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Strength of Materials: Bending

Before continuing on if you don't have an understanding of shear and moment diagrams and how to calculate area moment of inertias. I strongly recommend you look at those pages before continuing.

Bending of a part is a very common occurrence, and being able to calculate bending stresses will help an engineer determine if a design is feasible, or if it instead needs to be modified. During bending, in most cases a normal stress in tension and compression is created along with a transverse shear stress. The only time shear would not be a factor is if the beam is only under a moment. Transverse shear stress will be discussed separately.

Normal stress on a beam due to bending is normally referred to as bending stress. First off, bending stress consists of a compression stress along with a tensional stress. The type of stress changes at the neutral axis. There is no normal stress at the neutral axis. The neutral axis is always located at the beams centroid, which means it's not always directly in the center of the beam. For any situation of bending, the higher stress is on the point farthest away from the neutral axis. Refer to the figure below.

Stress Distribution on a beam due to bending

Depending on the beams setup, the maximum stress would be located at different points of the length of the beam. This point can be determined from the moment diagram which will show the point along the length of the beam that has the greatest moment. However, if the beam is a cantilever beam then the highest stress would always be located at the wall where the beam is connected, while if the beam is in simply supported configuration, then the highest stress would be half way down the length of the beam. To calculate the normal stress on a beam equation 1 would be used.

Equation to calculate normal stress on a beam due to bending (1)

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