Shear Stress On Surface Of Shaft Given Total Strain Energy In Hollow Shaft Calculator

Formula Used:

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

Strain Energy in body (U):

Modulus of rigidity of Shaft (G):

Outer Diameter of Shaft (d_outer):

Inner Diameter of Shaft (d_inner):

Volume of Shaft (V):

m³

Shear stress on surface of shaft (τ):

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1. What is Shear Stress on Surface of Shaft?

Shear stress on surface of shaft is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. It's a critical parameter in mechanical engineering for analyzing shaft performance under torsional loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the shear stress on the surface of a hollow shaft based on the stored strain energy, material properties, and geometric dimensions.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for designing shafts that can withstand torsional loads without failure, ensuring structural integrity and safety in mechanical systems.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Strain energy and modulus of rigidity must be positive values. Outer diameter must be greater than inner diameter for hollow shafts.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between solid and hollow shafts in this calculation?
A: For solid shafts, set inner diameter to zero. The formula automatically handles both solid and hollow shaft configurations.

Q2: What are typical values for modulus of rigidity?
A: Modulus of rigidity varies by material. Steel typically has G ≈ 79.3 GPa, aluminum ≈ 26 GPa, and copper ≈ 44 GPa.

Q3: How does shear stress relate to shaft failure?
A: Excessive shear stress can lead to yielding or fracture of the shaft material. The calculated stress should be compared to the material's yield strength with appropriate safety factors.

Q4: Can this formula be used for non-circular shafts?
A: No, this formula is specifically derived for circular shafts (both solid and hollow) under torsion.

Q5: What is the significance of strain energy in this calculation?
A: Strain energy represents the energy stored in the shaft due to elastic deformation under torsional loading, which is directly related to the shear stress distribution.