The GATE Grind

GATE 2021 ME (ME1) – Question 27

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

A cantilever beam of length, $L$, and flexural rigidity, $EI$, is subjected to an end moment, $M$, as shown in the figure. The deflection of the beam at $x=L/2$ is

Cantilever of length L with end moment M and coordinate x measured from the fixed end. See the attached source image.
  1. $ML^2/(2EI)$
  2. $ML^2/(4EI)$
  3. $ML^2/(8EI)$
  4. $ML^2/(16EI)$

Practise this question in The GATE Grind →

Show answer and explanation

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

Explanation

Bending moment is constant, so curvature is $v^{\prime\prime}=M/EI$. Integrate twice using v(0)=v′(0)=0 to obtain $v(x)=Mx^2/(2EI)$.

At L/2, $v=ML^2/(8EI)$, **C**.