1. What is Section Modulus of Circle?

The section modulus (Z) is a geometric property of a circular cross-section that describes its strength in bending. It's directly related to the moment of inertia and the distance from the neutral axis to the outermost fiber.

2. How Does the Calculator Work?

The calculator uses the circle modulus formula:

Where:

• \( Z \) — Section modulus (m³)
• \( d \) — Diameter of the circle (m)
• \( \pi \) — Mathematical constant (~3.14159)

Explanation: The formula shows that the section modulus increases with the cube of the diameter, meaning larger diameters provide significantly more bending resistance.

3. Importance of Section Modulus

Details: Section modulus is crucial in structural engineering for determining a beam's capacity to resist bending stress. It's used in the design of shafts, beams, and other structural elements.

4. Using the Calculator

Tips: Enter the diameter of the circular cross-section in meters. The value must be positive. The result will be in cubic meters (m³).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between section modulus and moment of inertia?
A: Moment of inertia (I) measures resistance to bending deformation, while section modulus (Z = I/y) measures resistance to bending stress (y = distance to extreme fiber).

Q2: How does section modulus affect beam strength?
A: Higher section modulus means greater bending strength. Doubling the diameter increases the section modulus by 8 times (2³).

Q3: What are typical applications of circular section modulus?
A: Used in design of circular shafts, columns, pipes, and any structural elements with circular cross-sections subject to bending.

Q4: Can this be used for hollow circular sections?
A: No, this formula is for solid circles. Hollow sections require subtracting the inner circle's contribution.

Q5: What units should I use?
A: Consistent units are essential. If diameter is in meters, result is in m³. For mm input, result would be in mm³.