# Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams
## 3 Results and Discussion
### Calibration
Since the aim of this study was to determine the model's ability to faithfully reproduce the CRACKING MOMENT and ULTIMATE MOMENT in the bending of pre-stressed concrete elements, we now compare the degree of fit of these parameters between the simulation and the experimental test. Table 4 summarizes both values for each element, as well as their degree of fit, calculating the differences in both absolute values and percentages with respect to the experimental value. The overall results of the simulation-experiment comparison show errors ranging from 0.24% to 15%, in both cracking and ultimate strength; it can be concluded, then, that overall, an acceptable degree of fit is obtained, with the average difference being between 6 and 7%. In addition, the overall comparison of the results show that the fit is very good along almost the entire load-deformation curve. It can be concluded that the load-deflection curves obtained in the bending simulations fit the experimental results reasonably well along their entire length. However, there are slight differences in some elements that are worth analyzing in order to understand the potential of the model. The main findings of the simulations are listed below, with emphasis on the greatest differences with respect to the ultimate strength of the elements. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multicolumn{4}{c}{**Cracking Moment (kN-m)**} & \multicolumn{4}{c}{**Ultimate Moment (kN-m)**} \\ \cline{2-9}  & **Exper.** & **Simul.** & **Difference** & **(\%)** & **Exper.** & **Simul.** & **Difference** & **(\%)** \\ \hline T13-1 & 2.60 & 2.99 & 0.39 & 15.00 & 5.30 & 5.19 & \(-0.11\) & \(-2.08\) \\ T13-2 & 3.43 & 3.60 & 0.17 & 4.96 & 6.53 & 6.49 & \(-0.04\) & \(-0.61\) \\ T18-1 & 4.51 & 4.25 & \(-0.26\) & \(-5.76\) & 8.15 & 7.14 & \(-1.01\) & \(-12.39\) \\ T18-3 & 6.46 & 6.27 & \(-0.19\) & \(-2.94\) & 12.64 & 12.67 & 0.03 & 0.24 \\ Overall joists & & & & 7.17 & & & & 3.83 \\ \hline TB35-3 & 37.60 & 36.14 & \(-1.46\) & \(-3.88\) & 66.45 & 58.55 & \(-7.90\) & \(-11.89\) \\ TB35-4 & 43.78 & 50.12 & 6.34 & 14.48 & 71.57 & 73.88 & 2.31 & 3.23 \\ TB35-5 & 63.65 & 61.20 & \(-2.45\) & \(-3.85\) & 96.45 & 92.70 & \(-3.75\) & \(-3.89\) \\ TB35-6 & 65.58 & 63.72 & \(-1.86\) & \(-2.84\) & 113.10 & 98.56 & \(-14.54\) & \(-12.86\) \\ Overall tubular joists & & & & 6.26 & & & & 7.97 \\ \hline Mean total & & & 6.71 & & & & 5.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the main bending results for cracking moment and ultimate moment, obtained experimentally and by simulation. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Calibration Value** \\ \hline Compressive strength & 48 MPa \\ Initial modulus of elasticity & 32,000 MPa \\ Tensile strength & 3.5 MPa \\ Fracture energy & 9.5 GPa \\ Pre-stressing losses & 35\% \\ Bond strength & 12 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Final values of the model calibration conducted in ATENA to simulate pre-stressed elements. Regarding the individual values obtained for the maximum moment, it can be seen that all the simulations yield a result similar to, or slightly lower than, that obtained experimentally, which in case of error, errs on the side of safety. This confirms that the ATENA tool is a perfect option for estimating the maximum resistance of the different elements. The errors of above 10% obtained for the elements T18-1, TB35-3 and TB35-6 may be explained as follows:  
* **Joist T18-1. **--This element lacks great strength, with an absolute difference in value between simulation and experiment of 1 kN-m. This difference is not particularly significant; it highlights the sensitivity in terms of the mean parameters considered in the calibration. The error with respect to the cracking moment was 5.8%. * **Tubular joist TB35-3 and TB35-6. **--The elements are stronger, with the differences obtained in the maximum load being \(-10\) y \(-17\) kN, respectively.