Modulus of Rigidity or Shear Modulus:

Modulus of rigidity is defined as the ratio of tangential stress to shear strain within the elastic limit.

If a tangential force \( F \) acts on a surface of the area \( A \), then the tangential stress is \( \displaystyle\frac{F}{A}\). This effect gives rise to the angle of shear \( \theta \). Then the Modulus of Rigidity \( \eta=\frac{Tangential\ Stress}{Shear\ Strain}=\frac{F/A}{\theta} \)

The shear strain \( \displaystyle\theta=\frac{l}{L} \), where \( l \) is the displacement of the vertical plane of the cube, \( L \) is the hight of the cube.

\eta=\frac{F/A}{l/L}=\frac{F\cdot{L}}{A\cdot{l}}