Nonlinear steel strains in cracked RC beams based on bond-stress profiles

Abstract

Steel–concrete bond is instrumental in transferring tensile forces to the concrete via the bond stresses, whose values and distribution along a steel bar vary with the level of the load applied to the reinforcement. To study the profile of the strains in the reinforcement, the variation of the bond-stress distribution is considered and the bond stresses are introduced according to Model Code 2010. The transfer length where the bond stresses are active is shown to be a function of the slip in the cracked sections. This slip can be evaluated from the concrete strains based on the plane-section hypothesis to take care of the strain compatibility between the concrete and the reinforcement. The equilibrium of the internal forces, the constitutive laws of the materials and the bond stress-slip law make it possible to model the kinematic interaction between the concrete and the reinforcement. An iterative algorithm is proposed to calculate the steel strains, and the effectiveness of the numerical procedure is checked against the test data coming from simply-supported RC beams tested in this research project or available in the literature. The results show that the nonlinear evolution of steel–concrete slip close to the cracks may increase the transfer length of the bond stresses by 50% under increasing loads, and the steel strains by up to 90% along the bonded length. As a result, the steel-strain profile becomes a slightly-nonlinear function of the load, which is also markedly affected by the crack pattern.