# Verification of Actual Prestressing in Existing Pre-Tensioned Members
## 5 Discussion  
As a part of the prestress losses evaluation, the stress in the prestressing wires, considering the expected prestress losses after one year (365 days), was determined according to the Eurocodes [43; 44; 45]. The maximal value of stress in prestressing steel of 1389 MPa was calculated using Equation (2), the end of the curing after three days, and relative humidity of 65%, were taken into account. Accordingly, Equation (3) enables determining the overall maximal prestressing force in specimens (P\({}_{\text{max}}\)). In these two equations, f\({}_{\text{p}}\) represents tensile strength, f\({}_{\text{p},0.1}\) is 0.1% proof-stress, and A\({}_{\text{p}}\) is the value of the cross-sectional area of prestressing steel.  
\[\sigma_{\text{p,max}}=\text{min}\ [0.80\times\text{f}_{\text{p}};0.90\times \text{f}_{\text{p},0.1}]=1389\text{ MPa} \tag{2}\]  
\[\text{P}_{\text{max}}=\Sigma\ [\sigma_{\text{p,max,i}}\times\text{A}_{\text{p}, \text{i}}]=428\text{ kN} \tag{3}\]  
Figure 19: Stress monitoring points in the numerical model.  
Figure 18: Stage 0: h = 0 mm (**a**); Stage 1: h = 10 mm (**b**); Stage 2: h = 20 mm (**c**); Stage 3: h = 30 mm (**d**).  
The standard value of prestressing force determined in compliance with the Eurocodes [43; 44; 45] after 365 days in one wire was 45.5 kN, whereas the overall residual prestressing force in the prestressed concrete sleeper (Pmt,theoretical) was 364.1 kN. The expected value of prestress losses in one wire was 7.9 kN and the total value (\(\Delta\)Pmt,theoretical) in all eight wires was 63.5 kN. Consequently, in a period of 365 days, the maximal prestressing force was expected to be decreased by 14.8%. Comparisons of stress relief results from the experimental measurements and numerical analysis are displayed in Figure 20. In this figure, stress relief curves from the numerical analysis (for prestress losses of 10, 15, and 20%) are compared to the experimentally measured values. As can be seen in Figure 21, the initial stress value does not influence the percentage stress relief rate. The example of stress change from numerical analysis for a specimen with expected prestress losses of 15% is presented in Figure 22. Obtained results from the numerical and experimental analyses suggest that percentage stress relief should not be influenced by the type of prestressed concrete member. A similar experiment was performed on post-tensioned beam and stress [23; 24]. Therefore, local stress change monitored in the area adjacent to performed saw-cuts should be universal.  
Figure 21: Stress relief rate for three depths of saw-cuts.  
Figure 22: Stress change for \(p=0.85\times\)P\({}_{\max}\). Stage 0 (**a**); Stage 1 (**b**); Stage 2 (**c**); Stage 3 (**d**).  
The methodology for assessment of prestress by the use of Barkhausen noise in wires is based on the measurement of Barkhausen noise emission in the prestressed state directly in the sleeper and fitting the data with calibration evolution (further details can be found in [39]). Barkhausen noise tends to grow versus tensile stress due to the realignment of domain walls into the direction of load. However, the wires matrix has been already fully strained along the wire length [16]. For this reason, this mechanism is consumed and the evolution between Barkhausen noise and amplitude of tensile stresses is reversed (further details can be found in [16]). The values of stress and prestress losses in the investigated wire from Specim 4 determined using the magnetic Barkhausen noise are listed in Table 3. In the middle, Point I, the prestress losses determined using the MNB technique represented 26.4 \(\pm\) 5.7%.