GATE ME 2021 Set 2 — Question 24
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Engineering Mechanics → Statics → Trusses (Joints & Sections)
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Question
A plane truss (, and ) is shown in the figure.
The forces in the members and , respectively, are ______________
Correct answer
(B) F√(2) (tensile) and F (compressive)
Solution
Take (pin) at the origin, (roller, vertical reaction only) at distance to the right, and , at height .Support reaction at S: moments about : (clockwise, from acting at height ) , so upward.Joint Q: no load and two non-collinear members (, ), so .Joint S: the only member at is the vertical member . The upward reaction must be balanced by member pushing down on the joint, so is in compression, .Joint R (members at down-left, vertical, zero force; load to the right):
- : , pulling towards , i.e. tension.
- : , where the compressive member pushes upward with ; consistent.
- (A) has in tension, which would leave the roller reaction unbalanced.
- (C) and (D) swap the magnitudes.
- (B) is correct.
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