# Modulus of rigidity

1. Jun 6, 2005

### chandran

what is modulus of rigidity and shear modulus? What do they define?

2. Jun 6, 2005

### Dr.Brain

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.

3. Jun 6, 2005

### Pyrrhus

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.

4. Jun 6, 2005

### Pyrrhus

Maybe you are refering 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".

Last edited: Jun 6, 2005
5. Aug 12, 2009

### sindhujahere

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

6. Oct 28, 2009

### rotin089

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

7. Oct 28, 2009

### FredGarvin

Last edited by a moderator: May 4, 2017
8. Jul 23, 2010