  Cracks in beams and shallow arches are modeled by massless rotational
springs. First, we introduce a specially designed linear operator that
"absorbs" the boundary conditions at the cracks. Then the equations of motion
are derived from the first principles using the Extended Hamilton's Principle,
accounting for non-conservative forces. The variational formulation of the
equations is stated in terms of the subdifferentials of the bending and axial
potential energies. The equations are given in their abstract (weak), as well
as in classical forms.
