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.

In this example, the steel bar will be transformed into an equivalent aluminum bar. To be equivalent, this new aluminum bar must have the same height and the same value of EI as the actual steel bar. The width of the equivalent aluminum bar will be modified to satisfy this requirement.