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Modulus of rigidity

  1. Jun 6, 2005 #1
    what is modulus of rigidity and shear modulus? What do they define?
  2. jcsd
  3. Jun 6, 2005 #2
    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..)

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

    2. Bulk Modulus is generally used for Liquids and Gases

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

    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.
  4. Jun 6, 2005 #3


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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.
  5. Jun 6, 2005 #4


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    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".
    Last edited: Jun 6, 2005
  6. Aug 12, 2009 #5
    what does the product of rigidity modulus and moment of inertia of a beam mean??
  7. Oct 28, 2009 #6
    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

  8. Oct 28, 2009 #7


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