# State-of-the-Art Review on Determining Prestress Losses in Prestressed Concrete Girders
## 2 Works Conducted by Researchers Worldwide
### Brief on Works Conducted by [PERSON] et al. (2018)  
The static approach was originally developed for detecting axial force in compressed steel beams [77]. Subsequently, it was employed for identifying prestress forces in PC girders [80]. In this last case, the reference model comprised a simply supported Euler-Bernoulli beam of 250 mm in width, 400 mm in height, and length \(L\) of 6.62 m, made with a high strength concrete, and prestressed by a straight unbonded tendon, where the prestress force \(N\) was assumed as an external compressive force eccentrically applied to the end constraints \(N\)_e_ (Figure 2a). The cross sectional second moment of the area of the PC beam's section \(I\) was equal to \(1.3333\times 10^{9}\) mm\({}^{4}\). Besides, a bending deflection \(v^{(1)}\) along the aforementioned beam's model, of 0.01 mm in accuracy, was properly approximated by multiplying the corresponding first-order deflection by the _\"magnification factor\"_ of the second-order effects, id est, according to the _\"compression-softening\"_ theory [40; 41; 42] (Figure 2b).  
Experiments on a PC beam specimen, having the test configuration above mentioned (Figure 2a,b), were arranged in the laboratory of the National Center for Research on Earthquake Engineering (NCREE) of Taipei, Taiwan [80], where a research program, based on testing uncracked PC bridge member prototypes, began in 2015 (Figure 3). All geometrical dimensions were checked by laser rangefinder and caliper, of 0.01 mm in tolerance, after the PC beam was fixed on the simple supports. First, deflected-shape measurements \(v^{(1)}\) along its span, obtained from 27 three-point bending tests with different applied prestress forces \(N\), measured by a load cell placed at both end constraints [86], were examined to verify the accuracy of the assumptions of the beam's model (Figure 2b). The span of the PC beam specimen was specifically instrumented to short term measure such static deflection shapes, with an accuracy of 0.01 mm, by a set of displacement transducers. Temperature and relative humidity of real environment of the PC beam were not continuously recorded during testing. Second, based on the _\"magnification factor\"_ formula of the _\"compression-softening\"_ theory [40; 41; 42], prestress force determinations were obtained using two series of vertical deflections \(v^{(1)}\), id est, those recorded at the quarter \(v_{2}{}^{(1)}\) and at the midspan \(v_{4}{}^{(1)}\) of the PC beam, respectively. Information regarding the flexural rigidity of the PC beam were in addition required. In detail, average values of the chord elastic modulus \(E_{\mathrm{aver}}\) of the high strength concrete, with an accuracy of 1 MPa, were estimated by compression tests on a series of cylinders cast at the same time of the PC beam [87] to determine its increment caused by the concrete's consolidation/hardening with time [52].  
Figure 1: Static NDT methods proposed by [PERSON] et al. [71; 74]: (**a**) cast iron disks suspended at the reference beam; (**b**) arrangement of the dial indicators for vertical deflection measurements during an experimental simulation. Copyright © 2012, 2013 Elsevier Ltd. Reprinted with permission.  
Figure 2: Reference model of the PC girder [80]: (**a**) deflection curve \(v^{(0)}\) after the application of the eccentric prestress force \(N\); (**b**) deflection curve \(v^{(1)}\) after the application of the vertical load \(F\) to the deflection curve \(v^{(0)}\). The dashed lines represent the initial deflection curves. Copyright © 2018, World Scientific Publishing Co. Pte Ltd. Reprinted with permission.