# Modulus of Rigidity & Shear Modulus: Definition & Meaning

• chandran
In summary: Shear strain is the change in length of an object that is subjected to shear forces. Shear stress is the force per unit area that is applied to an object to cause that change in length. Rigidity is the force required to produce a unit increment in length.
chandran
what is modulus of rigidity and shear modulus? What do they define?

There are three moduli of rigidity:
1. Young's Modulus
2.Bulk Modulus
3.Shear Modulus

Modulus is generally defined as Stress/Strain

1.Young's Modulus is generally used for solid materials( In problems, for wires..)

$Y= \frac{Longitudinal Stress}{Longitudinal Strain}$

2. Bulk Modulus is generally used for Liquids and Gases

$B= \frac{Volumetric Stress}{Volumetric Strain}$

3. Shear Modulus is used where tangential stress is applied and the object bends or tangentially bends making some angle with vertical.

I assume you know what stress and strain is.

suhrid
Rigidity is the required force to produce a unit incrementum of length.

In prismatic beams, the product of EA is known as axial rigidity.

$$\delta = \frac{PL}{EA}$$

where $\delta$ is the change in length, P is the force applied at the centroid, L is the original length, E is the modulus of elasticity (assuming the material is at the elastic-linear region) and A is the cross sectional area. Of course this is for Homogenous materials.

In general the rigidity will be a measure of a structural member "opposing the change in length", with rigidity it's often used flexibility, which is inverse to the rigidity.

Maybe you are referring to the modulus of elasticity in shear stress, also know as modulus of rigidity.

According to Hooke's Law in shear (elastic-linear region)

$$\tau = G \gamma$$

where $\tau$ is the shear stress, G is the modulus of rigidity or elasticity in shear and $\gamma$ is the angle of distorsion or the unit deformation.

The rigidity here is about measuring the structural element resistance to the "change of its shape".

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what does the product of rigidity modulus and moment of inertia of a beam mean??

can some one please tell me the derivation of modulus of rigidity or shear modulus i stuck
i need to finish with this equation:

thanks

Last edited by a moderator:
rotin089 said:
can someone tell me in brief about modulas of elasticiy along with pictures

## 1. What is the Modulus of Rigidity?

The Modulus of Rigidity, also known as Shear Modulus, is a measure of a material's resistance to shearing or twisting forces. It is the ratio of shear stress to the corresponding shear strain within the elastic limit.

## 2. What is the significance of the Modulus of Rigidity?

The Modulus of Rigidity is an important material property that helps determine a material's ability to withstand shearing or twisting forces. It is commonly used in engineering calculations to determine the stability and strength of structures and components.

## 3. How is the Modulus of Rigidity calculated?

The Modulus of Rigidity can be calculated by dividing the shear stress by the shear strain. It is typically expressed in units of force per unit area (such as N/m2 or Pa).

## 4. What factors can affect the Modulus of Rigidity?

The Modulus of Rigidity can be affected by various factors, including the type of material, its microstructure, and its temperature. Generally, materials with stronger intermolecular forces and a more rigid structure will have a higher Modulus of Rigidity.

## 5. How does the Modulus of Rigidity differ from the Modulus of Elasticity?

The Modulus of Rigidity is a measure of a material's resistance to shearing or twisting forces, while the Modulus of Elasticity (also known as Young's Modulus) is a measure of a material's stiffness under tensile or compressive forces. Both are important properties in understanding a material's behavior under different types of stress.

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