Shaft Dia (Bending+Torsion)
Per the third strength theory, find shaft diameter d from bending M, torque T, correction α and allowable shear τ.
Inputs
Formula
Fundamentals
Per the third strength theory, find shaft diameter d from bending M, torque T, correction α and allowable shear τ.
This tool computes Shaft Dia (Bending+Torsion) from the formula: Me = √(M²+(αT)²); d = ³√(16Me/(πτ))
History
Design theory of gears, threads and bearings matured with machine tools and standardisation (AGMA, ISO) since the Industrial Revolution.
Engineering applications
Used for transmission design, joint strength checks and component selection.
Glossary
| Bending moment M | Input parameter |
| Torque T | Input parameter |
| Correction α | Input parameter |
| Equiv. moment Me | Output result |
| Shaft dia. d | Output result |
How to use
- Fill in Bending moment M, Torque T, Correction α, Allowable shear τ in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Equiv. moment Me, Shaft dia. d in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：Me = √(M²+(αT)²); d = ³√(16Me/(πτ))
输入变量：
- Bending moment M
M— N·mm - Torque T
T— N·mm - Correction α
alpha - Allowable shear τ
tau— MPa
输出结果：
- Equiv. moment Me
Me— N·mm - Shaft dia. d
d— mm
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 Me = √(M²+(αT)²); d = ³√(16Me/(πτ))，取 Bending moment M = 40,000 N·mm；Torque T = 50,000 N·mm；Correction α = 0.6；Allowable shear τ = 40 MPa。
代入计算得：Equiv. moment Me = 50,000 N·mm；Shaft dia. d = 18.53 mm。
Key Points
- Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
- Compare stress with allowable stress and keep a safety factor (≥1.5, ≥2 for critical parts).
- For high speed/load also check lubrication, heat and fatigue life, not just static strength.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Bending moment M (N·mm) | M | N·mm | 40000 |
| Torque T (N·mm) | T | N·mm | 50000 |
| Correction α | alpha | 0.6 | |
| Allowable shear τ (MPa) | tau | MPa | 40 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Equiv. moment Me | Me | N·mm |
| Shaft dia. d | d | mm |
Applications
- Common engineering use cases