Calculate the shear modulus (modulus of rigidity) of a material using the relationship between shear stress and shear strain. Enter the shear stress (τ) and shear strain (γ) to get the shear modulus (G) — or solve for any unknown by providing the other two values. Based on the fundamental formula τ = G × γ, this tool covers materials like steel, aluminum, and more.
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The shear modulus (modulus of rigidity) has units of pressure — Pascals (Pa) in SI units. Because the values are typically very large, it is most commonly expressed in Gigapascals (GPa) or Megapascals (MPa). In imperial units, it is expressed in pounds per square inch (psi) or kip per square inch (ksi).
The shear modulus of steel is approximately 79–80 GPa (79,000–80,000 MPa). This high value reflects steel's resistance to shear deformation, making it a preferred material in structural and mechanical engineering applications where rigidity is critical.
You can calculate shear modulus (G) from Young's modulus (E) and Poisson's ratio (ν) using the formula: G = E / (2 × (1 + ν)). For example, steel with E ≈ 200 GPa and ν ≈ 0.26 gives G ≈ 79.4 GPa. This relationship holds for homogeneous, isotropic materials.
The shear modulus of aluminum is approximately 26 GPa (26,000 MPa) for common alloys. This is roughly one-third that of steel, meaning aluminum deforms more under the same shear stress, which is an important consideration in lightweight structural design.
The 6061-T6 aluminum alloy has a shear modulus of approximately 26 GPa (26,000 MPa). It is one of the most widely used aluminum alloys in aerospace and structural applications due to its good strength-to-weight ratio and machinability.
Yes, the modulus of rigidity (shear modulus) is an intrinsic material property that describes how a material resists shear deformation. It depends on the material's atomic bonding and crystal structure, not on the shape or size of the object. However, it can vary slightly with temperature and processing conditions.
Young's modulus (E) measures a material's resistance to tensile or compressive (normal) stress along an axis, while shear modulus (G) measures resistance to shear (tangential) stress. Both are elastic moduli and are related through Poisson's ratio for isotropic materials. Young's modulus values are typically about 2.5 times larger than shear modulus values for common metals.
Shear modulus is essential for calculating the angle of twist in a shaft subjected to torsion. The formula φ = TL / (GJ) relates the angle of twist (φ) to the applied torque (T), shaft length (L), shear modulus (G), and polar moment of inertia (J). A higher shear modulus means less angular deformation for the same applied torque.