H-Beam Area Moment of Inertia Calculator

Calculate Area Moment of Inertia









Definition

An H-beam is composed of three sections: two parallel flanges and a webbing. The beam's size describes its overall resistance to bending forces, measured by its area moment of inertia in in^4.

Formulas

The formula to calculate the area moment of inertia for the flanges is:

\[ I_{\text{flange}} = 2 \times (\text{Flange Length}^3 \times \text{Flange Width}) \]

The formula to calculate the area moment of inertia for the webbing is:

\[ I_{\text{webbing}} = \text{Webbing Length}^3 \times \text{Webbing Width} \]

The total area moment of inertia is:

\[ I_{\text{total}} = \frac{I_{\text{flange}} + I_{\text{webbing}}}{12} \]

Description

To find the area moment of inertia of an H-beam, you need to:

  1. Raise the length of each flange to the power of 3.
  2. Multiply this result by the width of the flange.
  3. Double this result because the beam has two flanges.
  4. Repeat the steps with the webbing between the flanges.
  5. Add the results from the flanges and the webbing.
  6. Divide this sum by 12 to find the area moment of inertia.

Example Calculation

For an H-beam with flanges of 6 inches length and 2 inches width, and webbing of 6.5 inches length and 2.2 inches width:

\[ I_{\text{flange}} = 2 \times (6^3 \times 2) = 2 \times 216 \times 2 = 864 \, \text{in}^4 \] \[ I_{\text{webbing}} = 6.5^3 \times 2.2 = 274.625 \times 2.2 = 604.18 \, \text{in}^4 \] \[ I_{\text{total}} = \frac{864 + 604.18}{12} = \frac{1468.18}{12} = 122.35 \, \text{in}^4 \]