An analytical model based on cross-sectional geometric characteristics for calculating crack opening displacement in reinforced concrete beams

To accurately calculate crack opening displacement (COD) in reinforced concrete beams, this study establishes a relationship between COD, cross-sectional rotation, and strain distribution by utilizing the geometric relationships of deformation in the cracked region. Based on the varying bond characteristics between the reinforcement and concrete, a method is developed to calculate COD by analyzing the nonlinear strain distribution in both materials and determining the sectional rotation of the cracked beam. This proposed method was validated through experimental tests on a cracked reinforced concrete beam model. The results indicate that, as the load increases, the bond stiffness between the reinforcement and concrete diminishes, leading to nonlinear changes in the tensile strain of the reinforcement. This results in an increasing slope of the crack opening displacement with increasing load, showing a clear nonlinear trend, even under small loads. However, a linear relationship is observed between crack opening displacement and structural deflection. The proposed method, based on the geometric relationship of sectional deformation, accurately predicts these nonlinear deformations, offering a novel approach for calculating crack opening displacements.