## 5 Analysis of Long-Term Prestressing Force (PF)
### Long-Term Prestress Losses in the Full-Scale Specim  
Figure 7 representatively shows the distribution of PF in the Smart Strand of T1-H1 (refer to Figure 4) that varies at four time points: right after short-term losses of prestress in Figure 2, and 91, 198, and 318 days after tensioning. In the legend of Figure 7, \"After short-term losses\" indicates the beginning of the long-term losses and thus corresponds to \"Tensioning + 0 days\". The measured distribution, which was obtained by connecting the PFs at FBGs (shown as bullets), was compared with that calculated by Eurocode 2 [38], which is one of the provisions analyzed in Figure 8. The theoretical values were calculated at 2-m intervals and interpolated. The theoretical jacking force of the strand, shown in Figure 7 and the following figures, was calculated by dividing the total jacking force measured in the multi-strand jack by the number of strands inserted into the corresponding duct. On the other hand, the actual jacking force in each strand was also measured using EM sensors. The measured jacking force of T1-H1 was 188 kN, which was higher than the theoretically estimated value of 180 kN. This aspect will be further analyzed below. The theoretical PF can be obtained by subtracting the loss of PF (prestress loss multiplied by the area of a strand) from the original PF. Even the measured and theoretical distributions after the short-term losses do not completely agree with each other, because the short-term losses differed between the theoretical values obtained by predictive equations and measurement. However, the analysis of the PF distribution, based on the short-term losses, is beyond the scope of this study and will be covered in  
Figure 8: PFs at mid-span in the full-scale specimen (T1-H1, H7, and H12). Figure 7: Distribution of PFs in the full-scale specimen (T1-H1). another study. The aforementioned difference between the measured and theoretical jacking forces is another factor that affects the subsequent long-term comparison. These intrinsic differences can be intentionally removed to make a reasonable comparison for long-term PFs, as is analyzed in Table 1, by introducing the difference of the PFs between two adjacent time steps. Note that the form of the PF distribution along the span of the specimen is unsymmetrical in both measurement and theory despite the symmetrical shape of the strand, as shown in Figure 7. Because all the strands were tensioned only at one end (left end), the unsymmetrical PF distribution is formed by the friction loss and anchorage-seating loss of Figure 2 and is maintained when subjected to other types of prestress losses. It is apparent that the PFs were decreased over time by the long-term losses of prestress in both measurement and theory. Although the two approaches gave a similar decreasing trend, the decrement in each time step varied between the two, as shown in Figure 7 and Table 1. However, the total long-term losses, until 318 days after tensioning, are very comparable at 7.0% and 6.3% of the jacking force in measurement and theory, respectively, at the mid-span. Therefore, Eurocode 2 [38] made a reasonable estimation of the long-term prestress losses, as will be confirmed again by comparing with other provisions in Figure 8.  
Figure 8 presents the PF variation at mid-span over time in both measurement and theory. H1, H7, and H12 of T1 in Figure 4 were representatively analyzed herein. Zero-day corresponds to the time after tensioning when the short-term losses had just occurred. The PFs measured at a specific time are different in three Smart Strands, including at the time of tensioning. This indicates that the PF of a strand can vary from strand to strand inside a duct due to the uneven interlocking between a strand and a wedge at the anchor head, although all the strands are tensioned simultaneously using a multi-strand jack. The PF variation of a strand in a duct was statistically analyzed by [PERSON] et al.