The GATE Grind

GATE 2023 ME – Question 17

Engineering Mechanics · Plane trusses and frames · 1 mark · Multiple choice

The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

four pin-jointed frames. (A) A quadrilateral with one diagonal. (B) A frame of 6 joints and 9 bars built from triangles. (C) Two square panels joined by two horizontal bars, where the left square has one diagonal, the middle panel has no diagonal and the right square has both diagonals. (D) Three square panels in a row, each with one diagonal.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) Option C in the figure

Explanation

A pin-jointed frame with $j$ joints is rigid and just stiff when it has $2j - 3$ bars, arranged so that it is built from triangles. (A) has 4 joints and 5 bars, and it is two triangles. (B) has 6 joints and 9 bars, built from triangles, and it is rigid. (D) has 8 joints and 13 bars with a diagonal in every panel, so it is rigid. In (C) the middle panel has no diagonal. The left and right squares are rigid on their own, but they are connected by only the two horizontal bars, so the parallelogram between them can change shape and the frame is non-rigid.