Keywords: non-linearity, composite beam, slip, uplift, timber.

A new finite element formulation for the non-linear analysis of the mechanical behaviour of a composite planar beam is presented. A modified principle of virtual work is employed in formulating our finite element method. The basic unknowns are strains [1]. The following assumptions are considered in the mathematical model: the composite structure, applied loading and deformations are planar; the material of each layer is taken to be non-linear and homogeneous, but can differ from layer to layer; interacting shear and normal contact tractions between the layers results from non-linear contact shear traction-slip and normal contact traction-uplift characteristics of the connectors; the geometrically linear Bernoulli beam theory is assumed for each layer; a sufficiently small interlayer slip is assumed and the contact between the layers where slip and uplift are realized, is modelled with an additional layer of small thickness.

The suitability of the present theoretical approach and its numerical solution for the analysis of a two-layer timber beams is verified by comparing the numerical solution with the experimental results of a full-scale laboratory test on a simply supported beam investigated by Planinc et al. [2]. An excellent agreement between the measured and the calculated results is observed for all levels of loading.

We investigated in detail the influence of different normal contact traction-uplift constitutive relationships on the load-deflection and the load-end slip curves. It was observed that, for the range of the normal contact traction-uplift constitutive relationships employed in the analysis, the effect on the geometrical shape of curves is negligible; and that a very small effect on the ultimate load capacity occurs. The normal contact traction distribution for different normal contact traction-uplift relationships differed somewhat in the localized region around the application point. The influence of different normal contact traction-uplift relationships on the shear traction in the contact surface was negligible.

A fundamental difference in the normal traction distribution was observed when the point of application of the force was taken either at the top or in the lower layer. If the top layer is loaded, the normal contact traction is negative and highly localized in the loaded zone. By contrast, when the load acts on the bottom layer, the normal contact traction is positive, having several times smaller amplitude.

1

I. Planinc, M. Saje, B. Cas, "On the local stability condition in the planar beam finite element", Structural Engineering and Mechanics, 12(5), 507-526, 2001.

2

I. Planinc, S. Schnabl, M. Saje, J. Lopatic, B. Cas, "Numerical and experimental analysis of timber composite beams with interlayer slip", Engineering Structures, 30, 2959-2696, 2008. doi:10.1016/j.engstruct.2008.03.007

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