Analytical solution for layered composite beams with partial shear interaction based on Timoshenko beam theory

• Two-layered beam with interlayer slip is considered.
• Timoshenko beam model is used.
• Slip-cross sectional rotation formulation is developed.
• Analytical solutions are given for deflection, slip and stresses.

The authors present an analytical solution for two-layered beam with interlayer slip. Timoshenko’s kinematic assumptions are used for both layers imposing the constraint of equal cross-sectional rotation. A linear constitutive equation between the horizontal slip and the interlaminar shear force is considered. The applied loads act in the plane of symmetry of composite beam and the material and geometrical properties do not depend on the axial coordinate. Analytical solution for the deflection, slip, cross-sectional rotation and internal forces are derived. The effect of the cross-sectional shear deformation to the deflection is analyzed. Closed form solutions are given for the stresses. A Rayleigh-Betti type reciprocity relation for composite shear deformable beam with interlayer slip is formulated, whose applications are illustrated by some examples.