# Experimental and Numerical Analysis of an Innovative Combined String-Cable Bridge
## 3 Test Results and Analysis
### Experimental Results
#### 3.1.2. Asymmetrical Loading  
Tables 7-9 show the values of the displacements of the bridge model loaded with temporary load asymmetrically over half the span length. The values of the displacements are presented according to the values of the pre-tension of the string: \(T_{1}\) = 0.472 kN; \(T_{2}\) = 1.084 kN; \(T_{3}\) = 1.506 kN. From the results presented in Tables 6-8, it is obvious that the bridge model deformed asymmetrically according to the placement of the live load (when the live asymmetric load was on the left side of the model, see Figure 9). The largest displacements occurred on the side loaded with the asymmetric load (nodes 3L, 5L, 7L). These displacements increased proportionally to the values of the load ratio \(\gamma\). For example, with string pre-tension \(T_{1}\) = 0.472 kN and increasing load ratio values from \(\gamma\) = 1 to \(\gamma\) = 3, model displacements in-creased from 18.55 mm to 33.3 mm (node 5L). It was experimentally established that the pre-tensioning of the string reduces the values of the maximum displacements. By increasing the string pre-tension values from \(T_{1}\) = 0.472 kN to \(T_{3}\) = 1.506 kN, the mentioned maximum displacements (node 5L) decreased (at \(\gamma\) = 1) by about 14%, at \(\gamma\) = 2 by about 11%, and at \(\gamma\) = 3 by about 7%. It should be noted that even with a load ratio of \(\gamma\) = 1, the maxi-mum displacements of asymmetric loading are larger than those of symmetrical loading by about 3.3 times. This means that in the case of asymmetric loading, kinematic displacements dominate [33]. Additionally, these kinematic displacements increase in proportion to the load ratio \(\gamma\) and the initial sag of the cable [37]. It should be noted that the innovative combined string-cable bridge system consisting of a string and a cable is \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multicolumn{3}{c}{**Shear Forces, kN**} \\ \cline{2-4}  & \(T_{1}\) = 0.472 kN & \(T_{2}\) = 1.084 kN & \(T_{3}\) = 1.506 kN \\ \hline String & 2.95 & 3.31 & 4.02 \\ \hline Cable & 3.30 & 3.49 & 3.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Axial forces in the string and cable by symmetrical loading. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Loading Type**} & \multicolumn{6}{c}{**Vertical Displacements, mm**} \\ \hline Measurement points of structure & 1L & 3L/9L & 5L/10L & 7L/11L & 7R/11R & 5R/10R & 3R/9R & 1R \\ Live load, asymmetrical \(\gamma\) = 1 & 0 & \(-\)10.78 & \(-\)17.11 & \(-\)15.69 & 6.63 & 10.11 & 3.23 & 0 \\ Live load, asymmetrical \(\gamma\) = 2 & 0 & \(-\)15.39 & \(-\)26.02 & \(-\)23.07 & 13.62 & 18.41 & 7.04 & 0 \\ Live load, asymmetrical \(\gamma\) = 3 & 0 & \(-\)18.74 & \(-\)32.05 & \(-\)28.21 & 18.09 & 23.79 & 9.16 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Vertical displacements of the model under string prestressing force \(T_{2}\) = 1.084 kN. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Loading Type**} & \multicolumn{6}{c}{**Vertical Displacements, mm**} \\ \hline Measurement points of structure & 1L & 3L/9L & 5L/10L & 7L/11L & 7R/11R & 5R/10R & 3R/9R & 1R \\ Live load, asymmetrical \(\gamma\) = 1 & 0 & \(-\)10.78 & \(-\)17.11 & \(-\)15.69 & 6.63 & 10.11 & 3.23 & 0 \\ Live load, asymmetrical \(\gamma\) = 2 & 0 & \(-\)15.39 & \(-\)26.02 & \(-\)23.07 & 13.62 & 18.41 & 7.04 & 0 \\ Live load, asymmetrical \(\gamma\) = 3 & 0 & \(-\)18.74 & \(-\)32.05 & \(-\)28.21 & 18.09 & 23.79 & 9.16 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Vertical displacements of the model under string prestressing force \(T_{3}\) = 1.506 kN. under consideration. The string has no kinematic displacements, so it \"stabilizes\" the displacements caused by the asymmetric load of the entire bridge model (basically cable displacements). Increasing string pre-tension values also increases this \"stabilizing\" effect. This is evident from the obtained experimental results (see Tables 7-9).