Volume Of Shaft Given Total Strain Energy In Hollow Shaft Calculator

Formula Used:

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

Strain Energy in body (U):

Joule

Modulus of rigidity of Shaft (G):

Pascal

Outer Diameter of Shaft (d_outer):

Meter

Shear stress on surface of shaft (τ):

Pascal

Inner Diameter of Shaft (d_inner):

Meter

Volume of Shaft (V):

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1. What is Volume Of Shaft Given Total Strain Energy In Hollow Shaft?

This calculator determines the volume of a hollow shaft based on the total strain energy stored in the shaft under torsion, using the modulus of rigidity, shear stress, and the inner and outer diameters of the shaft.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Shaft (m³)
\( U \) — Strain Energy in body (Joule)
\( G \) — Modulus of rigidity of Shaft (Pascal)
\( d_{outer} \) — Outer Diameter of Shaft (Meter)
\( \tau \) — Shear stress on surface of shaft (Pascal)
\( d_{inner} \) — Inner Diameter of Shaft (Meter)

Explanation: This formula relates the volume of a hollow shaft to the strain energy stored when the shaft is subjected to torsional stress, accounting for the material's rigidity and the geometric properties of the shaft.

3. Importance of Volume Calculation

Details: Calculating the volume of a shaft given strain energy is important in mechanical engineering design, particularly for determining the appropriate dimensions of shafts in torsion applications while considering energy storage capacity and material efficiency.

4. Using the Calculator

Tips: Enter all values in the specified units. Strain energy, modulus of rigidity, outer diameter, and shear stress must be positive values. Inner diameter can be zero for solid shafts.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in a shaft?
A: Strain energy is the energy stored in a shaft when it is deformed under torsional loading. It represents the work done by the applied torque.

Q2: How does hollow shaft differ from solid shaft in this calculation?
A: For solid shafts, set the inner diameter to zero. Hollow shafts have different stress distributions and can store more strain energy per unit volume.

Q3: What is modulus of rigidity?
A: Modulus of rigidity (G) is a material property that measures its resistance to shearing deformation. It's also known as the shear modulus.

Q4: When is this calculation most useful?
A: This calculation is particularly useful in mechanical design applications where energy storage in rotating shafts is important, such as in torsion springs or energy-absorbing components.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous, isotropic material behavior and applies to shafts with circular cross-sections under pure torsion within the elastic limit.