Shear modulus, which is also often referred to as the modulus of rigidity or torsion modulus, is a measure of the rigid or stiff nature of different types of solid materials. It is derived from the material's ratio of its shear stress value to that of shear strain. Shear stress is a value of how much force is applied to a square area of a material, usually measured in pressure values of pascals. Strain is the amount that the material has deformed under stress divided by its original length. The shear modulus value is always a positive number and is expressed as an amount of force per unit area, which is generally recorded as metric gigapascals (GPa) because the values are more practical than English equivalents.
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p -0.29,e-12.4e3mpa
Robert Hooke in 1660 discovered the stress strain relation known as Hooke's law. The shear tress relation ( stress = rigidity modulus x shear strain) is a logical extension of Hooke's law,
1. Young's modulus of elasticity, E, also called elastic modulus in tension 2. Flexural modulus, usually the same as the elastic modulus for uniform isotropic materials 3. Shear modulus, also known as modulus of rigidity, G ; G = E/2/(1 + u) for isotropic materials, where u = poisson ratio 4. Dynamic modulus 5. Storage modulus 6. Bulk modulus The first three are most commonly used; the last three are for more specialized use
The modulus of elasticity , E, relates tensile stress to tensile strain The modulus of rigidity, G, relates shear stress to shear strain The bulk modulus, K, relates compressive stress to volume strain The three are related using u, poisson ratio of material, that varies generally from 0 to 0.5 E = 9K/ (1 + 3K/G) G = E/2(1+u) G = 3(1-2u)K/2(1+u)
shear = 77GPa
there are different types of modulus it depends on what types of stress is acting on the material if its direct stress then then there is modulus of elasticity,if tis shear stress then its modulus of rigidity and when its volumetric stress it is bulk modulus and so on
Shear Stress divided by the Angle of Shear is equals to Shear Stress divided by Shear Strain which is also equals to a constant value known as the Shear Modulus. Shear Modulus is determined by the material of the object.
It is the ratio of shear stress to shear strain.
Shear modulus of soil is measured in pressure units, typically Pascals (Pa) or KiloPascals (KPa).
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p -0.29,e-12.4e3mpa
shear stress (t) is proportional to shear modulus (G) x shear strain (h) or t = Gh where h is shear angle/length
That is the shear modulus, G, related to Young elastic modulus ,E, as G = E/(2(1+u)) where u is Poisson ratio
Most steels have Young Modulus, E, of 30 million psi and Poisson ratio, u, of about 0.30 Shear Modulus = E/2/(1+u) = 30/2.6 = 11.5 million psi
Just as the modulus of elasticity , E, relates tensile stress to tensile strain, the modulus of rigidity, G, relates shear stress to shear strain. The modulus of rigidity, G, is, for isotropic materials, related to E as G = E/ (2(1+u)) where u = poisson ratio which varies from 0 to 0.5 and is usually 0.25-0.33 for many metals. tensile stress = Ee e = tensile strain shear stress = Gk k = shear strain