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GATE 2025 CE (CE2) – Question 46

Engineering Mechanics · Internal forces in structures · 2 marks · Multiple select

In the pin-jointed truss shown in the figure, the members that carry zero force are identified. Which of the following options is/are zero-force members?

a truss with a 60 kN downward load at joint B on the sloping top chord A-B-D-F, bottom chord members A-C-E-G-I (horizontal), the vertical members B-C, D-E, F-G and H-I, a column G-J-L on the left, a column I-K-M on the right with horizontal members F-H, J-K and L-M, and diagonals B-E, E-F, F-I, I-J and J-M. L is a pin support and M a roller support.
  1. BC
  2. EG
  3. FI
  4. JK

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Show answer and explanation

Correct answer: (A) BC; (D) JK

Explanation

At joint A (a free end with two non-collinear members and no load) both AB and AC are zero. At joint C the members AC and CE are collinear and the third member BC is the only one with a vertical component with no load applied, so BC = 0 (A is a zero-force member). At joint K the members IK and KM are collinear (vertical) and JK is the only horizontal one, so JK = 0 (D). Take the whole upper part supported by GJ, IJ and IK, and take moments about J: the 60 kN load gives a force in IK, and the horizontal equilibrium gives IJ = 0. At joint I the vertical member IK is then balanced by the vertical component of FI, so FI carries force, and at joint G the force in EG equals that in GI, which in turn balances the horizontal component of FI, so EG carries force as well.