The shear stress is the resistance developed by the object per unit resisting area to avoid the shear deformation caused by the application of the shear forces while the shear strain is the strain results due to the shear stress.
Contents:
Shear stress:
The shear stress indicates the internal resistance per unit area developed by the object to avoid shear deformation.
The shear stress in the object arises due to the application of the equal and opposite forces that acts tangentially to the resisting surface. Thus the shear stress also acts tangentially to the resisting surface.
The above figure shows the object subjected to the shear forces. Thus the shear stress acting on the object is given by,
`\text{Shear stress}=\frac{\text{Shear force}}{\text{Resisting area}}`
Shear strain:
The shear strain is the type of strain in the object caused due to the shear stress.
It is the rate of shear deformation in the object and is measured as a change in the angle between the planes of the object. It is measured in terms of radians.
The below figure indicates an object with its bottom plane fixed. The upper plane of the object is subjected to the shear force (F) which results in the displacement of the upper plane of the object.
The shear strain in the object (`\gamma`) is given by the following equation,
`\gamma=tan^{-1}(\frac{\text{Displacement of plane}}{\text{Perpendicular distance from opposite plane}})`
Shear stress vs Shear strain:
| Sr. No. | Shear stress | Shear strain |
|---|---|---|
| 1 | Shear stress indicates the internal resistive force developed by an object per unit resisting area against the shear deformation. | The strain arises due to the shear stress is known as shear strain. |
| 2 | Shear stress is the ratio of shear force to the respective resisting area. | Shear strain is the measure of shear deformation that occurs in the object. |
| 3 | Shear stress = `\frac{\text{Shear force}}{\text{Area}}` | It is equal to the inverse tan of the ratio of displacement of the plane to the perpendicular distance from the opposite plane. |
| 4 | It is denoted by the symbol ‘𝜏’ (tau). | It is denoted by the symbol ‘γ’ (gamma). |
| 5 | It has an SI unit of N/m². | It is expressed in terms of a radian. |
| 6 | Shear stress develops due to the application of shear forces. | It develops due to shear stress. |
| 7 | The shear stress in the object cannot be measured directly. | It can be measured directly. |
FAQs:
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How to obtain shear strain from the shear stress?
The shear strain can be calculated from the shear stress by use of the following equation:-
Shear strain (γ) = Shear stress (𝜏) ÷ Modulus of rigidity (G). -
How shear strain depends on the shear stress?
The shear strain in an object increases with the increase in shear stress.
