us23043 bridge models

Two almost identical models are created: Model 1 and Model 2. The only difference is that Model 1 has plate elements and Model 2 has beam ele-ments to model the cast-in-place slab.

5.5.1.1 Model 1: Slab modeled with plate elements

Model 1 is a highly detailed model of the bridge US23043. As the number of elements is much higher than usual, accurate results are expected. This model has beam elements for the precast AASHTO beams and diaphragms, truss elements for the piers and the prestressing tendons, and plate elements to simulate the cast-in-place slab. Figure 5.33 shows the 3D model that con-tains beam, truss, and plate elements.

Although the precast AASHTO type V beams end at point “A” and are supported at point “D,” the model supports the beams at point “B.” For the construction periods in which the structure acts as simple spans, a joint at point “B” is added, to admit relative rotations between the beams of the two adjacent spans.

Figure 5.32 US23043 Bridge, Maryland.

The beam properties do not change along the bridge. The slab, which is cast in a later stage, will not change the section properties of the beam ele-ments because the slab is modeled with additional eleele-ments.

The supports are modeled as truss elements and prevent the verti-cal displacements of the beam elements at these points. At the bottom end of the truss elements, all displacements and rotations are restricted.

Figure 5.34 shows the restricted displacements with X, Y, or Z and the restricted rotations with XX, YY, or ZZ at the end of the elements. In all 55 supports of the four spans, 11 beams have the same boundary condi-tions in the first construction stage. Once the diaphragms are added, all rotations of the beam are admitted. Then the lateral displacements are restrained only at the abutments and the longitudinal displacements at one end of the bridge.

Figure 5.33 Elements of US23043 Bridge model 1.

Figure 5.34 Part of US23043 Bridge model 1, boundary conditions.

The precast and prestressed AASHTO type V beams contain different numbers of strands, depending on the span length. Figure 5.35 shows the cross sections with the reinforcement for spans 1 and 2. The I-beam section on the left is at midspan, and the one on the right is over the supports. In the first two spans, 71 12,7-mm (1/2″) diameter strands are placed; 27 of these are draped.

In the model, the prestressing truss is situated at the centroid of strands.

And, while spans 3 and 4 are shorter than spans 1 and 2, the number of placed strands is smaller, which results in a different geometry of the trusses.

While spans 1 and 2 are prestressed with 71 strands and spans 3 and 4 with 43, the resulting forces applied on the truss elements are (1) F_1,2 = 9123.5 kN and (2) F_3,4 = 5525.5 kN.

The construction sequence of the bridge US23043 has six stages:

• Stage 1—Place precast I-beams from pier to pier.

• Stage 2—Cast midspan diaphragms, leaving a gap in the middle of the cross section.

• Stage 3—Pour the slab, except in the region of piers and in a gap in the middle of the cross section.

• Stage 4—Cast the gaps of the midspan diaphragms and the slab.

• Stage 5—Cast the pier diaphragms.

• Stage 6—Pour the slab in the regions of the piers.

Figure 5.35 Section of the AASHTO beams with strands.

In the model, these six stages are simplified into four. Stage 4 is included as a part of stages 2 and 3, and stages 5 and 6 are combined. To distin-guish between actual and modeled sequences, the stages in the modeled sequence will be assigned both a number and the letter m (i.e., stage 1m, stage 2m).

The construction schedule in the model, which is shown in Table 5.3, considers the minimal possible construction time that has to be allowed between the stages. According to the instructions on the construction plans, 40 hours must be allowed between each stage in the actual sequence, except between stages 3 and 4, where only 16 hours is required. The age of the precast AASHTO beam is assumed as 60 days, which is important for the creep and shrinkage analysis.

The slab is built with plate elements to analyze the actual force distri-butions more accurately. Because the bridge is skewed, triangle plate ele-ments are chosen. Between precast beams, two lines of plate eleele-ments are situated, which allow the transverse moment distribution in the slab to be obtained.

The nodes in the slab are at the same vertical location as the nodes in the beams, where elements with high rigidity connect them together. In total, 4200 plate elements are created in Model 1; 200 of them are from stage 4m.

5.5.1.2 Model 2: Slab modeled with beam elements

Model 2 is the same as Model 1, but the slab is represented by beam elements. These beam elements are located at the center of gravity of the slab, 1.1 m (3.6′) above the beam elements. Every second node of the slab elements is connected laterally with the next line of the slab elements.

These connections are also simulated with beam elements and have the same torsional and bending rigidity as the plate elements in the longitudi-nal direction.

Creep and shrinkage properties will be assigned only to the elements in the longitudinal direction. This is the essential difference between Models 1 and 2.

Table 5.3 Construction sequence in Model 1

Construction stage Day

Stage 1m 0

Stage 2m 1

Stage 3m 3

Stage 4m 8