GATE 2016 ME (ME1) – Question 43
The figure shows a beam cross section subjected to bending. Its area moment of inertia about its base is ______ mm⁴. All dimensions in the figure are in mm.
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Correct answer: 1873 to 1879
Explanation
Start with the10mm by10mm rectangle: Ibase=bh³/3=3333.333mm⁴. The two semicircular cut-outs together have areaπ·4² and horizontal-centroid second momentπ·4⁴/4. Their common centre lies5mm above the base, so removed I isπ·4⁴/4+π·4²·5². Remaining inertia is **1875.634mm⁴**.