Time-Dependent Analysis of Shear-Lag Effect in Composite Beams

Abstract

Taking into account the long-term behavior of the concrete, this paper proposes a model for analyzing the shear-lag effect in composite beams with flexible shear connection. By assuming the slab loss of planarity described by a fixed warping function, the linear kinematics of the composite beam is expressed by means of four unknown functions: the vertical displacement of the whole cross section, the axial displacements of the concrete slab and of the steel beam, and the intensity of the warping (shear-lag function). A variational balance condition is imposed by the virtual work theorem for three-dimensional bodies, from which the local formulation of the problem, which involves four equilibrium equations with the relevant boundary conditions, is achieved. The assumptions of linear elastic behavior for the steel beam and the shear connection and of linear viscoelastic behavior for the concrete slab lead to an integral-differential type system, which is numerically integrated. The numerical procedure, based on the step-by-step general method and the finite-difference method, is illustrated and applied to a composite beam to get information on the complex time-dependent behavior, including shear-lag and connection deformability effects.