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GATE 2023 CE (CE2) – Question 26

Structural Analysis · Principle of superposition, virtual work and Castigliano theorem · 1 mark · Multiple select

In the frame shown in the figure (not to scale), all four members (AB, BC, CD, and AD) have the same length and same constant flexural rigidity. All the joints A, B, C, and D are rigid joints. The midpoints of AB, BC, CD, and AD, are denoted by E, F, G, and H, respectively. The frame is in unstable equilibrium under the shown forces of magnitude P acting at E and G. Which of the following statements is/are TRUE?

unsupported square frame, with equal inward horizontal forces at the midpoints of its left and right sides.
  1. Shear forces at H and F are zero
  2. Horizontal displacements at H and F are zero
  3. Vertical displacements at H and F are zero
  4. Slopes at E, F, G, and H are zero

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Show answer and explanation

Correct answer: (A) Shear forces at H and F are zero; (B) Horizontal displacements at H and F are zero; (D) Slopes at E, F, G, and H are zero

Explanation

Symmetry makes the midpoints of the top and bottom members have zero horizontal displacement and zero shear. All side-midpoint slopes vanish by reflection symmetry; the top and bottom midpoints can move vertically as the frame deforms.

Official GATE 2023 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2023/CE2_ANS_GATE2023.pdf