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GATE 2022 ME (ME2) – Question 47

Engineering Mechanics · Plane trusses and frames · 2 marks · Multiple select

The lengths of members BC and CE in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude Q > 0 are applied as shown, each at the mid-length of the respective member on which it acts. Which one or more of the following members do not carry any load (force)?

BC vertical and CE horizontal form two sides of a square; horizontal GH engages diagonal BE through a frictionless pin in its slot at G. AB is horizontal, CD and EF are vertical supports. Q acts rightward on BC and downward on CE.
  1. AB
  2. CD
  3. EF
  4. GH

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Show answer and explanation

Correct answer: (B) CD; (D) GH

Explanation

Moments of BC and CE give horizontal and vertical end-force components of Q/2. Their equal components transmit through the diagonal without requiring GH; joint C then has canceling vertical components and requires no CD force. AB and EF each carry Q.