## 5 Numerical Simulation of the Long-Term Behavior of a Bridge
### Structural Effects of Long-Term Deformations  
The analysis of the structural behavior has been performed through a three-dimensional finite program applied, because of symmetry, to only one half of the bridge. The box girder of this bridge is considered a thick shell which is discretized by brick (8-node three-dimensional) finite elements and the generated mesh is shown in Figure 13. The prestressing tendons (see Figure 13) are modeled through beam elements connected rigidly to the nodes of the three-dimensional mesh (slip is allowed along each tendons). Non-prestressed reinforcing steel bars are not considered in the present discretization. The fineness of the mesh has been validated by checking that a finer mesh with the double of hexahedral elements would yield only a negligible improvement of the computed elastic deflections. The integration algorithm described in Section 2 reduces the creep problem to a series of elastic structural analyses in each time step. A finite element code developed by the first author was used to carry out the step-by-step elastic analysis. The introduction of prestress in each tendon was done by assigning the initial stress to the tendons through an equivalent thermal deformation. To reproduce  
Figure 13: Three-dimensional finite element mesh model of the bridge, the mesh of its different segments, and the mesh of the steel cables. the time sequence of segmental construction, the finite elements corresponding to different segments were activated at the time of their casting, which also introduced a different age of concrete for each segment. Each segment was activated taking into consideration the correction of level adopted during the construction procedure as reported in Table 1. These corrections have been introduced in the construction process for taking into account the cumulative deflection at the free end of the cantilever element and for obtaining the demanded level of the road. In other words, those corrections are introduced in order to compensate for the initial creep deflection at the free end of the cantilever beam, due also to the weight of the construction apparatus (see the first picture in Figure 12). During the deck construction the different type of post-tension tendons/bars (see Figure 12) were activated as described in the following. The free cantilever is built from the pier segment by adding up to 15 side segments, each one stabilized by the activation of two upper tendons, for a total of 32 upper cables. At the end of free cantilever construction, abutment segments and key center segment are connected by lower cables and pre-stressed bars for a total of 88 post-tension tendons/bars. Table 2 reports all the features of post-tension tendons and bars. The tendons of each segment were prestressed 2 days after the segment casting. The friction caused by curvature was neglected while the wobble friction was considered. The initial prestress diminishes also because of the relaxation of steel. However, this effect is not considered in the 3D finite element analyses, although it can be implemented in the numerical algorithm just imposing a reduction of the initial prestress in accordance with some formula taken from a code (for instance the EuroCode2 formula). The creep phenomenon is strongly influenced by the temperature value. In the numerical simulations however the effect of the temperature increase due to solar heating of the top slab is neglected as well as any effect of the environmental temperature variation on the concrete properties. Tensile cracking has not been taken into account because no significant tensile stresses arise in the numerical simulations and, therefore, the mechanical behavior can be assumed as linear elastic. The nonlinear effects for creep have not been considered because the stress levels are always below \(0.4f_{cm}\). In the numerical analysis the self-weight has been applied through a volume force (\(\gamma=25\) kN/m\({}^{3}\)).