# Shear Modulus

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:

\(\large{ \epsilon = \frac { \Delta x } { l_i } }\)

\(\large{ \sigma = \frac { F } { A } }\)

Tags: Equations for Strain and Stress Equations for Force Equations for Modulus