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GATE 2023 ME – Question 16

Mechanics of Materials · Deflection of beams · 1 mark · Multiple choice

The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

  1. $\frac{3EI}{L^3}$
  2. $\frac{2EI}{L^3}$
  3. $\frac{L^3}{2EI}$
  4. $\frac{L^3}{3EI}$

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Correct answer: (A) $\frac{3EI}{L^3}$

Explanation

The tip deflection of a cantilever under a tip load $W$ is $\delta = \frac{WL^3}{3EI}$. The stiffness is the load per unit deflection, $k = \frac{W}{\delta} = \frac{3EI}{L^3}$.