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The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
G is the modulus of rigidity (shear modulus) of the material J is the torsional constant. Inverting the previous relation, we can define two quantities; the torsional rigidity, = with SI units N⋅m 2 /rad. And the torsional stiffness,
The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters. Young's modulus [ edit ]
Relations for other moduli are found in the (λ, G) row of the conversions table at the end of this article. Although the shear modulus, μ, must be positive, the Lamé's first parameter, λ, can be negative, in principle; however, for most materials it is also positive. The parameters are named after Gabriel Lamé.
A36 steel has a Poisson's ratio of 0.26 and a shear modulus of 11,500 ksi (79.3 GPa). [7] A36 steel in plates, bars, and shapes with a thickness of less than 8 inches (203 millimeters) has a minimum yield strength of 36 ksi (250 MPa) and ultimate tensile strength of 58–80 ksi (400–550 MPa).
The shear modulus or modulus of rigidity (G or Lamé second parameter) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
Pure shear stress is related to pure shear strain, denoted γ, by the equation [3] =, where G is the shear modulus of the isotropic material, given by = (+). Here, E is Young's modulus and ν is Poisson's ratio.
G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in 2 (psi), or lbf/ft 2 or in ISO units N/mm 2. The product J T G is called the torsional rigidity w T.