# Estimation of Tendon Force Distribution in Prestressed Concrete Girders Using Smart Strand
## 1 Introduction  
The prestress force in a prestressed concrete (PSC) structure is mostly introduced by means of steel strand. Since such steel strands are the most important member of the PSC structure, their rupture is likely to degrade structural health. It is noteworthy that, despite its primary role, it has been challenging to directly measure the prestress distribution within the structure prior to the development of the smart strand [1; 2; 3; 4; 5]. The prestress force was estimated indirectly by a formula calculating the loss of prestress using the hydraulic pressure measured externally at the jacked end of the structure and the change in the length of the tendon before and after prestressing [6; 7; 8].  
The recent development of the smart strand, which can measure the strain of the strand all along its service from jacking, offers the possibility of accurately measuring the distribution of the prestress force in the tendon. The smart strand can be fabricated by attaching the optical fiber between the neighboring helical wires [4; 5] or by replacing the steel core wire with a core wire in which the optical fiber is embedded. In such case, the core wire is made by inserting the optical fiber inside a hollow steel tube [2] or by pultruding a carbon fiber reinforced polymer (CFRP) rod [1] or a glass fiber reinforced polymer (GFRP) rod [3] with the optical fiber monolithically. Moreover, the strain can be measured at the locations at which the fiber Bragg grating (FBG) is engraved in the optical fiber [1; 2] or all along the optical fiber using the Brillouin wave [9]. Figure 1 presents a typical configuration of the smart strand in which the steel core wire is replaced by a core wire with sensing function.  
As shown in Figure 2, the PSC girder is generally prestressed by several tendons. Each tendon experiences some loss in prestress force due to the friction and the anchorage slip during the prestressing process. This results to the occurrence of discrepancy between the prestress forces developed outside and inside the structure. Moreover, the prestress force in a previously jacked tendon diminishes due to the shrinkage of the concrete structure generated by the subsequent jacking of the other tendons. Since there was no way to measure the force in the tendon before the developmentof the smart strand, these losses of the prestress force were estimated by an indirect method [6]. However, the appearance of the smart strand opens up the possibility of measuring the change in the prestress force in the tendon all along the jacking process, thus directly computing the loss of the prestress force.  
Ideally, the smart strand should be installed in each tendon to directly measure the change of prestress force in the tendons. However, in practice, the smart strand is installed only in a limited number of the tendons because of the higher cost of the smart strand compared to the conventional strand. Accordingly, this study intends to propose a method for estimating the prestress force distribution in all the tendons of the PSC girder when only one smart strand is installed as shown in Figure 2.