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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 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 a new mathematical model for analytical investigation of global buckling behavior of slender concrete-filled steel tubular (CFST) columns with circumferential gaps and partial debonding between the concrete core and the steel tube. The analytical buckling load of circular and slender CFST columns with circumferential gaps and partial debonding is derived for the first time. The critical buckling load decreases as the magnitude and length of the circumferential gap increases. Nevertheless, it is shown that if the length of the circumferential gap is smaller than the length of the CFST column, this effect is less than 4%. On the other hand, for a fully delaminated CFST column, this effect can be up to approximately 40%. Similarly, the first buckling shape modes proved to be notably affected by the circumferential gap only if its length is greater than 75% of the CFST column length. The results can be used as a benchmark solution for the buckling problem of slender circular CFST columns with circumferential gaps and partial debonding between the materials. [ABSTRACT FROM AUTHOR]

This paper presents an exact model for studying the global buckling of concrete-filled steel tubular (CFST) columns with compliant interfaces between the concrete core and steel tube. This model is then used to evaluate exact critical buckling loads and modes of CFST columns. The results prove that interface compliance can considerably reduce the critical buckling loads of CFST columns. A good agreement between analytical and experimental buckling loads is obtained if at least one among longitudinal and radial interfacial stiffnesses is high. The parametric study reveals that buckling loads of CFST columns are very much affected by the interfacial stiffness and boundary conditions. [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]

Abstract: The present case study is an example of the use of reliability analysis to asses the failure probability of a tapered glulam beam. This beam is part of a true structure built for a super market in the town of Kokemäki in Finland. The reliability analysis is carried out using the snow load statistics available from the site and on material strength information available from previous experiments. The Eurocode 5 and the Finnish building code are used as the deterministic methods to which the probabilistic method is compared to. The calculations show that the effect of the strength variation is not significant, when the coefficient of variation of the strength is around 15% as usually assumed for glulam. The probability of failure resulting from a deterministic design based on Eurocode 5 is low compared to the target values and lower sections are possible if applying a probabilistic design method. In fire design, if a 60min resistance is required, this is not the case according to Eurocode 5 design procedures, a higher section would be required. However, a probabilistic based fire analysis results in bounds for the yearly probability of failure which are comparable to the target value and to the values obtained from the normal probabilistic based design. [Copyright &y& Elsevier]

A mathematical model is proposed and its analytical solution derived for the analysis of the geometrically and materially linear two-layer beams with different material and geometric characteristics of an individual layer. The model takes into account the effect of the transverse shear deformation on displacements in each layer. The analytical study is carried out to evaluate the influence of the transverse shear deformation on the static and kinematic quantities. We study a simply supported two-layer planar beam subjected to the uniformly distributed load. Parametric studies have been performed to investigate the influence of shear by varying material and geometric parameters, such as interlayer slip modulus (K), flexural-to-shear moduli ratios (E/G) and span-to-depth ratios (L/h). The comparison of the results for vertical deflections shows that shear deformations are more important for high slip modulus, for “short” beams with small L/h ratios, and beams with high E/G ratios. In these cases, the effect of the shear deformations becomes significant and has to be addressed in design. It also becomes apparent that models, which consider the partial interaction between the layers, should be employed if beams have very flexible connections. [ABSTRACT FROM AUTHOR]

The paper presents the analytical model of a linear two-layer composite beam with partially debonded interlayer contact. The interlayer contact may be also locally fully debonded. The two-dimensional model is materially and geometrically linear, and the governing equations are based on Reissner beam theory. In the partially debonded interlayer contact, only axial slips are allowed. The finger joints are modelled as linear springs. The analytical solution is presented. The kinematic and equilibrium variables are evaluated along the simply supported beam. A parametric study was carried out to analyse the effect of the strength of finger joints and interlayer contact. In addition, different lengths and positions of the fully debonded area of the interlayer contact were analysed, and their effects on selected kinematic and equilibrium variables were observed and commented on. It was shown that the presence of the fully debonded interlayer contact and finger joints significantly affects the behaviour of the beam as well as the stiffness properties of the interlayer contact and finger joints. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of strain-based finite elements for modelling composite beams with finger joints considering slip between the layers. The finite elements are derived according to Reissner beam theory based on the modified principle of virtual work where the displacements and rotations are eliminated from the problem and the axial deformation, shear deformation and curvature of the layers remain only functions to be approximated within the finite element. Lagrange polynomials are used as shape functions to approximate the deformations and various interpolation methods are applied to numerical examples, with the Lobatto integration scheme giving slightly better results than Equidistant. The experimentally measured mechanical properties needed as input data for the numerical model are given for the four glued laminated beech beams. The numerical model is thoroughly verified and validated. The results show that the presented finite element formulation is an efficient tool for practical and accurate calculations. • New finite elements for composite beams with slip and finger joints are proposed. • Numerical model is validated and verified with experimental results. • The finite elements exhibit no slip and shear locking. [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]