Engineering
Shaft Preliminary Design Calculator
Calculate solid-circular bending stress, torsional shear, von Mises stress, reduced allowable strength, required diameter, elastic twist, and power.
Outer-fibre bending stress-
Outer-surface torsional shear stress-
Combined von Mises stress-
Yield strength after entered reduction-
Reduced yield divided by design factor-
Reduced yield divided by combined stress-
Combined stress divided by allowable stress-
Required solid diameter at allowable stress-
Solid-shaft polar moment J-
Elastic angle of twist (degrees)-
Power at entered torque and speed-
Entered minus required diameter-
Decision view
Bending-torsion shaft stress and diameter check
Bending-torsion shaft stress and diameter checkOuter-fibre bending and torsional shear combine through von Mises stress, then the strength-reduced allowable stress determines the minimum solid-shaft diameter.
Exact scenario comparisonApplied torque T (N m) changes while all other entered assumptions remain constant.
| Applied torque T (N m) | Outer-fibre bending stress | Outer-surface torsional shear stress | Combined von Mises stress | Yield strength after entered reduction | Reduced yield divided by design factor | Reduced yield divided by combined stress | Combined stress divided by allowable stress | Required solid diameter at allowable stress | Solid-shaft polar moment J | Elastic angle of twist (degrees) | Power at entered torque and speed | Entered minus required diameter |
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How to use Shaft Preliminary Design Calculator
- Enter peak bending moment and torque on the same load basis.
- Enter solid diameter and material properties.
- Review stress, required diameter, twist, and power as separate criteria.
Calculator guide
Understanding Shaft Preliminary Design Calculator
A solid shaft under simultaneous bending and torque needs both normal and shear stress. This calculator combines them with the von Mises criterion and separately checks diameter, twist, and transmitted power.
Detailed calculation process
Detailed solid-shaft combined-stress calculation
The default example keeps moment, stress, strength, diameter, and twist units explicit.
General formula: sigma=32M/(pi d^3)tau=16T/(pi d^3)sigma_v=sqrt(sigma^2+3tau^2)S_a=S_y(1-r)/nd_req=[sqrt((32M)^2+3(16T)^2)/(pi S_a)]^(1/3) Bending normal stress and torsional shear are combined by von Mises; the same combined equation is inverted for diameter.
What each symbol means
Worked substitution with the default inputs
Substituting the required diameter back into the stress equations produces a von Mises stress of approximately 93.75 MPa.
Worked situations
Practical examples
- Increasing diameter reduces both stresses with the cube of diameter.
- A keyway allowance reduces available strength rather than increasing applied torque.
Better inputs
Useful tips
- Use N mm internally when checking hand calculations.
- Evaluate fatigue separately for fluctuating loads.
- Check shoulders and keyways with actual stress-concentration factors.
Before relying on the result
Limitations and common mistakes
- Fatigue, notches, critical speed, and deflection are excluded.
- The shaft is solid and circular.
- Bearing reactions and load spectra must be established elsewhere.
Reference
Key terms
- Von Mises stress
- Equivalent stress combining normal and shear components for a ductile-yield check.
- Polar moment
- Solid-round torsional section property pi d^4/32.
- Design factor
- Reduced strength divided by permitted equivalent stress.
Important note
Complete shaft design requires fatigue, stress concentrations, deflection, dynamics, fits, and the governing standard.
Frequently asked questions
Why does required diameter use a cube root?
Solid-round surface stresses vary inversely with diameter cubed.
Is angle of twist a safety limit?
No; compare it with the application's alignment and stiffness requirement.
Can this size a hollow shaft?
No. A hollow section needs different section properties.