# Shear Modulus

Shear modulus, abbreviated as G, also called modulus of rigidity or shear modulus of elasticity, 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.

## Formulas that use Shear Modulus

\(\large{ G = \frac { \tau } { \gamma } }\) | |

\(\large{ G = \frac { F\;l } { A\;\Delta x } }\) | |

\(\large{ G = \frac { 8 \; k_s \; n_a \; D^3 } { d^4 } }\) | (spring) |

### Where:

\(\large{ G }\) = shear modulus

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

\(\large{ F }\) = force that acts

\(\large{ l }\) = lateral length of the material without force applied

\(\large{ D }\) = mean coil diameter

\(\large{ n_a }\) = number of active coils

\(\large{ \gamma }\) (Greek symbol gamma) = shear strain

\(\large{ \tau }\) (Greek symbol tau) = shear stress

\(\large{ k_s }\) = spring constant

\(\large{ \Delta x }\) = transverse displacement

\(\large{ d }\) = wire size

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