GATE CE 2023 Set 2 — Question 57
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member to the vertical member at is _________ N (round off to one decimal place).
Correct answer
17.5 to 18.5
Solution
To find the horizontal component of the force transferred from member to member at point , we analyze the equilibrium of the horizontal member .
By Newton's third law, the force transferred from member to member at point is equal in magnitude and opposite in direction. The magnitude of the horizontal component is N.
1.Identify the forces acting on member :
- Reaction at : Horizontal component and vertical component .
- Force from the strut : Since is a two-force member (pinned at both ends with no intermediate loads), the force acts along the line .
- External load: N acting vertically downwards at point .
- Let be the origin .
- Point is at .
- Point is at .
- Point is m below , so its coordinates are .
- The angle that the strut makes with the horizontal is given by:
3.Apply equilibrium equations to member :
- Sum of moments about point must be zero:
4.Find the horizontal component at :
- Sum of horizontal forces must be zero:
- From the relation between components:
- Therefore, N. This is the force exerted by member on at .
By Newton's third law, the force transferred from member to member at point is equal in magnitude and opposite in direction. The magnitude of the horizontal component is N.
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