Uniform Strength in Beams

A beam is said to be of uniform strength if the bending stress is the same at every section along its longitudinal axis. This means that the beam is able to withstand the same amount of bending stress at any point along its length.

Understanding Bending Stress

Bending stress is the stress induced in a beam when subjected to bending moments. When a beam is loaded externally, it experiences bending, which causes one side of the beam to be in compression and the other side to be in tension. This results in the development of bending stress.

Why is Uniform Strength Important?

Uniform strength in beams is important for several reasons:

1. Safety: When a beam is subjected to external loads, it is crucial that the beam's strength is consistent throughout its length. If there are significant variations in bending stress along the beam, it can lead to localized failure or deformation, compromising the overall structural integrity. Uniform strength ensures that the beam can safely support the applied loads without any weak points.

2. Design Simplicity: Designing beams with uniform strength simplifies the structural analysis and design process. Engineers can assume a constant bending stress throughout the beam, which allows for easier calculation of the required beam dimensions, material selection, and reinforcement.

Why is Option D Correct?

Option D states that a beam is of uniform strength if the bending stress is the same at every section along its longitudinal axis. This statement is correct because the bending stress is a key factor in determining the strength and stability of a beam.

Options A, B, and C are incorrect because:

- Option A: The bending moment can vary along the beam, depending on the applied loads and supports. The bending moment is directly related to the bending stress but does not determine uniform strength on its own.

- Option B: The shear stress in a beam is not necessarily the same throughout the beam. The shear stress varies along the cross-section of the beam, reaching maximum values at the neutral axis and decreasing towards the top and bottom edges. Uniform shear stress is not a requirement for uniform strength.

- Option C: The deflection of a beam is related to the applied loads, beam geometry, and material properties. Deflection is not an indicator of uniform strength, as different sections of the beam can have the same deflection but different bending stresses.

In conclusion, option D is correct because uniform strength in a beam is achieved when the bending stress is the same at every section along its longitudinal axis. This ensures consistent strength and avoids localized failure or deformation.