Evaluation of bond–slip behaviour of embedded rebars through control field equations

Abstract

Anchorage of steel bars is critical in reinforced concrete design to ensure composite action between concrete and rebars. The force–slip relationship of rebars is another factor governing the failure mode and rotation of structural joints. These two aspects can be predicted by bond–slip models and depend on bond behaviour at the reinforcement–concrete interface. However, current bond–slip models show either low accuracy and limited applications due to simplified assumptions or complicated computation due to nested iteration loops. This paper proposes analytical models derived from control field equations, which are characterised by low computational cost, high accuracy and broad application. The control field equations describe force equilibrium of embedded rebars by second-order differential equations and give accurate predictions by incorporating the local bond stress–slip relationship. The proposed models are appropriate for adequate and inadequate embedment lengths of rebars and can describe the evolution of the bond–slip distribution along embedment length. Closed-form solutions can be obtained for perfect anchorage and obviate iterative nested computations. If closed-form solutions are unavailable, owing to free-end slip for short embedment length, a mathematical function in Matlab is used to solve non-linear control field equations and complicated nested iteration is avoided. Finally, the proposed models show good agreement with published experimental results.