  We study a planar thin brittle beam subject to elastic deformations and
cracks described in terms of a nonlinear Griffith energy functional acting on
$SBV$ deformations of the beam. In particular we consider the case in which
elastic bulk contributions due to finite bending of the beam are comparable to
the surface energy which is necessary to completely break the beam into several
large pieces. In the limit of vanishing aspect ratio we rigorously derive an
effective Griffith-Euler-Bernoulli functional which acts on piecewise $W^{2,2}$
regular curves representing the midline of the beam. The elastic part of this
functional is the classical Euler-Bernoulli functional for thin beams in the
bending dominated regime in terms of the curve's curvature. In addition there
also emerges a fracture term proportional to the number of discontinuities of
the curve and its first derivative.
