GATE CE 2024 Set 2 — Question 50
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Question
The horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load (V) of 10 kN can act at any point over the entire length of the beam.
The maximum magnitude of the moment reaction (in kN. m) that can act at the support P due to V is ____________ (in integer).
Correct answer
150 to 150
Solution
To find the maximum moment reaction at support P (), we consider the influence of the load kN at different positions.
kN.m.
For segment QRS, taking moments about R:
for (overhang RS).
Max occurs when is at S ( m):
kN (downward).
The moment at P due to this reaction is kN.m.
Comparing the two cases, the maximum magnitude of the moment reaction at P is 150 kN.m.
1.Load on segment PQ (0 ≤ x ≤ 15m):
The beam acts as a cantilever fixed at P and hinged at Q. The maximum moment at P occurs when the load is at the furthest point from P, which is the hinge Q ( m).kN.m.
2.Load on segment QRS (15m < x ≤ 30m):
The load on segment QRS creates a reaction at the hinge Q (), which is then transferred to segment PQ.For segment QRS, taking moments about R:
for (overhang RS).
Max occurs when is at S ( m):
kN (downward).
The moment at P due to this reaction is kN.m.
Comparing the two cases, the maximum magnitude of the moment reaction at P is 150 kN.m.
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