How to Calculate and Solve for Shear Modulus | Rock Mechanics

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.

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