# Safety Concept for Textile-Reinforced Concrete Structures with Bending Load
## 5 Reliability Calculation Results  
### General Observations  
The reliability index \(\beta\) is given as a function of the reinforcement ratio \(\rho_{\rm I}\) and the effective depth \(d\). The partial safety factors \(\gamma_{\rm T}\) vary between 1.0 and 1.5 so that the required safety level can be easily identified. To this end, the level at which these factors lead to a target reliability index \(\beta\) equal to 3.8 was determined, considering a reference period of 50 years.  
Figure 7 symbolically illustrates the results of the parametric studies. The curve in Figure 7 is divided into three states: A, B and C. The reliability index is approximately \(\beta\approx 3.9\) (state A) for reinforcement ratios up to \(\rho_{\rm I}\approx 2.0\%_{\rm oo}\). Then, the reliability index decreases approximately linearly until it reaches its minimum of \(\beta\approx 2.9\) (state B) for a reinforcement ratio of approximately \(\rho_{\rm I}\approx 4.75\%_{\rm oo}\). Afterwards, the reliability index slightly increases again (state C).  
In state A, the textile reinforcement governs the bending load capacity. Both parameters--the design value of the textile tensile strength \(f_{\rm td}\) in the ultimate limit state and the textile stress \(f_{\rm t}  
Figure 6: Flowchart for the calculation of the failure probability according to the Monte Carlo method.  
Figure 7: Results of the parametric studies: (**a**) reliability index; (**b**) contribution to failure.  
the design point \(x^{*}\)--govern the load-bearing capacity. In state C, the reverse occurs, and the design concrete compressive strength\(f_{\rm cd}\) in the ultimate limit state and the concrete compressive stress \(f_{\rm c}\)* at the design point \(x^{*}\) govern the load-bearing capacity. In state B, reflecting a textile failure, the design value of the textile tensile strength\(f_{\rm td}\) in the ultimate limit state governs the load-bearing capacity. However, the results show that concrete failure occurs with the same longitudinal reinforcement ratio. The reason for this is that the tensile strength of the reinforcement is underestimated in the calculation model due to the applied partial safety factor \(\gamma_{\rm T}\) in the ultimate limit state. In fact, the load-bearing capacity of the textiles is higher than the capacity of the concrete in state B. As the reinforcement ratio increases, the reversed conditions occur at failure load. The probability that a concrete failure occurs increases.  
In general, at any reinforcement ratio \(\rho_{\rm l}\), the cause of failure can be the concrete and the reinforcement. However, at low \(\rho_{\rm l}\) values, the current concrete compressive strength is not likely to be fully used. In this case, the textile reinforcement is governing in the event of failure. At high \(\rho_{\rm l}\) values, reversed conditions occur, and the concrete strength is usually critical for a failure event.  
In the following sections, the influence of selected parameters on the probability of failure is presented. In order to illustrate this influence, only the parameter being examined varies in each case. A detailed description of the calculations can be found in [9].