The GATE Grind

GATE 2018 CE (CE1) – Question 40

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

The simply supported uniform-EI beam PQ carries moments M and 2M as shown. The slope at P is ______.

Diagram for GATE 2018 CE (CE1) question 40
  1. 0
  2. $ML/(9EI)$
  3. $ML/(6EI)$
  4. $ML/(3EI)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $ML/(6EI)$

Explanation

Equilibrium gives $R_P=-3M/L$ and $R_Q=3M/L$. With the indicated clockwise couples as positive moment jumps, integrate the piecewise bending-moment function and impose zero endpoint deflections. Equivalently, $$\theta_P=-\frac1{LEI}\int_0^L(L-x)\mathcal M(x)\,dx=\frac{ML}{6EI}.$$ Answer C.