## 5 Discussion of Test Results
### Human Comfort and Vibration Serviceability Assessment Based on Existing Technical Documents
#### 5.3.1 Eurocode 0--Annex A2 and ISO Criteria  
The pedestrian comfort criterion of footbridges is conventionally defined by the Eurocode 0 (EC0)--Annex A2 in terms of an acceptable acceleration for any part of a given deck [21]. Anne A2 is specifically intended for bridges, while dedicated threshold accelerations (given as a function of the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Occupants \(p\)** & \multicolumn{3}{c}{**Loading Condition (Mean)**} & **Frequency** & **Damping \(\xi\)** \\ \hline
**Total** & **Standing** & **Walking** & \(R_{M}\) **(Equation (5))** & \(a_{peak}\) **(\%g)** & **Variation \(\Delta_{f}\) (\%)** & **Damping \(\xi\)** \\ \hline
1 & 0 & 1 & 0.182 & 7.13 & +8.34 & 2.163 \\
2 & 1 & 1 & 0.332 & 0.87 & +8.35 & 1.470 \\
3 & 2 & 1 & 0.546 & 0.91 & +6.39 & 2.095 \\
4 & 1 & 3 & 0.964 & 3.30 & +14.08 & 1.515 \\
6 & 3 & 3 & 1.350 & 3.27 & +11.96 & 2.220 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average frequency variation and damping for the system (P#1).  
vertical frequency \(f_{v}\)) are recommended for pedestrian structures. Generally, the acceleration peak must be limited to (values in m/s\({}^{2}\)):  
\[a_{max}=min\left\{\begin{array}{c}0.5\sqrt{f_{v}}\\ 0.7\end{array}\right. \tag{6}\]  
When the deck frequency exceeds 5 Hz, in addition, it may be assumed that no further verifications are required [21]. Simplified approaches are indeed recommended for pedestrian structures with \(f_{v}<3\) Hz.  
For the case-study system, based on Equation (6), the limit acceleration peak \(a_{max}=0.7\) m/s\({}^{2}\) can be hence taken into account (\(f_{v}=f_{es}=15.1\) Hz), and no additional vibrational checks are required. As shown in Figure 10, the EC0-A2 provisions and the experimental estimates for the examined structure result in fact in mostly satisfied serviceability performances, for all the considered test scenarios (i.e., with \"acceptable\" acceleration peak for 24 configurations, over 26). The exception is represented by the CN#3 and #4 scenarios (in-place jump, \(p=1\)), while few other configurations (four in total) are approaching the vibration acceptability limit. Two of them (CN#1 and #2) are still associated to an impulsive excitation (\(p=1\)), while the CN#8 and CN#11 configurations have a relatively high occupation density (with normal walking activity).  
For ordinary floors or special pedestrian structures requiring advanced calculation methods against vibrations, the Eurocode 0 follows the ISO recommendations [22]. There, the limit acceleration peaks (in %g) are provided as a function of the \"ISO baseline curve\", based on the destination of the structure, the class of use and the key movement features (see Figure 11). The proposed acceleration thresholds are more restrictive especially for the frequency range of 4 Hz to 8 Hz, where unpleasant effects are expected for the human body [51]. Certainly, the ISO method is simple and efficient for design practice. On the other hand, research studies highlighted that the approach (and other criteria in which the vibration thresholds are provided as a function of the structural frequency only) can have intrinsic limits when applied to pedestrian systems with reduced mass ([56; 57], etc.), like the walkway herein explored and glass structures in general.  
When the ISO criterion is applied to the examined system, see Figure 11, it is possible to notice that most of the CN#\(n\) configurations could still satisfy the recommended comfort limits. For few of them only (five in total, with four associated to an in-place jump (\(p=1\))) the threshold performance for  
Figure 10: Vibration serviceability assessment of the examined system, based on EC0-A2 provisions. Experimental acceleration peaks (average values, vertical direction), as a function of the number of occupants.  
\"indoor footbridges\" is exceeded. Three further conditions are approaching the limit peak, while the majority of them suggests a relatively good dynamic behavior of the structure.