Keywords: composite beam, interlayer slip, uplift, analytic solution, elasticity, mathematical model.

Layered planar beams belong to a group of composite structures. Composite beams are being increasingly employed in civil engineering. If specific material properties of various layers are optimally combined, the composite structure can be more efficient and cost-reducing. A variety of mathematical models and theories for the analysis of behaviour of composite beams have been developed during past decades.

This paper presents the analysis of a two-layer linear elastic beam, in which both the interlayer slip and uplift at an interface is considered. An original mathematical model is proposed and its analytical solution derived. Behaviour of composite beams depends to a large degree on the connection between the sub-elements. We assume linear relationships between the force and slip or uplift. An additional parameter of the model is thickness of the fictitious connecting layer much like in [1]. In principle, this parameter depends on layer material and the type of connection, and must be, for the actual beam, determined experimentally.

Our mathematical model of the composite beam assumes a continuously distributed connection at the contact of the layers. If the actual contact is point-wise, the statically equivalent distributed connection requires an average characteristic to be obtained.

Each layer of the composite beam is modelled by the classical linear beam theory. The key equations are the constraining equations between the layers. After these have been set up, the system of governing differential equations is reduced to a differential equation of the seventh order for slip at the interface. After the proper boundary conditions are considered, the solution of the boundary value problem is obtained in a closed analytical form.

The analytical solution makes it possible to carry out an extensive analysis of the effects of the transverse and shear contact stiffnesses and the thickness of the connecting layer on the stress and strain state of two-layer timber beams. It has been established that:

• The transverse contact stiffness between the layers has not only an essential influence on the tangential contact traction, but also significantly dictates uplift of the contact interface at the point of application of the force. It is somewhat surprising, however, that the transverse stiffness has only a minor influence on the equilibrium, deformation and kinematic quantities of the structural engineer's interest. Consequently, the delamination can be neglected in engineering design.
• The thickness of the connecting layer is also found to be a less important parameter that does not contribute to the accuracy of the strain and stress state of two-layer timber beams. Thus, it can be neglected in the engineering analysis.
• The axial force in the nails close to the point of application of an external force could be very large for small transverse contact stiffnesses.

1

Cas B., Bratina S., Saje M., Planinc I., "Non-linear analysis of composite steel-concrete beams with incomplete interaction", Steel and Composite Structures, 4(6), 489-507, 2004.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)