A space-exact beam element for time-dependent analysis of composite members with discrete shear connection

This paper presents a space-exact, time-discretized solution for the time-dependent analysis of composite beams with partial interaction. The time effects considered in this model are creep and shrinkage of the concrete slab. The constitutive model adopted to describe the time effects is linear viscoelasticity with time-dependent coefficients to account for ageing. By using the time-discretized form of the constitutive relations, the equilibrium equations in terms of the displacements at a generic instant are analytically solved. Based on the analytical expressions (exact in space) of the displacements and the internal forces, the space-exact stiffness matrix is deduced for a generic composite beam element. This stiffness matrix can be used in a displacement-based procedure for the time-analysis of continuous composite steel–concrete beams with arbitrary support and loading conditions. The present formulation requires a minimum number of elements depending on the support and loading conditions. The proposed hybrid analytical–numerical method is used to investigate both the short-term and the long-term deflections of simply supported composite beams in order to assess the calculation method proposed in Eurocode EN 1994-1-1 [21]. The effects of creep, shrinkage and degree of shear connection on the deflection of simply supported composite beams are also analyzed. The long-term deflection calculated with the analytical model based on the rules given in EN 1994-1-1 [21] is compared against the one predicted by the proposed model. It is found that EN 1994-1-1 [21] slightly underestimate the long-term deflection. It was also observed that the contribution of shrinkage to the deflection is more significant than suggested in EN 1994-1-1 [21].