Question

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?
\includegraphics[width=0.5\linewidth]{27.png}

• A. The magnitude of the vertical reaction force at A is larger than that at B.
• B. The magnitude of the vertical reaction force at B is larger than that at A.
• C. The magnitudes of the vertical reaction forces at A and B are equal.
• D. The reactions at points A and B are indeterminate.

Hint:

For a linearly varying load on a simply supported beam, the reaction force at the point closer to the larger part of the load will be higher.

Answer 1

The Correct Option is A

The problem describes a beam subjected to a triangular distributed load. In this case, the resultant of the triangular load acts at a distance of \( \frac{l}{3} \) from the larger end (point A) of the load distribution. The total load applied is: \[ {Total Load} = \frac{1}{2} q_0 l \] By applying the equations of equilibrium, we can calculate the reactions at A and B. Since the load is larger at point A and decreases linearly to zero at point B, the vertical reaction at A will be greater than the vertical reaction at B.