GATE CE 2024 Set 1 — Question 39
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
The beam shown in the figure is subjected to a uniformly distributed downward load of intensity between supports A and B.
📷 Figure: Beam with supports A, B, C, an internal hinge, and UDL
Considering the upward reactions as positive, the support reactions areCorrect answer
(A) R_A = (ql)/(2); R_B = (5ql)/(2); R_C = - ql
Solution
Let the hinge be at point H. The beam is divided into two parts: A-H and H-B-C.
1.Part A-H (length ): Taking moments about the hinge H, .
2.Equilibrium of the whole beam:
- Total downward load = .
- .
- Taking moments about A for the whole beam: .
- From , we have .
- Substitute into the moment equation: .
- Then .
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