Project ForgeStrength of Materials
Bending of Beams
GATE 2023
Hard
The area moment of inertia about the y-axis of a linearly tapered section is ______ m⁴. The section spans x=0 to x=12m, with full height 3m at x=0 tapering linearly to full height 6m at x=12m, symmetric about the x-axis.
3024 m⁴(± 1 accepted)
Explanation
Height as a function of x: H(x)=3+0.25x (linear from 3 at x=0 to 6 at x=12). I_y=∫₀¹² x²·H(x) dx=∫₀¹²(3x²+0.25x³)dx=[x³]₀¹²+0.0625[x⁴]₀¹²=1728+0.0625×20736=1728+1296=3024.
Source: GATE ME 2023 Official Paper (2023)
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