## 4 Validations
### Example 3: RC Tunnel Section (from [27])  
Example 3 is RC box structure without shear reinforcement, representative of a tunnel section tested by [27] and considered in [3]. The span to depth _a/d_ ratio of the roof portion falling in shear is 1.9. Figure 6(a) shows the geometry of the beam, and Table 2 gives the input parameters. Mean values of \(f^{\prime}_{c}\) and \(f_{y}\) are from the experiment and c.o.v values are identical to the ones used in [3], for comparison purposes with ANFEA results. Table 2 presents the results, where SRAM values correspond to the case 50% \(P_{u}\). Again, SRAM results were on the conservative side, with an underestimation of 11% of the experimental shear failure load. The result was also 19% lower if compared to numerical failure load obtained by ANFEA in [3] (ANFEA in this case overestimated the capacity of the tunnel section). Although a shear failure mode was observed for the roof portion as in previous example 2, different conclusions regarding SRAM Rosenblueth's analyses were obtained for this example. In fact, the four Rosenblueth's analyses results were different for this example, meaning that both \(f^{\prime}_{c}\) and \(f_{y}\) had influence on the final failure mechanism. The c.o.v of the structural resistance was slightly lower than the one obtained by ANFEA. Also, this c.o.v was half the one obtained in the first example, though identical input c.o.v were used in both examples for \(f^{\prime}_{c}\) and \(f_{y}\) (Table 2). The same conclusions regarding the differences between the examples were drawn in [3], and were attributed to the difference in the _a/d_ ratios between the two examples. It is believed that a smaller shear span ratio is favorable to the formation of a second resistance mechanism after the formation of the first shear crack. This second mechanism involves a direct concrete strut towards the support  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Input Data**} & \multicolumn{3}{c}{**Exp**} & \multicolumn{3}{c}{**SRAM**} & \multicolumn{3}{c}{**ANFE [3]**} \\ \hline \multirow{2}{*}{**Example**} & \(\mathbf{f}_{c}\) & \(\mathbf{f}_{y}\) & **COV** & **COV** & **V\({}_{\text{exp}}\)** & **R\({}_{\text{m}}\) = V\({}_{\text{u}}\)** & \(\widetilde{R}_{\text{\star+}}\)** & \(\widetilde{R}_{\text{\star-}}\) & \(\widetilde{R}_{\text{\text{\star}-}}\) & \(\widetilde{R}_{\text{\text{\star-}}}\) & \(\widetilde{R}_{\text{\text{\star-}}}\) & **COV** (\(\widetilde{R}\)) & **V\({}_{\text{ANFE}}\)** & **COV** (\(\widetilde{R}\)) \\ \hline \multirow{2}{*}{**Example**} & \multirow{2}{*}{37} & \multirow{2}{*}{465} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.09} & \multirow{2}{*}{585} & \multirow{2}{*}{424} & \multirow{2}{*}{460} & \multirow{2}{*}{460} & \multirow{2}{*}{353} & \multirow{2}{*}{353} & \multirow{2}{*}{0.13} & \multirow{2}{*}{535} & \multirow{2}{*}{0.10} \\  & & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{**Tunnel**} & \multirow{2}{*}{45} & \multirow{2}{*}{490} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.09} & \multirow{2}{*}{805} & \multirow{2}{*}{722} & \multirow{2}{*}{798} & \multirow{2}{*}{714} & \multirow{2}{*}{663} & \multirow{2}{*}{691} & \multirow{2}{*}{0.07} & \multirow{2}{*}{885} & \multirow{2}{*}{0.05} \\  & & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties and results for examples 2 and 3.  
and a tie action from the bottom layer longitudinal reinforcement of the roof. This effect can be clearly seen in Figure 7b, and explains the influence of \(f_{y}\) for this example.