1. What is Moment of Inertia?

The moment of inertia (I) is a property of a steel section that quantifies its resistance to bending. For hollow rectangular sections, it's calculated by subtracting the inner section's inertia from the outer section's inertia.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( I \) — Moment of inertia (m⁴)
• \( b \) — Outer width (m)
• \( h \) — Outer height (m)
• \( b' \) — Inner width (m)
• \( h' \) — Inner height (m)

Explanation: The formula calculates the second moment of area for a hollow rectangular section by subtracting the inner rectangle's moment of inertia from the outer rectangle's.

3. Importance of Moment of Inertia

Details: Moment of inertia is crucial in structural engineering for determining beam deflection, bending stress, and buckling resistance. Higher values indicate greater stiffness against bending.

4. Using the Calculator

Tips: Enter all dimensions in meters. For solid sections, set inner width and height to zero. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: How does moment of inertia affect beam design?
A: Higher I values mean less deflection under load, allowing longer spans or heavier loads for the same material.

Q3: What are typical I values for steel beams?
A: Common I-beams range from 10⁻⁶ m⁴ (small sections) to 10⁻³ m⁴ (large structural members).

Q4: How does hollow section compare to solid section?
A: Hollow sections often provide higher I-to-weight ratios, making them efficient for bending resistance.

Q5: Can this be used for other materials?
A: Yes, the formula applies to any material, but steel is most common due to its uniform properties.