## 6 Results and Discussion  
### Single Pedestrian HSI Analysis  
An 80 kg male subject walking along the reference structure with the anthropometric characteristics described in Table 6 was implemented for all simulation cases. The subject moves with a step length of 1.5 m at step frequency \(f_{w}\) = 2 Hz and double support duration between 33 and 50% for each gait cycle. Figure 4: Optimization Scheme. The ground reaction forces (GRFs) in the vertical and lateral directions as the pedestrian traverses the bridge are shown in Figures 5 and 6, respectively. The percentage differences for the GRFs, comparing the HSI with respect to those on a rigid surface, were calculated as the Root Mean Square Error (RMSE) over 10% intervals of the bridge span, as shown in Figure 7. As expected, the highest RMSE are found around the mid-span of the bridge, where the accelerations \(\vec{A}_{g}(t)\) are greater by 63.7% in the vertical direction and 23.42% in the lateral direction, with respect to the GRFs on rigid surfaces. The movements of the body segments are presented in Figures 8 and 9 and display typical patterns as reported in investigations [36]. The percentage differences for the angles corresponding to HSI with respect to those corresponding to the rigid surface were calculated and are very small when the pedestrian is near the bridge ends. Hence, the RMSE was calculated over the 40-60% span of the bridge, where the accelerations \(\vec{A}_{g}(t)\) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Mass [\%]** & \begin{tabular}{c} **Length** \\ **[mm]** \\ \end{tabular} & \begin{tabular}{c} *** CoM [\%]** \\ \end{tabular} & \begin{tabular}{c} **Ratio** \\ **Sagittal** \\ \end{tabular} & \
\begin{tabular}{c} **Ratio** \\ **Transverse** \\ \end{tabular} &
\begin{tabular}{c} **Ratio** \\ **Frontal** \\ \end{tabular} \\ \hline Head & 6.94 & 203.3 & 50.02 & 30.3 & 26.1 & 31.5 \\ Upper arm & 2.71 & 281.7 & 57.72 & 28.5 & 15.8 & 26.9 \\ Forearm & 1.62 & 268.9 & 67.51 & 43.88 & 12.31 & 42.93 \\ Trunk & 32.29 & 386.2 & 49.85 & 33.74 & 23.4 & 29.1 \\ Hip & 11.17 & 145.7 & 38.85 & 61.5 & 58.7 & 55.1 \\ Thigh & 14.16 & 422.2 & 40.95 & 32.9 & 14.9 & 32.9 \\ Shank & 4.33 & 434 & 43.95 & 25.1 & 10.2 & 24.6 \\ Foot & 1.37 & 190 & 44.15 & 25.7 & 24.5 & 12.4 \\ \hline \hline \end{tabular}  
* CoM is the Center of Mass of the element from distal to proximal point.  
\end{table} 
Table 6: Anthropometric data. Adapted from [37]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & **Element** & \(\mathbf{a_{0}}\) & \(\mathbf{a_{1}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{b_{3}}\) & \(\mathbf{a_{4}}\) & \(\mathbf{b_{4}}\) & \(\mathbf{a_{5}}\) & \(\mathbf{b_{5}}\) \\ \hline Head & 1.503 & \(-\)0.022 & \(-\)0.069 & \(-\)0.005 & 0.022 & \(-\)0.001 & 0.011 & \(-\)0.063 & 0.005 & 0.017 & 0.002 \\ Upper arm & 1.709 & 0.196 & \(-\)0.058 & 0.036 & 0.029 & \(-\)0.002 & \(-\)0.265 & \(-\)0.027 & \(-\)0.013 & 0.001 & 0.018 \\ Forearm & 1.81 & 0.195 & \(-\)0.058 & 0.036 & 0.029 & \(-\)0.002 & \(-\)0.264 & \(-\)0.027 & \(-\)0.013 & 0.001 & 0.018 \\ \(\theta_{i}\) & Trunk & 1.492 & \(-\)0.022 & \(-\)0.069 & \(-\)0.005 & 0.022 & \(-\)0.001 & 0.011 & \(-\)0.063 & 0.005 & 0.017 & 0.002 \\ Hip & 1.513 & 0.005 & \(-\)0.048 & 0.007 & 0.03 & 0.002 & \(-\)0.014 & \(-\)0.08 & \(-\)0.003 & 0.008 & \(-\)are influential, and are given in Table 8. In the case of angular movements in the frontal plane (Figure 9), the differences between the HSI and rigid surface are much greater than the differences in the sagittal plane. We believe that this is due to the lock-in phenomenon, for which the human model increases its lateral sway [24]. Figure 5: Vertical Ground Reaction Forces, HSI (Green solid line) and rigid surface (Black dotted line). (**a**) Forces over the entirety of the bridge, (**b**) Forces corresponding to four strides at mid-span. Figure 6: Lateral Ground Reaction Forces, HSI (Green solid line) and rigid surface (Black dotted line).