The behaviour of regular multi-span simply-supported bridges is strongly dependent on the behaviour of its piers. The response of a pier is governed, in general, by different mechanisms: flexure, shear, second order effects, lap-splice of longitudinal bars or their buckling. The flexural behaviour is an important part of the problem, and it can be characterised through the equivalent plastic hinge length and the Moment-Curvature law of the fixed end. In this paper, a procedure to calculate the Moment-Curvature relationship of circular RC sections is proposed which is based on defining the position of few characteristic points. The analytical formulation is based on adjusted polynomial functions fitted on a database of fibre-based analyses. The proposed solution is based on three parameters: dimensionless axial force, mechanical ratio of longitudinal reinforcement, geometrical ratio of transverse reinforcement. A benchmark case is presented to compare the solution to a FEM non-linear analysis. Even if it is based on few input data, this solution allows to have good indicators on the material performances (e.g. yielding, spalling, etc). For these reasons, the proposed approach is deemed to be particularly effective in performing quick yet accurate mechanics-based regional-scale assessment of bridges.