1. What is Torsional Section Modulus?

The Torsional Section Modulus (Zₚ) of a shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It represents the shaft's resistance to torsional deformation and is a key parameter in mechanical engineering design.

2. How Does the Calculator Work?

The calculator uses the Torsional Section Modulus formula:

Where:

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

Explanation: The formula calculates the torsional section modulus by dividing the polar moment of inertia by the radius of the shaft.

3. Importance of Torsional Section Modulus

Details: Torsional section modulus is crucial for designing shafts and other rotating components to ensure they can withstand torsional stresses without excessive deformation or failure.

4. Using the Calculator

Tips: Enter polar moment of inertia in m⁴ and radius of shaft in m. All values must be valid (J > 0, R > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is polar moment of inertia?
A: Polar moment of inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Q2: How is torsional section modulus used in design?
A: It is used to calculate the maximum shear stress in a shaft under torsion using the formula τ = T/Zₚ, where T is the applied torque.

Q3: What are typical units for torsional section modulus?
A: The SI unit is cubic meters (m³), but it may also be expressed in mm³ or in³ depending on the application.

Q4: Does this formula work for non-circular sections?
A: This specific formula is primarily for circular shafts. Non-circular sections have different formulas for torsional section modulus.

Q5: How does shaft radius affect torsional section modulus?
A: Torsional section modulus increases with increasing shaft radius, meaning larger shafts can withstand higher torsional loads.