The GATE Grind

GATE 2016 ME (ME2) – Question 43

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

A simply supported beam of length 2L carries midpoint moment M at x = 0, as shown. For $0\le x\le L$, $w=-Mx(L-x)(x+c)/(12EIL)$, where E is Young’s modulus, I is second moment of area, and c is to be determined. The slope at x = 0 is ______.

Diagram for GATE 2016 ME (ME2) question 43
  1. $ML/(2EI)$
  2. $ML/(3EI)$
  3. $ML/(6EI)$
  4. $ML/(12EI)$

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Show answer and explanation

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

Explanation

Expand the polynomial: w=−M[Lcx+(L−c)x²−x³]/(12EIL). At the simple right support x=L, bending moment is zero, so w-double-prime(L)=0 gives c=−2L. Then w-prime(0)=−Mc/(12EI)=**ML/(6EI), C**. The deflection boundary alone at x=L is automatically satisfied and cannot fix c.