Project ForgeStrength of Materials
Bending of Beams
GATE 2020
Hard
A cantilever of length l and flexural rigidity EI, stiffened by a spring of stiffness k at its tip, is loaded by a transverse force P at the tip (the spring also connects the tip to a rigid ground below). The transverse deflection under the load is
- APl³/(3EI) × [3EI/(3EI+2kl³)]
- BPl³/(3EI) × [(6EI−kl³)/(6EI)]
- CPl³/(3EI) × [(3EI−kl³)/(3EI)]
- Pl³/(3EI) × [3EI/(3EI+kl³)]
Explanation
The beam (equivalent tip stiffness 3EI/l³) and the spring (stiffness k) act in parallel between the tip and the fixed points, so their stiffnesses add: k_total=3EI/l³+k. Deflection δ=P/k_total=P/(3EI/l³+k)=Pl³/(3EI+kl³). Rewriting: =Pl³/(3EI)×[3EI/(3EI+kl³)] — option (D).
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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