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Structural systems of thin-walled steel members have gained increasing attention during the last decades. This increased attention is mainly due to an efficient material utilisation. However, the methods for structural analysis existing today concern primarily single member analysis that does not include the actual inter­action between members. Despite that, the modelling of the beams, columns, and especially the connections between them is essential for the assessment of the overall structural performance and for the ability to provide more economical design. This thesis presents a generic methodology to perform a first-order linear elastic analysis of thin-walled frame structures based on a modal decomposition of beam displacement modes. For this purpose, an advanced beam element and a detailed three-dimensional joint element model is developed. The main novelty is the abil­ity to transform the degrees of freedom at the interface between a beam and a joint into a reduced number of beam displacement mode-related degrees of free­dom. Accordingly, the efficiency of this procedure is achieved by having a limited number of degrees of freedom. However, detailed information is available due to decomposition into displacement modes. The beam element that is developed throughout the study enables an analysis of thin-walled prismatic members with either open or closed cross-sections and covers cross-sectional displacements related to distortion, Poisson effects, and shear. The formulation of the beam element is based on semi-analytic displacement solution modes, which are deduced by a new procedure that results in fundamental and distortional beam modes, with polynomial and exponential variations along the beam axis. Due to the kinematic assumptions, local shear transmission between non-aligned wall elements is accounted for, which is not typically seen in thin-walled beam formulations or shell models. Nonetheless, this is confirmed by a finite element analysis with solid elements. An overall good agreement is seen when comparing the obtained results with a commercial finite element software (Abaqus, 2016). In conclusion, the obtained results show that the methodology is attractive and well-suited for further development and practical use as it enables an enhanced structural analysis with advanced beam elements and joint models that allows the transfer of torsional and distortional displacement modes. Furthermore, a detailed analysis of various steel frames with a reasonable number of degrees of freedom can be carried out. The formulation is general and thereby suited for implementation in other approaches, which use displacement modes for analysing structural systems.

In modern structural steel frame design, the modelling of joints between beams and columns are based on very simple assumptions. The joints are most often assumed to behave as a perfect hinge or as a rigid joint. This means that in the overall static analysis relative rotations and changes in the moment curves due to joint deformations are neglected. This simplification eases the modelling but it is at the cost of losing a detailed understanding of the behaviour of the joint. This happens even though the European code has introduced the so-called component method in order to determine the rotational stiffness of a connection. Based on a modelling of any beam-to-column joint using finite shell elements and springs for single components such as bolts, it is the primary hypothesis that it is possible to formulate a generalized connection model with few degrees of freedom related to a relevant set of deformation modes. This hypothesis is based on the idea of modal decomposition performed in generalized beam theories (GBT). The question is – is it possible to formulate an eigenvalue problem with a solution corresponding to mode shapes for the deformation of the joint by using the finite element model and some type of GBT beam elements? It is believed that this is possible. The paper will address our investigations and show the progress of our research.