Modulus of Rigidity & Shear Modulus: Definition & Meaning

[chandran]

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

 

[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.

 

[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.

 

[Pyrrhus]

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".

 

[sindhujahere]

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

 

[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:

G=E/2(1+U) please help out if you can

thanks

 

[FredGarvin]

They are not derived quantities. They have specific definitions:
http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html
http://en.wikipedia.org/wiki/Shear_modulus
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/calc_elastic_constants.cfm
http://geophysics.ou.edu/geomechanics/notes/elast_const/elast_const.html

For the proof you are doing, you'll need to look at the definition of shear strain and how shear strain is related to shear stress in multiple dimensions.

 

[engineers]

can someone tell me in brief about modulas of elasticiy along with pictures