# FRP Bridges in the Flanders Region: Experiences from the C-Bridge Project
## 7 Dynamic Human-Structure Interaction  
The benefits of the low self-weight weight also come with a downside, which is the increased sensitivity to dynamic excitation by walking or jogging pedestrians. This can lead to vibrations, of which the acceleration may cause discomfort to (standing) pedestrians on the bridge. Therefore, there is a need for calculation models that accurately predict vertical acceleration, which is to be expected under a given pedestrian stream. Currently, such models exist, but may be over-conservative for web-core sandwich-type composite footbridges [53; 54; 55; 56; 57; 58]. As a result of the C-Bridge project, the actual accelerations measured on site are found to be lower, and the damping is found to be higher [59; 60; 61; 62; 63; 64] than predicted. The reason for this discrepancy is presumably the effect of human-structure interaction  
Figure 2: Longitudinal and transverse deflection under (**a**) a uniformly distributed load (LC3) and (**b**) a service vehicle (LC4). (HSI). Humans are mechanical systems of their own, which interact with the bridge. In particular, this leads to a human-induced damping in addition to the structural damping of the bridge. Its effect is, however, difficult to estimate and therefore forms the subject of ongoing research. Here, we present results from a 3D engineering software model that attempts to take into account the influence of human-structure interaction to estimate the vertical accelerations and, consequently, the comfort of the composite bridge. The model (Figure 3) is based on the web core sandwich panel FRP bridge in Puurs (See Section 6.1.1 and [44]). The structural damping of the bridge is modelled using Rayleigh damping, and a free vibration is induced on the bridge by means of a triangular impact load of short duration. Pedestrians are modelled on the bridge as single degree of freedom (SDOF) systems consisting of a nodal mass connected to its support by a damper and a spring. The SDOF system is characterized by a mass, spring constant, and damping ratio. It is assumed that 95% of a person's mass is sprung. With an average mass of 70 kg for one person, this results in a mass of 66.5 kg assigned to the nodal mass. A natural frequency of a person with one or two legs slightly bent, as is the case during walking, is equal to 3.25 Hz on average. The damping ratio of the SDOF system is equal to 30% based on [59,65]. From the mass, the natural frequency, and the damping ratio, the damping spring constant and damping coefficient can be calculated using dynamic equations describing a SDOF system, which are then assigned to the spring-damper element in the numerical model. In the simulations, a varying number of pedestrians is used in such a way that the pedestrian density ranges from 0 to 1.5 pedestrians per square meter. Additionally, the structural damping ratio of the bridge itself is varied, ranging from 0% to 5%. The resulting observed damping ratio in the free vibration as a function of pedestrian density for a pedestrian natural frequency of 3.25 Hz (walking pedestrian with bended knees) is shown in Figure 4.  
Figure 4 shows that the damping ratio is initially equal to the structural damping ratio, as expected, and subsequently increases steeply with increasing pedestrian density. Around 0.2 \(\mathrm{P/m^{2}}\), a peak is reached, after which the damping ratio declines gradually. Despite this decline, the observed damping ratio remains much higher than the structural damping ratio across the entire range of pedestrian densities. The maximum observed damping ratio can be a multiple of the basic structural damping ratio, especially if the latter value is low to begin with. Figure 3: Numerical model of web-core sandwich panel FRP bridge in Puurs with SDOF pedestrians. The human-induced damping effect was also observed during in situ vibration tests on different composite footbridges in Flanders [66,67].