GATE CE 2014 Set 1 — Question 40
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of 80 kN hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member QR, will be
Correct answer
(A) 30 kN Compressive
Solution
Coordinates: , , .
Let and be the forces in members PQ and PR.
At joint P, equilibrium equations are:
(assuming downward load is negative)Angles with horizontal:
For PQ:
For PR: (or from the other side)Using vectors for joint P:
Equilibrium at P:
-comp:
-comp:
Substitute :
Now consider joint R:
Forces acting are and .
The negative sign indicates compression. Thus, .
Let and be the forces in members PQ and PR.
At joint P, equilibrium equations are:
(assuming downward load is negative)Angles with horizontal:
For PQ:
For PR: (or from the other side)Using vectors for joint P:
Equilibrium at P:
-comp:
-comp:
Substitute :
Now consider joint R:
Forces acting are and .
The negative sign indicates compression. Thus, .
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