Extensions of the constrained Finite Strip Method for thin-walled members: closed sections and sections with rounded corners

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The objective of this paper is to provide a derivation for a constrained Finite Strip Method (cFSM) stability solutions that applied to thin-walled members with closed sections and sections with rounded corners. The current cFSM is able to provide the decomposed stability solutions for members with open sections – single branch and multi-branch. However, with the mode definitions and implementation adopted in current cFSM, there are limitations that inhabit its applications to other general sections, such as closed section, section with rounded corners, and curved sections. To overcome these limits, the traditional implementation approach of the Global (G), Distortional (D), and Local (L) modes through the warping displacement has been revisited and its relationship with the transverse displacements (i.e., Degree of Freedom, DOF) are then used to build the characteristics of these transverse displacements. Then, following the core assumptions of the mode definitions in current cFSM, a new implementation approach is adopted to establish the mode classes: through the transverse displacements instead of the warping displacement. Then, several other techniques are further introduced to enable the cFSM for overcoming the aforementioned limitations. First, the bredt shear strain for closed sections is incorporated along with the conventional in-place shear. Second, for section with rounded corners, the transverse DOFs, the controlling DOFs in the new implementation for the D modes are categorized into secondary DOFs (i.e., that can be determined from the controlling DOFs) whilst they are set as the controlling DOFs for L modes. Finally, numerical examples of several thin-walled steel members are illustrated to highlight the consistency of the new cFSM with current cFSM for open sections and the applicability to closed sections and sections with rounded corners.