Keywords: composite beams, interlayer slip, reinforced concrete, differential shrinkage, creep, finite element method, Reissner beam.

Composite structures are defined as structures built up by structural self carrying subelements connected by shear connectors to form an interacting unit. The behavior of composite members depends to a large degree on the type of connection between the subcomponents. Rigid shear connectors usually develop full composite action between the individual components of the member, thus conventional principles of analysis can be applied. Flexible shear connectors, on the other hand, generally permit development of only partial composite action; therefore the analysis procedure requires consideration of the interlayer slip between the subelements. Extensive results of analytical and experimental investigation of layered beams with interlayer slip have been reported (Ayoub [1], Girhammer and Gopu [2], Saiidi et al. [3], Silfwerbrand [4], Wheat and Calixto [5]). In all these studies, only a small attention was given to the effects of the combination of geometrically and materially nonlinear behavior and to the interaction between subelements.

In this paper, a finite element formulation for the nonlinear analysis of two-layer beams and beam-columns with interlayer slip is presented. In the analysis of this layered member, the following assumptions are introduced: (1) the member, the applied loads, and the deformations lie in a plane; the plane of the loads is the plane of symmetry of the member; (2) material properties of each layer are constant along the length, but they can differ from one layer to the other; (3) no separation occurs between layers at any point along the member; (4) there is no friction at the interface between the two layers; the interaction between the layers follows from the connector load-slip characteristics; (5) for each layer, a geometrically nonlinear Reissner's beam theory is assumed with small interlayer slip; geometrical (displacements and rotations) and deformation (membrane, bending) variables are finite; (6) materials in all layers and the load-slip characteristics of the interface are assumed to be nonlinear.

A variety of finite element formulations of planar beams could be found in literature. Most employ simplified versions of Reissner's equations. A common practice is to express the deformation variables in terms of the geometrical ones, , , using kinematic equations; then by inserting these expressions into the constitutive relations and after employing these equations in the principle of virtual work, one obtains the displacement-based principle of virtual work. Disadvantages of such formulations are well known in the finite element literature. Poor convergence, stress oscillations and several kinds of locking are just few of them. In contrast to the displacement-based formulation, the present finite element formulation of composite frames employs a modified principle of virtual work, in which the unknown functions are extensional strains of the axis of the the layers and the pseudocurvature of the reference axis of the composite beam. The present approach uses the concept of the consistent equilibrium of constitutive and equilibrium-based stress-resultants, and employs the deformation variables of the beam as the basic unknown functions of the problem (Planinc et al. [6]). Displacements and rotations need not be approximated. Any kind of locking, poor convergence and stress oscillations are absent in these finite elements.

To show the validity of the present theoretical results and to illustrate the accuracy and efficiency of the derived finite element formulation of composite frames, we consider a computationally demanding case: the differential shrinkage and creep in reinforced concrete composite beams. An excellent agreement is obtained between the experimental results presented by Silfwerbrand [4] and the present numerical ones even when using only a few finite elements in modelling the concrete composite beam.

1

A. Ayoub, "A two-field mixed variational principle for partially connected composite beam", Finite Elements in Analysis and Design, 37, 929-959, 2001. doi:10.1016/S0168-874X(01)00076-2

2

U. A. Girhammer, V. K. A. Gopu, "Composite beam-columns with interlayer slip - exact analysis", Journal of Structural Engineering ASCE, 119, 1265-1282, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:4(1265)

3

M. Saiidi, S. Vrontinos, B. Douglas, "Model for the response of reinforced concrete beams strengthend by concrete overlays", ACI Structural Journal, 87, 687-695, 1990.

4

J. Silfwerbrand, "Stresses and strains in composite concrete beams subjected to differential shrinkage", ACI Structural Journal, 94, 347-353, 1997.

5

D. L. Wheat, J. M. Calixto, "Nonlinear analysis of two-layered wood members with interlayer slip", Journal of Structural Engineering ASCE, 120, 1909-1929, 1994. doi:10.1061/(ASCE)0733-9445(1994)120:6(1909)

6

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

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