# Experimental and Numerical Analysis of an Innovative Combined String-Cable Bridge
## 4 Numerical Method and Comparison between Experimental Results
### Comparison of Experimental and Numerical Results  
After conducting experimental and numerical studies of the bridge model, it is possible to compare the obtained results. They are presented in Tables 14 and 15 in relative magnitudes (percentages) to evaluate the differences in the results (displacements) in both cases of analysis, taking into account the values of string prestressing. The differences in the maximum displacements place (at node 5L) due to asymmetric loading do not exceed 10%. Additionally, relatively large differences in displacements are observed in nodes 3L (3R) and 7L (7R). In the case of symmetrical loading, we also have small differences at the location of maximum displacements (mid-span), i.e., up to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{5}{c}{**Results**} \\ \cline{2-5}  & \(\mathbf{T_{1}=0.472\) kN} & \(\mathbf{T_{2}=1.084\) kN} & \(\mathbf{T_{3}=1.506\) kN} \\ \hline \(H_{\text{string}}\), kN, \(\gamma=1\) & \(-0.31\%\) & \(-1.85\%\) & \(-4.23\%\) \\ \hline \(H_{\text{string}}\), kN, \(\gamma=2\) & \(10.10\%\) & \(6.98\%\) & \(3.25\%\) \\ \hline \(H_{\text{string}}\), kN, \(\gamma=3\) & \(7.17\%\) & \(4.77\%\) & \(1.52\%\) \\ \hline \(H_{\text{cable}}\), kN, \(\gamma=7\) & \(7.93\%\) & \(1.15\%\) & \(6.65\%\) \\ \hline \(H_{\text{cable}}\) kN, \(\gamma=1\) & \(-8.58\%\) & \(-8.91\%\) & \(-7.41\%\) \\ \hline \(H_{\text{cable}}\) kN, \(\gamma=2\) & \(3.51\%\) & \(3.53\%\) & \(-14.15\%\) \\ \hline \(H_{\text{cable}}\) kN, \(\gamma=3\) & \(14.06\%\) & \(13.83\%\) & \(-4.89\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison results of numerical and experimental axial forces. Figure 11: Scheme of deformed model structure: (**a**) symmetrical loading; (**b**) asymmetrical loading. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Loading Type**} & \multicolumn{5}{c}{**Vertical Displacements, mm**} \\ \hline Local points of structure & 1L & 3L & 5L & \(7\)L & \(7\)R & \(5\)R & \(3\)R & \(1\)R \\  & & & & \(T_{1}=0.472\) kN & & & \\ Live load, symmetrical & 0 & 20\% & 10\% & 3\% & \(-2\%\) & \(1\%\) & \(11\%\) & \(0\) \\ Live load, asymmetrical \(\gamma=1  
3%, and we have much larger differences in areas outside of the maximum displacements. From such differences, we can see that the shape of the deformation of the experimental model did not fully correspond to the shape of the deformation of the FEM model, because the experimental model was equipped with massive support bearings that \"constrained\" rotations (deviations) and displacements at the same time, and this affected the shape of the deformation. Additionally, a 6 mm solid rod was used in the experiment (for the string and lower cable). In the model, the lower element (cable) was modeled as a truss element, which can only be stretched, and the string as a \"cable\" element. By modeling in this way, it was possible to pre-tension the string and perform non-linear calculations, while also evaluating the loading sequence. However, the designed nodes in the struts could create additional stiffness of the nodes and not fully correspond to the function of the hinge, because of which the structure could become stiffer than in the model. In the graph below (Figure 12), we can see the displacements of a symmetrically loaded structure obtained by numerical and experimental methods. We can see that the displacements obtained during the experiment are slightly smaller. Of course, the sizes of the displacement results obtained both numerically and experimentally are relatively very small compared to the dimensions of the whole bridge model, so it is normal that any minimal deviation here caused much larger errors. If the results of an asymmetrically loaded structure are examined, we can see that the maximum displacements of the structure coincide in the third of the span; when the structure is examined numerically and when it is examined experimentally, the shape of the deformation itself is different (Figure 13).