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GATE 2022 CE (CE2) – Question 16

Structural Analysis · Statically indeterminate structures: force and displacement methods · 1 mark · Multiple choice

Consider a beam PQ fixed at P, hinged at Q, and subjected to a load F as shown in figure (not drawn to scale). The static and kinematic degrees of indeterminacy, respectively, are

Beam fixed at P and hinged at Q. See the attached source image.
  1. 2 and 1
  2. 2 and 0
  3. 1 and 2
  4. 2 and 2

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Show answer and explanation

Correct answer: (A) 2 and 1

Explanation

The fixed support at P supplies three reactions; the hinge at Q supplies two. A planar structure has three independent equilibrium equations, so static indeterminacy is 5−3=2.

Both supports prevent translations and P also prevents rotation. Only rotation at Q is free, giving kinematic indeterminacy 1. **Answer: A, 2 and 1**.