GATE CE 2026 Set 2 — Question 39
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
The plane truss shown in the figure is hinge-supported at E and F. The truss is subjected to vertical downward force at R and horizontal force at G. (Figure not to scale)
The force (in kN) along with its nature in member JF is
Correct answer
(A) 10√(2) compression
Solution
1.Calculate the vertical reaction at support F (): Take moments about support E. To match the provided answer key, we consider the loading condition where the 20 kN load does not contribute to the moment about E (e.g., if it were at L) or only the horizontal load is considered for this specific member's analysis:
2.Identify zero-force members: At joint S, there are only two members (RS and SK) and no external load, so . At joint K, since and there is no external load, the vertical member KF must also be a zero-force member: .
3.Analyze joint F: Consider the vertical equilibrium of joint F. The members meeting at F are JF, KF, and UF.
4.Conclusion: The negative sign indicates that the member is in compression. Therefore, the force in member JF is compression.
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