Time-dependent analysis of composite beams with continuous shear connection based on a space-exact stiffness matrix

In this article, the time-dependent behavior of continuous composite beams with partial interaction is investigated using a space-exact, time-discretized finite element formulation. The effects of creep and shrinkage taking place in a concrete slab are considered by using age-dependent linear viscoelastic models. The Euler–Bernoulli’s kinematical assumptions are considered for both the connected members and the shear connection is modeled through a continuous relationship between the interface shear flow and the corresponding slip. Based on above key assumptions and the time-discretized form of the constitutive relationships, the governing differential equations are derived in terms of the displacements at a generic instant. These equations are analytically solved and the corresponding space-exact stiffness matrix is deduced for a generic composite beam element. This stiffness matrix may be utilized in a classical finite element procedure for the time-dependent analysis of composite beams with partial interaction. The present finite element formulation requires a minimum number of elements depending on the support and loading conditions. Finally, a time-dependent analysis of two-span continuous composite beams is presented. The results compare favorably with experimental data as well as previous numerical studies. It can be seen that shrinkage and creep can have a significant influence on the beam’s deflection.