###### Abstract  
Punching shear-reinforced flat slabs can fail in three modes: (1) inside the shear-reinforced zone, (2) outside the shear-reinforced zone, or (3) at the maximum punching shear capacity. By using the theory of structural systems reliability, this study investigates how these failure modes combined affect the safety level of reinforced concrete flat slabs with punching shear reinforcement, and ultimately, the variation of partial factors. Based on DIN EN 1992-1-1 together with the German National Annex DIN EN 1992-1-+NA(D), and by using distinct reliability-based methods (i.e., levels II and III), the variation in the system failure probabilities and, consequently, partial factors were analysed. The results indicated that partial factors can fluctuate significantly depending on the governing ultimate limit state function and the scatter of basic variables. Furthermore, they indicated that the chosen reliability-based method had a significant influence on the resulting safety level. The sensitivity analysis confirmed the premise that partial factors can be reduced without compromising socially accepted safety levels (e.g., recommended in DIN EN 1990). Ultimate benefits include material and cost savings and CO\({}_{2}\) emission reductions. Finally, the approach addressed in this paper offers a new perspective on the derivation of partial factors that can be considered by engineering practitioners. systems reliability; RC flat slabs; punching shear; punching shear reinforcement; partial factors; reliability-based analysis +
Footnote †: journal: Applied Sciences  
1. Failure inside the zone of punching shear reinforcement (i.e., failure in the surface crossing one or more rows of punching shear reinforcement);
2. Failure outside the zone of punching shear reinforcement (i.e., failure in the surface located in the region outside the punching shear reinforcement elements);
3. Failure at the maximum punching shear capacity (i.e., failure in the compression zone directly at the face of the column). The typical crack formations of these punching shear failure modes, with and without punching shear reinforcement, are illustrated in Figure 1.  
In Germany, the punching shear design provisions (with and without reinforcement) included in the European structural code DIN EN 1992-1-1 [4; 5] are supplemented by the National Annex NA(D) [6; 7]. In the following sections, this combination is abbreviated as DIN EN 1992-1-1+NA(D) [4; 5; 6; 7]. If a low amount of punching shear reinforcement is installed and a shear crack appears, the punching shear reinforcement will be activated. Due to the low amount of reinforcement, it will start to yield immediately and the crack width cannot be controlled. This lack of control can lead to immediate failure. This should be avoided through a minimum amount of punching shear reinforcement, which is established by the structural code. For larger amounts of punching shear reinforcement, a failure can occur at the maximum punching shear capacity, inside the shear-reinforced zone, or even outside the shear-reinforced zone, depending on the number of reinforcement rows. Despite the design being normally governed by the smallest punching shear resistance, the extent to which the above-described failure modes influence partial factors for building materials (i.e., concrete and reinforcing steel) can vary. When it is unclear which type of failure is decisive due to the scatter of basic variables (namely, material and geometric properties and model uncertainties), the use of reliability-based methods enables the assessment of failure probabilities and the corresponding reliability indices \(\beta\) (as a measure of structural safety level) for a structural system or component. The theory of structural systems reliability offers means to assess these failure probabilities and reliability indices \(\beta\) when a system is subjected to multiple failure modes (e.g., [8; 9; 10; 11; 12; 13]).