Modulus of Rigidity Calculator for Steel

Modulus of Rigidity Formula:

\[ G = \frac{\tau}{\gamma} \approx 79 \text{ GPa for steel} \]

Modulus of Rigidity (G):

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1. What is Modulus of Rigidity?

The Modulus of Rigidity (G), also known as shear modulus, is a measure of a material's elastic shear stiffness. For steel, it's approximately 79 GPa. It describes the material's response to shear stress.

2. How Does the Calculator Work?

The calculator uses the Modulus of Rigidity formula:

\[ G = \frac{\tau}{\gamma} \]

Where:

\( G \) — Modulus of Rigidity (Pascals)
\( \tau \) — Shear stress (Pascals)
\( \gamma \) — Shear strain (dimensionless)

Explanation: The equation shows the relationship between shear stress, shear strain, and the material's rigidity.

3. Importance of Modulus of Rigidity

Details: The modulus of rigidity is crucial in mechanical engineering for designing components that experience shear stress, such as shafts, beams, and fasteners.

4. Using the Calculator

Tips: Enter shear stress in Pascals and shear strain (dimensionless). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical modulus of rigidity for steel?
A: For most steels, it's approximately 79 GPa (79 × 10⁹ Pascals).

Q2: How does temperature affect the modulus of rigidity?
A: Generally, the modulus decreases with increasing temperature.

Q3: What's the difference between Young's modulus and modulus of rigidity?
A: Young's modulus describes tensile elasticity while rigidity modulus describes shear elasticity.

Q4: Can this calculator be used for materials other than steel?
A: Yes, but the typical value shown (79 GPa) is specific to steel. Other materials have different rigidity moduli.

Q5: How is shear strain measured?
A: Shear strain is the ratio of deformation to original dimension, typically measured in radians or as a dimensionless ratio.