Keyway fatigue behavior
Key depth, end shape, fit, fillet, surface, and notch sensitivity affect local fatigue. A single reduction cannot represent all geometries.
Engineering
Shaft Capacity Calculator
Solve the remaining torque capacity of a solid shaft after bending stress, design factor, and a declared keyway reduction are applied to a von Mises allowable.
SHAFT COMBINED CAPACITY
Find the torsional capacity left after bending consumes part of the stress allowance
Torque capacity cannot be assessed independently when the checked section also carries bending. This calculator derives an entered-model allowable stress, calculates nominal bending stress, and solves the von Mises relationship for the torsional capacity that remains.
Remaining torque capacity (N*m)-
Applied-torque utilization-
Torque margin (N*m)-
Reduced allowable stress (MPa)-
Bending stress (MPa)-
Capacity status-
ENGINEERING DECISION VIEW
See bending reserve converted into remaining torque capacity
If bending alone consumes the allowable, the page stops instead of reporting imaginary torsional capacity. A positive margin supports only this nominal-yield screen and must be followed by local fatigue, geometry, and deflection checks.
| Capacity step | Input / stress | Geometry / comparison | Result | Interpretation |
|---|
LIVE CALCULATION PROCESS
Formula, substitution, and reconciliation
sigma_allow = Sy/n x (1 - keyway reduction); tau_allow = sqrt((sigma_allow^2 - sigma_b^2)/3); Tcap = tau_allow*pi*d^3/16
The method first applies the entered design factor and declared keyway reduction to yield strength. Nominal bending stress is subtracted through the von Mises interaction, not by linearly subtracting percentages. The remaining allowable shear is converted to torque for a solid circular section.
HOW TO USE
Solve a traceable preliminary torque capacity
- Identify the exact solid section and enter its net diameter and simultaneous bending moment.
- Enter the material yield basis, design factor, and any explicitly approved screening reduction for a keyway.
- Enter the applied torque for the same load case and review bending stress before the remaining torque capacity.
- Use the utilization and margin to select the next detailed shaft check, not to waive fatigue or local-geometry analysis.
- Preserve the section drawing, moment and torque source, material basis, and reduction rationale so the calculated reserve is not detached from the actual feature.
SUBJECT FUNDAMENTALS
Capacity concepts used by the interaction solution
- Allowable stress
- Yield strength reduced by the entered design factor and explicit screening reduction.
- Interaction
- Combined-stress relationship in which bending reduces the shear stress available before the same equivalent limit is reached.
- Remaining capacity
- Torque corresponding to the shear portion left after bending demand is included.
- Utilization
- Applied torque divided by calculated remaining torque capacity.
- Keyway reduction
- Entered scalar reduction for preliminary screening; it is not a geometry-specific stress-concentration analysis.
- Positive margin
- Calculated capacity minus applied torque, meaningful only inside this stated nominal model.
CALCULATION METHOD
Solve the von Mises interaction instead of adding stress percentages
sigma_allow = Sy/n x (1 - keyway reduction); tau_allow = sqrt((sigma_allow^2 - sigma_b^2)/3); Tcap = tau_allow*pi*d^3/16
The method first applies the entered design factor and declared keyway reduction to yield strength. Nominal bending stress is subtracted through the von Mises interaction, not by linearly subtracting percentages. The remaining allowable shear is converted to torque for a solid circular section.
DEFAULT CASE AUDIT TRAIL
Symbols, units, substitution, and independent check
| Symbol | Meaning | Unit |
|---|---|---|
| d | Net solid-shaft diameter | mm |
| M | Applied bending moment | N*m |
| Ta | Applied torque | N*m |
| Sy | Entered yield strength | MPa |
| nd | Entered design factor | dimensionless |
| r | Remaining strength factor after reduction | dimensionless |
Default values
- d = 55 mm, M = 650 N*m, and Ta = 1,100 N*m.
- Sy = 355 MPa, nd = 1.80, and keyway reduction = 12%.
Unit conversion
- M = 650,000 N*mm; final torque capacity is converted from N*mm back to N*m.
- r = 1 - 0.12 = 0.88.
