A beam that can only bend on the Cantor set

In this work we address the following question: is it possible for a one-dimensional, linearly elastic beam to only bend on the Cantor set and, if so, what would the bending energy of such a beam look like? We answer this question by considering a sequence of beams, indexed by n, each one only able to bend on the set associated with the n-th step in the construction of the Cantor set and compute the Γ-limit of the bending energies. The resulting energy in the limit has a structure similar to the traditional bending energy, a key difference being that the measure used for the integration is the Hausdorff measure of dimension ln 2/ln 3, which is the dimension of the Cantor set.