modulus of rigidity

Shearing Deformation

Shearing Deformation
Shearing forces cause shearing deformation. An element subject to shear does not change in length but undergoes a change in shape.
 

shearing-deformation.jpg

 

The change in angle at the corner of an original rectangular element is called the shear strain and is expressed as
 

$\gamma = \dfrac{\delta_s}{L}$

 

The ratio of the shear stress τ and the shear strain γ is called the modulus of elasticity in shear or modulus of rigidity and is denoted as G, in MPa.
 

$G = \dfrac{\tau}{\gamma}$

 

The relationship between the shearing deformation and the applied shearing force is
 

$\delta_s = \dfrac{VL}{A_s G} = \dfrac{\tau L}{G}$

 

where V is the shearing force acting over an area As.