## 5 Analysis of Long-Term Prestressing Force (PF)
### Long-Term Prestress Losses in the PSC Girder Bridge  
Similar to the full-scale specimen, the theoretical estimation obtained by Eurocode 2 [38] and the measurement of PF were compared in Figure 9 at a few different time points. The bullets in the measured PF indicate the locations of FBGs, whereas the theoretical values were produced at 5-m intervals. Because the actual PF of each strand was not measured using an EM sensor, only the theoretical jacking force is presented. Figure 9: Distribution of PFs in the PSC girder bridge. Although both approaches produced a decreasing PF trend, the measured PF distribution was more irregular than that of the theory. This implies that the PF distribution is, in reality, more complex, and hence its theoretical estimation is more difficult. Despite the tensioning at both ends, the measured distribution does not assume the perfect symmetry that is theoretically predicted with respect to the center, and the strands seem to be entangled at the right end region, as implied by the irregularity of the distribution. The situation in the actual PSC girder bridge is further complicated by the effect of construction stages on the variation of the PF distribution; some construction stages can increase the PF, as opposed to the prestress losses. Therefore, the decreasing trend of the PF over time is not clear in some parts of the two graphs with consecutive times in Figure 9. This aspect will be further analyzed below. In the allowable stress design of PSC members, concrete stresses at the top fiber and the bottom fiber are adjusted to within a range of allowable stresses by the appropriate design of prestressing tendons. However, if the actual PF is significantly different from that estimated during the design, and if the marginal concrete stress is not sufficient, the concrete stresses can possibly exceed the allowable range, sometimes resulting in the cracking or crushing of concrete. The comparison shown in Figure 9 explains how and why this adverse outcome can occur in reality. Figure 10 compares PFs at the mid-span between the predictive equations and the measurement. The figure suggests that several major construction stages caused significant PF fluctuations, in addition to the decreasing trend induced by long-term prestress losses. For example, when the additional dead loads were applied, including the deck and barrier, the PF tended to increase due to the deformation of the PSC girder and the accompanied elongation of the embedded prestressing tendon. On the contrary, the secondary prestressing, which is a special technique applied to extend the span [40], reduced the existing PF introduced at the primary prestressing stage due to elastic-shortening loss. Furthermore, the composite action of the girders and deck increases the complexity because of the change in cross-sectional constants for stress calculation and the difference in the long-term behavior of the girders and deck. The same correction factors as those considered in the analysis of the full-scale specimen were applied to the predictive equations, including the volume to surface ratio (110 mm) of the girder. Consequently, the ultimate creep coefficient, 2.35, and the ultimate shrinkage strain, \(780\times 10^{-6}\) m/m, were reduced to 1.23 and \(259\times 10^{-6}\) m/m, respectively, in ACI 209R. Overall, Equation (11) of Eurocode 2 [38] was in good agreement with the measured values, similar to the full-scale specimen. Figure 10 also presents the theoretical PFs of Eurocode 2 with or without the additional consideration of the effect of a few major construction stages on the PF. However, the accurate evaluation of the PF, as affected by each construction stage, can be difficult because of the complex structural behavior in reality. In this respect, the responses of Smart Strands can also be utilized to assess the structural safety during  
Figure 10: PFs at mid-span in the PSC girder bridge. construction and in service because they are critical in the structural health monitoring (SHM) of PSC structures.