# Numerical Analysis of the Beam-Column Resistance Compared to Methods by European Standards
## 1 Introduction  
The high strength properties of steel are one of the greatest advantages of constructional steel compared to the other materials used in civil engineering, and allows us to design lighter, slender and, therefore, more economical structures. However, the material's utilization is also reaching its limits. The resistance of steel members subjected to a combination of axial compressive forces and bending moments, the so-called beam columns, is affected by stability problems, which occur with increasing slenderness of structural elements. The basis of this scientific discipline was set by [PERSON] in the 18 th century [1]. Since then, thanks to the hard work of researchers dealing with buckling phenomena, development in this field of study has gone a long way, as various design approaches have been developed to include these phenomena into design calculations. The equivalent column method was adopted in European standards for design of steel members subjected to an axial compressive force and bending moment about either or both principal axes of cross-section, as summarised in papers [2, 3, 4]. This design approach is simple and general for a wide range of applicability. On the other hand, these attributes cause the loss of accuracy in a variety of load cases, and discrepancies can occur due to the complexity of creation of the equivalent member. Therefore, a huge amount of effort is still dedicated by researchers to either optimise or replace this design procedure, which recently resulted in the development of several alternative design approaches. The first alternative method for verification of beam columns susceptible to out-of-plane buckling was proposed by [PERSON] et al. [5, 6], on the basis of a derivation performed by [PERSON] and [PERSON] [7]. The result of this derivation was a design formula based on the well-known Ayrton-Perry format. However, as the authors themselves acknowledged that for practical applications the proposal for in-plane buckling of beam-columns has to be derived, covering the combined effects of in-plane and lateral torsional buckling modes [5]. The overall interaction concept [8], the direct strength method [9] and continuous strength method [10] are other design methods, which are being currently developed. These design methods are based on a similar approach to the general method included in clause 6.3.4 of EN 1993-1-1:2005 [11], which uses generalised relative slenderness as the key parameter for interaction between resistance and instability. The main advantages of these design methods are their ability to account for beneficial strain hardening effects of stocky members and avoidance of complex and burdensome calculation of effective cross-sectional properties in the case of local buckling of slender cross-sections. Nowadays, as more sophisticated numerical software is commonly used in design practice, the possibility of inclusion of local and global imperfections [12; 13; 14] directly into numerical analysis is more relevant. So, as the imperfections are already included in the nonlinear global analysis, the consecutive verification for stability effects is not necessary. However, this advantage seems to be less significant with the growing complexity and size of the numerical models, because in these cases the computational time is markedly increasing. It seems that the design method of Eurocode 9 has been forgotten in the shadow of the aforementioned design methods. Even though aluminium and steel are two different materials, because of their similar mechanical behaviour similarities in the concepts of calculating aluminium and steel constructions can be seen. The possibility of application of a unified design method according to Eurocode 9 [15] was, therefore, presented for steel members by [PERSON] [16]. The fact that this design method was originally used for verification of steel members in Sweden is another proof for its possible utilization for steel members.