Project ForgeStrength of Materials
Bending of Beams
GATE 2011
Hard
For the same triangular cantilever beam (uniform thickness t, width b at the wall tapering to a point at the free end, length l, Young's modulus E, load P at the free end), the maximum deflection of the beam is
- A24Pl³/(Ebt³)
- B12Pl³/(Ebt³)
- C8Pl³/(Ebt³)
- 6Pl³/(Ebt³)
Explanation
With x measured from the free end, M(x)=Px and I(x)=bxt³/(12l) (from the previous part). The curvature M(x)/(EI(x)) = Px/(E·bxt³/(12l)) = 12Pl/(Ebt³) is CONSTANT along the whole beam (x cancels) — the beam bends into a circular arc. Double-integrating with the fixed-end boundary conditions y(l)=0, y'(l)=0 gives ymax=y(0)=6Pl³/(Ebt³).
Source: GATE ME 2011 (2011)
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