  We present a geometrically exact nonlinear analysis of elastic in-plane beams
in the context of finite but small strain theory. The formulation utilizes the
full beam metric and obtains the complete analytic elastic constitutive model
by employing the exact relation between the reference and equidistant strains.
Thus, we account for the nonlinear strain distribution over the thickness of a
beam. In addition to the full analytical constitutive model, four simplified
ones are presented. Their comparison provides a thorough examination of the
influence of a beam's metric on the structural response. We show that the
appropriate formulation depends on the curviness of a beam at all
configurations. Furthermore, the nonlinear distribution of strain along the
thickness of strongly curved beams must be considered to obtain a complete and
accurate response.
