The image above represents shear modulus.

To compute for shear modulus, two essential parameters are needed and these parameters are **young’s modulus (E) **and **Poisson’s ratio (v).**

The formula for calculating the shear modulus:

G = ^{E} / _{2(1 + v)}

Where:

G = Shear Modulus

E = Young’s Modulus

v = Poisson’s Ratio

Let’s solve an example;

Find the shear modulus when the young’s modulus is 32 and the Poisson’s ratio is 24.

This implies that;

E = Young’s Modulus = 32

v = Poisson’s Ratio = 24

G = ^{E} / _{2(1 + v)}

G = ^{32} / _{2(1 + 24)}

G = ^{32} / _{2(25)}

G = ^{32} / _{50}

G = 0.64

Therefore, the **shear modulus **is **0.64.**

**Calculating the Young’s Modulus when the Shear Modulus and the Poisson’s Ratio is Given.**

E = G (2 + 2v)

Where:

E = Young’s Modulus

G = Shear Modulus

v = Poisson’s Ratio

Let’s solve an example;

Find the young’s modulus when the shear modulus is 12 and the Poisson’s ratio is 10.

This implies that;

G = Shear Modulus = 12

v = Poisson’s Ratio = 10

E = G (2 +2v)

E = 12 (2 + 2(10))

E = 12 (2 + 20)

E = 12 (22)

E = 264

Therefore, the **young’s modulus **is **264.**

Continue reading How to Calculate and Solve for Shear Modulus | Rock Mechanics