## 7 Conclusions  
A three-dimensional model of the HSI was developed that consists of a whole-body biomechanical model of human gait and a structural system represented as a simple supported beam. The proposed model was used in an optimization algorithm that minimizes the mechanical energy expenditure required by a pedestrian to walk across the structure. The structural response, considering HSI, was implemented by combining inverse dynamics to predict the kinematics and kinetics of human gait and direct dynamics to solve the differential equations of the coupled system.  
Multibody models such as that of [PERSON] et al. (2016) [PERSON] et al. (2016) demonstrate that predictive gait models using inverse dynamics have up to 8 times faster execution speed compared to commercial multibody models using direct dynamics. For the model presented in this research, the primary factor contributing to the computational expense is the solution of the differential equations governing the structural system and HSI. Nevertheless, the integration of direct and inverse dynamics efficiently reduces the overall time required for each optimization iteration. The computational efficiency of the model was evidenced in the simulation times obtained during the study. Each gait pattern was simulated in approximately 12 s on the computer described in Section 5, demonstrating the feasibility of the model for practical analysis compared to other approaches that require significantly longer processing times [PERSON] et al. (2016).  
The predictions of body movements and ground reaction forces considering HSI were based solely on three simple gait characteristics: average walking speed (\(V_{w}\)), frequency (\(f_{w}\)), and step length, as well as the anthropometric data of the person and physical characteristics of the structure. It should be noted that none of the human body movements were predefined for a specific motion, and their behaviors were determined solely by the optimization process. The only constraints that were imposed corresponded to physically realizable gait patterns. The results suggest that human gait is a biological process of energy minimization, as other authors have suggested [PERSON] et al. (2016).  
The proposed model effectively simulates the kinematics and kinetics of human gait and accurately captures the dynamic response of structures subjected to HSI effects. It is important to note that the vertical force pattern (see Figures 5 and 6) exhibits a different number of peaks compared to the existing force patterns reported in the literature. However, this discrepancy is commonly observed in models with high leg stiffness at low walking speeds, where a greater number of force peaks is generated as the walking speed decreases [PERSON] et al. (2016).  
The results of the simulation of the HSI demonstrate the potential of this approach for modelling HSI effects pedestrian bridges. As such, it is a viable methodology for the evaluation and understanding of the impact of HSI. A comparison of the results of simulations of a person walking on a rigid surface and walking on a flexible bridge revealed significant differences in the contact forces induced by pedestrians traversing the structure. In particular, differences of 63% and 23% for vertical and lateral forces respectively, highlight the influence of HSI effects on contact forces and their implications for structural response.  
Finally, as shown in Figure 15, pedestrian bridges that are not expected to have excessive vibrations may experience frequency synchronization problems if high occupancy levels are reached and the natural frequency of the coupled system decreases. This highlights the importance of taking this factor into account during the design and construction phases in order to prevent serviceability issues arising from HSI phenomena.