## 5 Conclusions  
In this study, 3D FE modeling and analysis were performed for short-, medium-, and long-span bridges to calculate the long-term deflections of PSC bridges considering the combined effects of creep, shrinkage, and cracking of concrete. To consider the nonuniform shrinkage effect, a simplified method using an equivalent load is proposed herein. After performing a moisture transport analysis and calculating the resulting deflection owing to the nonuniform shrinkage strain, the equivalent load for producing the same deflection is calculated. The equivalent load is then applied to a model for  
Figure 21: Principal tensile stress of Koror–Babeldaob Bridge on the 160 th day.  
Figure 20: Variation of mid-span deflection with time of Koror–Babeldaob Bridge.  
a combined nonlinear structural analysis incorporating creep, uniform shrinkage, and cracking to thereby calculate the long-term deflections of PSC bridges. From several example analyses in this study; the following conclusions can be drawn:  
1. Nonuniform shrinkage contributes to a significant portion of the long-term deflection of PSC bridges, especially in medium- to long-span bridges with large girder sections.
2. The cracking of concrete has a significant impact on the long-term deflections of PSC bridges because it reduces the stiffness of the girder. In addition, the deflection caused by the nonuniform shrinkage induces more cracks and enhances them to propagate, resulting in an increase in the long-term deflection owing to the combined action of the creep.
3. The equivalent load approach yields results very close to the experimental data by incorporating the above-mentioned nonuniform shrinkage effect, especially for lightly reinforced PSC girders. For heavily reinforced PSC girders, however, the equivalent load approach shows a slight deviation from the experimental data owing to the increased restraint from reinforcements. Therefore, the arrangement and number of reinforcements are crucial for predicting the nonuniform-shrinkage-induced deflection by the equivalent load method.
4. Despite a slight deviation in the calculated deflections of heavily reinforced PSC girders, the results can be on the safe side for the design calculation, and therefore, this approach is very effective for calculating long-term deflections while considering the nonuniform shrinkage strain, without the need for the complicated and expensive coupling of moisture transport and structural analyses.  
Conceptualization, F.N.B. and S.Y.J.; methodology, F.N.B. and S.Y.J.; software, F.N.B.; validation, F.N.B., S.Y.J. and S.-I.K.; formal analysis, F.N.B.; investigation, F.N.B.; resources, F.N.B. and S.Y.J.; data curation, F.N.B.; writing--original draft preparation, F.N.B.; writing--review and editing, F.N.B. and S.Y.J.; visualization, F.N.B. and S.Y.J.; supervision, S.Y.J. and S.-I.K.; project administration, F.N.B., S.Y.J. and S.-I.K.; funding acquisition, S.Y.J. and S.-I.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Doctoral Program of the University of Science and Technology (UST) and the R&D program of Korea Railroad Research Institute, Republic of Korea.  
We would like to thank [PERSON] (Senior Researcher, Korea Railroad Research Institute) for sharing his insight and experiences in the numerical analysis.  
The authors declare no conflict of interest.