Shear Modulus Formula

What is Shear Modulus?

Shear modulus (G) represents the ability of any material to respond to shear stress. It means how much deformation a material will undergo under the influence of applied shear force. The higher the shear modulus, the greater is the stiffness of the material and hence the lesser its deformation.

Formula  

Where, 

• G is shear modulus in N.m-2

• F is the force acting on the body

• l is the initial length

• ∆x is the change in length

• A is the area

A shear modulus is useful for the small deformation of the material by using less shearing force which is capable to return to its original state. But not for the big sharing force because it causes permanent deformations of the object.

Example: 

Shear modulus value for Steel is 7.9×1010

Shear modulus value for plywood is 6.2×108

From the above explanation, it is clear that the steel is more rigid as compared to plywood.

Shear Modulus Unit is  Pa and Dimensional formula is M1L-1T-2

Solved Example:

Example 1: Find the Shear modulus, given that stress experienced by a body is 5×104Nm2 and strain is 4×10-2.

Solution:

Given,

 Stress = 5×104 Nm2

 Strain =  4×10-2

 shear modulus (G) =Shear stress/Shear strain

 shear modulus (G) = (5×104)/ (4×10-2)

 shear modulus (G)  = 1.25×106Nm2

Understanding shear modulus therefore gives a student studying materials science and engineering a way to predict the manner in which materials will behave under different forces; thus, an engineer could design safer, more effective structures and components.