In real-world engineering, components are rarely perfect cylinders or uniform beams. They include keyways, shoulders, holes, notches, and grooves — all of which introduce local stress intensification. This phenomenon is measured using the Stress Concentration Factor (SCF), known in engineering as K<sub>t</sub>.
If ignored, stress concentrations can lead to crack initiation, premature fatigue failure, and unexpected structural damage, especially in high-load environments like mining machinery.
What Is a Stress Concentration Factor (K<sub>t</sub>)?
The stress concentration factor is a multiplier that accounts for increased localized stress caused by geometric irregularities. It relates the maximum local stress to the nominal (calculated) stress.
Kt=σmaxσnomK_t = \frac{σ_{max}}{σ_{nom}}
Where:
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σmaxσ_{max} = Actual peak stress at the discontinuity
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σnomσ_{nom} = Nominal stress assuming uniform geometry
Common Causes of Stress Concentrations
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Keyways in shafts
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Shoulder steps and diameter changes
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Bolt holes or cross-holes
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Grooves or snap-ring seats
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Sharp corners or fillets
Even minor changes in geometry can raise stress by 30–300% at specific locations.
Why SCFs Matter in Mining and Heavy Industry
Mining components — like crusher shafts, conveyor drive axles, or dragline arms — operate under extreme and repeated loading conditions. Any small stress riser can lead to:
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Surface cracks under cyclic torque
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Fracture initiation in keyway roots
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Bearing journal wear at undercuts
Using K<sub>t</sub> ensures safety in these harsh environments.
When and How to Use K<sub>t</sub>
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Fatigue Analysis:
SCFs are critical when calculating fatigue life, particularly for components with millions of stress cycles. -
Design Validation:
After initial sizing, apply K<sub>t</sub> at key locations to check whether actual stress exceeds material limits. -
Selection of Fillet Radii:
Increasing corner radii significantly reduces K<sub>t</sub>, improving component life.
Typical K<sub>t</sub> Values for Shafts
| Feature | K<sub>t</sub> Range |
|---|---|
| Sharp shoulder | 1.5–2.5 |
| Keyway | 2.0–3.5 |
| Cross-drilled hole | 2.7–4.0 |
| Groove with fillet | 1.3–2.0 |
| Under-milled section | 1.8–2.4 |
Higher K<sub>t</sub> values → higher fatigue risk → require stronger materials or larger diameters
Best Practices to Minimize Stress Concentrations
✅ Add fillets to all sharp corners
✅ Use relief grooves where steps occur
✅ Position keyways away from high bending zones
✅ Avoid sudden changes in cross-section
✅ Perform FEM analysis in complex cases
Real-World Example:
A mining conveyor shaft has a 60 mm diameter and includes a keyway. The calculated shear stress is 40 MPa. If the K<sub>t</sub> due to the keyway is 2.5:
σactual=Kt×σnom=2.5×40=100MPaσ_{actual} = K_t × σ_{nom} = 2.5 × 40 = 100 MPa
The material and safety factor must now support 100 MPa, not 40. This changes material choice and fatigue predictions.
Conclusion
Stress concentration factors are small numbers with huge impact. By incorporating K<sub>t</sub> into shaft and axle design — especially in mining equipment exposed to repetitive loads — engineers can prevent unexpected failures and extend service life.
Ignoring K<sub>t</sub> might save time on paper but will cost much more in downtime, repair, and risk.