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.
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:
\[ I_{\text{total}} = \frac{I_{\text{flange}} + I_{\text{webbing}}}{12} \]
To find the area moment of inertia of an H-beam, you need to:
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:
\[ I_{\text{flange}} = 2 \times (6^3 \times 2) = 2 \times 216 \times 2 = 864 \, \text{in}^4 \] \[ I_{\text{webbing}} = 6.5^3 \times 2.2 = 274.625 \times 2.2 = 604.18 \, \text{in}^4 \] \[ I_{\text{total}} = \frac{864 + 604.18}{12} = \frac{1468.18}{12} = 122.35 \, \text{in}^4 \]
