This study focuses on prestressed reinforced concrete bridges equipped with post-tensioned internal tendons. The response of these structures in service is expected to be elastic but it can show some degree of nonlinearity due to tendons relaxation or critical event occurring on the pre-stressing system, conditions which are impossible to be detected unless specific accurate inspections are performed. This study focuses on a recently proposed methodology exploiting the abilities of the Hilbert-Huang Transform (HHT) to extract the instantaneous properties of vibration under bridge operational traffic conditions. In particular, it is assessed the capability of the proposed approach to derive the nonlinear relationship between internal force and displacement of the bridge exploiting only deformation data recorded during vehicle passages, with the final objective of providing a tool for relating prestressing losses to variations in the dynamic response. For this aim, a benchmark case study is considered and its response under realistic, simulated, traffic scenarios is analysed proving the suitability of the tool to accurately reconstruct the constitutive law of the system.