The GATE Grind

GATE 2025 AE – Question 27

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 1 mark · Multiple choice

A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from $q_0$ at A to zero at B, as shown in the figure. Which one of the following options is correct?

A beam AB of length $l$ with a pin support at A and a roller at B. The load acts downwards and decreases linearly from $q_0$ at A to zero at B.
  1. The magnitude of the vertical reaction force at A is larger than that at B.
  2. The magnitude of the vertical reaction force at B is larger than that at A.
  3. The magnitudes of the vertical reaction forces at A and B are equal.
  4. The reactions at points A and B are indeterminate.

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Show answer and explanation

Correct answer: (A) The magnitude of the vertical reaction force at A is larger than that at B.

Explanation

The resultant load is $W = \frac{q_0 l}{2}$ and acts at the centroid of the triangle, $\frac{l}{3}$ from A. Moments about B give $R_A = \frac{2}{3}W$ and $R_B = \frac{1}{3}W$, so A carries more. The beam is statically determinate.