1. What is the Radius Given Torsional Section Modulus Formula?

The formula R = J/Zp calculates the radius of a shaft using the polar moment of inertia (J) and the polar modulus (Zₚ). This relationship is fundamental in torsion analysis of circular shafts.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R \) — Radius of Shaft (m)
• \( J \) — Polar Moment of Inertia (m⁴)
• \( Z_p \) — Polar Modulus (m³)

Explanation: The formula establishes the relationship between the geometric properties of a circular shaft and its torsional section modulus.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for determining the torsional strength and stiffness of circular shafts in mechanical design and structural analysis.

4. Using the Calculator

Tips: Enter polar moment of inertia in m⁴ and polar modulus in m³. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is polar moment of inertia?
A: Polar moment of inertia is a measure of an object's ability to resist torsion and is dependent on the shape and size of the cross-section.

Q2: What is polar modulus?
A: Polar modulus is the ratio of the polar moment of inertia to the radius of the shaft, representing the shaft's resistance to torsional stress.

Q3: When is this formula applicable?
A: This formula applies specifically to circular shafts undergoing torsional loading.

Q4: Are there limitations to this formula?
A: This formula is valid only for circular cross-sections and assumes homogeneous, isotropic material properties.

Q5: How does radius affect torsional strength?
A: Larger radius shafts generally have higher torsional strength and stiffness due to increased polar moment of inertia.