GATE CE 2021 Set 2 — Question 30
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure.
The vertical reaction at support X (in kN, in integer) is ___________
Correct answer
30 to 30
Solution
The beam has an internal hinge at O. We can split the beam into two parts: OY and XO.
1.Analyze part OY:
- It is a simply supported beam with a hinge at O and a roller at Y.
- Length , UDL .
- Taking moments about O: .
- Vertical equilibrium: (upwards on OY).
- It is a cantilever fixed at X with a point load acting downwards at O and a UDL.
- (downwards on XO).
- Vertical equilibrium: .
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