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GATE 2020 ME (ME1) – Question 15

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

For any load P > 0 and no appreciable deformation (no appreciable change in member angles), which members carry zero force in the shown truss?

Diagram for GATE 2020 ME (ME1) question 15
  1. BF and DH only
  2. BF, DH and GC only
  3. BF, DH, GC, CD and DE only
  4. BF, DH, GC, FG and GH only

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Show answer and explanation

Correct answer: (C) BF, DH, GC, CD and DE only

Explanation

At unloaded joint B, AB and BC are collinear, so BF = 0. At unloaded D, CD and DE are collinear, so DH = 0. At G, FG and GH are collinear, so GC = 0. At roller E, the support reaction is normal to the 45° inclined support and collinear with HE. Joint equilibrium therefore gives DE = 0; equilibrium at D then gives CD = 0. The complete zero-force set is BF, DH, GC, CD and DE. **Answer: C.**