Search

This paper presents a novel analytical solution for the buckling load in 3D of columns that fills a gap in the existing literature by accounting for shear deformation and spatial effects. The latter means that a column can be supported and buckle in any direction. We build on the foundational work of Simo and use a 3D beam model to derive a set of equations that form the basis for our analytical solution. The paper outlines the axioms of the Simo model, presents the corresponding equations, and describes the linearization procedure in details. By linearizing the equations we obtain a set of algebraic equations with boundary conditions, which we manipulate into an analytical solution for the buckling load. An illustrative example using a column with an elliptical cross-section shows how different boundary conditions and the spatial orientation of the column influence the buckling load. This research work not only contributes to the verification of numerical programs, but also provides engineers with a valuable tool for optimizing structural configurations. [ABSTRACT FROM AUTHOR]

This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic columns with preexisted longitudinal cracks and finite adhesion between the cracked sections. Consequently, the analytical solution for the buckling loads is derived for the first time. The critical buckling loads are calculated for two different types of connections between the cracked sections, namely for slipping only and simultaneous slipping and uplifting between them. The parametric study is performed to analyze the effect of the crack length on the critical buckling loads. It is shown that the critical buckling load can be greatly affected by the crack length and type of the connection between the cracked sections. Finally, the presented results obtained can be used as a benchmark solution. [ABSTRACT FROM AUTHOR]

This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic longitudinally cracked columns with finite axial adhesion between the cracked sections. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated for different crack lengths and various degrees of the contact adhesion. It is shown that the critical buckling loads can be greatly affected by the crack length and degree of the connection between the cracked sections. Finally, the presented results can be used as a benchmark solution. [ABSTRACT FROM AUTHOR]

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution. [ABSTRACT FROM AUTHOR]

This paper presents an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The model is based on the exact buckling model, response surface method, and Monte Carlo simulations. The probability of failure is investigated for a different number of random variables, sample points, and various degrees of response surfaces. The results show that the probability of failure is considerably affected by the type (deterministic or probabilistic) of the loading and its distribution. [ABSTRACT FROM AUTHOR]