# State-of-the-Art Review on Determining Prestress Losses in Prestressed Concrete Girders
## 2 Works Conducted by Researchers Worldwide
### Numerical Investigations  
Numerical studies were conducted by addressing the effect of prestress force on the dynamics of PC girders. During simulation of a moving force identification method which assumed the effects of prestressing, [PERSON] and [PERSON] [39] found that the natural frequencies of a PC bridge decrease with an increase in prestress force. This is well-known as the \"_compression-softening_\" effect and, in general, occurs in Euler-Bernoulli beams and PC members preserved against crack formation [40; 41; 42]. [PERSON] et al. [43] investigated prestress loss identifications in PC girders based on the measurement variations of natural frequencies. Comparison between the experimental results obtained by [PERSON] et al. [32] and the previsions of their model validated their method. [PERSON] and [PERSON] [44] analyzed the time-domain response of a PC girder under dynamic excitation. By comparing their results of numerical simulations with theoretical findings, the authors identified the prestress force in the time domain by displacement and strain measurements. According to their findings, the natural frequencies decrease as the prestressing increases. [PERSON] and [PERSON] [45] developed a nonlinear solution for modeling the behavior of PC girders with a bonded or an unbonded tendon. Based on the derived governing equations, the authors proved that prestressing does not influence the natural frequencies of PC girders. [PERSON] [46] underlined that the increase of a PC girder's stiffness (and frequency) depends on the tendon's eccentricity, thus inducing greater moment and stiffening effect along the member. [PERSON] et al. [47] investigated the prediction of early warning signs of deterioration in a PC beam caused by prestress losses. The investigators pointed out that vibration frequencies of PC girders significantly change only under the effects of crack initiation or crack re-opening. [PERSON] et al. [48] validated the experiments done by [PERSON] et al. [37] and [PERSON] et al. [49] by a Finite Element (FE) model, where the influence of prestressing on the natural frequencies was simulated by the existence of early-age shrinkage cracks inside the concrete. [PERSON] et al. [50; 51] found that the fundamental frequency of uncracked PC girders with a parabolic tendon is unaffected by the prestress force because the course of the \"_compression-softening_\" theory being cancelled out by the increase of elastic modulus due to the concrete's consolidation/hardening with time [52]. [PERSON] et al. [53] investigated the flexural performance of two PC girders under uncracked and cracked conditions for further applications of SHM. In relation to the uncracked state, the authors affirmed that changes in natural frequency due to prestress losses are negligible. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Author** & **Year** & **Vibration Test** & **Result and Finding** \\ \hline [PERSON] [31] & 1991 & UnCracked PC girders & Increase in prestress force slightly increases the natural frequencies \\ \hline [PERSON] et al. [32] & 1994 & UnCracked PC girder & (_as above_) \\ \hline [PERSON] et al. [33] & 2000 & UnCracked PC girders & (_as above_) \\ \hline [PERSON] and [PERSON] [34] & 2006 & UnCracked PC girder & (_as above_) \\ \hline [PERSON] and [PERSON] [35] & 2009 & Cracked PC girders & Increase in prestress force slightly decreases the natural frequencies \\ \hline [PERSON] et al. [36] & 2010 & Cracked PC girder & Increase in prestress force slightly increases the natural frequencies \\ \hline [PERSON] et al. [37] & 2010 & UnCracked PC girders & (_as above_) \\ \hline [PERSON] et al. [38] & 2015 & UnCracked PC girders & (_as above_) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Laboratory investigations on the relation between prestress force and dynamics of Prestressed Concrete (PC) girders. Looking at the relevant works above mentioned, id est, at [PERSON] and [PERSON] [45], [PERSON] [46], [PERSON] et al. [47], and [PERSON] et al.