# Numerical Analysis of the Beam-Column Resistance Compared to Methods by European Standards
## 3 Verification According to European Standards
### Resistance of Beam-Columns with IPE 100 Type of Cross-Section  
#### 3.1.1 Axial Compression and Major-Axis Bending Laterally Restrained  
The objective of these loading conditions is to study the flexural buckling in the plane of bending about the major axis. This type of failure occurs for beam-columns with double symmetric I sections subjected to a combination of axial compressive force and bending moment only if the sufficient lateral restraints are present. The lateral restraints were modelled in the place where web and flanges are connected, as can be seen in Figure 7.  
Method 2, according to Eurocode 3, also differentiates between members susceptible and not susceptible to torsional deformations. Therefore, the appropriate interaction factors _kij_ have to be used.  
The interaction curves according to design approaches compared to the results of numerical analysis are presented on the Figures 8-12. There is also introduced an equivalent member in the case of a pinned-fixed beam column.  
Figure 8: Interaction curves for laterally restrained beam-columns with IPE 100 cross-section.  
Figure 7: Lateral restraints of beam-columns.  
Figure 11: Interaction curves for laterally restrained beam-columns with IPE 100 cross-section.  
Figure 10: Interaction curves for laterally restrained beam-columns with IPE 100 cross-section.  
Figure 9: Interaction curves for laterally restrained beam-columns with IPE 100 cross-section.  
As can be seen, in the case of pin ended beam-column Methods 1 and 2 of Eurocode 3 are calibrated correctly. The interaction curves have the same tendencies as the curves obtained by the numerical analysis, especially in the high levels of axial force. Moreover, Methods 1 and 2 generally provide conservative resistances for all load cases. The difference in these methods is in the case of the pinned-fixed beam column being higher, but the results are always on the safe side compared to numerical analysis. The accuracy of these methods is highly dependent on the _kij_ interaction factors, which for both methods evaluated in a different way. The differences in resistances between these two methods are also the consequence of different values of interaction factors.  
The interaction curves according to the method of Eurocode 9 are generally unsafe for all load cases. The resistances are on the safe side mostly for beam columns with relative slenderness \(\overline{\lambda}_{y}=2.0\). Despite these results, it can be seen that interaction curves have the same character as the curves acquired by the numerical analysis.  
The beneficial effect of the bending moment diagram on the beam-column resistance can be seen from the comparison of the numerical curves for different load cases, as it plays a role in the extent of yielding at the ultimate limit state [4]. This is most notable for the slenderness ratio \(\overline{\lambda}_{z}=0.5\), where the beam-columns subjected to concentrated load in the middle of the span reached the highest values of resistance. This effect is accounted in the Eurocode 3 by means of the \(Cm\) factor. However, it can be seen that this effect is not included in the interaction formulae for the method of Eurocode 9, as this method provided the same values of resistances for all load cases.