To be equivalent, the transformed cross section must yield the same bending strains as the actual cross section.

Bending strains are defined by:

where y = coordinate measured from the neutral surface and ρ = radius of curvature.

It's also clear that ρ must be the same in the transformed cross section. The radius of curvature is defined by:

M must be the same in both cases, leaving EI as the only variable that can be modified.