## 5 Analysis of Long-Term Prestressing Force (PF)
### Long-Term Prestress Losses in the Full-Scale Specim
[19] Therefore, the averaged value of the PFs in the three Smart Strands was also provided in Figure 8 to reduce any bias. The predictive equations for the long-term prestress losses induced by creep and shrinkage, that were introduced in Section 3, were compared with the measurements: ACI 209R [36], ACI 423.10R [34], and Eurocode 2 [38]. In contrast to ACI 209R and Eurocode 2, ACI 423.10R only suggests the ultimate creep and shrinkage losses without time function. However, relaxation loss was intentionally not \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Distance (m)**} & **1** & **4** & **7** & **10** & **13** & **16** & **19** \\ \hline \multirow{8}{*}{**Measurement**} & Tensioning & 188 & 188 & 188 & 188 & 188 & 188 & 188 \\ \cline{2-9}  & After short-term & 167.2 & 168.8 & 166.5 & 172.4 & 172.5 & 167.5 & 168.4 \\  & losses & [11.1]1  & [10.2] & [11.4] & [8.3] & [8.2] & [10.9] & [10.4] \\ \cline{2-9}  & Tensioning + 91 & 162.6 & 165.3 & 163.6 & 167.5 & 167.6 & 163.6 & 164.1 \\
**[difference** & days & [2.7] & [2.1] & [1.8] & [2.8] & [2.8] & [2.3] & [2.6] \\ \cline{2-9}  & Tensioning + 198 & 155.9 & 159.4 & 157.9 & 161.7 & 161.9 & 157.8 & 158.0 \\  & days & [4.1] & [3.6] & [3.5] & [3.5] & [3.5] & [3.6] & [3.7] \\ \cline{2-9}  & Tensioning + 318 & 155.3 & 158.7 & 156.9 & 160.3 & 160.9 & 156.7 & 157.1 \\  & days & [0.4] & [0.4] & [0.6] & [0.8] & [0.6] & [0.7] & [0.6] \\ \hline \multirow{8}{*}{**Theory 3 (kN)**} & Tensioning & 180 & 180 & 180 & 180 & 180 & 180 & 180 \\ \cline{2-9}  & After short-term & 151.4 & 154.1 & 155.8 & 158.2 & 158.6 & 157.2 & 154.9 \\ \cline{2-9}  & losses & [15.9] & [14.4] & [13.5] & [12.1] & [11.9] & [12.7] & [13.9] \\ \cline{2-9}  & Tensioning + 91 & 145.9 & 148.6 & 149.8 & 151.8 & 152.6 & 151.6 & 149.3 \\ \cline{2-9}  & days & [3.6] & [3.5] & [3.8] & [4.1] & [3.8] & [3.5] & [3.6] \\ \cline{2-9}  & Tensioning + 198 & 143.9 & 146.6 & 147.8 & 149.7 & 150.5 & 149.6 & 147.2 \\ \cline{2-9}  & days & [1.4] & [1.3] & [1.4] & [1.4] & [1.4] & [1.3] & [1.3] \\ \cline{2-9}  & Tensioning + 318 & 142.5 & 145.3 & 146.4 & 148.2 & 149.1 & 148.3 & 145.8 \\ \cline{2-9}  & days & [1.0] & [0.9] & [1.0] & [1.0] & [0.9] & [0.9] & [1.0] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PFs at the location of FBGs in the full-scale specimen (T1-H1). considered in the equations to make a reasonable comparison with the Smart Strands, where the relaxation loss is not directly measured, as mentioned previously. Although the ultimate creep coefficient of ACI 209R is 2.35, it was reduced to 1.11 by incorporating such correction factors as loading age, ambient relative humidity (65%), and volume to surface ratio (231 mm). Likewise, the ultimate shrinkage strain of 780 \(\times\) 10\({}^{-6}\) m/m was reduced to 150 \(\times\) 10\({}^{-6}\) m/m by considering the correction factors, including relative humidity and volume to surface ratio, and by deducting the shrinkage that occurred before tensioning. Regarding Equation (10) of ACI 423.10R used for predicting ultimate shrinkage strain, the above three factors are already integrated into the equation. The detailed calculation of creep and shrinkage included in Equation (11) of Eurocode 2 involves a very complicated procedure, incorporating several correction factors, such as relative humidity, concrete compressive strength, loading age, type of cement, and notional size, which approximately corresponds to double the volume to surface ratio. The deduction of the shrinkage prior to tensioning was also separately considered. Among the three equations considered, Eurocode 2 showed relatively good agreement with the averaged measurement values, partly because Equation (11) takes into account the long-term PF variation by applying the advanced technique of the age-adjusted effective modulus method (AEMM) [41] for more accurately calculating creep.