A fixed beam of length 'L' is subjected to two concentrated loads: 'W' at \(\rm \frac{L}{4}\) from the left support (A) and '2W' at \(\rm \frac{3L}{4}\) from the left support (A). The beam is fixed at both ends (A and B). Which of the following statements is correct regarding the reactions at the supports?

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A fixed beam of length 'L' is subjected to two concentrated loads: 'W' at \(\rm \frac{L}{4}\) from the left support (A) and '2W' at \(\rm \frac{3L}{4}\) from the left support (A). The beam is fixed at both ends (A and B). Which of the following statements is correct regarding the reactions at the supports?

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The reactions at both A and B are independent of the applied loads.
The reactions at A and B are equal and opposite.
The reaction at A is greater than the reaction at B.
The reaction at B is greater than the reaction at A.

Answer 1

Concept:

In a fixed beam, both ends are restrained against rotation and vertical movement. When point loads are applied, the support reactions and fixed-end moments depend on:

Load magnitude
Load position
Span length

Reactions are determined using equilibrium equations and moment distribution. The fixed supports create redundant conditions, so compatibility is also used or standard formulas.

Given:

Beam length L
Load W at from A
Load 2 W at 3L/4 from A
Fixed at both ends A and B
This makes the heavier load (2W) closer to support B.
Because 2W is nearer to B, the reaction at support B must be larger to maintain equilibrium.
The beam being fixed causes moments and shears to distribute, but the closer and heavier load dominates the local reaction.

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