Shear Stress In Shaft Given Torque Transmitted By Shaft Calculator

Shear Stress Formula:

\[ \tau = \frac{16 \times T_{shaft}}{\pi \times d_s^3} \]

Shear Stress in Shaft:

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1. What is Shear Stress in Shaft?

Shear stress in a shaft is the force per unit area that tends to cause deformation of the material by slippage along planes parallel to the imposed stress. It's a critical parameter in mechanical design that determines the shaft's ability to withstand torsional loads.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \tau = \frac{16 \times T_{shaft}}{\pi \times d_s^3} \]

Where:

\( \tau \) — Shear stress in shaft (Pa)
\( T_{shaft} \) — Torque transmitted by shaft (N·m)
\( d_s \) — Diameter of shaft (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: This formula calculates the maximum shear stress in a circular shaft subjected to pure torsion, based on the torque applied and the shaft diameter.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for designing shafts that can safely transmit power without failure. It helps engineers determine appropriate shaft dimensions and material selection for various applications.

4. Using the Calculator

Tips: Enter torque in Newton-meters and shaft diameter in meters. Both values must be positive numbers. The calculator will compute the shear stress in Pascals.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 16/π factor in the formula?
A: The 16/π factor comes from the polar moment of inertia calculation for a circular cross-section and the relationship between torque and shear stress.

Q2: Does this formula apply to hollow shafts?
A: No, this specific formula is for solid circular shafts. Hollow shafts require a different formula that accounts for inner and outer diameters.

Q3: What are typical shear stress limits for shaft materials?
A: Shear stress limits vary by material. Steel shafts typically have allowable shear stresses between 40-100 MPa, while aluminum may be 20-50 MPa, depending on the specific alloy and application.

Q4: How does shaft diameter affect shear stress?
A: Shear stress is inversely proportional to the cube of the diameter. Doubling the diameter reduces shear stress by a factor of 8.

Q5: When is this formula not applicable?
A: This formula assumes pure torsion, homogeneous material, and circular cross-section. It may not be accurate for shafts with keyways, splines, or other stress concentrators.