# Probabilistic Studies on the Shear Strength of Slender Steel Fiber Reinforced Concrete Structures
## 7 Conclusions  
Uncertainties are inevitable in any structural engineering problems. Uncertainties may arise from the properties of the material parameters, random nature of the loadings, imperfect resistance modelling, lack of experience and human factors. Previous studies have shown that the resistance predictions from the existing shear design models for SFRC beams differ from the experimentally observed shear strength. The shear models contain significant uncertainty due to the failure to represent the phenomenology of shear resistance accurately. Proper modelling and description of model uncertainties are critical since model uncertainty significantly influences reliability performance [29; 35]. The present study is focused on the quantification of model uncertainty related to the current shear resistance predictive models for SFRC beams without shear reinforcement. The study also presents a systematic derivation of global partial safety factors to account for the effects of model uncertainties in the shear resistance of SFRC beams following the semi-probabilistic approach recommended in EN 1990 for reliability-based design. The models investigated include the best estimate predictive model of (1) fib Model Code 2010, (2) German guideline (DAStB), and (3) [PERSON] et al. [27] mechanical model. The model uncertainty statistics were developed by comparing mean predicted shear capacity with experimental capacity. The best model is the model with the lowest bias (i.e., mean value closest to 1), minimum dispersion (standard deviation closest to zero) and milder sensitivities to shear parameters. The following concluding remarks are drawn:  
* The model uncertainty related to the DAStB model has a mean value of \(\mu_{M}=1.08\) (the closest to the optimal value of 1) and the lowest dispersion (\(\sigma_{M}=0.31\)). On the other hand, the MC-10 and [PERSON] et al., models displayed the highest mean value (\(\mu_{M}=1.13\)) (largest conservative bias) and the most substantial dispersion, comparatively. * The [PERSON] et al., model showed weak to moderately weak trend with all the shear parameters investigated in this study. MC-10 and DAStB models showed some correlation of the model uncertainty with the beam effective depth \(d\), shear span to effective depth \(a/d\) and the reinforcement ratio \(\rho_{l}\), corresponding to unwanted trends in the model uncertainty with these parameters. * The shear span to effective depth ratio \(a/d\) was found to be the most influential parameter (highest correlation coefficient). The strong decreasing trend of safety bias as the shear span to effective depth ratio \(a/d\) increases, is a cause for concern. Further assessment of this trend was conducted by computing model uncertainty statistics for different subsets of beams with \(a/d\) ratio. The parameter range analysis indicates that the statistics of the model uncertainty (mean value, standard deviation and coefficient of variation) decreases with increasing \(a/d\) ratio. * The probability distribution fitting indicates that the derived model uncertainty random variables can be modelled using a lognormal distribution. * Global partial safety factors accounting for the model uncertainty in shear resistance models for SFRC beams were proposed. Partial safety factors ranging from 1.13-1.23, 1.17-1.22 and 1.38-1.64 were recommended for beams with short, medium and slender shear span lengths, respectively.