# Shear Modulus

Written by Jerry Ratzlaff on . Posted in Thermodynamics 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