  It has been proved by the authors that the (extended) Sadowsky functional can
be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip of
height $\varepsilon$, as $\varepsilon$ tends to 0. In this paper we show that
this Gamma-convergence result is stable when affine boundary conditions are
prescribed on the short sides of the strip. These boundary conditions include
those corresponding to a M\"obius band.
