For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., \( 2b = 20 \, \text{mm} \). Thickness is 0.6 mm.
The second moment of area about a horizontal axis passing through the centroid is _________ mm\(^4\).
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For thin-walled sections, the total moment of inertia can be found by adding the moments of inertia of the individual parts (flanges and web).
For a thin-walled I section, the second moment of area about the horizontal axis passing through the centroid is the sum of the moments of inertia of the two flanges and the web. The second moment of area for each part is given by:
\[
I_{\text{flange}} = \frac{b h^3}{12} \quad \text{(for a rectangle of width \( b \) and height \( h \))},
\]
where \( b = 20 \, \text{mm} \) and thickness of flange is \( 0.6 \, \text{mm} \).
For the web:
\[
I_{\text{web}} = \frac{b h^3}{12} \quad \text{(for the web with similar dimensions as the flange)}.
\]
Thus, the total second moment of area is approximately \( 2700 \, \text{mm}^4 \).
Thus, the second moment of area about a horizontal axis passing through the centroid is approximately \( 2700 \, \text{mm}^4 \).
