Modulus Of Rigidity Of Shaft Given Total Strain Energy Stored In Shaft Calculator

Formula Used:

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

Shear Stress on Surface of Shaft (τ):

Pascal

Length of Shaft (L):

Meter

Polar Moment of Inertia of Shaft (J):

Meter⁴

Strain Energy in Body (U):

Joule

Radius of Shaft (r):

Meter

Modulus of Rigidity of Shaft (G):

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1. What is Modulus of Rigidity?

Modulus of rigidity of shaft 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 ability to resist shear deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( G \) — Modulus of rigidity of shaft (Pascal)
\( \tau \) — Shear stress on surface of shaft (Pascal)
\( L \) — Length of shaft (Meter)
\( J_{shaft} \) — Polar moment of inertia of shaft (Meter⁴)
\( U \) — Strain energy in body (Joule)
\( r_{shaft} \) — Radius of shaft (Meter)

Explanation: This formula calculates the modulus of rigidity based on the relationship between shear stress, shaft dimensions, polar moment of inertia, and stored strain energy.

3. Importance of Modulus of Rigidity Calculation

Details: Accurate calculation of modulus of rigidity is crucial for designing shafts and mechanical components that undergo torsional loading, ensuring they can withstand applied shear stresses without excessive deformation.

4. Using the Calculator

Tips: Enter all values in appropriate units. Shear stress in Pascal, length in meters, polar moment of inertia in meter⁴, strain energy in joules, and radius in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of modulus of rigidity?
A: Modulus of rigidity measures a material's resistance to shear deformation. Higher values indicate greater stiffness against shear forces.

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 shear deformation.

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: Why is polar moment of inertia important in this calculation?
A: Polar moment of inertia determines a shaft's resistance to torsional deformation, directly affecting how it stores strain energy under torsion.

Q5: Can this formula be used for non-circular shafts?
A: This specific formula is derived for circular shafts. Different formulas apply for shafts with non-circular cross-sections.