GATE CE 2026 Set 2 — Question 18
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Question
The horizontal beam shown in the figure has fixed supports at and . Internal hinges are provided at locations and . The beam supports vertically downward concentrated loads as well as uniformly distributed loads, as shown in the figure.
(Figure not to scale)The upward vertical reaction (in kN) at the support is
Correct answer
(A) 23
Solution
To find the upward vertical reaction at support , we can analyze the beam by segments separated by the internal hinges and .
The vertical reactions at and due to this load are:
Apply vertical equilibrium () to segment :
Therefore, the upward vertical reaction at support is .
1.Analyze segment :
Segment is a simply supported beam between hinges and with a length of (). A point load of acts at its center .The vertical reactions at and due to this load are:
2.Analyze segment :
This segment is fixed at and has a hinge at . The forces acting on it are:- The downward reaction from segment at hinge , which is .
- A uniformly distributed load (UDL) of over the segment (length ). Total UDL .
Apply vertical equilibrium () to segment :
Therefore, the upward vertical reaction at support is .
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