Mechanical Behaviors Of Partial-interaction Composite Beams Using Timoshenko’s Beam Theory

Based on the kinematic assumptions of Timoshenko’s beam theory, this paper firstly presents the principle of virtual work and reciprocal theorem of work of the composite beams with partial interaction.Then the principle of minimum potential energy and minimum complementary energy are derived and proved. The variational principles for the fi-equency of free vibration and critical load of buckling are also deduced afterward as well as the mixed variational principle with two types of variables. These variational formulae are all rendered in terms of shearing force, bending moment and axial force as well as corresponding deflection, rotation angle and interlayer slip, which can be applied conveniently for analyzing of composite beams. According to the proposed variational principles, the governing equations of static bending, free vibration and buckling can be obtained for the partial-interaction composite members as well as the corresponding boundary conditions. Finally, some numerical examples are presented and compared with the other solutions available in literatures to demonstrate the present theory.Similar to the homogeneous beams, there is not only Euler-Bernoulli beam theory but also Timoshenko beam theory which takes the shear deformation into account for the analysis of partial-interaction composite beams. By analyzing the constitutive relationships and equations of equilibrium, this work derives the relationships of solutions between single-span Euler-Bernoulli and Timoshenko partial-interaction composite beams. The integral constants are also presented for different boundary conditions. Through the results. The Timoshenko partial-interaction composite beam’s solutions could be readily obtained as long as the ones of the corresponding Euler-Bernoulli counterparts were known.The shear connectors of simply supported partial-interaction composite beams are redistributed along the span with "triangular shape" in order to decrease the interlayer slip. Then the differential equation of interlayer slip is derived and solved, which is suitable for not only Timoshenko partial-interaction composite beams but also Euler-Bernoulli ones. Through numerical calculation and analysis, it is found that the interlayer slip decreases significantly for the beams with triangular shaped connectors, which may provide basis and new idea for the design of shear connectors for partial-interaction composite beams.