1. What is Moment of Inertia?

The moment of inertia (I) is a property of a beam's cross-section that quantifies its resistance to bending. For a rectangular beam, it depends on the base width and height of the beam.

2. How Does the Calculator Work?

The calculator uses the moment of inertia formula:

Where:

• \( I \) — Moment of inertia (kg m²)
• \( b \) — Base width of the beam (m)
• \( h \) — Height of the beam (m)

Explanation: The formula shows that the moment of inertia increases with the cube of the beam height, making height much more influential than width in determining bending resistance.

3. Importance of Moment of Inertia

Details: Moment of inertia is crucial in structural engineering for calculating beam deflection, bending stress, and determining appropriate beam sizes for given loads.

4. Using the Calculator

Tips: Enter the base width and height in meters. Both values must be positive numbers. The result will be in kg·m² units.

5. Frequently Asked Questions (FAQ)

Q1: Why is height cubed in the formula?
A: The cubic relationship shows that increasing height dramatically increases stiffness, as material farther from the neutral axis contributes more to bending resistance.

Q2: How does orientation affect moment of inertia?
A: A beam oriented with its height vertical has much greater bending resistance than the same beam laid flat (height horizontal).

Q3: What are typical values for beams?
A: Values range widely based on size - from 10^-6 kg·m² for small components to 10^-2 kg·m² for large structural beams.

Q4: Does material affect moment of inertia?
A: No, this formula calculates geometric moment of inertia. Material properties are accounted for separately in stress calculations.

Q5: How is this different from polar moment of inertia?
A: This calculates bending resistance (area moment of inertia). Polar moment of inertia (J) relates to torsional resistance and uses a different formula.