1. What is the Radius Calculation Formula?

The formula \( R = \frac{\tau_{max} \times J}{T} \) calculates the radius of a shaft given the maximum permissible shear stress, polar moment of inertia, and applied torque. This is essential in mechanical engineering for designing shafts that can withstand specific stress levels.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R \) — Radius of the shaft (m)
• \( \tau_{max} \) — Maximum permissible shear stress (Pa)
• \( J \) — Polar moment of inertia (m⁴)
• \( T \) — Applied torque (N·m)

Explanation: This formula calculates the minimum radius required for a shaft to withstand a given torque without exceeding the maximum permissible shear stress.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for designing mechanical components that can safely transmit torque without failure due to excessive shear stress.

4. Using the Calculator

Tips: Enter maximum shear stress in Pascals, polar moment of inertia in meters to the fourth power, and torque in Newton-meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is maximum permissible shear stress?
A: Maximum permissible shear stress is the highest shear stress a material can withstand without permanent deformation or failure.

Q2: What is polar moment of inertia?
A: Polar moment of inertia is a measure of an object's ability to resist torsion about a specific axis.

Q3: How does torque affect shaft radius?
A: Higher torque requires a larger shaft radius to maintain the same maximum shear stress level.

Q4: What units should be used for inputs?
A: Use Pascals for stress, meters to the fourth power for polar moment, and Newton-meters for torque.

Q5: Can this formula be used for hollow shafts?
A: Yes, but the polar moment of inertia calculation differs for hollow shafts compared to solid shafts.