The constitutive equation describes how the direct stress s and direct strain e within the beam are related.
Direct means perpendicular to a beam cross section; if we were to cut the beam at a given location, we would find a distribution of direct stress acting on the beam face,
Beam theory typically uses the simple 1-dimensional Hooke's Equation,
Note that the stress and strain are functions of the entire beam cross section (i.e. they can vary with y).