GATE 2025 ME – Question 57
A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per m throughout the length as shown in the figure given below. The bending moment at the mid-point of the beam is_____ N m (rounded off to the nearest integer).
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Correct answer: 0
Explanation
The applied couples add up to $1 \times 1 = 1$ N m, so the supports must give a balancing pair of vertical reactions $R = \frac{1}{1} = 1$ N, in opposite directions. At the mid-point, the reaction at one support gives a moment of $1 \times 0.5 = 0.5$ N m. The applied couples on that half contribute $1 \times 0.5 = 0.5$ N m in the opposite sense. The two cancel, so the bending moment at the mid-point is 0.