Figure 3.

Bending of a beam. The deflection is Δ, the thickness T, the width a, and the length of the beam L. The transverse deflecting force, F, is applied to one end of the beam. The position, y, is measured from the other, clamped end. For any cross section at a given y, the strain will vary with position x away from the neutral line, being zero on the line itself. Further away from the line, the strain may exceed γ_o, and the response will be hard. The sections closer to the clamp, at small y, are more distorted, and the crossover γ_o will be closer to the neutral axis. It is this variation of elastic response across the beam, on going down the beam, that makes the problem of the overall response nontrivial.