Constrained spline Finite Strip Method for thin-walled members with open and closed cross-sections

The present paper aims at introducing the constrained spline Finite Strip Method (csFSM). The proposed approach is basically a spline Finite Strip Method (spline FSM) that allows the modal decomposition. Similarly to the constrained Finite Strip Method (cFSM), some mechanical assumptions are made in order to constrain the general spline FSM model to buckle in specific modes, for example to enforce the member to buckle in the local-plate mode, or distortional mode. Derivation of matrices that define the distortional (D) and global (G) modes for thin-walled members with unbranched open and closed cross-sections is the main objective of this paper. To define these subspaces, a standard practice is followed which consists in forming RGD, the constraint matrix of the combined GD space, then, RG and RD the constraint matrices of pure global and distortional buckling modes, respectively. Mechanical criteria are used to derive RGD and RG matrices, while orthogonality conditions are used to derive RD matrix. The implementation of the mechanical criteria is done by using FEM procedure rather than the cFSM one. Moreover, some practical aspects on how to constrain a spline FSM model are also discussed, including how to force the torsional mode of closed cross-sections. Numerical examples of modal decomposition are provided for a column - beam problem, with standard boundary conditions. The distortional and global buckling loads obtained are found to be in good agreement with those calculated via the cFSM and the Generalized Beam Theory (GBT). The paper concludes with a discussion on the applicability of csFSM in cold-formed steel member design.