A beam of uniform strength may be obtained by

Explanation:

In general, beams have uniform cross-sections throughout their length. When they are loaded, there is a variation in bending moment from section to section along the length. The stress in extreme outer fiber (top and bottom) also varies from section to section along their length.

The extreme fibers can be loaded to the maximum capacity of permissible stress, but they are loaded to less capacity. Hence, in beams of the uniform cross-section, there is a considerable waste of materials.

To avoid this waste of material, the beam is suitably designed such that the extreme fibers are loaded to the maximum permissible stress by varying the cross-section it will be known as a beam of uniform strength.

The beam is said to be in uniform strength if the maximum bending stress is constant across the varying section along its length.

The bending stress in extreme fiber can be calculated by using the bending formula:

$\sigma =\frac{M}{Z}$

For rectangular sections, Z = bd²/6

Based on the above formula, to have the beam of uniform strength, its cross-section varies in the following way:

1. Changing the depth (by keeping the width constant) throughout the length of the beam
2. Changing the width (by keeping the depth constant) throughout the length of the beam.
3. By changing both width and depth suitably.