Numerical substitution
- Reduced allowable stress = 355 / 1.80 x 0.88 = 173.556 MPa.
- Bending stress = 32 x 650,000 / (pi x 55^3) = about 39.80 MPa.
- Remaining shear = sqrt((173.556^2 - 39.80^2) / 3) = about 97.53 MPa.
- Torque capacity = remaining shear x pi x 55^3 / 16 / 1,000 = about 3,187 N*m.
Named intermediate results
- Reduced allowable von Mises stress: 173.556 MPa.
- Bending demand: about 39.80 MPa.
- Remaining torsional capacity: about 3.19 kN*m.
Independent check:Substituting the calculated capacity torque back into sqrt(sigma_b^2 + 3 tau^2) returns the reduced allowable stress; the 1,100 N*m default demand remains below capacity.
DEEPER ANALYSIS
Why real shaft capacity can be lower
Load spectrum and reversals
Repeated torque, rotating bending, starts, stops, and shock loads require alternating and mean-stress treatment.
Section and material condition
Heat treatment, decarburization, residual stress, corrosion, wear, repairs, and dimensional tolerances can invalidate the nominal input.
WORKED DECISION CASES
Two preliminary capacity decisions
Coupling upgrade screen
A higher-torque coupling is proposed on an existing shaft. The calculation shows bending already consumes much of the entered allowance, so a detailed shoulder and keyway fatigue review is commissioned.
Diameter option comparison
Two concept diameters are checked with the same load case. Because capacity scales strongly with diameter cubed, the ledger shows why a small diameter change materially affects torque margin.
Shaft capacity terminology
- Allowable
- Design comparison value derived under a stated rule, not an inherent material constant.
- Torque capacity
- Torque corresponding to the remaining nominal shear allowance at the selected section.
- Bending utilization
- Share of the entered equivalent-stress allowance consumed by bending.
- Keyway
- Axial slot used to transmit torque through a key, creating local section loss and stress concentration.
- Design factor
- Entered divisor between yield strength and the preliminary allowable basis.
- Interaction equation
- Mathematical rule for combining simultaneous stress components.
EVIDENCE AND DATA LINEAGE
Keep the geometry and allowable derivation with the capacity result
Retain the drawing revision, local diameter, keyway and shoulder details, applied moment and torque diagrams, load-case timing, yield specification, heat treatment, design-factor source, reduction-factor rationale, unit conversions, unrounded stresses and capacity, and the subsequent fatigue and deflection checks.
LIMITS AND EXCLUSIONS
What the solved torque capacity excludes
- No local stress concentration, fatigue, fracture, wear, fretting, deflection, critical speed, torsional vibration, connection, key, spline, or coupling capacity is calculated.
- The model is limited to a nominal elastic solid circular section and an entered yield-based von Mises allowable.
- The user-supplied design factor and keyway reduction are not validated or selected by the calculator.
RELIABLE SOURCES
References for the method and its boundaries
FREQUENTLY ASKED QUESTIONS
Questions about the remaining torque capacity
Why does the calculator stop when bending exceeds allowable?
The von Mises equation has no real remaining shear solution once nominal bending reaches the entered allowable.
Is the keyway percentage a standard value?
No. It is an explicit user-entered screening assumption and must not replace geometry-specific analysis.
Can I set bending moment to zero?
Yes, for a pure-torsion screen, provided the real section truly has negligible bending.
Why does diameter have such a large effect?
Nominal bending and torsional stresses vary inversely with diameter cubed for a solid circular section.
Does capacity include fatigue?
No. It is a nominal static-yield interaction only.
Can I use ultimate strength instead of yield?
Not with this stated ductile-yield model unless the governing design method explicitly establishes a different basis.
RELATED CALCULATORS
Continue the engineering review
Shaft Safety Factor Calculator
Calculate the factor at one entered combination rather than solving capacity.
Shaft Loss Calculator
Evaluate heat and delivered power without confusing energy loss with strength reserve.
IMPORTANT NOTE
Do not rate or overload equipment from this preliminary capacity alone
Final shaft capacity requires the governing standard, verified load spectrum, full geometry, material and manufacturing condition, fatigue and dynamics, inspection, and responsible engineering approval.