## 4 Numerical Examples and Discussion
### Long-Term Deflection of Long-Span Cantilever PSC Bridge (Koror-Babeldaob Bridge) (Case C)
The deflection owing to the non-uniform shrinkage is extracted every 0.5 m at the top slab and is formulated as a function of the length of the bridge. From this data, the moment and equivalent load are derived, as shown in Figure 19c,d. In the structural analysis using _Model-2_, because the bridge was built using a segmental construction method, the self-weight and prestressing load were gradually applied for 220 days. Other permanent loads, such as the weight of the pavement and guardrail load, were applied 20 days after the completion of the segmental construction. The total analysis period was 10,000 days. The load adjusting factor for the equivalent load was calculated as 0.8 and was applied on the 14 th day. Figure 18: RH distribution in the girder section and variation of mid-span deflection owing to nonuniform shrinkage with time and along the span of Koror–Babeldaho Bridge. In Figure 20, the analysis results are compared against the measured data (shown by the red squares) and the original design calculation (shown with the purple line). The original estimation of the deflection was calculated using a simplified approach based on the American Association of State Highway Officials design guidelines [26]. In this approach, the creep and shrinkage are assumed to start after the completion of bridge construction. Accordingly, the elastic deflection owing to all permanent loads is calculated first, and the long-term deflection is estimated by multiplying the elastic deflection by the assumed creep coefficient. The total elastic deflection after an assumed 10% prestress loss was 370 mm, and multiplying this by a creep coefficient of 1.3 gave the final long-term deflection as 481 mm. Figure 20 shows the results for the deflection calculation using different methods. As shown, the analyses considering cracking provide results that are very close to the measured data. The relatively steeper slope in the period from the 30 th to 220 th day in the analyses considering cracking is caused by the gradual increment of permanent loads during this period. In contrast, the results from the analysis using the built-in MC2010 model show a long-term deflection under 250 mm, which is the lowest value and is too far away from the measured data. This indicates that a design and analytic approach that does not consider cracking (even a current one) cannot correctly predict an excessive deflection in a case where the stiffness degradation owing to cracking is the main cause of the excessive deflection. Figure 19: Variation of 2 nd moment of area, deflection owing to nonuniform shrinkage, and equivalent moment and load along the span of Koror–Babeldaob Bridge. The cracking starts at the face of the second pier and at a location 66 m away from that point, as shown in Figure 21. The principal stress exceeds the tensile strength of concrete, i.e., 3.2 MPa. This is in good agreement with the report by [PERSON] [26], i.e., cracking and failure occur near the same location. The nonuniform shrinkage induced deflection is upward, and thus, the final deflection from the equivalent load analysis (_C&US+NUS+Cracking_) is less than that from the analysis without considering the non-uniform shrinkage (_C&US+Cracking_). However, it is worth noting that the nonuniform shrinkage induces a considerable amount of additional deflection in long-span PSC bridges. It is expected that this additional deflection induces more cracks, further reducing the stiffness of the girder, and consequently, enhances the long-term deflection.