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The paper presents a static analysis of the buckling and post-buckling state of thin-walled cold-formed steel (TWCFS) lipped channel section beam-columns subjected to eccentric compression. Eccentricity is taken into consideration relative to both major and minor principal axes. An analytical–numerical solution to the buckling and post-buckling problems is described. The solution is based on the theory of thin plates. Equations of equilibrium of section walls are derived from the principle of stationary energy. Then, to solve the problem, the finite difference (FDM) and Newton–Raphson methods are applied. Linear (buckling) and nonlinear (post-buckling) analyses are performed. As a result, pre- and post-buckling equilibrium paths are determined. Comparisons of the obtained numerical results, FE simulation results, and experimental test results are carried out and presented in comparative load-shortening diagrams. Additionally, a comparison of the buckling forces and buckling modes obtained from theoretical analysis and experiments is presented. [ABSTRACT FROM AUTHOR]

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For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations. These components are nonlinearly dependent on the plate deflection. The magnitudes of components of transverse forces for the four theories under consideration were compared. [ABSTRACT FROM AUTHOR]

The present paper deals with the interactive buckling of thin-walled lipped channel (LC) beams under the bending moment in the web plane when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) was adopted for LC beams. The structures were assumed to be simply supported at the ends. A modal method of solution to the interactive buckling problem within Koiter's asymptotic theory, using the semi-analytical method (SAM) and the transition matrix method, was applied. LC-beams, from short through medium-long via long to very long beams, were considered. The paper focuses on the influence of the secondary global buckling mode on the load carrying capacity for the steel LC-beams under bending. [ABSTRACT FROM AUTHOR]

In the present paper, a methodology for determination of a value of the bifurcation shortening and the corresponding bifurcation load of the real thin-walled laminated column under compression with initial imperfections, using an axial shortening versus squared deflection amplitude plot, is presented. A plate model of the column has been assumed. It has been shown that the post-buckling state is described with a linear relationship on this plot, whereas a value of the bifurcation shortening corresponds to a free term of the straight line approximating the post-buckling state on the plot and is proportional to the bifurcation load. Detailed calculations have been conducted for short composite angle columns under uniform compression. The eigenvalue problem and the non-linear post-buckling problem have been solved with the semi-analytical method (SAM) based on Byskov-Hutchinson's method and the finite element method (FEM). The bifurcation shortening and the corresponding bifurcation load have been determined. An effect of the imperfection amplitude on the post-buckling behaviour of laminated thin-walled angle columns has been analysed. General configurations of laminate plies have been selected. All columns have been simply supported at both ends. A very good agreement between the results attained with both the methods for solving the non-linear problem has been obtained. [ABSTRACT FROM AUTHOR]