Modelling the complete behaviour of dapped-end connections along re-entrant corner cracks

Reinforced concrete dapped-end connections, which are common in existing Gerber-beam bridges, typically feature an inclined corner crack at service loads due to high stress concentrations in the re-entrant corner. These cracks exacerbate corrosion issues and increase the stresses in the dapped-end reinforcement, which in the event of further deterioration and increased loading may lead to yielding and failure of the connection. This paper proposes a kinematics-based model that predicts the opening of the corner crack based on first principles: compatibility, equilibrium, and constitutive relationships. The model stems from an earlier model for strength of dapped-end connections failing along re-entrant corner cracks and extends it to predict the crack widths under increasing load up to failure. The modelling assumptions are discussed, and the crack width predictions are extensively validated using 42 large-scale tests. The results show good agreement between measured and predicted crack widths, as well as the peak flexural resistance of dapped-end connections. The average experimental-to-predicted ratio for the flexural strength is 0.98 and the coefficient of variations is 8.8%.