Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects

Abstract

This paper is focused on elastic stability problems of partial composite columns: the conditions for the axial load not to introduce any pre-bending effects in composite columns; the equivalence, similarities and differences between different sandwich and partial composite beam theories with and without the effect of shear, with and without the effect of axial extensibility, and also the effect of eccentric axial load application. The basic modelling of the composite beam-column uses the Euler-Bernoulli beam theory and a linear constitutive law for the slip. In the analysis of this reference model, a variational formulation is used in order to derive relevant boundary conditions. The specific loading associated with no prebending effects before buckling is geometrically characterized, leading to analytical buckling loads of the partial composite column. The equivalence between the Hoff theory for sandwich beam-columns, the composite action theory for beam-columns with interlayer slip and the corresponding Bickford-Reddy theory, is shown from the stability point of view. Special loading configurations including eccentric axial load applications and axial loading only on one of the sub-elements of the composite beam-column are investigated and the similarity of the behaviour to that of imperfect ordinary beam-columns is demonstrated. The effect of axial extensibility on kinematical relationships (according to the Reissner theory), is analytically quantified and compared to the classical solution of the problem. Finally, the effect of incorporating shear in the analysis of composite members using the Timoshenko theory is evaluated. By using a variational formulation, the buckling behaviour of partial composite columns is analysed with respect to both the Engesser and the Haringx theory. A simplified uniform shear theory (assuming equal shear deformations in each sub-element) for the partial composite beam-column is first presented, and then a refined differential shear theory (assuming individual shear deformations in each sub-element) is evaluated. The paper concludes with a discussion on this shear effect, the differences between the shear theories presented and when the shear effect can be neglected.

Energy methods for curved composite beams with partial shear interaction

“…For admissible variation of u, ϕ 1 , ϕ 2 , which are δu, δϕ 1 and δϕ 2 are arbitrary expect where the kinematic boundary conditions are specified. Since with arbitrary admissible variation of u,…”

“…It may be the connection between the beam components is perfect only in normal direction and the connection is not perfect in tangential direction. A lot of works deal with numerical and analytical solution of straight layered composite beam with imperfect shear connections [1][2][3][4][5][6][7][8]. In papers [1][2][3][4] variational principles for layered straight beams with imperfect shear connections are formulated and used to get approximate solutions.…”

“…A lot of works deal with numerical and analytical solution of straight layered composite beam with imperfect shear connections [1][2][3][4][5][6][7][8]. In papers [1][2][3][4] variational principles for layered straight beams with imperfect shear connections are formulated and used to get approximate solutions. We note that there are a lot of works on the static problems of layered curved composite beams with perfect shear connections, such as [9][10][11][12][13][14][15].…”

Stability analysis of three-layer shear deformable partial composite columns

“…Schnabl and Planinc (2011) investigated the buckling of two-layer Timoshenko beams including the extensibility effect and Haringx's theory, with a differential shear model (with the possibility to have different rotation kinematics for each layer). Challamel and Girhammar (2011) considered both the uniform and the differential shear beam model and compared both Engesser's and Haringx's approach for various boundary conditions. Le et al (2012) also considered the differential shear beam model with Engesser's theory and they obtained similar results as proposed by Challamel and Girhammar (2011) .…”

“…Challamel and Girhammar (2011) considered both the uniform and the differential shear beam model and compared both Engesser's and Haringx's approach for various boundary conditions. Le et al (2012) also considered the differential shear beam model with Engesser's theory and they obtained similar results as proposed by Challamel and Girhammar (2011) . Komijani et al (2013) studied thermal buckling behaviour of two-layer shear deformable beams with partial interaction between the layers.…”