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GATE 2026 ME – Question 41

Engineering Mechanics · Free-body diagrams and equilibrium · 2 marks · Multiple choice

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

A beam with a hinge. Roller support A is at the left end. A 10 kN load is 0.5 m from A. The hinge is a further 0.5 m along. Roller support B is 0.2 m past the hinge. A 25 kN load is a further 0.2 m along, and pin support C is 0.6 m beyond that load.
  1. 5
  2. 10
  3. 20
  4. 15

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Show answer and explanation

Correct answer: (A) 5

Explanation

Measure from A: the 10 kN load is at 0.5 m, the hinge at 1.0 m, support B at 1.2 m, the 25 kN load at 1.4 m and support C at 2.0 m. The bending moment at the hinge is zero. For the left part, taking moments about the hinge gives $R_A \times 1.0 = 10 \times 0.5$, so $R_A = 5$ kN, and the hinge passes 5 kN downward onto the right part. For the right part, taking moments about B gives $-5(0.2) + 25(0.2) - R_C(0.8) = 0$, so $R_C = 5$ kN.