## 4 Probabilistic Analyses
### ECOV Analyses  
According to the ECOV format detailed in Section 2.2, the global resistance factor and the design resistance value for the normal force and moment of the slender columns are computed considering two safety levels characterized by target reliability indexes of 3.8 and 4.2 (see Table 6). These reliability levels have been selected due to the assumption of moderate (\(\beta=3.8\)) and low (\(\beta=4.2\)) relative costs of safety measures and great consequences of failure for a considered classical public building and a reference period of 50 years according to EN 1990.  
Furthermore, two model uncertainty factors were considered for NLFEM. For the nominal stiffness method and the NLFEM, a model uncertainty factor equal to 1.10 was first considered since such models are considered here as high uncertainties given the fact that the NLFEM results have shown poor agreement with the experimental results. Nevertheless, the Model Code [27] recommends a model uncertainty factor of 1.06 for refined numerical analysis such as non-linear finite element analysis since such modeling approaches are regarded as low uncertainties models. Accordingly, calculations considering the low model uncertainty factor for NLFEM are also presented for the purpose of benchmarking.  
Figure 12: Statistical structural responses and PDFs obtained according to EN1992-1 non-linear finite element analyses: (**a**) BOKU Group: University of Natural Resources and Life Sciences Vienna, Institute of Structural Engineering, (**b**) STUBA Group: Slovak University of Technology in Bratislava, Department of Concrete Structures and Bridges, (**c**) U-MINHO Group: University of Minho, Institute for Sustainability and Innovation in Structural Engineering (ISISE) and (**d**) UNIZG-FCE Group: University of Zagreb Faculty of Civil Engineering, Department of Structural Engineering.  
For exceptional cases when models are validated through assessment of an existing structure and no uncertainties are observed, a model uncertainty factor of 1.10 is recommended. This could be the case for the experimental campaign. Nonetheless, given deviations in the results provided by the experimental campaign, a low model uncertainty factor was considered when applying the ECOV format to the outputs of the experiments.  
The ECOV format results are displayed in Table 6 and the model uncertainty factor is of crucial importance. Employing the ECOV method as suggested by the Model Code, and considering a model uncertainty factor of 1.06 and a target safety index of 3.8, leads to an overestimation of the slender column axial capacity for most of the developed NLFEM, except for the model developed by the UNIZG-FCE where the design normal force is below the design value obtained from the experimental campaign results (i.e., 235.41 kN). For the same target safety level when considering a model uncertainty factor of 1.1, the overestimation of the normal force is only observed for the model developed by BOKU. Concerning the higher safety index, i.e., 4.2, the design value overestimation was observed only for the BOKU prediction for high uncertainty models (\(\gamma_{Rd}=1.1\)). For low uncertainty models (\(\gamma_{Rd}=1.06\)), the overestimation is observed for the U-MINHO and BOKU NLFEM. As previously stated, the nominal stiffness method provides results that are too conservative, with a design normal force representing approximately 70% of the design normal force provided by the experimental campaign results.  
According to such findings, higher model uncertainty factors (i.e., \(\gamma_{Rd}>\)1.1) are recommended for the design and safety assessment of slender columns using standard NLFEM. Further research is also suggested to investigate more sophisticated numerical models for the prediction of the carrying capacity of slender columns.