Enter Tube Data
Example Data Table
| Outer Diameter | Inner Diameter | Length | Shear Modulus | Torque | Stiffness | Twist |
|---|---|---|---|---|---|---|
| 50 mm | 40 mm | 500 mm | 79 GPa | 120 N·m | ≈ 1,492 N·m/rad | ≈ 4.61° |
| 2.0 in | 1.6 in | 24 in | 11,500 ksi | 900 lbf·in | ≈ 1,010 lbf·ft/rad | ≈ 3.06° |
| 80 mm | 60 mm | 1.2 m | 26 GPa | 250 N·m | ≈ 2,180 N·m/rad | ≈ 6.57° |
Formula Used
This calculator uses the standard torsion relationships for a hollow circular tube.
- Polar moment of area: J = (π/32) · (Do4 − Di4)
- Torsional rigidity: GJ
- Torsional stiffness: k = GJ / L (torque per radian)
- Angle of twist: θ = T · L / (GJ)
- Outer-surface shear stress: τ = T · ro / J with ro = Do/2
How to Use This Calculator
- Select a dimension unit, then enter the outer diameter.
- Choose inner diameter or wall thickness as input.
- Enter tube length and the material shear modulus.
- Optionally enter torque to get twist and stress.
- Optionally enter a target angle to get torque.
- Press Calculate, then download CSV or PDF if needed.
Article
1) What Torsional Stiffness Means
Torsional stiffness (k) is the tube’s resistance to twisting. It links applied torque (T) and twist angle (θ) using T = k·θ when θ is in radians. Higher stiffness reduces angular deflection, improves alignment, and helps keep couplings, gears, and shafts within allowable twist limits under load.
2) Core Inputs Used in This Calculator
The calculator uses outer diameter (Do), inner diameter (Di) or wall thickness (t), length (L), and shear modulus (G). Typical shear modulus values: steel ≈ 79 GPa, aluminum ≈ 26 GPa, titanium alloys often ≈ 44 GPa. Units are converted internally for consistent results.
3) Polar Moment of Area for Hollow Tubes
Tube geometry enters through the polar moment J = (π/32)(Do4 − Di4). Because diameters are raised to the fourth power, small diameter changes can significantly increase stiffness. For example, increasing Do by 10% can raise J by roughly 46% when Di scales similarly.
4) Stiffness and Rigidity Relationships
Torsional rigidity is GJ (N·m2). Stiffness is k = GJ/L (N·m per rad). Doubling length halves stiffness, while doubling G doubles stiffness. This calculator reports both GJ and k so you can compare materials and geometries quickly.
5) Twist Angle and Required Torque Options
If you enter torque, it computes twist: θ = T·L/(GJ). If you enter a target twist, it computes the required torque: T = k·θ. This “full option” workflow supports sizing a tube for a maximum allowed twist or predicting twist for a known drive torque.
6) Shear Stress Check for Practical Design
The calculator also estimates outer-surface shear stress using τ = T·ro/J. This is useful for screening against material yield or allowable stress. For a given tube, stress rises linearly with torque and outer radius, and drops as J increases.
7) Example Use Case With Real Numbers
Consider a steel tube with Do=50 mm, Di=40 mm, L=500 mm, G=79 GPa, and T=120 N·m. The calculator returns stiffness near 1,500 N·m/rad and a twist around 4.6°. These values help verify that your shaft twist stays within performance targets.
FAQs
1) What is the difference between torsional rigidity and torsional stiffness?
Rigidity is GJ and depends on material and geometry. Stiffness is k = GJ/L, so it also depends on length. Longer tubes are less stiff even if GJ is unchanged.
2) Which diameter affects stiffness more, outer or inner?
Both matter through D4, but increasing outer diameter usually boosts stiffness more than decreasing inner diameter by the same small amount. Geometry changes are amplified because of the fourth-power term.
3) Can I use wall thickness instead of inner diameter?
Yes. Select the thickness option and enter t. The calculator computes Di as Do − 2t. Ensure thickness is not so large that the computed inner diameter becomes zero or negative.
4) Why does the calculator ask for shear modulus, not Young’s modulus?
Torsion uses G directly. If you only know Young’s modulus E, you can estimate G = E / (2(1+ν)) using Poisson’s ratio ν, typically 0.30 for many steels.
5) How do I choose the twist unit for best results?
Use degrees for quick interpretation, but internally equations use radians. This calculator handles conversions. For engineering checks, ensure your allowable twist is specified consistently, especially when comparing different lengths.
6) Is the stress result enough for final shaft design?
It is a helpful screening value for elastic torsion. Final design should also consider fatigue, stress concentrations, keyways/splines, combined loading, and safety factors. Use the stress output as an early validation step.