Von mises stress vs Shear stress – Difference [Explained]

The main distinguishing point for von mises stress vs shear stress is that von mises stress resists the distortion in the object while shear stress resists the shear deformation in the object.

Let’s take a look at them before knowing how they differ from each other.

In this article, we’re going to discuss:

• Von-mises stress:
• Shear stress:
• Von mises stress vs Shear stress – Difference:
• FAQ:

Von-mises stress:

Von mises stress is equivalent stress calculated from the distortion energy of objects. The total strain energy of the object is classified on the basis of the nature of deformation occurring in the object i.e. the strain energy related to the change volume (`U_{v}`) and the strain energy responsible for the change in the shape of the object (distortion energy, `U_{d}`).

`U_{\text{Total}} = U_{v} + U_{d}`

Out of them, the von-mises stress is based on the distortion energy (`U_{d}`), which is given by,

`\sigma = \sqrt{\sigma_{1}^{2} + \sigma_{2}^{2} + \sigma_{3}^{2} – \sigma_{1}\sigma_{1} – \sigma_{2}\sigma_{3}-\sigma_{3}\sigma_{1}}`

Where `\sigma_{1}`, `\sigma_{2}`, `\sigma_{3}` are the principal stresses acting on member.

The theory of failure based on von-mises stress is used for the design of ductile materials.

Shear stress:

Shear stress is stress developed into the object to avoid failure due to the shear forces. The shear deformation in an object causes because of the sliding of layers of the object over each other. The shear stress developed in an object helps to resist this sliding of layers.

Shear stress is denoted by the symbol ‘`\tau`’ and measured in terms of N/m².

Mathematically it is expressed as,

`\tau = \frac{\text{Shear force (F)}}{\text{Resisting Area (A)}}`

In this case, the forces act parallel to the plane of deformation.

Von mises stress vs Shear stress – Difference:

Sr. No.	Von-mises stress	Shear stress
1	The von-mises stress resists the distortion or change in the shape of the object.	The shear stress resists the deformation caused by shear forces.
2	It is equivalent stress calculated from the distortion energy absorbed by an object.	It is actual stress experienced by an object.
3	It is used in the von-mises theory of failure.	It is used in the maximum shear stress theory of failure.
4	The failure theory based on von-mises stress is less conservative in comparison with the maximum shear stress theory.	The maximum shear stress theory is more conservative in comparison with von-mises stress theory.
5	It is difficult to calculate von-mises stress.	It is easy to find shear stress.

FAQ: