Project ForgeStrength of Materials
Bending of Beams
GATE 2011
Hard
A triangular-shaped cantilever beam of uniform thickness t and length l is fixed at the wall, where its width is b, tapering linearly to a point at the free end. A concentrated load P is applied at the free end. The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is
- Abxt³/(6l)
- bxt³/(12l)
- Cbxt³/(24l)
- Dxt³/12
Explanation
The plan-view width at distance x from the free end (linearly tapering from 0 at the free end to b at the fixed end, length l) is w(x)=bx/l. For a rectangular cross-section w(x)×t bending about the axis parallel to w, I(x)=w(x)t³/12=bxt³/(12l).
Source: GATE ME 2011 (2011)
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