MODAL DECOMPOSITION OF INSTABILITIES AND ITS APPLICATIONS IN ANALYSIS AND DESIGN OF COLD-FORMED STEEL STRUCTURES

The construction industry has witnessed a widespread of cold-formed steel structures (CFS) in the recent years. However, despite its advantages due to the thin-walled nature of such kind of structures they are highly susceptible to instabilities including coupled instabilities. Currently the modal decomposition method used to analyse these coupled instabilities still has space of improvement. For example, the method generates overly rigid distortional and global modes, and an increased computational effort is needed when dealing with complex cross-sections. Regarding the design of CFS, the existing design code is cumbersome to implement since different empiral formulas are proposed for different types of buckling. In addition, an overly conservative prediction of the ultimate load is obtained for sections where there is significant disparity between the slenderness values of different parts. The aim of the project is to improve the modal decomposition methods and to exploit its application aspects in the analysis and design of CFS undergoing coupled instabilities. First, two new modal decomposition methods are developed, namely the polarisation method and the nodal force method. Both of the methods are based on the finite strip method (FSM), and are aimed at overcoming the disadvantages of the existing method. Second, the nodal force method is applied to analyse the deformed shape of CFS columns in the post-buckling stage, in which the contributions of buckling modes are traced until the column fails. This lays a foundation for the development of design approaches dealing with coupled instabilities. In addition, the modal decomposition method is applied to the statistical analysis of geometric imperfections of CFS specimens, which leads to a scientific charactorisation of geometric imperfections. Finally, a design approach is developed based on the concept of the direct strength method (DSM). In the proposed design approach, the initial post-buckling stiffness is considered as an input parameter in addition to the critical load. These input parameters are then used to establish a multi-linear model approximating the elastic post-buckling behaviour, which is linked to the ultimate load using empirical formulas. In the proposed design approach, two improvements are made. First, a unified design formula is used for different types of buckling, which are distinguished by the difference in post-buckling stiffness. Second, the overly conservative prediction of the ultimate load, when one part of the section is significantly slender, is avoided. This is due to the fact that in these cases, the reduction of the stiffness when buckling occurs is comparably minor.