# Observing Material Properties in Composite Structures from Actual Rotations
## 3 Results
### Example 3: Application to a Simplified Model of a Composite Bridge  
To show the application of the proposed methodology to a real structure, the problem of the construction of a bridge by the balanced cantilever method is studied in Section 4. In these structures, deflections should be anticipated in advance in order to calculate how to build the precamber structures in the different segments. To update this precamber structure for every step during its construction, complete topographic surveying is usually performed. Therefore, an inverse analysis can be employed for providing information for this model updating process. However, shear effects might not play a very important role for a fully developed cantilever; neglecting the effects of the shear rotation in the first segment will lead to the unreliable estimation of the bending stiffness. It is important to highlight that a simplified model of the Yunbao Bridge over the Yellow River in China (see Figure 6) is chosen to demonstrate the feasibility of the proposed methodology. Future research objectives include working with real on-site measurements to enhance the applicability of the method to real structures. Implementing this application will require the creation of more elaborate models. The structure span is 90 m long, but only an intermediate construction stage is considered in this example. The studied construction stage includes the construction of two symmetric cantilevers. The length of each deck segment is 4.5 m and the length of the segment over the pile is 2.5 m. The total length of the model is 29.5 m. The effects of creep and shrinkage in the concrete are overlooked. The connection between the concrete and the steel is assumed as rigid (total connection), and the relative slip between both materials is neglected. Hence, the steel sections of segments contribute very little to the axial and bending stiffness of the composite cross-section. Following [PERSON] assumptions for this structure [10] shear is transferred only by the steel webs. Therefore, the value of the Poisson's ratio in this example is considered for steel and equal to 0.3. In addition, [PERSON]'s modulus is considered 35 GPa. It is important to emphasize that all measurements are generated in numerical form, and the representation of the bridge structure is a simplification. To validate the method's applicability in monitoring real-world structures, on-site data from actual structures will be analyzed in the future. The mechanical and material properties of Example 3 by the method of the transformed section are listed in Table 4[46]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Average** & **CoV** & **Standard Deviation** \\ \hline EI\({}_{1}\) & 1.000 & \(8.783\times 10^{-7}\) & \(8.783\times 10^{-7}\) \\ EI\({}_{2}\) & 1.000 & \(9.118\times 10^{-7}\) & \(9.117\times 10^{-7}\) \\ GA\({}_{\text{V}1}\) & 1.000 & 0.000 & 0.000 \\ GA\({}_{\text{V}2}\) & 1.000 & 0.000 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Obtained results from random initial values of example 2. Actual on-site data is not considered in this structure and the structural response is simulated numerically. The load test used simulates the movement of the formwork traveler (Figure 7). The weight F of the formwork traveler (weight of formwork included) is considered 60% of the weight of the segment (1041 kN). The effect of each form traveler in the deck is considered in two vertical forces. The values of these two forces are 0.25F and 1.25F (226 kN upwards and 1267 kN downwards). The load case of the bridge model is calculated by reducing the effects of stage i (Figure 7a), from stage i + 1 (Figure 7c), wherein the formwork traveler is moved forward to the next segment. The load cases of the stages i and i + 1 are expressed in Figure 7b,d, respectively. The consequent load case introduced in the simulation is shown in Figure 8e. It is important to highlight that the vertical resultant of such forces on each side of the cantilever is zero.