# Estimation of Tendon Force Distribution in Prestressed Concrete Girders Using Smart Strand
## 4 Experimental Validation and Discussions  
The validity of the proposed method is verified experimentally as shown in Figure 7. The shape and size of the specimen are those of the girder adopted in the numerical analysis (Figure 4). The girder specimen is prestressed by three 12-strand tendons. The prestress force is 2109 kN in Tendon #1, 2045 kN in Tendon #2, and 2032 kN in Tendon #3. Jacking is done sequentially from Tendon #1 to Tendon #2 to Tendon #3. Tendon #1 and Tendon #2 are equipped smart strands having 7 FBGs, and Tendon #3 is installed with a smart strand having 5 FBGs. Figure 8 plots the strains measured by the smart strands at each jacking stage. The strain is seen to decrease as much as the position becomes farther from the jacked end because of the friction within the tendon. In addition, the strain reduces at the jacked end due to the anchorage slip that occurred after setting. However, the measured strain does not fit exactly with the prestress force distribution predicted by the formula considering the friction due to the intertwisting of the strands inside the tendon. Optimization was conducted by the proposed method using the values measured by the smart strand of Tendon #1. The results provided a curvature friction coefficient of 0.123/rad, a wobble friction coefficient of 0.0037/m, an anchorage slip of 4.65 mm, and a concrete elastic modulus of 25.2 GPa. The strain distribution in each tendon could then be obtained based upon the optimization results. Figure 9 compares the measured prestress force distributions with the optimized ones from the start to the end of the jacking process. In the graphs, the gray lines represent the 95% confidence interval for the prestress force distribution of each strand. These lines were obtained from the average prestress force of the tendon resulting from optimization and standard deviation calculated by Equation (11). The optimization results are seen to resemble the measured values but to not be in perfect coincidence. This can be attributed to the fact that the prestress force of each individual strand in the tendon is normally distributed and then the measured values of the smart strands is not necessarily identical to the average values of each tendon. This explains the apparent difference between the experimental values and the optimized average values. Moreover, the optimized value can have a certain level of error in the determination due to fluctuation of the measured value, as can be seen from the numerical verification. However, most of the values measured by the smart strands fall within the 95% confidence interval obtained from the optimized average prestress force. This proves that the proposed method can be applied even in the case where the measured value is not the average prestress force and indicates that the method can be used to estimate the prestress force distribution in the tendon. Figure 7: Shape of specimen and jacking process. Figure 8: Strains measured by smart strands at each jacking stage: (**a**) Jacking of Tendon #1; (**b**) Setting of Tendon #1; (**c**) Jacking of Tendon #2; (**d**) Setting of Tendon #2; (**e**) Jacking of Tendon #3; (**f**) Setting of Tendon #3. Figure 9: Comparison between experiment and optimization per jacking stage (gray lines represent 95% confidence interval): (**a**) Tendon #1: Jacking of Tendon #1; (**b**) Tendon #1: Setting of Tendon #3; (**c**) Tendon #2: Jacking of Tendon #2; (**d**) Tendon #2: Setting of Tendon #3; (**e**) Tendon #3: Jacking of Tendon #3; (**f**) Tendon #3: Setting of Tendon #3. However, as shown in Section 3.2, the accuracy degrades when the measured strains diverge significantly from the average. Further study shall investigate the relation between the extent by which the measured strains diverge from the average and the accuracy of the proposed method. The prestress force varies continuously not only during jacking but also all along the service life of the structure, and influences the behavior of the structure [15,16].