Total Strain Energy In Hollow Shaft Due To Torsion Calculator

Formula Used:

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

Shear Stress On Surface Of Shaft (τ):

Pascal

Outer Diameter Of Shaft:

Meter

Inner Diameter Of Shaft:

Meter

Volume Of Shaft:

Cubic Meter

Modulus Of Rigidity Of Shaft (G):

Pascal

Strain Energy In Body (U):

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1. What Is The Strain Energy Formula For Hollow Shaft?

The strain energy stored in a hollow shaft due to torsion is calculated using the formula that considers shear stress, shaft dimensions, material properties, and volume. This energy represents the work done in deforming the shaft under torsional loading.

2. How Does The Calculator Work?

The calculator uses the strain energy formula:

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

Where:

\( U \) — Strain Energy in body (Joule)
\( \tau \) — 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)
\( G \) — Modulus of rigidity of Shaft (Pascal)

Explanation: The formula calculates the energy stored in a hollow cylindrical shaft when subjected to torsional stress, accounting for both inner and outer diameters.

3. Importance Of Strain Energy Calculation

Details: Calculating strain energy is crucial for understanding the energy absorption capacity of shafts under torsion, designing safe mechanical systems, and predicting failure points in rotating machinery components.

4. Using The Calculator

Tips: Enter all values in appropriate SI units. Ensure shear stress, diameters, volume, and modulus values are positive. The inner diameter must be less than or equal to the outer diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in mechanical systems?
A: Strain energy is the energy stored in a material when it is deformed elastically. It represents the work done on the material to cause the deformation.

Q2: How does hollow shaft differ from solid shaft in strain energy?
A: Hollow shafts can store more strain energy per unit weight compared to solid shafts, making them more efficient for torsional applications where weight is a concern.

Q3: What factors affect strain energy in shafts?
A: Material properties (modulus of rigidity), geometric dimensions (diameters and length), and applied shear stress all influence the amount of strain energy stored.

Q4: When is this formula applicable?
A: This formula applies to linearly elastic materials undergoing small deformations where Hooke's law is valid and the shaft has a uniform cross-section.

Q5: How is strain energy related to shaft safety?
A: The strain energy calculation helps engineers ensure that shafts can safely absorb and dissipate energy without exceeding material limits or causing failure.