  The objective of this research is the development of a geometrically exact
model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The
complete metric of the beam is utilized in order to include the effect of
curviness on the nonlinear distribution of axial strain over the cross section.
The exact constitutive relation between energetically conjugated pairs is
employed, along with four reduced relations. The isogeometric approach, which
allows smooth connections between finite elements, is used for the spatial
discretization of the weak form. Two methods for updating the local basis are
applied and discussed in the context of finite rotations. All the requirements
of geometrically exact beam theory are satisfied, such as objectivity and
path-independence. The accuracy of the formulation is verified by a thorough
numerical analysis. The influence of the curviness on the structural response
is scrutinized for two classic examples. If the exact response of the structure
is sought, the curviness must be considered when choosing the appropriate beam
model.
