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GATE 2021 ME (ME2) – Question 24

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

A plane truss PQRS (PQ = RS, and $\angle PQR=90^\circ$) is shown in the figure. The forces in the members PR and RS, respectively, are

Square truss PQRS of side L, pinned at P and on a roller at S, with diagonal PR and a rightward force F at R. See the attached source image.
  1. $F\sqrt2$ tensile, F tensile
  2. $F\sqrt2$ tensile, F compressive
  3. F compressive, $F\sqrt2$ compressive
  4. F tensile, $F\sqrt2$ tensile

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Show answer and explanation

Correct answer: (B) $F\sqrt2$ tensile, F compressive

Explanation

At unloaded joint Q, the two perpendicular members PQ,QR have zero force. At R, diagonal PR must supply leftward force F, requiring tensile force F√2 at 45°.

Its downward component is F, balanced by upward compression in RS. **PR=F√2 tensile, RS=F compressive (B)**.