_{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.}

Flexural buckling is one of the main problems steel structures are faced with in ensuring an economic design. In Europe, the buckling resistance is calculated using an imperfection factor based on the section type, fabrication method, and steel grade. The current European design standards contain guidelines for the imperfection factor for sections made of steels with yield strength up to and including 700 MPa. However, the current design codes are based mainly on tests performed on steels with yield strength below 460 MPa. Therefore, the applicability of the methodology was reassessed. This paper reviewed the background documentation of the European flexural-buckling design methodology and discussed the current design practice described in the American National Standard. A total of 72 flexural-buckling experiments performed on cold-formed, hot-finished, and welded sections made of steel with yield strength in the range 690–960 MPa were collected and analyzed. Four models for estimating the resistance of high-strength steel struts subjected to pure compression were statistically evaluated based on the collected data. Finally, a recommendation for the estimation of flexural-buckling resistance of high-strength steel members is presented.

Regular convex polygon sections (RCPS) are commonly used as towers supporting transmission lines, stadium lightning and street lamps. Their use provides advantages in the bearing capacity and can simplify erection. Over the last 50 years experimental studies have been conducted to check the applicability of the plate theory to stocky polygonal columns. The paper presents the processed data gathered from compression tests found in the literature. Results from 70 specimens tested under pure compression were statistically analysed. Specimens with yield strength varying from 235 to 700 MPa and angles varying from 144 to 175.5 (5 to 40 sides) were investigated. The local non-dimensional slenderness was calculated using buckling lengths according to EN 1993-1-3 and EN 1993-1-5 with values ranging from 0.55 to 4.52. The objective of the paper was to compare the plate buckling resistance predictions to the experimental results. The paper concludes with a buckling width recommendation for evaluating the critical stress as calculated according to EN 1993-1-3 or EN 1993-1-5.

Stability in a structural mechanics context has posed a continuous problem throughout history for mathematicians, engineers and architects. Flexural buckling is one of the main problems steel structures are faced with in order to ensure an economic design. Different equations have been derived to estimate critical loads that could lead to collapse of compressed members. The buckling resistance of compressed struts are calculated in Europe using the European buckling curves. The method of calculating the resistance implies the use of a reduction factor based on 5 different buckling curves. These buckling curves differ based on type of cross-section, fabrication method and steel grade. The method has been generally accepted since it proved to be reliable and versatile. The current design codes are assigning the same relevant buckling curve to the sections made of steels with yield stress of above 460 MPa. This conservative approach is one of the reasons that discourages the use of high-strength steels in common structural applications, since the designer does not see a direct benefit from the additional steel strength. The first part of the paper briefly describes the origin of the European buckling curves. The second part presents two analytical models for calculating flexural buckling limit loads. Flexural buckling experiments performed on welded box and I-sections made of high-strength steel, with the yield stress in the range of 690-960MPa. The third part analyses the existing buckling experiments and statistically evaluates the models proposed for estimating the resistance of high-strength steel struts subjected to pure compression. The final part addresses the potential future research in the context of developing adequate flexural buckling curves for high strength steel (HSS) members.

Development of the wind energy industry continues to push the need for innovative solutions in terms of structural requirements. High-performance materials are thus needed to improve the efficiency of the structures and to ease the erection costs. The materials used for the towers have not improved significantly in the past years mainly because the design guidelines do not allow the efficient use of the high-strength steels. Lattice wind turbine towers could benefit from cost reductions if cold-formed high-strength steels would be used. Currently high-strength steel members have the same reductions factors for the relevant flexural buckling curve for cold-formed members regardless of the strength of steels. The paper discusses the approach towards the current European buckling curves and draws attention to potential limitations. The residual stresses present in rectangular hollow sections are discussed based on the method of fabrication. Different patterns of residual stresses are investigated by means of finite element simulations. The results indicate that the design codes slightly underestimate the flexural buckling resistance of high-strength steel members in the medium slenderness range.

The pursuit for cheaper energy is leading the current wind tower design to increased heights. Common wind turbine tower designs would generate unjustified costs for transportation and erection leading to inefficient use of materials. In order to reduce these costs, several simplified erection methods have been proposed. One of such is the hybrid lattice-tubular steel tower. For economic feasibility, built-up cold-formed polygonal cross-sections have been proposed for the lattice part. This article presents a numerical investigation of the failure modes of closed polygonal cross-sections. The first part contains a presentation of structural systems which incorporate elements composed of plates and cold-formed members. The evaluation of the polygonal sections is done by means of finite element analysis considering local and global geometrical imperfections and residual stresses generated in the fabrication procedure. A comparative study is performed between several finite element models to propose a corresponding European buckling curve for calculating the flexural buckling resistance. The results show that the design of polygonal sections can be done according to European buckling curves methodology.

Steel cylindrical shell structures are used in a large variety of civil engineering applications such as off- shore platforms, tanks, silos, wind turbine towers, etc. The local stability of such structures and their sensitivity to imperfections is a well-known problem. In current engineering practice the design method is based on the selection of an imperfection class for the shell and subsequently calculating a reduction factor,χ, to the resistance of the shell. One such methodology is supplied by the EN1993-1-6; special conditions are given to pressurized tubes subjected to meridional compression.

Past studies have focused on the stability of cylindrical shells with internal pressure. The stability problem of a long cylinder considering the internal pressure as a simple static load was addressed. Thus, the approaches considered the fluid as compressible.

The purpose of the present work is to investigate numerically the potential benefit of using an incompressible fluid fully enclosed in a circular cylindrical shell. The constraint imposed by the presence of the liquid in the interior of a shell will be referred to as “hydraulic constraint”. As liquids are nearly incompressible, the buckling of a liquid-filled shell has to satisfy the condition that the integral of all the displacements normal to the shell surface is equal to the volume variation of the contained liquid. The volume variation of the shell interior has to be equal to the dilation of the shell due to liquid pressure increments associated to the onset of geometrical instability. Additionally, the weight of the contained liquid causes additional circumferential tension in the cases of vertically placed cylinders.

The methodology followed is the numerical analysis of cylindrical shells by means of the ABAQUS Finite Element code and a comparison with the methods given in the Eurocode.