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Home / Physics / Shear Modulus Of Rigidity - Definition, Formula, Example & FAQs

Shear Modulus Of Rigidity - Definition, Formula, Example & FAQs

Last Updated on Jan 23, 2025
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Understanding Shear Modulus

The shear modulus or modulus of elasticity is a way to measure the mechanical properties of solids. It is one among other elastic moduli like Young’s modulus and bulk modulus. The shear modulus provides us with the ratio of shear stress to shear strain in a body.

  • It is measured in the SI unit pascal or Pa.
  • The dimensional formula of shear modulus is M1L-1T-2.
  • It is denoted by G.

The shear modulus can be used to describe how a material resists transverse deformations. However, this is applicable only for small deformations. After these, the material can return to its original state. This is because large shearing forces can lead to permanent deformations (no longer an elastic body).

The Formula for Modulus Of Rigidity

In this formula:

  • is the shear stress.
  • F represents the force acting on the object.
  • A is the area on which the force is acting.
  • is the shear strain.
  • is the transverse displacement.
  • l is the initial length.

Units:

  • The modulus of rigidity is measured in the SI unit pascal or Pa.
  • It is often expressed in terms of gigaPascal (GPa).
  • Alternatively, it can also be expressed in pounds per square inch(PSI).

An Overview of Modulus Of Rigidity

The modulus of rigidity is an elastic coefficient that results in lateral deformation when a shear force is applied. It provides a measure of a body's rigidity. The table below gives an overview of rigidity modulus.

Definition: The shear modulus is the ratio of shear stress to shear strain in a body.
Symbol: G, S, or μ
SI unit: Pascal (Pa), N/m2
Formula: Shear stress/shear strain
Dimension formula: M1L-1T-2

Examples of Modulus Of Rigidity

Let's consider a few examples to understand how the shear modulus defines the rigidity of different materials.

  • The shear modulus of rubber is 0.3×106 Pa
  • The shear modulus of aluminium is 25×109 Pa

This implies that aluminium is significantly more rigid than rubber, almost 83333 times more rigid!

How to Calculate It

Let's say we have a block of an unknown material placed on a table (with the square face on the table). It is under a shearing force. Using the given data, we can calculate the shear modulus of the material.

Dimensions of the block = 50 mm x 50 mm x 15 mm

Shearing Force = 0.200 N
Displacement = 4 mm

Calculation:

We substitute the values in the formula:

Shear stress:

 

Shear strain:

So, shear modulus,

= 1200 N/m2.

Here are some more topics you might find interesting:

The Relationship Between Elastic Constants

The elastic moduli of a material, such as Young’s Modulus, Bulk Modulus, and Shear Modulus, are specific forms of Hooke’s law. This law states that the strain experienced by a material due to the applied stress is proportional to that stress. Therefore, we can express the relationship between elastic constants using the equation below:

2G(1+υ) = E = 3K(1−2υ)

Here,

  • G is the Shear Modulus
  • E is the Young’s Modulus
  • K is the Bulk Modulus
  • υ is Poisson’s Ratio

 

 

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Frequently Asked Questions

If the shear modulus of material 1 is x pascals and Material 2 is 30x pascals. It means that material 2 is more rigid than material 1.

The value of shear modulus is constant for a given material and is independent of the applied shear force.

The shear modulus is related to other elastic moduli as 2G(1+υ) = E = 3K(1−2υ) where, G is the Shear Modulus, E is the Young’s Modulus, K is the Bulk Modulus, υ is Poisson’s Ratio

The modulus of rigidity is defined as the ratio of shear stress to shear strain in a body.

Shear strain is a dimensionless physical quantity and hence has no unit.
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