## 4 Results and Discussion
### Reference Footridge Performance, Including HSI  
The spatio-temporal dynamic behavior structural responses of the reference footbridge under HSI effects due to human-induced gait loads, described in Section 2.1, were experimentally evaluated using RTHS as a testing methodology, as described in Section 3. In order to show the complete structural response during the crossing of pedestrians (TSs), the structural displacement and acceleration under gait loads induced by TS\({}_{1}\) at the contact point between the pedestrian and the footbridge and in the middle span were determined and processed, as shown in Figures 8 and 9. Lateral structural accelerations at the contact point for the three gait velocities, evaluated in time history and frequency response (1.20 m\(\cdot\)s\({}^{-1}\)--orange, 1.50 m\(\cdot\)s\({}^{-1}\)--blue, and 1.80 m\(\cdot\)s\({}^{-1}\)--green), determined an inverse relation between structural response times and gait velocity of the TSs. Likewise, the fundamental frequency that composes the structural response was close to 1.0 Hz, as shown in Figure 8 (top left). A similar behavior was observed when evaluating the lateral structural displacement at the contact point of the ST\({}_{1}\) and its frequency response (Figure 8, top right). In addition, the lateral structural displacement and acceleration in the structural middle span exhibited frequential behavior similar to the fundamental frequency around 1.0 Hz, and a free vibration behavior of the footbridge was identified once the pedestrian left the structure, allowing the identification of the structural damping, as presented in Figure 8 (bottom). It is important to note that while an approximately constant step length was maintained during the experiments, this step length was not restricted and could vary from step to step. This variability in step length arises due to the coupling between the test subjects and the structure, influenced by the effects of human-structure interaction (HSI). Such interaction can result in longer or shorter step lengths depending on the synchronization and adaptation of the subject to the movement of the footbridge. Figure 6: Parametric analysis of human-induced gait loads. Peak lateral human-induced gait loads vs. gait velocity of TSs (**left**); and peak vertical human-induced gait loads vs. gait velocity of TSs (**right**). Figure 7: Behavior of human-induced vertical gait loads on rigid and flexible surfaces. Time history and spectral response of human-induced vertical gait loads on rigid surfaces (**top**); spectral response of human-induced lateral gait loads on the reference footbridge for the three gait velocities: 1.20 (**middle left**), 1.50 (**middle center**), and 1.80 m\(\cdot\)s\({}^{-1}\) (**middle right**); and ST\({}_{1}\)-induced vertical gait loads on the reference footbridge for the three gait velocities: 1.20 (**bottom center**), 1.50 (**bottom left**), and 1.80 m\(\cdot\)s\({}^{-1}\) (**bottom right**). Similarly, vertical structural accelerations at the contact point for the three gait velocities were evaluated in time history and frequency response, which determined a direct relation between structural response times and gait velocity of the TS1 (1.20 m\(\cdot\)s\({}^{-1}\)--orange, 1.50 m\(\cdot\)s\({}^{-1}\)--blue, and 1.80 m\(\cdot\)s\({}^{-1}\)--green). Likewise, the fundamental frequency that composes these acceleration structural responses was close to 2.0 Hz, as shown in Figure 9 (bottom left). A similar behavior was observed when evaluating the vertical structural displacement at the contact point of ST1 and its frequency response (Figure 9, bottom right). Additionally, the vertical structural displacement and acceleration in the structural  
Figure 8: General lateral structural response of the reference footbridge under human-induced gait loads with HSI effects by ST1.