Explanation Of The Stress Concentration Factor

Stepped shafts are a very common application in mechanical systems. In stepped shaft mechanisms, the change of the diameter of the shaft is abrupt. Because of this abrupt change, a place called a ‘stress concentration zone’ occurs on the shaft. 

This place must be considered in the strength analyses of shafts. In torsion analysis, stress concentration zones are very important. 

In here, we explain;

  • What is the stress concentration factor and how it is calculated, 
  • How to calculate the shear stress on the stress concentration zones of shafts. 

What The Stress Concentration Factor?

The stress concentration factor is the factor that is considered for the abrupt diameter change zones for the stepped shafts. Stress concentration factors are the unitless factors that are used in maximum shear stress calculations. 

Stress concentration factor depends on two parameters; 

  • The ratio of the diameters of the shafts that are connected in stepped shaft mechanisms(D/d),
  • The ratio of the radius of the fillet that added to this stress concentration zone, to the smallest diameter of the stepped shaft(r/d). 

As you understand from above, fillets are added as a design principle to alleviate the stress concentration. You can use the graph below to calculate the stress concentration factor for your stepped shaft design;

You can find the approximate value of the stress concentration factor from the graph above. You must calculate the two parameters defined above to find the stress concentration factor. 

Also, you can define a goal stress concentration factor and you can see the approximate value of the fillet radius from the graph above for your application.

Maximum Shear Stress Calculation For The Stepped Shafts

Shear stress calculations for shafts are very important. You must compare the maximum shear stress with the maximum allowable stress of the shaft material to see whether the built system is safe. 

To calculate the maximum shear stress with the stress concentration factor, in the stress concentration zone of the stepped shafts, you can use the calculator below.

Maximum Shear Stress

The use of the calculator above is very simple. You just need to enter the required values inside the brackets then click on the ‘Calculate!’ button to see the result. 

The first value that you need to enter is the stress concentration factor that you calculated above. 

The second value is the torque of the shaft that is being transmitted. 

The third value is the smallest diameter in the stepped shaft system. 

The fourth value is the polar moment of inertia value of the smallest diameter. 

You can type the values in the recommended units inside the parenthesis both in SI or US Customary. You can use the MB Unit Converter tool to convert your units to consistent values. 


The explanation of the maximum shear stress originated because of the stress concentration sections of stepped shafts. 

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

You can find out much more calculators like in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Do not forget to leave your comments and questions below about the stress concentration factor and maximum shear stress calculations. 

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