Shear Stress At Surface Of Shaft Given Total Strain Energy In Shaft Due To Torsion Calculator

Formula Used:

\[ \tau = \sqrt{\frac{U \times 4 \times G}{V}} \]

Strain Energy in body (U):

Joule

Modulus of rigidity of Shaft (G):

Pascal

Volume of Shaft (V):

Cubic Meter

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 torsion analysis of shafts and mechanical components.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \sqrt{\frac{U \times 4 \times G}{V}} \]

Where:

\( \tau \) — Shear stress on surface of shaft (Pascal)
\( U \) — Strain Energy in body (Joule)
\( G \) — Modulus of rigidity of Shaft (Pascal)
\( V \) — Volume of Shaft (Cubic Meter)

Explanation: This formula calculates the shear stress at the surface of a shaft based on the total strain energy stored in the shaft due to torsion, the material's modulus of rigidity, and the volume of the shaft.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for designing shafts and mechanical components to ensure they can withstand torsional loads without failure. It helps in determining the safety factor and optimal dimensions for mechanical designs.

4. Using the Calculator

Tips: Enter strain energy in joules, modulus of rigidity in pascals, and volume in cubic meters. All values must be positive and valid for accurate results.

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 torsion. It represents the work done in deforming the shaft.

Q2: What is modulus of rigidity?
A: Modulus of rigidity (also known as shear modulus) is a material property that measures its resistance to shearing deformation. It's the ratio of shear stress to shear strain.

Q3: Why is shear stress maximum at the surface?
A: In torsion, shear stress is maximum at the outer surface of the shaft because this is where the deformation is greatest due to the maximum distance from the neutral axis.

Q4: What units should I use for input values?
A: Use joules for strain energy, pascals for modulus of rigidity, and cubic meters for volume to get shear stress in pascals.

Q5: Can this formula be used for non-circular shafts?
A: This specific formula is derived for circular shafts under torsion. Different formulas apply for shafts with other cross-sectional shapes.