GATE 2022 AE – Question 61
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 mm. Thickness is 0.6 mm. The second moment of area about a horizontal axis passing through the centroid is ______ mm4.
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Correct answer: 2800
Explanation
For a thin-walled section, the second moment of area about the horizontal centroidal axis is found from the flanges (parallel-axis theorem) and the web.
**Geometry.** Two flanges of width 20 mm and thickness 0.6 mm, and a web 20 mm high and 0.6 mm thick. By symmetry, the centroid is at mid-height of the web, so each flange is 10 mm from the centroidal axis.
**Flanges** (thin, so their own $I$ is neglected):
$$I_f=2\times(20\times0.6)\times10^2=2\times12\times100=2400\ \text{mm}^4 .$$
**Web:**
$$I_w=\frac{0.6\times20^3}{12}=\frac{0.6\times8000}{12}=400\ \text{mm}^4 .$$
$$I=2400+400=\mathbf{2800\ mm^4}.$$