  We study existence and uniqueness of distributional solutions to the
differential equation of the Euler-Bernoulli rod with discontinuous
coefficients and right-hand side. Upon checking the validity of a solution the
occurring products of singular coefficients with the distributional solution
have no obvious meaning. When interpreted on the most general level of the
so-called hierarchy of distributional products, it turns out that existence of
a solution forces a minimum regularity to hold. Curiously, the choice of the
distributional product concept is thus incompatible with the possibility of
having a discontinuous displacement function as a solution. We also give
conditions for unique solvability.
