BWIM with constant and variable velocity: theoretical derivation

The designs for live loads of bridges are specified by the codes. The codes are based upon data collected from traffic loads, after some adjustments, using a survey on truck weights in a weighing station. In recent decades, the characteristics of trucks can be found either by pavement weigh-in-motion or bridge weigh-in-motion (BWIM) systems. There are several algorithms used to perform BWIM; one of them is the area method (Helmi et al. in J Civ Struct Health Monit 4(3):195–208, 2014). The area method was developed based on the assumption that trucks move on the instrumented span with constant velocity. This paper includes a review of the theoretical derivation of the area method with constant velocity. Theoretical derivation for the case of variable velocity is derived and presented in this paper.