## 5 Results  
### System Reliability Analyses for Fixed Partial Factors  
Figures 4-7 show the results of the system reliability analyses for varying amounts of punching shear reinforcement. Each system reliability was calculated according to the methods described in Section 4.3.2 for different partial factors for concrete \(\gamma_{\rm C}\). The grey columns of Figures 4-7 respectively refer to the three failure modes discussed in Section 1: \(V_{\rm Rd,ccs}\) (failure mode (i)), \(V_{\rm Rd,out}\) (failure mode (ii)) and \(V_{\rm Rd,max}\) (failure mode (iii)). The variation of the amount of punching shear reinforcement considered in the analysis range between a minimum of 824 mm\({}^{2}\), which was determined according to DIN EN \begin{table}
\begin{tabular}{l c} \hline
**Design Parameters** & **Values** \\ \hline Concrete compressive strength\(f_{\rm ck}\) & 35 N/mm\({}^{2}\) \\ Yield strength fy & 500 N/mm\({}^{2}\) \\ Effective depth \(d\) & 280 mm \\ Column dimensions c\(\emptyset\) & 500 mm \\ Slab width \(h\) & 320 mm \\ Cross-sectional reinforcement area of the first & Varying between 1334 mm\({}^{2}\) (min.) \\ and second rows & and 6000 mm\({}^{2}\) (max.) \\ Flexural reinforcement ratio \(\rho_{1}\) (\({}^{\ast}\)) & 0.8\% \\ \(u_{0}/d\) & 5.61 \\ \hline \end{tabular} \({}^{(\ast)}\) It was considered an even distribution of the flexural reinforcement (i.e., equally distributed) over a distance equal to the column width plus 3\(d\) on each side.  
\end{table} 
Table 4: Assumptions for the design of the structural system. 1992-1-1+NA(D) [4; 5; 6; 7], and 6000 mm\({}^{2}\). The \(\beta\) target value of 3.8 was taken from DIN EN 1990 [22] and refers to the recommended value for a reliability class 2 (RC2) and a 50-year reference period. This RC2 is associated with the consequence class 2 (CC2), which is mostly related to common structures where the consequences of failure are medium (e.g., residential and office buildings, public buildings). Figure 4 shows the results of the system reliability analysis that considered the partial factor \(\gamma_{\rm C}\) equal to 1.5. Here, it can be observed that for all the reinforcement amounts, the calculated \(\beta\) values varied between 4.8 and 5.7 (approximately), meaning that the safety level of the system was always above the \(\beta\) value of 3.8 recommended in DIN EN 1990 [22]. Figure 4 also shows that the safety levels increase quite sharply for the reinforcement amounts of 5000 mm\({}^{2}\) and 6000 mm\({}^{2}\). Additionally, the results highlight that the \(\beta\) values generated through simple bounds and the simulation methods were quite similar for small amounts of reinforcement. This similarity could be an indication that the first-order methods already produced quite accurate results for the failure modes addressed in this investigation. For higher amounts of reinforcement, the \(\beta\) values generated through simple bounds were slightly higher than those produced through simulation methods. It was particularly noticeable that for the punching shear reinforcement with a cross-section of 5000 mm\({}^{2}\) in the first two rows, the simple bounds were only marginally wider than the bounds obtained for small amounts of reinforcement. Additionally, it can be observed that for reinforcement amounts lower than 4000 mm\({}^{2}\), the failure outside the zone of punching shear reinforcement \(V_{\rm Rd,out}\) was governing the system failure. However, 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. The failure mode inside the zone of punching shear reinforcement \(V_{\rm Rd,cs}\) never became dominant across the range of reinforcement amounts considered. By reducing the partial factor \(\gamma_{\rm C}\) to 1.35 (Figure 5), it was noticeable that the overall system safety level decreased despite still being above the 3.8 \(\beta\) threshold.