Formula Used:
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The Modulus of Rigidity (also known as shear modulus) is the measure of the rigidity of a body, given by the ratio of shear stress to shear strain. It represents a material's response to shear stress and is denoted by G.
The calculator uses the formula:
Where:
Explanation: This formula calculates the modulus of rigidity based on the maximum permissible shear stress, shaft dimensions, and the resulting angle of twist.
Details: Calculating the modulus of rigidity is crucial for material selection in engineering applications, designing mechanical components subjected to torsion, and ensuring structural integrity under shear forces.
Tips: Enter maximum shear stress in Pascals, length of shaft in meters, angle of twist in radians, and radius of shaft in meters. All values must be positive numbers.
Q1: What is the typical range of modulus of rigidity values?
A: Modulus of rigidity values vary widely by material. For example, steel has G ≈ 79.3 GPa, aluminum ≈ 26 GPa, and rubber ≈ 0.0003-0.004 GPa.
Q2: How does modulus of rigidity relate to other elastic moduli?
A: For isotropic materials, modulus of rigidity (G) relates to Young's modulus (E) and Poisson's ratio (ν) as: G = E/(2(1+ν)).
Q3: When is this calculation particularly important?
A: This calculation is essential in designing shafts, springs, and other components that experience torsional loading in mechanical systems.
Q4: What factors can affect the accuracy of this calculation?
A: Material homogeneity, temperature effects, and accurate measurement of the angle of twist can affect calculation accuracy.
Q5: Can this formula be used for all materials?
A: This formula applies to materials that exhibit linear elastic behavior under shear stress and follows Hooke's law for shear deformation.