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GATE 2020 ME (ME2) – Question 38

Mechanics of Materials · Deflection of beams · 2 marks · Multiple choice

A cantilever of length l and flexural rigidity EI is stiffened by a spring of stiffness k and loaded by transverse tip force P as shown. Find its deflection under P.

Diagram for GATE 2020 ME (ME2) question 38
  1. $\frac{Pl^3}{3EI}\frac{3EI}{3EI+2kl^3}$
  2. $\frac{Pl^3}{3EI}\frac{6EI-kl^3}{6EI}$
  3. $\frac{Pl^3}{3EI}\frac{3EI-kl^3}{3EI}$
  4. $\frac{Pl^3}{3EI}\frac{3EI}{3EI+kl^3}$

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Correct answer: (D) $\frac{Pl^3}{3EI}\frac{3EI}{3EI+kl^3}$

Explanation

The cantilever tip stiffness is kb=3EI/L³. Spring and beam resist the same displacement in parallel, so $\delta=P/(k_b+k)=PL^3/(3EI+kL^3)$. This is **D**. Adding flexibilities would describe elements in series and would increase rather than decrease deflection.