Cyclic Stresses in Mechanics; Definition, Uses and Calculator

Cyclic stress is one of the most encountered types of loadings in classical mechanics. So, dynamic systems which have lots of moving parts in them have lots of different kinds of them that we calculate. Also, there are different calculations related to cyclic stresses and their ratios in engineering calculations. 

What is Cyclic Stress?

Cyclic stresses.
Graphical illustrations of cyclic stresses(Image Source: Researchgate.).

These stresses can take place as axial stresses such as tensile and compressive stresses, bending stresses, and torsional stresses. Furthermore, if the value of these stresses varies along the time as a sinusoidal wave, we can talk about cyclic stress on that part. 

For example for a rotating shaft in both directions, we can say that there is cyclic stress on that shaft. Also in both directions, twisting loading is applied to the shaft. So, torsional stresses are applied to the shaft. 

We calculate them generally in the fatigue calculations of structural elements. In fatigue calculations, we calculate the endurance of the structural elements in different cyclic loading conditions. Before starting the fatigue calculations, we need to define these stresses in a good manner. 

Parameters of Cyclic Loads and Stresses

In these stresses, there are some parameters that we define and calculate. These parameters are; 

  • σmax: The maximum stress value that the cyclic stress loading has. 
  • σmin: The minimum stress value in a stress range. 
  • σm: The mean stress in them which we calculate with the maximum and minimum stress values.
  • σr: The range of the stress in them. We calculate the stress range in cyclic stress as; 

σr = σmax-σmin

  • σa: In them, we calculate the stress amplitude value by dividing the stress range into 2. 
  • R: Stress ratio is the ratio of the minimum and maximum stresses in them. 

The General Patterns

In engineering calculations, constant-amplitude stresses are generally calculated and used. And in general, the most common stress patterns are; 

  • Completely Reversed: Furthermore, in this case of cyclic stresses, the mean stress is 0 and the stress ratio is -1. The maximum and minimum stresses have the same absolute values in opposite signs. 
  • Nonzero Mean: In this case of these stresses, the mean stress is not equal to 0 which can be negative or positive, and the stress ratio is not equal to -1 which can be also negative and positive. 
  • Released Tension: In this case, the minimum stress value is 0 and the maximum stress value is positive. The mean stress is equal to half of the maximum stress value. The stress ratio is equal to 0. The reason that is called released tension is, that tensile stress is always in action, and in the minimum stress, tensile stress is released to 0. 
  • Released Compression: In this case, the maximum stress is equal to zero and the minimum stress value has a negative sign. So, the stress ratio is infinite and the mean stress is equal to the division of the minimum stress value with 2. And also, the name released compression came from releasing the compressive stress at the maximum stress value. 

Cyclic Stress Calculator

Cyclic stresses are mainly used in fatigue calculations and the parameters of them which are mentioned above must be calculated again and again. Also, we prepared a handy calculator to calculate all the parameters related to them. 


Type of the Cyclic Stress

The use of this calculator is very simple above. Firstly, you just need to enter the required maximum and minimum stress values inside the brackets and click on the ‘Calculate!’ button to see all the required parameters and patterns of cyclic stress type according to these parameters. 


Above all, as you see above, it is very simple to calculate the cyclic stresses for fatigue analyses in classical mechanics. 

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

So, you can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

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