modulus of rigidity


by chandran
Tags: modulus, rigidity
chandran
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#1
Jun6-05, 06:30 AM
P: 139
what is modulus of rigidity and shear modulus? What do they define?
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Dr.Brain
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#2
Jun6-05, 07:40 AM
P: 543
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..)

[latex]Y= \frac{Longitudinal Stress}{Longitudinal Strain}[/latex]

2. Bulk Modulus is generally used for Liquids and Gases

[latex]B= \frac{Volumetric Stress}{Volumetric Strain}[/latex]

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
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#3
Jun6-05, 08:39 AM
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Rigidity is the required force to produce a unit incrementum of length.

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

[tex] \delta = \frac{PL}{EA} [/tex]

where [itex] \delta [/itex] 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
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#4
Jun6-05, 11:28 AM
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modulus of rigidity


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)

[tex] \tau = G \gamma [/tex]

where [itex] \tau [/itex] is the shear stress, G is the modulus of rigidity or elasticity in shear and [itex] \gamma [/itex] 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
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#5
Aug12-09, 02:07 AM
P: 1
what does the product of rigidity modulus and moment of inertia of a beam mean??
rotin089
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#6
Oct28-09, 09:55 AM
P: 5
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
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#7
Oct28-09, 12:24 PM
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P: 5,095
They are not derived quantities. They have specific definitions:
http://www.engineeringtoolbox.com/mo...ity-d_946.html
http://en.wikipedia.org/wiki/Shear_modulus
http://www.efunda.com/formulae/solid..._constants.cfm
http://geophysics.ou.edu/geomechanic...ast_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
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#8
Jul23-10, 10:45 AM
P: 1
[QUOTE=rotin089;2414500]can someone tell me in brief about modulas of elasticiy along with pictures


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