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

Formula Used:

\[ G = \frac{(\tau^2) \times ((d_{outer}^2) + (d_{inner}^2)) \times V}{4 \times U \times (d_{outer}^2)} \]

Shear stress on surface of shaft (τ):

Pascal

Outer Diameter of Shaft:

Meter

Inner Diameter of Shaft:

Meter

Volume of Shaft:

Cubic Meter

Strain Energy in body:

Joule

Modulus of rigidity of Shaft (G):

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1. What is 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:

\[ G = \frac{(\tau^2) \times ((d_{outer}^2) + (d_{inner}^2)) \times V}{4 \times U \times (d_{outer}^2)} \]

Where:

\( G \) — Modulus of rigidity of Shaft (Pascal)
\( \tau \) — Shear stress on surface of shaft (Pascal)
\( d_{outer} \) — Outer Diameter of Shaft (Meter)
\( d_{inner} \) — Inner Diameter of Shaft (Meter)
\( V \) — Volume of Shaft (Cubic Meter)
\( U \) — Strain Energy in body (Joule)

Explanation: This formula calculates the modulus of rigidity for a hollow shaft based on the relationship between shear stress, shaft dimensions, volume, and strain energy stored in the material.

3. Importance of Modulus of Rigidity Calculation

Details: Calculating the modulus of rigidity is crucial for understanding material behavior under shear stress, designing mechanical components, and ensuring structural integrity in engineering applications involving torsion.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that outer diameter is greater than inner diameter (for hollow shafts), and all values are positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between modulus of rigidity and Young's modulus?
A: Modulus of rigidity measures resistance to shear deformation, while Young's modulus measures resistance to linear deformation under tension or compression.

Q2: Can this calculator be used for solid shafts?
A: Yes, for solid shafts, set the inner diameter to zero.

Q3: What are typical values for modulus of rigidity?
A: For steel: ~79.3 GPa, for aluminum: ~26 GPa, for rubber: ~0.0003-0.004 GPa, depending on the specific material composition.

Q4: Why is strain energy important in this calculation?
A: Strain energy represents the energy stored in the material due to deformation, which is directly related to the material's stiffness and modulus of rigidity.

Q5: What factors can affect the accuracy of this calculation?
A: Material homogeneity, temperature effects, measurement accuracy of input parameters, and assumptions in the theoretical model can affect the calculation accuracy.