  We present a nonlinear model of weakly curved rod, namely the type of curved
rod where the curvature is of the order of the diameter of the cross-section.
We use the approach analogous to the one for rods and curved rods and start
from the strain energy functional of three dimensional nonlinear elasticity and
do not presuppose any constitutional behavior. To derive the model, by means of
$\Gamma$-convergence, we need to propose how is the order of strain energy
related to the thickness of the body $h$. We analyze the situation when the
strain energy (divided by the order of volume) is of the order $h^4$. That is
the same approach as the one when F\"oppl-von K\'arm\'an model for plates and
the analogous model for rods are obtained. The obtained model is analogous to
Marguerre-von K\'arm\'an for shallow shells and its linearization is the linear
shallow arch model which can be found in the literature.
