_{The European standards dealing with design rules and recommendations for steel structures have been under revision in the past years due to the increased use of high-strength steels. High-strength steels popularity increased at a steady pace in the last decades since they allow for more light-weighted solutions than conventional steels. However, the material reduction ultimately increases the structural slenderness, which in turn has implications on the load bearing capacity if not properly accounted for. Flexural buckling is one of the main challenges steel structures are faced with in order to ensure an economic design. The European design standard EN 1993-1-1 uses an equivalent imperfection factor based on section type, fabrication method and steel grade for the flexural buckling resistance design of a steel member. The European design standards contain guidelines for the selection of the imperfection factor for structural elements made of steels with nominal yield strength up to and including 700 MPa. However, the current design codes are mainly based on tests performed on steels with nominal yield strength below 460 MPa. As higher steel grades are being more commonly used due to their increased global availability, design rules need to be revised and validated. The design standards in force in Europe and in USA do not provide additional rules for steel with nominal yield strength above 700 MPa. The applicability of the current design rules to higher steel grades needs to be assessed as new design standards are being prepared in Europe.This thesis focuses on the weak axis flexural column buckling resistance for high-strength steel sections aiming to propose a general design model to be applied to both mild steels sections and high-strength steel sections. The background, aim and the limitations of the study are explained in the first chapter. In the second chapter, a literature review was presented in which the limitations and the implications of the existing design models were analysed and discussed. Experimental data was collected from available literature in order to identify the need of a new model. The literature review revealed that a general agreement was found between the researchers stating that the European buckling curves are more conservative for columns made of high-strength steel than those made of mild steels and that a change can be justified for welded and cold-formed high-strength steel columns. A similar agreement was found stating that the American standard AISC 360 is not as conservative as the European standard in regard to the weak axis flexural buckling resistance of high-strength steel columns. However, unlike the European standard, the American standard uses a compressive resistance factor that reduces the allowed design resistance by 10\%. Based on the test results a compressive resistance factor was also proposed that could be applied to high-strength steel columns.  In the third chapter, a statistical analysis was performed to compare the resistance determined experimentally with the resistance calculated using the European and American design standards for mild and high-strength steels. The statistical analysis showed that higher steel grades are penalised more with increasing steel grade. This effect becomes more relevant as higher steel grades are more commonly used in practice. Furthermore, a large data scatter was observed in the global slenderness range 0.4 to 1.2 where the influence of the residual stresses on the compressive resistance is highest. Thus, a hypothesis that the residual stresses caused by welding and cold-forming are not proportional to the yield strength was formulated. The analysis also revealed a lack of experimental data for welded I/H-sections with nominal yield strengths above 700 MPa subjected to weak axis flexural buckling.The posed hypothesis was verified through compressive tests of seven welded high-strength H-sections manufactured with S960 (Strenx960). The experimental work is described in the forth chapter. The manufactured specimens aimed to fill the gap of experimental data for weak axis flexural buckling in the medium slenderness range  0.6 to 1.2. Additionally, welded I/H-sections are known to be more sensitive to residual stresses than for example hollow sections. The higher sensitivity emphasizes the different residual stress to yield strength ratio. For comparison purposes, four equivalent S355 welded columns were also tested. Material tests, imperfections measurements and residual stress measurements were also performed. The residual stress measurements confirmed that the residual stresses do not increase proportional to the yield strength. Furthermore, it was found that the design standards underestimated the compressive resistance of the high-strength steel columns while overestimating the resistance of the mild-strength steel columns when characteristic values were used. A holistic design method was proposed to predict the flexural buckling resistance over the weak axis for the tested columns. The design model proposed herein is based on the Ayrton-Perry model to which a reduction factor is applied as a function of the local and global slenderness. The resistance calculated using the proposed model was compared to the experimentally determined resistance of the welded high-strength steel columns collected from literature. In the fifth chapter, a residual stress model was proposed to be used for finite element modelling and validated through a series of finite element analysis. The proposed residual stress model assumes that the longitudinal residual stresses around the weld do not exceed a tensile stress value which is the smallest between the yield strength of the steel and 420 MPa. The proposed magnitudes of residual stresses were defined based on measurements collected from literature and reconfirmed through experimental data. The results obtained from the finite element analysis showed overall good agreement with the test results for the S960 columns. The final chapter contains a summary of the thesis and answers the research questions. The main conclusions were discussed and recommendations for future research were proposed.}