Keywords: multilayered planar beams, composites, interlayer slip, transverse shear deformation, exact analysis, elasticity.

Due to their economy of construction and a good bearing capacity, layered composite systems are widely used in buildings and bridges. The behaviour of layered structures largely depends on the flexibility of connection between the layers. Rigid connectors develop a full action between the individual components, so that conventional principles of the solid beam analysis can be employed. Flexible connectors, on the other hand, permit the development of only a partial interaction. As a result, an interlayer slip develops, with a sufficient magnitude to have a major effect on the deflection and stress distribution of the composite system.

The building codes allow that a structural engineer can perform a fully linear analysis for the determination of stress resultants. In a linear analysis, the governing equations of the mathematical model are linear and can be solved analytically. Many exact analytical solutions of simply supported, layered planar beams for combinations of simple loading cases and simple boundary conditions have been presented in professional literature, e.g.Cosenza and Pecce[1], Fabbrocino[2], Girhammar and Gopu[3], Girhammar and Pan[4], Goodman and Popov[5], Jasim and Mohamad[6], Newmark[7], Ranzi and Bradford[8], Smith and Teng[9], Wang[10]. There seems to be no exact solution reported on multilayered simply supported beams with consideration of transverse shear deformation. The principal novelty of the present paper is to fill the gap with the rational incorporation of transverse shear deformation into one-dimensional finite-strain multilayered beam theory. With this effect incorporated, the theory is more harmonious than the corresponding classical theory of multilayered beams where transverse shearing strains are not taken into account. Our formulation of the planar layered beam uses the following assumptions: (1) material is linear elastic; (2) displacements, strains and rotations are small; (3) shear deformations are taken into account (the 'Timoshenko beam'); (4) strains vary linearly over each layer; (5) the layers are continuously connected and slip modulus of the connection is constant; (6) friction between the layers is not considered; (7) the number of layers is arbitrary; (8) the shapes of the cross-sections are symmetrical with respect to the plane of deformation and remain unchanged in the form and the size during deformation.

The analytical solution of the generalized equilibrium equations of a structure is obtained by solving a set of inhomogeneous ordinary linear differential equations with constant coefficients along with the boundary conditions and the boundary values for interlayer slips and normal contact stresses.

The exact solution of multilayered beams is general, but relatively easy to comprehend. It is illustrated by an analysis of the mechanical behaviour of a number of two-layer simply supported beams composed from different materials. In additon, the influence of transverse shear deformation is studied and thus various parametric studies are made.

1

E. Cosenza, M. Pecce, "Shear and normal stresses interaction in coupled structural systems", Journal of Structural Engineering, ASCE, Vol. 127, 84-88, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:1(84)

2

G. Fabbrocino, G. Manfredi, E. Cosenza, "Modelling of continuous steel-concrete composite beams: computational aspects", Computers & Structures,Vol. 80, 2241-2251, 2002. doi:10.1016/S0045-7949(02)00257-2

3

U. A. Girhammar and V. A. Gopu, "Composite beam-columns with interlayer slip-exact analysis", Journal of Structural Engineering, ASCE, Vol. 119, No. 4, 1265-1282, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:4(1265)

4

U. A. Girhammar and D. Pan, "Dynamic analysis of composite member with interlayer slip", International Journal of Solids and Structures, Vol. 30, No. 6, 797-823, 1993. doi:10.1016/0020-7683(93)90041-5

5

J. R. Goodman and E. P. Popov, "Layered wood systems with interlayer slip", Wood Science, Vol. 1, No. 3, 148-158, 1969.

6

N. A. Jasim and A. A. Mohamad, "Deflections of composite beams with partial shear connection", The Structural Engineer, Vol. 75, No. 4, 58-61, 1997.

7

N. M. Newmark, C. P. Siess, I. M. Viest, "Test and analysis of composite beams with incomplete interaction", Proceedings of the Society for Experimental Stress Analysis, Vol. 1, 75-92, 1951.

8

G. Ranzi, M. A. Bradford, B. Uy,,"A general method of analysis of composite beams with partial interaction", Steel and Composite Structures, Vol. 3, No, 3, 169-184, 2003. doi:10.1016/j.compstruc.2006.07.002

9

S. T. Smith, J. G. Teng, "Interfacial stresses in plated beams", Engineering Structures, Vol. 23, 857-871, 2001. doi:10.1016/S0141-0296(00)00090-0

10

Y. C. Wang, "Deflection of steel-concrete composite beams with partial shear interaction", Journal of Structural Engineering, ASCE, Vol. 124, No. 10, 1159-1165, 1998. doi:10.1061/(ASCE)0733-9445(1998)124:10(1159)

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