  We consider three-dimensional elastic frames constructed out of
Euler-Bernoulli beams and describe a simple process of generating joint
conditions out of the geometric description of the frame. The corresponding
differential operator is shown to be self-adjoint. In the special case of
planar frames, the operator decomposes into a direct sum of two operators, one
coupling out-of-plane displacement to angular (torsional) displacement and the
other coupling in-plane displacement with axial displacement (compression).
  Detailed analysis of two examples is presented. We actively exploit the
symmetry present in the examples and decompose the operator by restricting it
onto reducing subspaces corresponding to irreducible representations of the
symmetry group. These "quotient" operators are shown to capture particular
oscillation modes of the frame.
