Analytical Model of Crack Opening in Reinforced Concrete Structures Based on DCE

This study focused on the advanced analysis of the crack resistance of reinforced concrete structures and provides proposals for improvement of the theory of calculation of reinforced concrete structures for serviceability and ultimate limit state. Despite the fact that the crack opening is a key parameter of reinforced concrete structures that frequently determines the reinforcement area, the design models and theory of calculation of this parameter are still not sufficiently perfect. The recent studies performed worldwide with the use of more advanced instrumentation have shown that the accuracy of theoretical prediction of crack opening in structures experiencing a complex stress–strain state, and especially structures made of high-strength concrete, fiber-reinforced concrete, lightweight concrete, and etc., remains unsatisfactory. This study analyzed and summarizes experimental studies of crack resistance of reinforced concrete structures and reveals new physical regularities in the deformation of concrete and steel reinforcement in zones adjacent to the crack. It introduces hypotheses that account for these regularities and proposes a general block model for calculating the width of irregular and single cracks in reinforced concrete structures under different stress states. In this model, crack opening is modeled by the double-cantilever element (DCE), which allows incorporation of the corresponding experimentally revealed effects and at the same time combines deformation parameters of both the theory of reinforced concrete and fracture mechanics. The DCE is two conventionally separated rigid cantilevers that include the crack surfaces, and are embedded on one side in the concrete at the neutral axis. On the other side, they are connected with reinforced steel bars crossing the crack. Using this model, a method for calculating the crack opening width in reinforced concrete structures with different types of cracks is proposed. The paper demonstrates the results of experimental investigations of crack resistance of simply supported and cantilever beams made of ordinary, light, and high-strength concrete. These results confirm the effects considered in the calculation model and the hypotheses accepted in the theory. The study also provides a physical explanation of the phenomena under consideration and shows acceptable agreement between theoretical and experimental values of crack opening calculated according to the proposed theory.