# Research on Human Exposure to Transport-Induced Vibration in Buildings
## 3 Weighting Function Problem
\begin{table}
\begin{tabular}{l l c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Excitation Source**} & \multirow{2}{*}{\begin{tabular}{c} **VDV\({}_{\text{tn}}\)** \\ **(W\({}_{\text{b}}\) acc. BS [18])** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **VDV\({}_{\text{tn}}\)** \\ **(W\({}_{\text{k}}\) acc. ISO [16])** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **VDV\({}_{\text{tn}}\)** \\ **(W\({}_{\text{m}}\) acc. ISO [17])** \\ \end{tabular} } \\ \hline
1 & Tram 105 N (2 wag.) & 0.0788 & 0.0707 & 0.0346 \\
2 & Tram 105 N (2 wag.) & 0.1143 & 0.1083 & 0.0584 \\
3 & Tourist bus & 0.2172 & 0.2705 & 0.1567 \\
4 & Tram EU8N (further track) & 0.0454 & 0.0427 & 0.0217 \\
5 & Tram 105 N (3 wag.) & 0.0697 & 0.0644 & 0.0321 \\
6 & Tram 105 N (2 wag.) & 0.0747 & 0.0684 & 0.0375 \\
7 & Tram EU8N (further track) & 0.0416 & 0.0382 & 0.0202 \\
8 & Tram GT8S & 0.0458 & 0.0425 & 0.0219 \\
9 & Tram EU8N (further track) & 0.3187 & 0.3183 & 0.1726 \\
10 & Heavy truck & 0.0756 & 0.0731 & 0.0392 \\
11 & Tram 105 N (3 wag.) & 0.1227 & 0.1186 & 0.0609 \\
12 & Heavy truck & 0.1015 & 0.1008 & 0.0574 \\
13 & Tram E1-C3 & 0.0581 & 0.0541 & 0.0276 \\
14 & Tram 105 N (3 wag.) & 0.0886 & 0.0804 & 0.0404 \\
15 & Tram 105 N (3 wag.) & 0.0735 & 0.0682 & 0.0390 \\
16 & Tram GT6 & 0.0588 & 0.0551 & 0.0299 \\
17 & Tram 105 N (3 wag.) & 0.0768 & 0.0708 & 0.0348 \\
18 & Heavy truck & 0.2049 & 0.2017 & 0.1050 \\
19 & Heavy truck & 0.3375 & 0.3446 & 0.1745 \\
20 & Tram 105 N (3 wag.) & 0.0638 & 0.0599 & 0.0316 \\
21 & Heavy truck & 0.2349 & 0.2327 & 0.1251 \\
22 & Heavy truck & 0.2966 & 0.2955 & 0.1575 \\
23 & Heavy truck & 0.0867 & 0.0857 & 0.0469 \\
24 & Tram EU8N (further track) & 0.0392 & 0.0370 & 0.0199 \\  & Tram GT8S (closer track) & & & \\
25 & and Tram 105 N 3 wag. & 0.0914 & 0.0867 & 0.0474 \\  & (further track) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The VDVs according to different weighting functions. Figure 6: Experimental building “A” located in Krakow. The results listed in Table 2 refer to single event values. To evaluate the day/night exposure, \(\mathrm{VDV_{day}}\) or \(\mathrm{VDV_{night}}\) should be calculated using the following equation:  
\[\mathrm{VDV_{day/night}}=\left(\sum_{k=1}^{k=N}\mathrm{VDV^{4}}\right)^{0.25} \tag{4}\]  
where \(k\) is a single event and \(N\) is the number of events during the day/night. Daily and night exposure to vibrations were calculated as follows:  
* Using \(W_{\mathrm{b}}\) acc. [18]: \(\mathrm{VDV_{b}}\), \(40^{\prime}=0.444\); \(\mathrm{VDV_{b}}\), day = 0.983-adverse comments probable; \(\mathrm{VDV_{b}}\), right = 0.695 (half intensity of tram and cars passages)-adverse comments probable. * Using \(W_{\mathrm{k}}\) acc. [16]: \(\mathrm{VDV_{k}}\), \(40^{\prime}=0.454\); \(\mathrm{VDV_{k}}\), day = 1.005-adverse comments probable; \(\mathrm{VDV_{k}}\), right = 0.711 (half intensity of tram and cars passages)-adverse comments probable. * Using combined \(W_{\mathrm{m}}\) acc. [17]: \(\mathrm{VDV_{m}}\), \(40^{\prime}=0.243\); \(\mathrm{VDV_{m}}\), day = 0.538-adverse comments possible; \(\mathrm{VDV_{m}}\), right = 0.381 (half intensity of tram and cars passages)-adverse comments possible. The comparison of daily and night exposure to vibrations according to different documents is presented in Table 3.  
Conclusions from the measurements are as follows:  
Assessment of human exposure to vibrations in buildings made using VDV analysis should take into account the signal analysis weighting function \(W_{\mathrm{b}}\). It is possible to take the weighting function \(W_{\mathrm{k}}\) into consideration because the differences between \(W_{\mathrm{b}}\) and \(W_{\mathrm{k}}\) are small and in the range of 5 and 25 Hz values of both of these functions, they are the same. Using \(W_{\mathrm{m}}\), smaller values are obtained than using \(W_{\mathrm{b}}\) or \(W_{\mathrm{k}}\). Heavy trucks and buses generates higher VDVs than tram passages.