Shaft stress concentration factor

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What is Stress concentration?

Mechanical elements such as shafts, gears, support brackets threaded fasteners etc often have 3D features that change its size and shape to fullfill its purposes such as stepped shaft shoulder for ball bearing, shaft keyways for keys, grooves for retainer rings and O-rings.

Stress concentration
Stress concentration

These sudden change geometry points under its load conditions often create localised stress fields where the part typically fails. This localised stress is called Stress concentration and those features are sometimes referred to as Stress concentrators or stress raisers or risers.



What is Stress concentration factor?

A stress concentration factor normally denoted as Kt quantifies the stress concentration in a part and is defined as the ratio of the maximum stress to the nominal or reference stress.

Kt = σmaxnom

Nominal stress (σnom) is the stress without the stress concentrators suchas grooves while the maximum stress (σmax) is the maximum stress with the stress raiser feature.

Stress concentration factor

Stepped shaft with fillet

Stress concentration factor for stepped shaft - Axial force
Stress concentration factor for stepped shaft – Axial force (source :Collins, J. (2010))
Stress concentration factor for stepped shaft - Torsional load
Stress concentration factor for stepped shaft – Torsional load (source :Collins, J. (2010))
Stress concentration factor for stepped shaft - Bending moment
Stress concentration factor for stepped shaft – Bending moment (source :Collins, J. (2010))



  • Collins, J. (2010). Mechanical design of machine elements and machines. Hoboken, NJ: Wiley
  • Pilkey, W. D.(2005). Formulas for stress, strain and structural matrices 2nd Edition John Wiley & Sons

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