  We consider a family of three-dimensional stiffened plates whose dimensions
are scaled through different powers of a small parameter $\varepsilon$. The
plate and the stiffener are assumed to be linearly elastic, isotropic, and
homogeneous. By means of $\Gamma$-convergence, we study the asymptotic behavior
of the three-dimensional problems as the parameter $\varepsilon$ tends to zero.
For different relative values of the powers of the parameter $\varepsilon$, we
show how the interplay between the plate and the stiffener affects the limit
energy. We derive twenty-three limit problems.
