Which geometric factor most affects bending stress in a beam?

The height of the beam is the geometric factor that significantly influences bending stress. When analyzing bending in beams, the bending stress (σ) can be found using the formula:

σ = M*c/I

where:

• M is the bending moment,
• c is the distance from the neutral axis to the outermost fiber (which is half the height of the beam if the beam is rectangular), and
• I is the moment of inertia of the beam's cross-section.

As the height of the beam increases, the value of c also increases, resulting in a larger bending stress for the same bending moment. Additionally, the moment of inertia (I) increases with the height of the beam, but the effect of c is more pronounced in terms of bending stress calculations, particularly because stress is directly proportional to the distance from the neutral axis.

In practical engineering applications, a taller beam can carry larger loads without reaching the same bending stress as a shorter beam of the same width and material properties. Therefore, increasing the height is a common method to improve the bending capacity of a beam.

This understanding clarifies why height is a pivotal geometric factor in determining the bending stress experienced by a beam under load.