D⁴ − d⁴) / 32.
- Convert torque from N·m to N·mm by multiplying by 1000.
- Peak nominal shear stress = torque × (D/2) / J. Twist (radians) = torque × length / (G × J).
- Example: 40 mm solid shaft, 500 mm long, 200 N·m and G = 80000 MPa gives 15.915494 MPa and 0.284966°.
Limitations
- Circular, uniform, linear elastic shaft only.
- Keyways, shoulders, bending, fatigue, buckling and critical speed are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- torsion
- shaft twist
- polar inertia
Who it is for
- Designers
- Maintenance engineers
What you get
- Polar area moment J
- Peak nominal shear stress
- Twist
Interpreting the result
- Use the nominal result as one load-case input, then assess discontinuities and combined loading.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 244–249, 295–303. 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
Shear, torque and rosettes
In Strain Gauges and Load Cells by the Numbers
What it covers: Why gauges at 45° measure shear, how torque transducers work on a shaft, and how a three-gauge rosette gives the principal strains and stresses on a surface whose stress directions are unknown.
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