## 7 Laboratory Tests and Numerical Simulations Result and Discussion
### Results of Numerical Simulations  
The results of numerical simulations and their comparison with the results of the laboratory test are reported in this section.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Beam Type** & **Dapped End Status** & \
\begin{tabular}{c} **Ultimate STM Load** \\ **[kN]** \\ \end{tabular} &
\begin{tabular}{c} **Ultimate Experimental** \\ **Load [kN]** \\ \end{tabular} \\ \hline Orthogonal & Sound end & 150 & 175 (+17\%) \\ reinforcement & Damaged end & 65 & 120 (+85\%) \\ \hline Inclined & Sound end & 160 & [-] \\ reinforcement & Damaged end & 70 & 120 (+72\%) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between strut & tie (STM) and experimental results.  
Figure 19a shows the comparison between load-displacement curves of the experimental result and their FEM model of the beams tested in static scheme 1. It can be seen that orthogonal and inclined reinforcement almost have the same behaviour until yielding as it was desired from design. The numerical simulation also fairly approximates the experimental result before yielding.  
In the beam with orthogonal reinforcement, when the load of 120 kN is reached, the experimental curve shows a short plastic plateau, that corresponds to the opening of the big crack evidenced in Figure 18a,b. This plateau is not visible in the FEM model as the load increases until a collapse load is 12% higher than the experimental one.  
In the beam with inclined reinforcement, when the load of 120 kN is reached, the experimental evidence shows a long plastic plateau that corresponds to the opening of the crack shown in Figure 18d. The FEM model again cannot find this plateau as the load increases until the collapse load is about 32% higher than the experimental one.  
Figure 19b shows the comparison between the experimental result of the beam with orthogonal reinforcement in static scheme 2 and its FEM model. In this case, an initial load-unload phase (blue curve) was made in the FEM model to simulate the starting condition equal to the experimental one (static scheme 2 is conducted after a full load on scheme 1). Moreover, in this case, the experimental and numerical results are in good agreement in the elastic and cracking propagation phase, but the FEM model is again unable to capture the plastic field that develops due to the collapse surface evidenced in Figure 18c. The collapse load of the numerical model is about 50% higher than the experimental evidence.  
In both schemes, FEM models are unable to capture the failure mechanism on the casting joint that seems to cause the collapse of the beams in reality. Different mesh sizes were tested to study the mesh dependency of the problem. A cohesive-friction interface was also introduced between the web and flange to simulate a reduction of tensile resistance without succeeding in improving the numerical solution. The numerical prediction of the failure load of concrete structures with brittle mechanisms (shear failures or D regions) is well-known in the literature [42; 43]. Errors up to 30% in the prediction of the ultimate load can be achieved using commercial software and are well documented.  
Figure 20 shows that the numerical crack pattern reproduces fairly well the experimental evidence in every static scheme that has been investigated. This result, in addition to the very good agreement of load-deflection curves shown in Figure 19, demonstrates the good performance of the numerical models until the sudden collapse that cannot be evidenced numerically.  
Figure 19: Comparison between experimental results and numerical simulation of a beam with orthogonal reinforcement. (**a**) Static scheme 1. (**b**) Static scheme 2.