Pure bending, neutral layer, neutral axis

Pure and simple bending

Pure bending is bending under a constant bending moment with zero shear force, for example the central portion of a beam loaded by two equal loads symmetrically placed. Simple bending is general bending in which the bending moment varies along the beam and shear force is also present.

 P              P      pure bending between the loads
 |              |
 v______________v
 A  a   |   L   | a  B    SF = 0, BM = Pa between loads

Neutral layer and neutral axis

• Neutral layer (surface): the layer of fibres that is neither stretched nor shortened during bending, so its stress and strain are zero. The fibres above it are in compression and those below it in tension for a sagging beam.
• Neutral axis (NA): the line of intersection of the neutral layer with a cross-section of the beam. Bending stress varies linearly from zero at the NA to the maximum at the extreme fibres.

Position of the neutral axis

For linearly elastic material the net axial force over the section is zero, $\int \sigma\,dA = 0$, hence $\int y\,dA = 0$. The neutral axis therefore passes through the centroid of the cross-section. For unsymmetrical sections (such as a T-section) it is not at mid-depth, so the maximum tensile and compressive stresses differ.