Verzasca 2 Bridge analysis results

The vertical bending moments in the beam along the bridge axis are shown as results. All the results are given in kN-m. To simplify the discussions in this section, the spans are still counted from left to right, span 1 between abutment A and pier 1 and span 6 between pier 5 and abutment B.

5.4.3.1 Model 1: Continuous girder with constant cross section

The vertical moments of this simple model (Figure 5.24) serve as starting points for the discussion of the results of the next models. Model 1 is built in one single stage and has a uniform dead load of 219.3 kN/m acting on the entire structure. The moments are distributed according to the span

Figure 5.24 Moment distribution, Verzasca 2 Bridge model 1.

5.4.3.2 Model 2: Continuous girder with skew supports

Model 2 takes into account the skew supports. It is easy to recognize the better distribution of the negative moments by increasing the bending moment over piers 2 and 4, from 25,850 to 26,596 kN-m and from 19,355 to 22,739 kN-m, while decreasing over pier 3 from 28,625 to 27,913 kN-m.

Because the abutments are placed perpendicularly to the bridge axis, the moments over piers 1 and 5 increase as well (Figure 5.25).

The torsional moments in the beam due to the skew supports are shown in Figure  5.26. While these moments are not essential in the subject of creep, they will not be taken into consideration in Models 3 and 4, but are taken into account in Model 5, as the superstructure is modeled three-dimensionally.

5.4.3.3 Model 3: One girder built in a single stage

Compared with Model 1, where the beam had a continuous cross section, the higher moment of inertia in the region of the piers causes higher nega-tive moments (Figure 5.27).

Figure  5.28 shows the vertical moments in the beam caused by the post-tensioning procedure. In this case all tendons are also stressed at the same time. As explained in Section 5.4, the tendons overlap in the region of the piers. Thus the positive moments are much higher than the negatives, although the distance to the neutral axis is 50% larger at midspan than over the pier. The moments caused by time-dependent effects in Model 3 can be neglected as the entire bridge was cast in one single stage.

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Figure 5.25 Moment distribution, Verzasca 2 Bridge model 2.

588 588 588 588 588 588 588 588

762762 762 762762 762762 762 762 762

−1023 −1023 −1023 −1023 −1023 −1023

−354 −354 −354 −354 −354 −354 −354

−117 −117 −117 −117 −117 −117

136 136 136 136 136 136 136

Figure 5.26 Torsional moment distribution, Verzasca 2 Bridge model 2.

5.4.3.4 Model 4: Girder built with actual construction stages span was built ending as simply supported, the negative moments over the piers are caused by only one span and the positive moments are higher.

For example, the negative moments over pier 5 are about 1500 kN-m after

−319 −1888

Figure 5.27 Vertical moments due to structural weight, Verzasca 2 Bridge model 3.

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Figure 5.28 Vertical moments due to post-tensioning, Verzasca 2 Bridge model 3.

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Figure 5.29 Accumulated moments due to structural weight and creep effect, Verzasca 2 Bridge model 4.

the first stage, and not 0, because the first construction stage ends 3.75 m over the support. Once span 6 is built continuously to span 5 in the second stage, the negative moment over pier 5 increases to around 7800 kN-m.

Due to the structural weight of span 4, the moment over pier 5 decreases to 3700 kN-m and increases again with the structural weight of span 3, and so on. In Figure 5.30, the distribution shows the addition of all moments due to structural weight and post-tensioning, each in its corresponding static system. Note that the cracking moment of the beam is around 12,600 kN-m for section 1 and 16,380 kN-m for section 2 next to the diaphragms.

5.4.3.5 Model 5: Three girders skew supported

The results of Model 5 are similar to the results of Model 4, but now the moments are distributed to three beams, whereas they were all on the same beam in Model 4. The moments in the middle beam are 33% higher than those in the beams at the sides. This can be explained by the fact that the moment of inertia in the middle beam is 33% higher.

The skew supports that are not taken into account in Model 4 also affect the distribution of the moments in the different beams. This effect is recog-nizable in both end spans. The front beam has larger negative moments over pier 5, because it is nearer to abutment B. Exactly the same effect occurs over pier 1, where the back beam receives more negative moments, due to a shorter first span.

Creep and shrinkage not only cause a redistribution of the internal forces but are also essential factors whenever displacements are evaluated. For the purpose of comparison, incremental displacements of all 19 stages in the con-struction sequence are accumulated once for the elastic displacements and once more for displacements due to creep and shrinkage, for AASHTO and for CEB-FIP. Then displacements are divided into vertical and horizontal components.

From the vertical displacements shown in Figure 5.31, the construction sequence can be reenacted. The peaks are located where the construction stages changed. The sequence was from span 5 leftward to span 1.

The vertical displacements are mainly due to creep and the horizontal due to shrinkage effects. The horizontal displacements due to shrinkage

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Figure 5.30 Accumulated moments due to structural weight and post-tension, Verzasca 2 Bridge model 4.

increase continuously from pier 4 in contrast to the displacements due to the post-tensioning. The displacements at abutment A reach 33 mm (1.54″) with AASHTO and 29  mm (1.14″) with CEB-FIP specifications and are proportional to the shrinkage coefficients at the time of five years.

The vertical displacements due to creep are more difficult to interpret because of the number of changes in the internal forces during construc-tion. In general, CEB-FIP yields higher deformations due to creep than AASHTO.

5.5 3d illustrated exaMPle of us23043 Precast Prestressed concrete BeaM Bridge—Maryland

American practice places precast beams from pier to pier and then casts the diaphragms and the slab in the second step. The bridge US23043 was built in 2001 in the state of Maryland. It is located on Route 113 and was part of a multiphase project to create a bypass for the town of Showell. Figure 5.32 shows the perspective view of US23043 Bridge.

The 137.5-m (450′) long bridge consists of four spans, two of 38.12 m (125′) and two of 30.5  m (100′). The supports and the abutments are Figure 5.31 Vertical displacements due to structural weight and post-tensioning, Verzasca 2

Bridge model 5.

skewed with an angle of 30° to the bridge axis. The section consists of 11  precast and prestressed I-beams and a cast-in-place slab. The same VBDS program as in Section 5.4 is used in this analysis.