# Shear Strain

on . Posted in Classical Mechanics

Shear strain, abbreviated as $$\gamma$$ (Greek symbol gamma), a dimensionless number, (measured in radians), is opposing forces acting parrallel to the cross-section of a body.  It is a measure of the deformation or displacement that occurs within a material when subjected to shear stress.  It represents the change in shape or distortion experienced by the material due to the applied shear force.

Shear strain is closely related to shear stress, the relationship between shear stress and shear strain is described by the material's shear modulus, also known as the modulus of rigidity or elastic modulus in shear.  The shear modulus represents the material's ability to resist deformation under shear stress.  Different materials exhibit different responses to shear strain, depending on their mechanical properties.  Elastic materials, such as metals and some polymers, can experience shear strain and return to their original shape when the shear force is removed.  In contrast, plastic materials, like certain plastics and fluids, may undergo permanent deformation or flow under shear strain.

Shear strain is an important concept in fields such as solid mechanics, materials science, and structural engineering.  It plays a crucial role in analyzing the behavior of materials and structures subjected to shear forces, such as beams, plates, and geological formations. ## Shear strain formula

$$\large{ \gamma = \frac{ \Delta y }{ l_i } }$$     (Shear Strain)

$$\large{ \Delta y = \gamma \; l_i }$$

$$\large{ l_i = \frac{ \Delta y }{ \gamma } }$$

Symbol English Metric
$$\large{ \gamma }$$  (Greek symbol gamma) = shear strain $$\large{deg}$$   $$\large{rad}$$
$$\large{ \Delta y }$$ = transverse displacement $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l_i }$$ = initial length $$\large{ in }$$ $$\large{ mm }$$ 