Unified Flexural Design Method for Deep and Shallow Beams Using Non-Linear Grid Model

Abstract

The fundamental design theory of reinforced concrete deep beams is not consistent with that of shallow beams due to non-compliance with the plane section assumption. This paper proposes a grid model that is valid for the flexural capacity prediction and reinforcement design of both shallow and deep beams, which unifies the design process and extends the sectional analysis to deep beams. The grid model is actually based on structural analysis such that stress distribution can be calculated automatically without the plane section assumption. In order to apply sectional design principles, it assumes that design of the critical section is independent of the status of other sections, which means that other sections will remain elastic when the critical section fails. As a result, by inserting the concerned section into the grid model with non-linear material constitutive relationship and failure criteria, the capacity prediction and reinforcement design on that section can be achieved. The axial grid in the grid model guides the design of the flexural reinforcement in two kinds of layouts. Two series of experiments are listed to validate the model. The results of the proposed method are also compared with other wellestablished methods, for example traditional sectional method, layered section approach and strut-and-tie model (STM) method.