## 5 Results
### System Reliability Analyses for Fixed Partial Factors
Figure 5 shows that the lowest reliability index (\(\beta\) = 4.3) was attained for a rather low amount of reinforcement (i.e., 1334 mm\({}^{2}\)). It is also visible that for reinforcement amounts higher than 2000 mm\({}^{2}\), the variations in the \(\beta\) values were relatively small. For reinforcement  
Figure 4: Systems reliability analysis for a partial factor \(\gamma_{\rm C}\) of 1.5.  
cross-sections of 4000 mm\({}^{2}\) and 5000 mm\({}^{2}\), the variations remained marginal and the maximum \(\beta\) value (\(\beta\) = 4.7) was found for the highest amounts of reinforcement considered (i.e., 5000 mm\({}^{2}\) and 6000 mm\({}^{2}\)). In fact, Figure 5 shows that the different reliability-based methods generated very similar results for the entire spectrum of reinforcement cross-sections. As seen in the results illustrated in Figure 4 (for a partial factor \(\gamma_{\rm C}\) of 1.5), the failure outside the zone of punching shear reinforcement \(V_{\rm{Rd,out}}\) was governing the system failure for reinforcement amounts lower than 4000 mm\({}^{2}\). For higher amounts of reinforcement (i.e., 5000 mm\({}^{2}\) and 6000 mm\({}^{2}\)), the failure at the maximum punching shear capacity \(V_{\rm{Rd,max}}\) became dominant. Similar to the previous analysis, the failure mode inside the zone of punching shear reinforcement \(V_{\rm{Rd,cs}}\) never became dominant. Note that here, only the MC-SuS was used for reasons of computational efficiency. Figure 6 shows that a further reduction of the partial factor \(\gamma_{\rm C}\) to 1.3 also led to an overall reduction of the system safety levels for all the reinforcement cross-sections considered. To some extent, it can be argued that this reduction was marginal since the maximum \(\beta\) values decreased to values around 4.3-4.5. However, an exception was visible for the safety level corresponding to the reinforcement amount of 1334 mm\({}^{2}\), where the \(\beta\) value was only marginally above the 3.8 threshold. These results seemed to indicate that a reduction of partial factors was not proportional (i.e., linear) to a reduction in the safety level across all the reinforcement amounts. As with the use of higher partial factors, here the failure outside the zone of punching shear reinforcement \(V_{\rm{Rd,out}}\) also governed for reinforcement amounts lower than 4000 mm\({}^{2}\). For higher amounts of reinforcement (i.e., 5000 mm\({}^{2}\) and 6000 mm\({}^{2}\)), the failure at the maximum punching shear capacity \(V_{\rm{Rd,max}}\) was again dominant. The failure mode inside the zone of punching shear reinforcement \(V_{\rm{Rd,cs}}\) is never dominant. The results of a further reduction of the partial factor \(\gamma_{\rm C}\) to 1.2 are plotted in Figure 7. This figure shows that the system safety levels are now below the threshold value (\(\beta\) = 3.8) for reinforcement amounts smaller than 2000 mm\({}^{2}\) and for reinforcement amounts of 5000 mm\({}^{2}\) and 6000 mm\({}^{2}\). By comparing the \(\beta\). values produced by the different reliability-based methods, it was visible that for the reinforcement amount of 4000 mm\({}^{2}\), the simple bounds seemed to be slightly larger than for the remaining reinforcement amounts. Note that it is normally accepted that when one failure mode is not dominant in relation to the other failure modes, the simple bounds are generally too wide, which could be less inter  
Figure 5: Systems reliability analysis for a partial factor \(\gamma_{\rm C}\) of 1.35.  
esting for practical use (e.g., [56]). Nonetheless, since these bounds were only marginally wider and the results of the lower bounds were practically the same as the values generated using the simulation methods, the variation in the safety level for the reinforcement amount of 4000 mm\({}^{2}\) in the first two rows was further analysed in detail. It should also be noted that here, the above-described trends for the governing failure modes are maintained: The failure mode inside the zone of punching shear reinforcement \(V_{\text{Rd,cs}}\) never became dominant.