Inner Diameter Of Shaft Given Total Strain Energy In Hollow Shaft Calculator

Formula Used:

\[ d_{inner} = \sqrt{\frac{U \cdot 4 \cdot G \cdot (d_{outer}^2)}{(\tau^2) \cdot V} - d_{outer}^2} \]

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

Volume Of Shaft (V):

Cubic Meter

Inner Diameter Of Shaft (d_inner):

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1. What Is The Inner Diameter Of Shaft Given Total Strain Energy In Hollow Shaft Formula?

The formula calculates the inner diameter of a hollow shaft based on strain energy, modulus of rigidity, outer diameter, shear stress, and volume. It's essential in mechanical engineering for designing shafts that can withstand torsional loads while storing specific strain energy.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ d_{inner} = \sqrt{\frac{U \cdot 4 \cdot G \cdot (d_{outer}^2)}{(\tau^2) \cdot V} - d_{outer}^2} \]

Where:

\( d_{inner} \) — Inner Diameter of Shaft (Meter)
\( U \) — 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)
\( V \) — Volume of Shaft (Cubic Meter)

Explanation: The formula derives from the relationship between strain energy stored in a hollow shaft under torsion and its geometric and material properties.

3. Importance Of Inner Diameter Calculation

Details: Calculating the inner diameter is crucial for optimizing shaft design to ensure it can store the required strain energy without failure, balancing weight, strength, and material usage.

4. Using The Calculator

Tips: Enter all values in consistent SI units. Ensure strain energy, modulus of rigidity, outer diameter, shear stress, and volume are positive values for accurate calculation.

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 subjected to torsional deformation, calculated based on the work done by the applied torque.

Q2: Why use a hollow shaft instead of a solid one?
A: Hollow shafts offer better strength-to-weight ratio, reduced material usage, and sometimes better resistance to torsion compared to solid shafts of the same outer diameter.

Q3: What affects the modulus of rigidity?
A: The modulus of rigidity is a material property that depends on the type of material used for the shaft. It remains constant for a given material under elastic deformation.

Q4: How is shear stress related to shaft diameter?
A: Shear stress in a shaft under torsion varies linearly with the radius from the center, with maximum stress occurring at the outer surface.

Q5: Can this formula be used for non-circular shafts?
A: No, this formula is specifically derived for hollow circular shafts. Different formulas apply to shafts with other cross-sectional shapes.