## 3 Results
### Application on the Real Bridge  
To show the applicability of the proposed methodology in complex structures, an intermediate stage of the balanced cantilever construction method was analyzed and the results are presented in this section. In this construction method, the deflections of the bridge segments have to be forecasted. This makes it possible to build the segments with the proper precamber. These predeformations are updated for each construction step after a topographical survey. This data can be used by inverse analyses for model updating to increase the accuracy of the precamber calculations. According to [PERSON]  
Figure 9: Percentage error between the estimated inertia using the OM method \(\overline{I}\) with the actual one \(I\) for three beams in terms of the slenderness (\(L/h\) ratio). et al. [51], neglecting the shear effects in the balanced cantilever construction method during the erection of the first bridge segments may lead to inaccurate estimations of the bending stiffnesses. The structure chosen for this example was a simplified model of an intermediate construction stage of the Yunbao Bridge over the Yellow River in China [52] (see Figure 10a). This bridge was erected with a novel construction technology called asynchronous pouring construction (APC), which was proposed on the basis of traditional balanced cantilever construction [53]. The Yunbao bridge has a total length of 906 m divided into the following spans: 48 m + 9 \(\times\) 90 m + 48 m. The deck is continuous, and its cross-section corresponds with a composite box girder. The height of the deck ranges between 5.5 m (at the supports) and 2.7 m (at mid-span). The deck in the analyzed construction stage was 29.5 m long and it was composed of seven segments (three 4.5 m-long segments at each side joined to a central 2.5 m-long section over the pile). The formwork traveler was located at the end of each lateral span, as presented in Figure 10b. It is important to highlight that the prestressing of the balanced cantilever erection was not studied, as this load was not limited to the first-order shear deformation effects investigated in this study. To study higher-order shear deformations, the effects of the prestressing load will be studied in future works. A simplified geometry of the real bridge was analyzed. The connection between the concrete and the steel was assumed to be rigid, and the relative slip between both materials was neglected. The effects of prestressing on the shear rotation were overlooked in this example; these effects on shear rotations will be addressed in future studies. The cross-section of the composite deck is presented in Figure 11a and the mechanical and material properties are listed in Table 3. The FEM of this structure is presented in Figure 11b and it included eight nodes and seven beam elements. Each of these elements was defined with [PERSON]'s modulus E, inertias I and shear areas A\({}_{\
u}\), as shown in this sub-figure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Elements 1 and 7** & **Elements 2 and 6** & **Elements 3 and 5** & **Element 4** \\ \hline \(EA\) (N) & \(4.33\times 10^{11}\) & \(4.38\times 10^{11}\) & \(4.43\times 10^{11}\) & \(4.46\times 10^{11}\) \\ \(GA_{\
u}\) (N) & \(1.10\times 10^{10}\) & \(1.25\times 10^{11}\) & \(1.43\times 10^{11}\) & \(1.53\times 10^{11}\) \\ \(EI\) (N\(\cdot\)m\({}^{2}\)) & \(1.34\times 10^{12}\) & \(1.69\times 10^{12}\) & \(2.13\times 10^{12}\) & \(2.38\times 10^{12}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of the FEM of the bridge. Figure 10: Example of application: (**a**) Yunbao Bridge under construction [52] and (**b**) a sketch of the analyzed construction stage. The load of the formwork traveler considered in the structure is presented in Figure 12a. In this figure, the weight of the formwork traveler F (1041 kN) was assumed to be 60% of the maximum weight of the deck segment.