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A vertical load of 10 kN acts on a hinge located at a distance of $L/4$ from the roller support $Q$ of a beam of length $L$ (see figure). The vertical reaction at support $Q$ is

1. 0.0 kN
2. 2.5 kN
3. 7.5 kN
4. 10.0 kN

Correct answer: 2.5 kN

Solution

For a simply supported beam with a point load, reactions are found using equilibrium. Since the load is at a distance $L/4$ from support Q, it is at $3L/4$ from the other support, so the reaction at Q is proportional to the opposite arm.

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