# Shear Modulus

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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.

## Shear Modulus formulas

 $$\large{ G = \frac { \tau } { \gamma } }$$ $$\large{ G = \frac { F\;l } { A\;\Delta x } }$$ $$\large{ G = \frac { E }{ 2 \; \left( 1 \;+\; \mu \right) } }$$ $$\large{ G = \frac { 8 \; k_s \; n_a \; D^3 } { d^4 } }$$ (spring)

### Where:

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

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

$$\large{ E }$$ = elasticity

$$\large{ F }$$ = 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

$$\large{ \mu }$$  (Greek symbol mu) = Poisson's Ratio

$$\large{ \gamma }$$  (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