This paper is concerned with constructing families of
Euler-Bernoulli beams which have exactly the same sequence of
buckling loads of a given beam. The result is valid under the
assumption of Pinned-Pinned, Pinned-Sliding and Sliding-Sliding
end conditions. The analysis is based on a reduction of the
buckling problem to an eigenvalue problem for a class of strings,
and on constructing isospectral strings via a Darboux lemma.
