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Modulus of Rigidity Formula:
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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 is often denoted by G and is an important property in materials science and engineering.
The calculator uses the Modulus of Rigidity formula:
Where:
Explanation: The formula calculates the modulus of rigidity by dividing the torsional rigidity by the polar moment of inertia of the material.
Details: Accurate calculation of modulus of rigidity is crucial for designing mechanical components subjected to torsional loads, analyzing material behavior under shear stress, and ensuring structural integrity in engineering applications.
Tips: Enter torsional rigidity in N·m² and polar moment of inertia in m⁴. Both values must be positive numbers greater than zero.
Q1: What is the physical significance of Modulus of Rigidity?
A: Modulus of Rigidity represents a material's resistance to shearing deformation. Higher values indicate stiffer materials that resist shear deformation more effectively.
Q2: How does Modulus of Rigidity differ from Young's Modulus?
A: Young's Modulus measures resistance to linear deformation (tension/compression), while Modulus of Rigidity measures resistance to shear deformation (sliding of layers).
Q3: What are typical values of Modulus of Rigidity for common materials?
A: Steel: ~80 GPa, Aluminum: ~26 GPa, Rubber: ~0.0003 GPa. Values vary significantly depending on material composition and treatment.
Q4: When is this calculation particularly important?
A: This calculation is critical in designing shafts, springs, and other components subjected to torsional loads in mechanical engineering applications.
Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic materials and linear elastic behavior. It may not accurately predict behavior for anisotropic materials or under large deformations.