Beam is said to be uniform strength if at every section along its longitudinal axis, the bending stress is same.

Introduction:
In structural engineering, when a beam is subjected to bending, it experiences internal forces and moments. These internal forces create stress within the beam, which is known as bending stress. The relationship between the bending stress and the bending moment is an important consideration in the design and analysis of beams.

Explanation:
The correct answer is option 'A' - the stress in a beam due to simple bending is directly proportional to the bending moment. This can be explained using the following points:

1. Definition of Bending Stress:
Bending stress is the stress induced in the beam due to the application of external forces, causing it to bend. It is defined as the ratio of the internal moment to the section modulus of the beam.

2. Equation for Bending Stress:
The equation for bending stress in a beam is given by:
Stress = (Bending Moment * Distance from Neutral Axis) / Section Modulus
where,
- Bending Moment: The moment produced by the external forces acting on the beam.
- Distance from Neutral Axis: The perpendicular distance from a point on the beam to the neutral axis.
- Section Modulus: A property of the cross-sectional shape that relates to the beam's ability to resist bending.

3. Relationship between Bending Stress and Bending Moment:
From the equation for bending stress, it is clear that the stress is directly proportional to the bending moment. As the bending moment increases, the stress in the beam also increases. Similarly, if the bending moment decreases, the stress in the beam decreases.

4. Significance of Bending Moment:
The bending moment is a measure of the internal forces in the beam caused by the external loads. It determines the amount of bending stress that will be induced in the beam. Therefore, any change in the bending moment will directly affect the stress in the beam.

Conclusion:
In conclusion, the stress in a beam due to simple bending is directly proportional to the bending moment. As the bending moment increases, the stress in the beam also increases. This relationship is important to consider in the design and analysis of beams to ensure they can withstand the applied loads without failure.