## 5 Numerical Simulation of the Long-Term Behavior of a Bridge
### Structural Effects of Long-Term Deformations
During the construction phases the weight of the mobile launching wagon were considered by means of a vertical force of 750 kN acting at the head of the overhang, and therefore, with a bending moment dependent on the size of a segment. At the end of the construction, an additional permanent load due to the pavement and superstructure equal to 35.8 kN/m is applied on the top surface of the upper slab. The input parameters required for creep and shrinkage analysis depend upon the model adopted, however, usually they are: The 28-day elastic modulus of concrete, \(E_{c}\), or the required design strength  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Segment** & **Central Span [mm]** & **Side Span [mm]** \\ \hline
2 & 10.5 & 6.7 \\
3 & 4.4 & 7.1 \\
4 & 14.1 & 7.3 \\
5 & 24.3 & 8.1 \\
6 & 24.2 & 8.2 \\
7 & 23.9 & 8.3 \\
8 & 3.9 & 8.4 \\
9 & 23.6 & 8.6 \\
10 & 13.1 & 17.5 \\
11 & 11.7 & 15.8 \\
12 & 9.2 & 2.6 \\
13 & 5.4 & \(-\(f_{c28}\), from which \(E_{c}\) can be estimated; the starting age of drying, taken as \(t^{\prime}=2\) days, which corresponds to the segmentalrection cycle; the average environmental humidity \(h=0.6\); the effective thickness of cross-sections, \(D=2V/S\) (\(V/S\) is the volume/surface ratio) see Tables 3 and 4; some concrete composition parameters (especially for model B3). The age at the start of drying is taken here as 2 days, which is the time of formwork removing in the segmentalrection cycle of 7 days. For the EC2 model the following values have been utilized: \(f_{cm}\) = 62.90 MPa, \(f_{ck}\) = 54.90 MPa, and cement of class N so \(\alpha=0\), \(\alpha_{ds1}=4\), \(\alpha_{ds2}=0.12\) (see the Appendix A for all the details). For the ACI model the 28-day mean compressive strength of \(f_{cm28}\) = 62.90 MPa is adopted with the coefficients reported in the Appendix B. For the B3 model using in Equation (A39) the 28-day mean cylinder compressive strength of \(f_{cm28}\) = 62.90 MPa and the concrete composition we have \(q_{1}=1.598~{}\times~{}10^{-5}\), \(q_{2}=9.248~{}\times~{}10^{-5}\), \(q_{3}=5.026~{}\times~{}10^{-7}\), \(q_{4}=7.107~{}\times~{}10^{-6}\), \(\alpha_{1}=1.1\), \(\alpha_{2}=1.2\), \(k_{s}=1.0\), \(\epsilon_{\rm geo}=6.87~{}\times~{}10^{-4}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Section** & **Area [m\({}^{2}\)]** & **Segment Length [m]** & **Volume [m\({}^{3}\)]** & **D [mm]** \\ \hline Diaphragm & 70.667 & 0.5 & 35.333 & 2437.007 \\
1 & 23.111 & 3.5 & 80.891 & 603.483 \\
2 & 19.117 & 4 & 76.468 & 514.435 \\
3 & 17.812 & 4 & 71.252 & 499.910 \\
4 & 16.590 & 4 & 66.363 & 485.120 \\
5 & 15.446 & 4.5 & 69.511 & 470.055 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometric characteristics of the bridge cross section and effective thickness, \(D=2V/S\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Segment** & **Upper Slab [mm]** & **Lateral Slab [mm]** & **Lower Slab [mm]** \\ \hline Diaphragm & 2304.70 & 4502.73 & 2200.00 \\
1 & 517.82 & 865.58 & 1237.01 \\
2 & 306.77 & 880.87 & 1143.65 \\
3 & 306.82 & 885,71 & 1042.86 \\
4 & 306.85 & 891,24 & 948.36 \\
5 & 304.73 & 897.59 & 860.17 \\