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GATE 2025 ME – Question 27

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

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

A truss with joints A, B, C and D. C is a pin support at the bottom left and D is a roller support at the bottom right, 1 m from C. A is directly above D at a height of 1 m, and a horizontal force F = 1000 N acts at A. B lies on the line CA, at 90° to BD, and CAB makes 45° at C.
  1. BD
  2. BC
  3. BA
  4. AD

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Show answer and explanation

Correct answer: (A) BD

Explanation

At joint B only three members meet, BC, BA and BD, and there is no external load on B. Members BC and BA lie along the same straight line, so they carry equal force. The third member, BD, is at an angle to them, so the force balance at B perpendicular to the line CA forces the force in BD to be zero.