Bridge assessment and monitoring are important subjects nowadays. While the monitoring of displacement can be challenging, the bridge monitoring based on strain measurement is preferred. The latter can be obtained directly by sensors such as fiber optics. This kind of sensors has some advantages such as precision, high sampling frequency, and durability. In order to analyze quickly the measurement results from this sensor, we have developed an analytical model of a bridge structure to study the influence of the vehicles (loads, velocity) on the behavior of the structure. This paper presents the aforementioned model which allows us to calculate rapidly the dynamic responses (displacement, average strain, acceleration…) of a beam-like structure under a vehicle load by using a transfer matrix of two successive beam segments. Moreover, a damage detection and localization method based on distributed long-gauge strain sensors is proposed. Next, the results of the model are compared with the measured data of a multi-girder prestressed concrete bridge located in France. The comparison shows that the model is efficient for fast computing of the bridge responses. Finally, numerical results of the aforementioned method will be discussed.