Modulus of Rigidity of Rod Given Strain Energy in Rod Calculator

Formula Used:

\[ G = \frac{(\tau^2) \times L}{2 \times J \times U} \]

Torque on Rod or Shaft (τ):

N·m

Length of Rod or Shaft (L):

Polar Moment of Inertia (J):

m⁴

Strain Energy in Rod or Shaft (U):

Modulus of Rigidity (G):

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1. What is the Modulus of Rigidity?

The Modulus of Rigidity (also known as shear modulus) is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is and its resistance to shearing stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{(\tau^2) \times L}{2 \times J \times U} \]

Where:

\( G \) — Modulus of rigidity (Pa)
\( \tau \) — Torque on rod or shaft (N·m)
\( L \) — Length of rod or shaft (m)
\( J \) — Polar moment of inertia (m⁴)
\( U \) — Strain energy (J)

Explanation: This formula calculates the modulus of rigidity based on the torque applied, length of the rod, polar moment of inertia, and the strain energy stored in the rod.

3. Importance of Modulus of Rigidity Calculation

Details: Calculating the modulus of rigidity is crucial for understanding material properties, designing mechanical components, and predicting how materials will behave under torsional stress.

4. Using the Calculator

Tips: Enter torque in N·m, length in meters, polar moment of inertia in m⁴, and strain energy in joules. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of modulus of rigidity?
A: It measures a material's resistance to shearing deformation - how much it will deform when subjected to shear stress.

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 angular deformation (shear).

Q3: What are typical values for modulus of rigidity?
A: For steel: ~79 GPa, aluminum: ~26 GPa, rubber: ~0.0003-0.004 GPa. Values vary significantly between materials.

Q4: When is this calculation particularly important?
A: In designing shafts, springs, and any components subject to torsional loading where shear deformation is a concern.

Q5: How does temperature affect modulus of rigidity?
A: Generally, modulus of rigidity decreases with increasing temperature as materials become less rigid when heated.