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GATE 2020 CE (CE1) – Question 40

Structural Analysis · Deflections of determinate beams, frames and trusses · 2 marks · Multiple choice

The shown cantilever PQ of uniform flexural rigidity EI has concentrated moment M at midpoint R. Find free-end Q deflection.

Diagram for GATE 2020 CE (CE1) question 40
  1. $ML^2/(6EI)$
  2. $ML^2/(4EI)$
  3. $3ML^2/(8EI)$
  4. $3ML^2/(4EI)$

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Show answer and explanation

Correct answer: (C) $3ML^2/(8EI)$

Explanation

Bending moment is M from the fixed end to L/2, and zero beyond. A unit tip load gives virtual moment L − x. Thus $\delta_Q=\int_0^{L/2}M(L-x)/(EI)\,dx=3ML^2/(8EI)$. **C**.