Shear Stress at Surface of Shaft given Total Strain Energy Stored in Shaft Calculator

Formula Used:

\[ \tau = \sqrt{\frac{U \times (2 \times G \times r_{shaft}^2)}{L \times J_{shaft}}} \]

Strain Energy in Body (U):

Modulus of Rigidity of Shaft (G):

Radius of Shaft (r_shaft):

Length of Shaft (L):

Polar Moment of Inertia of Shaft (J_shaft):

m⁴

Shear Stress on Surface of Shaft (τ):

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1. What is Shear Stress at Surface of Shaft?

Shear stress on the surface of a shaft is the force per unit area tending to cause deformation of the material by slippage along planes parallel to the imposed stress. It's a critical parameter in torsion analysis of shafts.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \sqrt{\frac{U \times (2 \times G \times r_{shaft}^2)}{L \times J_{shaft}}} \]

Where:

\( \tau \) — Shear stress on surface of shaft (Pa)
\( U \) — Strain energy in body (J)
\( G \) — Modulus of rigidity of shaft (Pa)
\( r_{shaft} \) — Radius of shaft (m)
\( L \) — Length of shaft (m)
\( J_{shaft} \) — Polar moment of inertia of shaft (m⁴)

Explanation: This formula calculates the maximum shear stress at the surface of a shaft based on the total strain energy stored in the shaft under torsion.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial for designing shafts that can withstand torsional loads without failure. It helps determine if a shaft will yield or fracture under applied torque.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all inputs are positive values. The calculator will compute the shear stress at the surface of the shaft.

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: Why is shear stress maximum at the surface?
A: In torsion, shear stress varies linearly from zero at the center to maximum at the outer surface of the shaft.

Q3: What is polar moment of inertia?
A: Polar moment of inertia is a measure of a shaft's resistance to torsion. For a solid circular shaft, J = πr⁴/2.

Q4: When is this formula applicable?
A: This formula applies to shafts with circular cross-sections undergoing elastic torsion within the proportional limit.

Q5: How does modulus of rigidity affect shear stress?
A: Higher modulus of rigidity means the material is stiffer and will experience lower shear strain for the same shear stress.