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