Home Back

Modulus Of Rigidity Given Maximum Permissible Shear Stress Calculator

Formula Used:

\[ G = \frac{\tau_{max} \cdot L_{shaft}}{\theta \cdot R} \]

Pa
m
rad
m

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Modulus of Rigidity?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{\tau_{max} \cdot L_{shaft}}{\theta \cdot R} \]

Where:

Explanation: This formula calculates the modulus of rigidity based on the maximum permissible shear stress, shaft dimensions, and the resulting angle of twist.

3. Importance of Modulus of Rigidity Calculation

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.

4. Using the Calculator

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.

5. Frequently Asked Questions (FAQ)

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.

Modulus Of Rigidity Given Maximum Permissible Shear Stress Calculator© - All Rights Reserved 2025