GATE 2026 CE (CE2) – Question 18
The horizontal beam shown in the figure has fixed supports at F and L. Internal hinges are provided at locations G and J. The beam supports vertically downward concentrated loads as well as uniformly distributed loads, as shown in the figure.
[Figure: A horizontal beam F-G-H-J-K-L with fixed supports at F (left end) and L (right end) and internal hinges at G and J. F to G is 4 m and G-H, H-J, J-K and K-L are 2 m each. A 5 kN/m uniformly distributed load acts on F to G, a 20 kN downward load acts at G, a 30 kN downward load acts at H, and a 4 kN/m uniformly distributed load acts on K to L. The figure is not to scale.]
The upward vertical reaction (in kN) at the support L is
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Correct answer: (A) 23
Explanation
The part G-H-J sits between two hinges, so it behaves like a simply supported beam. Its 30 kN load at the mid-point H gives 15 kN to the hinge at G and 15 kN to the hinge at J. The part J-K-L is a cantilever fixed at L. It carries the 15 kN from the hinge at J and the distributed load on K-L of 4 x 2 = 8 kN, so the vertical reaction at L is 15 + 8 = 23 kN. The 20 kN at G and the load on F-G are carried by the fixed support at F and do not affect L.