# State-of-the-Art Review on Determining Prestress Losses in Prestressed Concrete Girders
## 2 Works Conducted by Researchers Worldwide
### Prestress Force Determinations Obtained by [PERSON] et al. (2018)  
Table 4 lists the prestress force determinations \(N_{a}\) obtained using the vertical deflections \(v_{2}\)(1) and corresponding experimental values \(\Psi=F\,L^{3}/E_{\text{aver}}\)\(I\) in Equation (8a) (Test 1), as well as the vertical deflections \(v_{4}\)(1) and corresponding parameters \(\Psi\) in Equation (8b) (Test 2), respectively. Equations (8a) and (8b) are illustrated in [PERSON] et al. (2018). In specific, the nine test combinations represent the best prestress force determinations among the three test repetitions performed (Section 3.1). The chord elastic modulus \(E_{\text{aver}}\) of the high strength concrete, for each day of execution of the experiments (Section 3.1), was utilized as parameter in the identification process. The corresponding first-order vertical deflections were instead estimated by Equations (4a) and (4b), as similarly reported in [PERSON] et al. (2018). Table 4 additionally shows the related percentage errors \(\Delta=\left(N_{a}-N\right)/N\). In general, poor estimates \(N_{a}\) were obtained when prestressing \(N\) equal to 617 and 620 kN were assigned (Figure 2a,b). Vice versa, the test combinations with prestressing that induced second-order effects greater than 6.5%, id est, when \(N\geq 721\) kN, furnished excellent identifications of prestress forces \(N_{a}\). In fact, in this last case, estimation errors were lower, in absolute value, than 6.1%. Sensitivity analyses were elaborated for the prestress force determinations based on Equations (8a) and (8b). The vertical deflections \(v_{2}\)(1) and \(v_{4}\)(1), calculated with 0.01 mm in accuracy by Equations (3a) and (3b) reported in [PERSON] et al. (2018), and parameter \(\Psi\) were modified to generate possible experimental errors. In detail, deflections \(v_{2}\)(1), \(v_{4}\)(1), and \(\Psi\) were alternatively multiplied by 0.99 and 1.01 to reproduce 14 combinations of simulated values for nine different assumed prestress forces \(N\). The average value of the applied vertical loads, \(F_{\text{aver}}=22.6\) kN (Figure 2b), was taken into account in the manipulations. Figure 4 depicts a comparison between the worst determined \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{**Test 1-\(v_{2}\)(1)**} & \multicolumn{3}{c}{**Test 2-\(v_{4}\)(1)**} \\ \cline{3-8}  & & & & **Deflections at a Quarter** & **Deflections at the Midspan** \\ \hline Days of & \(E_{\text{aver}}\) & \(N\) & \(F\) & \(N_{a}\) & \(\Delta\) & \(N_{a}\) & \(\Delta\) \\ Concrete Curing & (MPa) & (kN) & (kN) & (kN) & (\%) & (kN) & (\%) \\ \hline \multirow{3}{*}{426} & \multirow{3}{*}{34,870} & 620 & 20.2 & 777 & 25.3 & 789 & 27.3 \\ \cline{3-8}  & & 620 & 22.6 & 857 & 38.2 & 857 & 38.2 \\ \cline{3-8}  & & 617 & 25.0 & 386 & –37.4 & 550 & –10.9 \\ \hline \multirow{3}{*}{427} & \multirow{3}{*}{37,618} & 724 & 20.1 & 729 & 0.7 & 732 & 1.1 \\ \cline{3-8}  & & 721 & 22.6 & 721 & 0.0 & 761 & 5.5 \\ \cline{3-8}  & & 721 & 25.1 & 715 & –0.8 & 718 & –0.4 \\ \hline \multirow{3}{*}{433} & \multirow{3}{*}{38,791} & 820 & 20.2 & 846 & 3.2 & 823 & 0.4 \\ \cline{3-8}  & & 820 & 22.9 & 825 & 0.6 & 825 & 0.6 \\ \cline{3-8}  & & 820 & 25.1 & 824 & 0.5 & 870 & 6.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prestress force determinations \(N_{a}\) based on Equation (8a) (Test 1) and Equation (8b) (Test 2), and corresponding measured parameters for each test day (80). Copyright © 2018, World Scientific Publishing Co. Pte Ltd. Adapted with permission. Figure 3: Three-point bending tests on a PCI girder conducted in the laboratory of NCREE, Taiwan (80): **(a)** indoor test rig; **(b)** application of a FBG-Differential Settlement Measurement (DSM) liquid-level system for vertical deflection measurements along the span. Copyright © 2019 Elsevier Ltd. Adapted with permission. and assumed values \(N\) conducted using vertical deflections \(v_{2}\)(1) and \(v_{4}\)(1), both of which yielded a constant error of about \(\pm 107\) kN.