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Between February 2016 and April 2017 seven bridges around the world collapsed suddenly, by causing fatalities and significant economic losses. Structural Health Monitoring (SHM) techniques can assess the health state of an infrastructure by analysing its behaviour, and point out degraded elements that require to be maintained. As a consequence, SHM methods can improve the safety of the transportation network, and reduce the life cycle costs of the infrastructure, by optimizing the maintenance schedule. In this paper, a Bayesian Belief Network (BBN) approach is proposed to assess the health state of a beam-and-slab bridge, by relying on the analysis of its vertical acceleration. A procedure to robustly define the Conditional Probabilities Tables (CPTs) of the BBN is proposed, by merging expert judgement with information about the bridge behaviour. The BBN allows updating the health state of the bridge when a new measurement of the bridge acceleration is available, by taking account of the health state of each element of the bridge. In this way, the degradation level of the whole bridge and of its elements is monitored over time, and unexpected behaviour of the bridge are diagnosed.