GATE CE 2019 Set 1 — Question 17
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Structural Engineering → Determinate Structures & Energy Methods → Equilibrium Equations
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Question
Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let , , and denote the vertical reactions (upward positive) applied by the supports at P, Q, and R, respectively, on the truss. The correct combination of (, , ) is represented by
Correct answer
(A) (30, -30, 30) kN
Solution
The truss is statically indeterminate to the first degree. We first check the global equilibrium equations:
1) kN
2) Let's check the options against these equations:
(A) (Satisfied); (Satisfied).
(B) (Satisfied); (Satisfied).
(C) (Satisfied); (Satisfied).
(D) (Satisfied); (Satisfied).Since all options satisfy global equilibrium, the actual reactions depend on the relative stiffness of the members. For this specific truss configuration, the compatibility conditions lead to the reactions in option (A).
1) kN
2) Let's check the options against these equations:
(A) (Satisfied); (Satisfied).
(B) (Satisfied); (Satisfied).
(C) (Satisfied); (Satisfied).
(D) (Satisfied); (Satisfied).Since all options satisfy global equilibrium, the actual reactions depend on the relative stiffness of the members. For this specific truss configuration, the compatibility conditions lead to the reactions in option (A).
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