# Experimental and Numerical Analyses of Timber-Steel Footbridges
## 2 Parametric Study of Timber Footbridges
Bridge deck type II removes some of the disadvantages of bridge deck type I. Bridge deck type III seems to be the least demanding from a structural viewpoint, and if hot-rolled IPE profiles could be used in the bridge superstructure, it would be the most advantageous in terms of steel consumption. However, due to the longitudinal placement of bridge covering on the stringers' upper flanges, the wide-flange profiles of the HEA type must be used. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Span**} & \multirow{2}{*}{**Main Girder Cross-Section** **[mm]**} & \multirow{2}{*}{**Compared Values**} & \multicolumn{4}{c}{**Footbridge Deck Type**} \\ \cline{5-8}  & & Resistance & \(\sigma_{\rm d}/\rm f_{\rm d}\) & [-] & 0.88 & 0.83 & 0.81 \\ \cline{3-8}  & & Deflection & \(\rm\delta_{\rm k}/\rm\delta_{\rm lim}\) & [-] & 0.47 & 0.55 & 0.50 \\ \cline{3-8}
12 & \multirow{2}{*}{150/900} & Stability & \(\rm\alpha_{\rm cr}\) & [-] & 16.05 & 22.84 & 24.70 \\ \cline{3-8}  & & Dynamic & \(\rm f_{\rm VI}\) & [Hz] & 6.32 & 6.48 & 6.21 \\ \cline{3-8}  & & \(\rm f_{\rm H1}\) & [Hz] & 8.89 & 7.38 & 8.03 \\ \hline \multirow{4}{*}{16} & \multirow{4}{*}{180/1200} & Resistance & \(\sigma_{\rm d}/\rm f_{\rm d}\) & [-] & 0.84 & 0.71 & 0.76 \\ \cline{3-8}  & & Deflection & \(\rm\delta_{\rm k}/\rm\delta_{\rm lim}\) & [-] & 0.57 & 0.53 & 0.64 \\ \cline{3-8}  & & Stability & \(\rm\alpha_{\rm cr}\) & [-] & 17.75 & 26.75 & 17.36 \\ \cline{3-8}  & & Dynamic & \(\rm f_{\rm VI}\) & [Hz] & 5.51 & 5.95 & 5.98 \\ \cline{3-8}  & & \(\rm f_{\rm H1}\) & [Hz] & 4.96 & 6.82 & 6.45 \\ \hline \multirow{4}{*}{20} & \multirow{4}{*}{220/1500} & Resistance & \(\sigma_{\rm d}/\rm f_{\rm d}\) & [-] & 0.73 & 0.60 & 0.66 \\ \cline{3-8}  & & Deflection & \(\rm\delta_{\rm k}/\rm\delta_{\rm lim}\) & [-] & 0.64 & 0.59 & 0.71 \\ \cline{3-8}  & & Stability & \(\rm\alpha_{\rm cr}\) & [-] & 22.75 & 29.23 & 17.00 \\ \cline{3-8}  & & Dynamic & \(\rm f_{\rm VI}\) & [Hz] & 5.00 & 5.39 & 5.22 \\ \cline{3-8}  & & \(\rm f_{\rm H1}\) & [Hz] & 3.68 & 5.39 & 5.22 \\ \hline \multirow{4}{*}{24} & \multirow{4}{*}{260/1800} & Resistance & \(\sigma_{\rm d}/\rm f_{\rm d}\) & [-] & 0.68 & 0.58 & 0.62 \\ \cline{3-8}  & & Deflection & \(\rm\delta_{\rm k}/\rm\delta_{\rm lim}\) & [-] & 0.69 & 0.60 & 0.75 \\ \cline{3-8}  & & Stability & \(\rm\alpha_{\rm cr}\) & [-] & 29.42 & 31.28 & 16.87 \\ \cline{3-8}  & & \(\rm f_{\rm VI}\) & [Hz] & 5.01 & 5.21 & 5.13 \\ \cline{3-8}  & & \(\rm f_{\rm H1}\) & [Hz] & 3.55 & 5.20 & 4.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of results of the parametric study. Therefore, it can be concluded that all three types of bridge decks show a similar steel consumption. When deciding on a specific type of bridge deck, it is, therefore, necessary to consider the speed and simplicity of bridge assembly and the guaranteed degree of safety and durability. Finally, it could be concluded that a rigid connection between the cross-girders and the main girders should be sufficient to protect the latter against lateral-torsional stability loss. Therefore, this connection is a very important detail which ensures the overall stiffness of the superstructure and improves its dynamic properties. The design of this connection must, therefore, minimise twist in the end node of the cross-girder. In the present study, the joint was considered fully rigid in the vertical direction. On the other hand, the connections of wooden structural members are usually considered to be nominally hinged, which is due to a slip of the joint created with dowel-type fasteners. It may be expected that the true stiffness of the joint is somewhere between these two extremes. Since this detail appeared to be essential for the design of the above-mentioned footbridge type, further attention was paid to it in our research.