# Numerical Analysis of the Beam-Column Resistance Compared to Methods by European Standards
## 2 Numerical Analysis
### Validation of the FEM Model  
Validation of this modelling approach was performed using the experimental analysis performed by [PERSON] and [PERSON] [30]. This experimental programme contains a description of 42 hot-rolled wide-flange columns subjected to axial force and bending moments. Most of the columns were subjected to bending moments about their major principal axis, except two specimens, T25 and T27, which were subjected to a bending moment about their minor principal axis. The boundary conditions were pin ended in the plane of applied bending moments and almost fixed in the perpendicular plane, as the buckling length was approximately 0.6 L for this plane. The five load cases investigated by this experimental analysis can be seen on Figure 6.  
Figure 5: Distribution of residual stresses for hot rolled I and H profiles.  
The loading components were applied independently of each other. Most of the specimens were first loaded to a certain level by an axial force, and after that the application of bending moments was continued until failure.  
Appropriate material properties and column dimensions were adopted in the numerical analysis for each member, as various cross-sections and steel properties were used for the specimens. Also, a linear residual stress distribution according to Figure 5. for members with a ratio \(h/b\leq 1.2\) was used. As the initial geometric imperfections are not presented in this report, the initial bow imperfections were applied in the shape of first buckling mode with an amplitude of L/1000.  
To sum up, a total of 16 specimens were used for this validation, covering a wide range of load cases and also relative slenderness and axial force ratios. The ultimate resistances of specimens from experimental analysis were compared to the ultimate resistances gathered by numerical analysis. The comparison of these specimens can be seen in Table 1. The specimens, which were firstly loaded by a bending moment and then by an increasing axial force till failure, are denoted by \"*\", and the specimens which were pinned in the plane of the minor axis are denoted by \"z\".  
As can be seen, the resistances given by the numerical analysis are in good agreement with the resistances gathered by the experimental loading tests. A similar level of accuracy was also achieved in an analysis performed by [PERSON] [31]. The deviations were both higher and also lower than the resistances from the experimental analysis with a maximum deviation of 13%. Also it can be seen that whether the resistances were higher or lower than the \"real\" resistances was not dependent on the load case, as the specimens T8 and T12 had the same relative slenderness and boundary conditions and the difference between their deviations was 9%. Therefore it can be stated that the model provides consistently accurate results, as the resistances are not strictly on the safe or unsafe side. The reason for these deviations could be the difference between the real and assumed geometrical imperfections involved in the numerical analysis, as they were not reported by authors.  
Moreover, a good agreement has to be highlighted in the case of specimen T2, where the bending moment resistance achieved by the experimental test was higher than the analytical cross-sectional plastic resistance. Therefore, it can be concluded that this model also provides good results in cases where the large plastic strains should be considered.  
Figure 6: Load cases investigated by [PERSON] and [PERSON]; simply supported beam-column with unequal end moments (**a**); pinned-fixed beam-column (**b**); simply supported beam-column with equal end moments (**c**); simply supported beam-column with linear bending moment distribution (**d**); centrically loaded beam-column (**e**).