# Structural Behaviour of Concrete Deep Beams Reinforced with Aluminium Alloy Bars
## 3 Results and Discussion  
### Validation  
The experimental study conducted by [PERSON] and [PERSON] [4] and described in Section 2.1 was validated by the developed FE model, which was also detailed in Section 2.2. Table 2 gives the experimental results in terms of load capacity (P\({}_{\text{Exp. }}\)) at failure and its deflection (\(\delta_{\text{Exp. }}\)) at mid-span, which were compared to those (P\({}_{\text{FE}}\) and \(\delta_{\text{FE}}\)) predicted by the FE model. It should be noted that some of tests were repeated to provide reliability [4]. For example, the AIL-2 specimen was the same as the specimen of AIL-3, and the AIH-2 specimen was the same as the AIH-3 specimen. These beams were hereinafter considered as one beam for FE validations. As reported in Table 2, the FE model which was created to simulate the behaviour of AA RC beams predicted the actual load-bearing capacity with a mean value of 1.00. The standard deviation was also a relatively smaller value of 0.05. A high correlation would mean the FE model could be reliable for predicting the behaviour under the tested conditions. The deflection response of FE-modelled beams was also in good correlation with that of tested beams (see Figure 4). As previously mentioned, the experimental programme was the only one in the published literature based on the author's knowledge. Hence, the experimental results reported by [PERSON] and [PERSON] [4] were able to validate against the proposed FE model. Figure 4 demonstrates the relation between load-deflection curves obtained from physical tests carried out by [PERSON] and [PERSON] [4] and the simulated load-deflection curves from the developed FE model. As can be seen in Figure 4, the experimental curve (black) and FE curve (blue) have similar initial slopes, meaning that uncracked stiffness, which directly depends on the parameters (i.e., cross-sectional dimensions, elastic modulus, and boundary conditions), was accurately simulated. After the development of cracks, both \begin{table}
\begin{tabular}{c c c c c c} \hline
**Specimen** & **P\({}_{\text{Exp.}}\) (kN)** & **\(\delta_{\text{Exp.}}\) (mm)** & **P\({}_{\text{FE}}\) (kN)** & **\(\delta_{\text{FE}}\) (mm)** & **P\({}_{\text{FE}}\)/P\({}_{\text{Exp}}\)** \\ \hline AIL-1 & 46.3 & \(\geq\)15 & 47.6 & \(\geq\)15 & 1.03 \\ AIL-3 & 50 & \(\geq\)18 & 47.7 & \(\geq\)18 & 0.95 \\ AIH-1 & 88 & \(\geq\)30 & 81.7 & 9.2 & 0.93 \\ AIH-3 & 86 & 12.6 & 80.4 & 10.4 & 0.93 \\ AIIM-1 & 65.2 & \(\geq\)20 & 68.4 & \(\geq\)20 & 1.05 \\ AIIM-2 & 63.9 & \(\geq\)20 & 66.3 & \(\geq\)20 & 1.04 \\ AIIL & 50.4 & \(\geq\)15 & 52.7 & \(\geq\)15 & 1.05 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison between experimental and FE results. Figure 3: The developed FE model. experimental and FE-simulated curves became nonlinear. Even though there were slight deviations near peak load and in the post-peak response, these were relatively small. Overall, the FE model provided a good correlation with the experimental data. The comparison between crack patterns at failure observed during the physical tests conducted by [PERSON] and [PERSON] [4] and those obtained from FE analyses is given in Figure 5. It should be noted that the crack patterns of all beams were not reported; hence, all beams would not be able to be compared. As can be seen in Figure 5, AIIM-1 failed in flexure, as evidenced by the cracks being concentrated in the centre and some branching outward,  
Figure 4: Experimental and FE-predicted load–deflection curves. similar to the simulation. AIH-1 also failed in flexure, and had apparent damage, with crushed concrete in the concrete compression zone. The more apparent shear cracks at failure were observed during physical testing rather than FE simulation. The FE simulation and the physical test indicate a good agreement in terms of crack location and orientation at failure. The FE model captures crack propagation patterns reasonably well, though the crack paths of physical testing are slightly more irregular. All FE-simulated beams failed in flexure.