## 3 Experimental Verification
### Experimental Results during the Post-Tensioning Process
#### 3.3.2 Discussions  
Overall, two sources are considered responsible for inducing such errors, including the variation in the modulus of elasticity of concrete, and the strain gauge measurement error. First, the error may have originated from the variation in the concrete modulus of elasticity EC. The elastic modulus of concrete is a critical parameter, since it determines the strain and displacement relationship in the section analysis, especially when the concrete is in the elastic region. The elastic modulus value can be calculated based on the compressive strength of the concrete using the empirical formulas provided in the different design standards and codes. However, these existing empirical equations predict the elastic modulus of concrete with an inevitable error [25]. In this paper, the concrete properties were obtained based on the experimental tests of six cylinders with a diameter of 100 mm and a height of 200 mm, in compliance with the Australian Standards 1012.8.1 (AS 2014a) [26] and AS 1012.9 (AS 2014b) [27]. The compressive strength of the concrete obtained on the day of the test was 41.5 MPa, which was taken as the average of six concrete cylinders [22]. The elastic modulus of concrete is 3.047 \(\times\) 10\({}^{10}\) Pa, which is calculated based on AS 3600: 2018 [28] from the compressive strength of the concrete. However, it should be pointed out that it is clearly stated that the elastic modulus of concrete has a range of \(\pm\)20% from the mean value [28]. Therefore, the error analysis was conducted to analyze the influence of the variation in the elastic modulus of the concrete on the prediction results of the prestress force. Based on the range of the elastic modulus of concrete, the prestress force of the beam obtained from the proposed approach is recalculated based on Equation (5), and the relative errors of the prestress force between the theoretical calculation and experimental results are computed and listed in Table 3.  
Table 3 shows the relative errors in the predicted prestress force corresponding to the different errors in elastic modulus of the concrete in the variation range given in the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**ENAL\({}_{2}\) (mm)** & **EF (kN)** & **TF\({}_{2}\) (kN)** & **RE\({}_{2}\)** & **ENAL\({}_{3}\) (mm)** & **EF (kN)** & **TF\({}_{3}\) (kN)** & **RE\({}_{3}\)** \\ \hline
305.05 & 61.57 & 64.17 & 4.22\% & 314.72 & 61.57 & 70.93 & 15.20\% \\
297.54 & 107.11 & 108.7 & 1.48\% & 303 & 107.11 & 119.72 & 11.77\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between the measured and calculated prestress forces of the beam. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variation**} & \multirow{2}{*}{**EC (Pa)**} & \multicolumn{2}{c}{**S2**} & \multicolumn{2}{c}{**S3**} \\ \cline{3-6}  & & **RE\({}_{2,62}\)** & **RE\({}_{2,107}\)** & **RE\({}_{3,62}\)** & **RE\({}_{3,107}\)** \\ \hline \(-\)20\% & 2.438 \(\times\) 10\({}^{10}\) & \(-\)18.77\% & \(-\)20.06\% & \(-\)10.42\% & \(-\)11.97\% \\ \(-\)10\% & 2.742 \(\times\) 10\({}^{10}\) & \(-\)7.86\% & \(-\)9.29\% & 1.65\% & \(-\)0.09\% \\
10\% & 3.352 \(\times\) 10\({}^{10}\) & 13.97\% & 12.26\% & 25.78\% & 23.65\% \\
20\% & 3.656 \(\times\) 10\({}^{10}\) & 24.88\% & 23.03\% & 37.85\% & 36.52\% \\ Original & 3.047 \(\times\) 10\({}^{10}\) & 3.06\% & 1.48\% & 13.72\% & 11.77\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error analysis considering variations in modulus of elasticity of concrete. Australian Standard (AS) 3600:2018 [28]. The subscripts numbers of error indicator RE (i.e., 2 and 3) represent the segments S2 and S3, and the numbers (i.e., 62 and 107 kN) stand for the two prestressing force levels. Assuming the estimated elastic modulus based on the obtained average concrete strength in the test is accurate, a variation of the elastic modulus leads to significant variations in the estimated prestress force.