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GATE 2019 CE (CE1) – Question 17

Structural Analysis · Principle of superposition, virtual work and Castigliano theorem · 1 mark · Multiple choice

For the pin-jointed plane truss shown, RP, RQ and RR denote vertical support reactions at P, Q and R, with upward positive. Find (RP, RQ, RR) in kN.

Diagram for GATE 2019 CE (CE1) question 17
  1. (30, −30, 30)
  2. (20, 0, 10)
  3. (10, 30, −10)
  4. (0, 60, −30)

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Correct answer: (A) (30, −30, 30)

Explanation

Take upward reactions positive. Joint equilibrium in the two left support members gives horizontal components −45 and +45 kN and vertical components −45 and +15 kN, hence $R_P=30$ kN. Whole-truss vertical equilibrium then gives $R_Q+R_R=0$. Taking moments about P gives $6R_Q+9R_R=30(3)=90$. Therefore **(RP, RQ, RR) = (30, −30, 30) kN, A**.