In this paper, one first presents the main steps involved in the formulation and numerical implementation of a GBT-based finite element incorporating the geometric stiffness reduction associated with applied stresses displaying non-uniform (linear, quadratic or cubic) longitudinal distributions. Then, taking full advantage of the GBT modal features, the above finite element is employed to investigate the influence of the longitudinal stress gradients on the local-plate, distortional and global buckling behavior of thin-walled steel beams. In particular, one presents and discusses numerical results concerning the buckling behavior of simply supported lipped channel cold-formed steel beams subjected to various non-uniform bending moment diagrams. For validation purposes, one also compares some GBT-based critical stresses with values reported in the literature.
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