1. What is Modulus of Rigidity?

The Modulus of Rigidity (also known as shear modulus) is a measure of a material's elastic shear stiffness. It describes the material's response to shear stress and is defined as the ratio of shear stress to shear strain.

2. How Does the Calculator Work?

The calculator uses the Modulus of Rigidity formula:

Where:

• \( G \) — Modulus of Rigidity (Pascals)
• \( F \) — Applied force (Newtons)
• \( L \) — Length of deformation (meters)
• \( A \) — Cross-sectional area (m²)
• \( \theta \) — Angle of deformation (radians)

Explanation: The formula calculates how much a material deforms under shear stress relative to its original shape.

3. Importance of Modulus of Rigidity

Details: The modulus of rigidity is crucial in engineering design, particularly for materials subject to twisting or shearing forces. It helps predict material behavior under mechanical stress.

4. Using the Calculator

Tips: Enter force in Newtons, length in meters, area in square meters, and angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for modulus of rigidity?
A: Steel has G ≈ 79 GPa, aluminum ≈ 26 GPa, rubber ≈ 0.0003 GPa. Values vary widely between materials.

Q2: How does modulus of rigidity relate to Young's modulus?
A: For isotropic materials, \( G = \frac{E}{2(1+\nu)} \), where E is Young's modulus and ν is Poisson's ratio.

Q3: What's the difference between shear modulus and modulus of rigidity?
A: They are the same property with different names - both refer to resistance to shear deformation.

Q4: Can modulus of rigidity be negative?
A: No, a negative value would imply the material expands when compressed, which is physically impossible.

Q5: How is angle measured for this calculation?
A: The angle should be in radians (1 radian ≈ 57.3 degrees) and represents the deformation angle.