# Safety Concept for Textile-Reinforced Concrete Structures with Bending Load
## 5 Reliability Calculation Results
### Influence of the Effective Depth \(d\)
As an advantage, this means that the proposed safety factor \(\gamma_{\mathrm{T}}\) can generally be derived for textiles impregnated with epoxy resin. Figure 15 shows the reliability indices determined in the parametric studies as a function of the reinforcement ratio and the effective depth. Figure 15a shows the reliability indices calculated with a partial safety factor \(\gamma_{\mathrm{T}}\) equal to 1.3 for the textile reinforcement and \(\gamma_{\mathrm{C}}\) equal to 1.5 for the concrete. In the area of the black contour lines, the estimated reliability indices are larger than the threshold of 3.8; in the area of the red contour lines, the estimated reliability indices are smaller. It can be seen that especially thinner members (\(d<60\) mm) are within this area of insufficient safety level. Figure 15b shows the results achieved under the assumption of a reduced effective depth \(d_{\mathrm{eff}}\) for thinner members. The red contour lines, indicating reliability indices below the threshold of 3.8, are significantly diminished. The target reliability index \(\beta_{\mathrm{target}}\) of 3.8 is now only undercut in a small area, which is characterized by a reinforcement level of about 4%0 and an effective depth of 75 mm. The reliability indices within this area have values of approximately 3.7. From the authors' point of view, these results are acceptable, because the deviation from the threshold of 0.1 lies within the range of the calculation methods applied. For example, the MC-IS results in reliability indices about 0.1 higher than the FORM used; thus, a sufficiently high safety level can be assumed. Figure 14: Reliability indices calculated according to FORM for the effective depth \(d\) and the reduced effective depth \(d_{\mathrm{red}}\). Based on the results presented, a value of \(\gamma_{\rm T}\) equal to 1.3 is proposed as a partial safety factor for epoxy resin impregnated textile reinforcement. The partial safety factor \(\gamma\)C for the concrete can be assumed equal to 1.5, which is the same value normally used for the design of steel-reinforced concrete constructions. For thin textile-reinforced structural members with an effective depth \(d\leq 60\) mm, it is recommended to apply a reduced effective depth \(d_{\rm eff}\). This paper discussed the safety concept for textile-reinforced concrete structures with bending load. For a general design, the shear capacity has also to be considered. The described probabilistic procedure can used with the existing design models [31; 32; 33; 34; 35; 36] to derive appropriate partial safety factors for other failure modes. Conceptualization, S.R., M.R. and J.H. ; methodology, S.R. and M.R. ; writing--original draft preparation, S.R. ; writing--review and editing, M.R. ; visualization, S.R. and M.R. ; supervision, M.R. and J.H. ; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript. This research was funded by BMBF, grant number 03 ZZ0321C. The authors give their thanks to solidian GmbH for donation of the carbon grid reinforcement used for the experiments. The authors are particularly thankful for the financial support by the BMBF during the project C3 V1.2. The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.