Analytical solutions for the viscoelastic response of composite beams including partial interaction

This paper addresses the issue of the deformations that occur in composite steel-concrete beams caused by the quasi-viscoelastic effects of creep and shrinkage of the concrete slab, and in which the effects of partial shear interaction (PI) at the interface between the slab and the steel joist are included in the analysis. By making recourse to an algebraic representation of the viscoelastic response of the concrete, the formulation in this paper leads to a unique and useful solution of the problem in closed form, which follows from the establishment of a second order linear differential equation. The solution therefore does not require a discretisation along the beam as is usually required for numerical techniques, but only one discretisation in the time domain, and furthermore the resulting solution is generic in the sense that it may be applied for a variety of loading and restraint conditions. Specific solutions, which are validated against a numerical technique reported elsewhere, are presented for the cases of a simply supported beam, an encastré beam and for a propped cantilever.