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GATE 2026 CE (CE1) – Question 39

Structural Analysis · Deflections of determinate beams, frames and trusses · 2 marks · Multiple choice

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height.

What is the absolute value of the maximum bending moment (in kN-m) in the frame?

A portal frame with a hinge support at the bottom left and a roller support at the bottom right. The columns are 3 m high, and the beam is 4 m long. A 50 kN horizontal force acts to the right at the top left corner, and a 90 kN downward load acts at the middle of the beam, 2 m from each end.
  1. 165
  2. 150
  3. 240
  4. 195

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Show answer and explanation

Correct answer: (A) 165

Explanation

Take moments about the left hinge. The right roller gives only a vertical reaction $R_B$, so $R_B \times 4 = 90 \times 2 + 50 \times 3 = 330$ and $R_B = 82.5$ kN. The moment at the top of the left column is $50 \times 3 = 150$ kN m. Under the 90 kN load, the beam moment is $R_B \times 2 = 165$ kN m. At the right corner the moment is zero because of the roller. The maximum is 165 kN m.