1. What is the Diameter of Shaft Given Torsional Shear Stress Formula?

This formula calculates the required diameter of a shaft based on the torsional moment and allowable torsional shear stress. It ensures the shaft can withstand applied torsional loads without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Diameter of shaft (m)
• \( M_{t_{shaft}} \) — Torsional moment in shaft (N·m)
• \( \tau \) — Torsional shear stress in shaft (Pa)
• \( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: This formula derives from the torsion equation for circular shafts, ensuring the maximum shear stress doesn't exceed the material's allowable stress.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft sizing is crucial for mechanical systems to transmit torque efficiently while preventing failure due to excessive shear stress.

4. Using the Calculator

Tips: Enter torsional moment in N·m and torsional shear stress in Pa. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is torsional moment?
A: Torsional moment is the torque applied to a shaft that causes it to twist about its axis.

Q2: What is torsional shear stress?
A: Torsional shear stress is the stress developed in a material when subjected to twisting forces.

Q3: Why is the formula raised to the power of 1/3?
A: The 1/3 power comes from the relationship between shaft diameter and its polar moment of inertia in torsion calculations.

Q4: What units should be used?
A: Use consistent SI units: N·m for torque and Pa for stress to get diameter in meters.

Q5: Does this formula account for safety factors?
A: No, this formula gives the minimum diameter based on stress alone. Engineering practice requires applying appropriate safety factors.