Discrete-Like Crack Simulation of Reinforced Concrete Incorporated with Analytical Solution of Cyclic Bond Model

Abstract

This paper presents solutions of second-order ordinary differential equations on bond problems to estimate crack widths of reinforced concrete (RC) members subjected to repeated cyclic loads. Up to now, bond behaviors under repeated cyclic loads have usually been calculated by a difference scheme. In contrast, this research adopts analytical solutions of the differential equations to calculate bond behaviors in finite element models where a number of concrete cracks occur. The conventional differential equation for the bond problem has been available only under monotonic loading conditions. This paper extends the equation to cases where the reinforcement becomes plastic and the bond is subject to unloading/reloading conditions. The bond stress-slip relationship is modeled by a multilinear model that is composed of an envelope made of five lines, unloading/reloading paths, and a negative friction path. The solution of the differential equation is classified into 25 cases when the bond stress-slip relationship is on the envelope and seven cases when on the unloading/reloading paths or the negative friction path. The solutions are implemented into the smeared crack-based finite-element method (FEM) to evaluate the crack widths of a RC beam subject to repeated cyclic flexural/shear loads. The FEM program is incorporated with the discrete-like crack procedure developed by the authors and calculates stress redistributions due to cracking using the solutions of the differential equations. Typical distributions of reinforcement stress, bond stress, and slip along the reinforcement are presented.