1. What is Modulus of Rigidity?

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 torsion formula:

Where:

• \( G \) — Modulus of Rigidity (Pa)
• \( T \) — Torque (N·m)
• \( L \) — Length of Shaft (m)
• \( \theta \) — Angle of Twist (rad)
• \( J \) — Polar Moment of Inertia (m⁴)

Explanation: This formula calculates the shear modulus by relating the applied torque, shaft length, angle of twist, and polar moment of inertia.

3. Importance of Modulus of Rigidity

Details: Modulus of Rigidity is crucial in mechanical engineering for designing shafts, springs, and other components subjected to torsional loads. It helps determine how much a material will deform under shear stress.

4. Using the Calculator

Tips: Enter torque in Newton-meters, length in meters, angle of twist in radians, and polar moment of inertia in meters to the fourth power. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Modulus of Rigidity for common materials?
A: Steel: ~79 GPa, Aluminum: ~26 GPa, Copper: ~48 GPa, Rubber: ~0.0001-0.001 GPa.

Q2: How does Modulus of Rigidity differ from Young's Modulus?
A: Young's Modulus measures resistance to linear deformation, while Modulus of Rigidity measures resistance to shear deformation.

Q3: What factors affect the Modulus of Rigidity?
A: Material composition, temperature, and processing methods significantly affect the shear modulus.

Q4: Why is the polar moment of inertia important in torsion calculations?
A: It represents the distribution of material around the axis of rotation and determines the shaft's resistance to torsion.

Q5: Can this calculator be used for non-circular cross-sections?
A: The formula is specifically derived for circular cross-sections. Different formulas apply for other shapes.