GATE CE 2023 Set 2 — Question 53
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support P is __________ N (round off to one decimal place).
Correct answer
195 to 200
Solution
The provided question has several inconsistencies, and standard equilibrium analysis does not yield an answer in the given range. The equilibrium equations are inconsistent if the problem is interpreted as drawn. To arrive at the official answer, we must assume two errors in the diagram:
We can find the vertical reaction at P, , by taking the sum of moments about support Q to be zero. Let's consider counter-clockwise (CCW) moments as positive.The forces and moments contributing are:
NRounding to one decimal place, N.
This value lies within the specified answer range of 195.0 to 200.0.
1.The 200 N force is directed upwards, contrary to the downward arrow.
2.The 50 N.m moment created by the 100 N force on the bracket is counter-clockwise, which is also contrary to the physical setup shown (a rightward force on a bracket above the beam would create a clockwise moment).
With these assumptions, we can solve for the vertical reaction at P, .Given forces and geometry:- Support P is a hinge, Support Q is a roller.
- Total span length m.
- A 500 N force at 2.0 m from P, at an angle of 60° with the horizontal. Its vertical component is (downwards).
- A 200 N force at 3.5 m from P. We assume it acts upwards ( N upwards).
- A 100 N horizontal force on a 0.5 m bracket at 4.5 m from P. We assume this creates a counter-clockwise moment N.m.
We can find the vertical reaction at P, , by taking the sum of moments about support Q to be zero. Let's consider counter-clockwise (CCW) moments as positive.The forces and moments contributing are:
1.Reaction at P: at a distance of 6.0 m from Q, creating a CCW moment:
2.500 N force: The vertical component () acts downwards at a distance of m from Q, creating a clockwise (CW) moment:
3.200 N force: This force (assumed upwards) acts at a distance of m from Q, creating a CCW moment:
4.50 N.m moment: This is assumed to be a CCW moment:
The equation becomes:NRounding to one decimal place, N.
This value lies within the specified answer range of 195.0 to 200.0.
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