Analytic solution for the bond stress-slip relationship between rebar and concrete

Abstract

This paper presents a three stage bond stress-slip relationship between rebar and concrete under static and dynamic loads, with coordinate values at key points determined by an analytic solution. Based on the elastic mechanic solutions of a thick-walled cylinder under uniform pressure, radial stress and radial slip at the end of the elastic stage is proposed. When concrete cracks, the fictitious crack model of fracture mechanics is used to consider the softening behavior of concrete under tension. The radial stress and radial slip at the partial cracked stage and full cracked stage is presented, and the bond stress is deduced from the radial stress based on the equilibrium of forces. By assuming the rebar between adjacent ribs is a circular truncated cone, the relationship between slip and radial strain is established. Meanwhile, as an additional external constraint in the thick-walled cylinder model, the restraint of stirrups is taken into account. For the dynamic effect, the dynamic tensile strength and elastic modulus of concrete is introduced to consider the effect of the loading rate. The bond strength calculated by the presented model is compared with the experimental results, and the errors are generally within 15%. The presented bond stress-slip relationship is then used to simulate pull-out test specimens, including the effect of stirrups and loading rates by ABAQUS software. The comparison between simulated and experimental results shows that the proposed bond stress-slip relationship can successfully predict the bond stress-slip between rebar and concrete.