## 5 Discussion of Test Results
### Human Comfort and Vibration Serviceability Assessment Based on Existing Technical Documents
#### 5.3.2 SETRA Guideline  
In accordance with the SETRA document, a first classification of a given pedestrian system should be carried out as a function of the frequency of the structure, see Table 4 and [23]. The desired comfort level must be then satisfied by checking the expected acceleration peak \(a_{max}\) in service conditions. Four classes of use can be in fact detected, depending on the occupation density of the system object of analysis:  
For a mean occupation in the order of \(d=0.5\) p/m\({}^{2}\) (see Table 2), a \"class III\" of use can be taken into account for the case-study walkway. Given the experimental frequency of the empty system (\(f_{\text{cs}}=15.1\) Hz), however, and according to SETRA recommendations, the structure can be classified in a  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Frequency Assessment** & \multicolumn{3}{c}{**Acceleration Assessment**} \\ \hline
**Range** & **Frequency (Hz)** & **Resonance Risk** & **Range** & **Acceleration Peak (m/s\({}^{2}\))** & **Comfort Level** \\ \hline F1 & 1.7-2.1 & Maximum & A1 & 0–0.5 & Maximum \\ F2 & 1–1.7 or 2.1–2.6 & Medium & A2 & 0.5–1 & Medium \\ F3 & 2.6–5 & Low & A3 & 1–2.5 & Minimum \\ F4 & 0–1 or \textgreater{}5 & Negligible & A4 & \textgreater{}2.5 & Not acceptable \\ \hline \hline \end{tabular}
\end{table}
Table 4: Reference frequency and acceleration ranges (vertical direction) for the comfort assessment according to [23].  
Figure 11: Vibration serviceability assessment of the examined system, based on ISO recommended limits. Experimental acceleration peaks (average values, vertical direction), as a function of the corresponding frequency.  
\"frequency range 4\" with \"negligible risk\" of resonance and null discomfort for the occupants. Specific dynamic analyses are in fact required by SETRA only for pedestrian systems that fall in the classes I-to-III, or when the vertical frequency is lower than 5 Hz, disregarding the structural typology and the fundamental dynamic features.  
The maximum acceleration peak \(a_{max}\) due to a single, equivalent occupant should be in fact calculated as:  
\[a_{max}=\frac{1}{2\xi}\cdot\frac{4p(t)w_{d}}{\rho_{s}\pi} \tag{7}\]  
where \(w_{d}=1.65\) m is the available width of the deck and \(\rho_{s}\) the total linear density (sum of deck and pedestrian). The harmonic pedestrian load \(p(t)\) should be then estimated based on the class of use (III) and frequency range (4) of the examined walkway. Its general definition gives:  
\[p(t)=Pcos\big{(}2\pi f_{p}\big{)}\frac{n^{\prime}}{S}\psi \tag{8}\]  
with \(P=280\) N the pedestrian force (class III), \(S\) the walking surface (\(1.65\times 2.65=4.375\) m\({}^{2}\)); \(f_{p}\) the walking frequency (with 1.6-2.4 Hz for \"normal\" activity). In Equation (8), \(n^{\prime}\) is the equivalent number of perfectly synchronized pedestrians (corresponding to a stream of \(n\) pedestrians), given by:  
\[n^{\prime}=10.8\sqrt{\xi n}\big{(}\text{for }d<1\text{p}/\text{m}^{2}\big{)} \tag{9}\]  
with \(\xi\), the critical damping. Finally, \(\psi\) is the reduction coefficient that accounts for the probability that \(f_{p}\) (or its second harmonic) approaches \(f_{os}\). For a vertical frequency \(f_{os}<1\) Hz or \(>2.6\) Hz, however, the SETRA document suggests \(\psi=0\), hence \(p(t)=0\) (Equation (7)) and \(a_{max}=0\), based on Equation (8).  
In Figure 12, comparative results are proposed for the experimental acceleration peaks of the glass walkway, as a function of \(p\) and \(f_{os}\). Differing from EC0-A2 and ISO provisions, it can be noticed that the majority of CN#\(n\) configurations are associated to \"maximum\" comfort, while six of them fall in the \"medium\" level. Again, the configurations with \"medium\" vibration performance are characterized by an in-place jump (\(p=1\)), see Figure 12b. Few others, however, are related to high occupation density and normal walking conditions (CN#8 and #11).