# Shear Modulus

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Shear modulus, abbreviated as G, also called modulus of rigidity, is the ratio of the tangential force per unit area applied to a body or substance to the resulting tangential strain within the elastic limits.

### Shear Modulus Formula

$$\large{ G = \frac { \sigma } { \epsilon } }$$

Where:

$$\large{ G }$$ = shear modulus

$$\large{ A }$$ = area on which the force acts

$$\large{ F }$$ = force that acts

$$\large{ l_i }$$ = initial length

$$\large{ \epsilon }$$  (Greek symbol epsilon) = shear strain

$$\large{ \sigma }$$  (Greek symbol sigma) = shear stress

$$\large{ \Delta x }$$ = transverse displacement

Solve for:

$$\large{ \epsilon = \frac { \Delta x } { l_i } }$$

$$\large{ \sigma = \frac { F } { A } }$$