Dynamic And Static Problems For Composite Beams With Partial Interaction

Of the various types of structural system, steel-concrete composite beam developed from the steel and concrete mainly consists of three components including the steel girder, the steel-concrete slab and the shear connectors. Due to the individual advantage that steel mainly bears the tension force and the steel-concrete slab mainly bears the compression, the steel-concrete composite beam is superior to steel or concrete when they are used exclusively. To improve the performance of the composite beam, this paper aims at analyzing in depth the static and dynamic behavior of the composite beam with interlayer slip, including vibration, buckling, shear-lag and torsion.This paper presents the state space formulation by adopting the generalized displacements and generalized forces as the basic variables for the vibration of the Euler-Bernoulli and Timoshenko partial-interaction composite beam. The formulation can deal with the boundary conditions and the continuity conditions conveniently and avoid the derivative of the load function in the equation as reported in literature. Based on the concept of symplectic inner product, two orthogonality relations for the free vibration modes of the partial-interaction composite beam are established. The procedure of solving the natural frequencies and free vibration modes, the analytical solution to the inhomogeneous state equation by virtue of mode superposition method and the joints coupling matrix method for single and multi-span composite beams are also presented. Then the buckling, natural frequency and modes are calculated and the analysis is further extended to nonuniform composite beams.For unsymmetric box-girder composite beam, we suggest to use different longitudinal displacement functions for the top slab, web, bottom slab and flange. Based on the symplectic system mechanics, the Hamilton formulas of the partial-interaction Timoshenko composite beam with the shear-lag effect are established, which can be degenerated into the full-interaction situation. The shear-lag effect of the single or multi-span, uniform or nonuniform composite box-girder beams is then conveniently analyzed by virtue of joints coupling matrix.The free torsion and constraint torsion of partial-interaction composite beams are also investigated. Based on the principle of minimum potential energy, the governing equation and the boundary conditions are derived. The analytical solution of warping function for the free torsion of bars with rectangular section is presented, in which we use the proper exponential functions instead of hyperbolic functions to avoid the numerical instability. The finite element formulation is also presented to analyze the free torsion of composite beams with arbitrary section. The solution of the constraint torsion which can be degenerated into the free torsion situation is obtained by iteration.