# modulus of rigidity

by chandran
Tags: modulus, rigidity
 P: 139 what is modulus of rigidity and shear modulus? What do they define?
 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..) $Y= \frac{Longitudinal Stress}{Longitudinal Strain}$ 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.
 HW Helper P: 2,280 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.
HW Helper
P: 2,280

## 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)

$$\tau = G \gamma$$

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".
 P: 1 what does the product of rigidity modulus and moment of inertia of a beam mean??
 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
 Sci Advisor 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.
 P: 1 [QUOTE=rotin089;2414500]can someone tell me in brief about modulas of elasticiy along with pictures

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