Tension Chord Model Modification for Uniaxial Unloading and Reloading in Elastic and Plastic States

The bond properties between concrete and steel reinforcement influence structural stiffness and deformation behavior as a result of tension stiffening. In specific cases, the load-bearing capacity of engineering structures depends on the deformation behavior and may be affected by load history because of unloading and reloading (UR) cycles. The bond stress-slip relationship of the original tension chord model was modified to make it applicable for general UR cycles in the elastic and plastic states of the reinforcing steel by reducing the admissible bond shear stress, thus taking into account the progressive and irreversible damage to the concrete around the ribbed bar attributable to yielding and the load history. The residual tension stiffening in the elastic state is influenced by the degree of slip reversal, for which an analytical function was found that is dependent on the crack spacing, bond strength, and stress levels before and after unloading. The proposed analytical model was successfully validated with experimental results.