GATE CE 2025 Set 2 — Question 46
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
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?
Correct answer
(A) BC; (D) JK
Solution
To identify zero-force members in a pin-jointed truss, we apply the following rules:
1.If three members meet at a joint where two are collinear and no external load or reaction is applied at that joint, the third (non-collinear) member is a zero-force member.
2.If only two non-collinear members meet at a joint with no external load or reaction, both are zero-force members.
Applying these rules to the given truss:- Joint C: Members and are collinear. Member is the third member meeting at this joint. Since there is no external load or reaction at joint , member is a zero-force member. (Option A is correct)
- Joint E: Members and are collinear. Member is the third member. No external load at , so is a zero-force member.
- Joint J: Members and are collinear. Member is the third member meeting at this joint. Since there is no external load or reaction at joint , member is a zero-force member. (Option D is correct)
- Joint K: Members and are collinear. Member is the third member. Since is already identified as zero-force, this is consistent.
- Joint G: Members and are not collinear, and there is a diagonal member (or , , meet). Simple inspection does not yield as zero.
- Joint I: Members , , and meet. None are necessarily collinear or zero-force based on inspection.
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