For a given neutral plane radius, r, (E/r) is a constant and the summation has only y as a variable. The quantity S b y² dy is known as the 'geometric moment of inertia' or the 'second moment of area' of the beam, I. The bending moment can therefore be written:
M = (E / r) I.

The maximum stress in the beam occurs at the 'top' and 'bottom' surfaces and has the value: s_max = {H h / 2 I}.

When designing a structure, s_max should be below the yield stress of the material , and below the buckling stress of the beam in compression. Since I is shape dependent, s_max can be controlled by proper selection of the beam geometry.