## 4 Results and Discussion
### Load-Displacement Curve  
Table 4 and Figures 10 and 11 compare the loads and displacements obtained from the FEA and experimental data of beams S1-2 and S1-4. This analysis employed a 20 mm mesh size for the concrete beam following the completion of the mesh convergence analysis. Figure 10 compares the results of FEA and experimental outcomes for the RC beam S1-2 at various load stages, encompassing the first cracking, service, and failure loads. The crack patterns and mode of failure exhibit substantial agreement between the simulation and experiment. The results indicate that the beam failed in flexure, with cracking initiating at the midspan and propagating toward the beam's ends, which is a characteristic feature of flexural failure. During the initial stage, as the structure reached the cracking load, the FEA results exhibited good agreement with the experimental findings. The deviation between the FEA and EXP was approximately 8.7%, as detailed in Table 4. Specifically, the cracking load in the experimental test measured 60.93 kN, while in the FEA model it was 66.23 kN. Regarding the corresponding displacement, the cracking displacement from the FEA aligned closely with the experimental result, showing only a 3.58% discrepancy. Specifically, the values of those displacements were 1.999 mm from FEA and 1.93 mm from the experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Beam** & & **FEA** & **EXP** & **Error (\%)** \\ \hline \multirow{4}{*}{S1-2} & Cracking load (KN) & 66.23 & 60.93 & 8.70\% \\ \cline{2-5}  & Crack displacement (mm) & 1.999 & 1.93 & 3.58\% \\ \cline{2-5}  & Ultimate load (KN) & 228.673 & 226.32 & 1.04\% \\ \cline{2-5}  & Ultimate displacement (mm) & 19.2377 & 20.333 & 5.39\% \\ \hline \multirow{4}{*}{S1-4} & Cracking load (KN) & 43.1 & 39.154 & 10.08\% \\ \cline{2-5}  & Crack displacement (mm) & 1.279 & 1.421 & 9.99\% \\ \cline{2-5}  & Ultimate load (KN) & 221.96 & 205.7 & 7.90\% \\ \cline{2-5}  & Ultimate displacement (mm) & 20.42 & 20.71 & 1.40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparing FEA and experimental results: analyzing loads and displacements of the beam S1-2. Figure 10: Comparing the load–displacement curves between FEA results and experimental findings [28] for the beam S1-2. In the next stage, as cracks emerged, the stiffness of the RC beam decreased. The beam's capacity to bear loads kept rising until it hit the ultimate load, marked by multiple cracks in the beam and the reinforcements reaching the yield load. At this point, the FEA results closely matched the experimental results, with a deviation of just 1.04%. The ultimate load was 228.673 KN in the FEA result and 226.32 KN in the experimental result. When considering the corresponding displacement at the ultimate load, there was a 5.39% difference between the FEA and experimental results, measuring 19.2377 mm and 20.33 mm, respectively. It is clear that, in general, the load-displacement curve from the FEA aligns closely with the experimental curve. However, the two curves have a noticeable gap, specifically in the load range of 60 KN to 170 KN. This difference can be attributed to voids and defects present in the experimental RC beam. These imperfections affect the results, deviating from the ideal behavior assumed by the isotropic material used in the FEA model. Around a load of 170 KN, there is a decline in the stiffness of the curve of the FEA model. This reduction is linked to the emergence of cracks in the concrete. These cracks cause a decrease in stiffness, and this change is accounted for in the FEA model by utilizing the CDP model for the concrete beam. Table 4 and Figure 11 present a comparison of results between the FEA model and the experiment, specifically focusing on the load-displacement curve at the cracking and ultimate points. When comparing with beam S1-2, it is evident that there is a more significant difference in the cracking and ultimate points between the FEA and the EXP results.