Strain Energy Of Shear Stresses On Bodies

Shear stress and strain is a very important aspect of classical mechanics. They are generally used in different analyses and calculations. One of these calculations is the strain energy calculations. Strain energies can be stored in different bodies because of different loadings. One of these loads is the shear stress and strain because of it. 

In safety calculations, Castigliano’s theorem can be used and this theorem depends on the strain energies of different loading conditions. On a mechanical system, if Castigliano’s theorem is used, you can calculate the strain energy due to the shear stresses based on this explanation here. 

Explanation Of The Shear Strain Energy Calculations

To explain these kinds of things, some theoretical assumptions are required. 

Think about a box that undergoes shear force ‘P’ from one side. Because of this shear force, there will be shear stress-induced and this shear stress generally calculated upon the shear strain value in which the angular distortion of the box element. 

Illustration of cube(Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.415).

The ‘G’ is the modulus of rigidity of the material of the cube. ‘V’ is the volume of the cube. ‘τ’ is the shear stress-induced on the box because of the shear force. And the stored shear strain energy is calculated with the formulation below;

The theory is explained over a cube because the cube shape is the most used engineering stress element. 


As you see above the explanation of the shear strain energy on bodies on the theoretical basis is very simple. 

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