A point of inflexion/inflection in a beam deflected shape corresponds to when the bending moment in the beam equals

A point of inflection in a beam's deflected shape corresponds to when the bending moment in the beam equals zero.

Here's a step-by-step explanation:

1. A beam under load will bend and deflect. This deflection is not uniform and will vary along the length of the beam.

2. The bending moment at any point along the beam is a measure of the bending effect at that point due to the applied loads.

3. At points where the bending moment is maximum or minimum, the curvature of the beam is greatest. These points are not points of inflection.

4. A point of inflection is a point on the curve (the deflected shape of the beam) where the curve changes concavity. In other words, it's where the curve changes from being concave up to concave down, or vice versa.

5. At these points of inflection, the bending moment is zero. This is because the bending moment is proportional to the curvature of the beam, and at points of inflection, the curvature is zero (the beam is