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If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "hogging", and a positive moment will cause "sagging". It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is, the point of transition from hogging to sagging or vice versa.
An evenly loaded beam, bending (sagging) under load. The neutral plane is shown by the dotted line. In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension.
Loads imposed on structures are supported by means of forces transmitted through structural elements. These forces can manifest themselves as tension (axial force), compression (axial force), shear, and bending, or flexure (a bending moment is a force multiplied by a distance, or lever arm, hence producing a turning effect or torque).
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
Therefore the first moment of the cross section about its neutral axis must be zero. Therefore the neutral axis lies on the centroid of the cross section. Note that the neutral axis does not change in length when under bending. It may seem counterintuitive at first, but this is because there are no bending stresses in the neutral axis.
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