## 4 Numerical Examples and Discussion
### Calculation of Long-Term Deflection of Medium-Span PSC Box Girder (Case B)
The variations in the mid-span deflection with time by different analysis methods are presented in Figure 13. The hydro-shrinkage constant for the best fit of the results of the equivalent load analysis (_C&US+NUS+Cracking_) was found to be \(3\times 10^{-3}\). The higher hydro-shrinkage constant value (relative to that for the short-span PSC beam (case A)) is attributed to the higher environmental RH as pointed out by [PERSON] [22], and the use of ground-granulated blast furnace slag as a concrete binder. Figure 12: RH distribution in the girder section and variation of mid-span deflection owing to nonuniform shrinkage and equivalent load with time in the medium-span PSC box girder. As can be seen in Figure 13, the staggered analysis and combined analysis using the equivalent load for nonuniform shrinkage (_C&US+NUS+Cracking_) gave the results closest to the measured data up to 380 days. In contrast, the analysis using the built-in MC2010 model for creep and uniform shrinkage (_C&US_) without considering cracking and the analysis considering creep and uniform shrinkage together with a stiffness reduction of the concrete by cracking (_C&US+Cracking_) failed to predict the long-term deflection. The cracking initiates in the support area, when the self-weight and the prestressing force is applied on the 5 th day (see Figure 14). The analysis without considering cracking (_C&US_) results in a lower upward deflection (camber) at the erection relative to the other analyses. The analysis considering cracking but not nonuniform shrinkage (_C&US+Cracking_) overestimates the upward deflection. The nonuniform shrinkage has a more significant contribution to the downward deflection throughout the analysis period than that in the short-span PSC beam case (case A) owing to the larger girder section. The final deflection owing to nonuniform shrinkage alone is only 4.5 mm in the moisture transport analysis but is raised to 9.5 mm in the combined analysis (_C&US+ NUS+Cracking_) and to 5.7 mm in the staggered analysis, owing to the combined action of cracking and creep as discussed in Section 4.2. Figure 13: Variation of mid-span deflection with time in the medium-span PSC box girder. The difference between the results of the staggered analysis and those of the equivalent load analysis (\(C\&US\) + \(NUS\) + \(Cracking\)) is larger than that in the short-span PSC beam (case A) described in Section 4.2. The difference was 0.7 MPa in the compressive stress values and 3.8 mm the deflection values at the end of the analysis period. Additionally, unlikely to be the case in 4.2, the upward deflection by the staggered analysis is larger than that by the equivalent load analysis, and the final deflection by the staggered analysis is smaller. This is because there are more reinforcing bars that are uniformly distributed in the top and bottom flanges in this PSC box girder than in the short-span PSC beam. That is, restraint to shrinkage strain is higher, and the downward or upward deflection is more restrained by the well-distributed reinforcements with higher reinforcement ratio. Therefore, smaller additional tensile strain due to nonuniform shrinkage occurs at the bottom of the girder in the staggered analysis than that in the equivalent load analysis. Additional tensile stress is induced at the top flange and additional compressive stress is induced at the bottom of the girder. This stress distribution is opposite to that in the equivalent load analysis. Consequently, larger upward deflection is obtained in the staggered analysis (as compared to the equivalent load analysis) as shown in Figure 13. This suggests that the section shape, dimensions, and reinforcement details considerably affect the nonuniform shrinkage induced deflection of the PSC girder. Shear cracking is visible at erection but only in the support area. The other section remains uncracked for the entire analysis period, as shown in Figure 14. Thus, the significance of the stiffness reduction owing to cracking is minimal at later stages.