The modulus of rigidity is the ratio of

Longitudinal stress to longitudinal strain
Volume stress to volume strain
Shearing stress to shearing strain
Tensile stress to tensile strain
Shearing stress to shearing strain  The modulus of rigidity, also known as shear modulus, is defined as the ratio of shear stress to shear strain of a structural member. This property depends on the material of the member: the more elastic the member, the higher the modulus of rigidity.

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