Research on the relationship between comprehensive characteristics of cracks and stiffness of RC beams

The relationship between crack comprehensive characteristics and the stiffness of RC beams is investigated through experimental tests and numerical simulations. A synthetic parameter, the surface damage ratio (SDR), is proposed to represent the comprehensive characteristics of cracks, including crack width, length and location. Crack propagation in RC beams is simulated using a dual-damage parameter plastic damage model. A method for calculating the width and length of cracks is developed based on integral point strains and element equivalent length. The accuracy of this method is verified by comparing it with the results of four-point bending tests on RC T-beams and rectangular beams. Correlation analysis indicates that the cracks in different zones have varying impacts on beam stiffness, with crack length in the bending area and crack width in the shear area having a greater impact than others. To consider the comprehensive characteristics of cracks and their impact on beam stiffness, the SDR, the ratio between the entire crack area and the intact area of the beam surface, is proposed. The proposed parameter is shown to increase linearly with load, resulting in beam stiffness degradation following a power law. The accuracy and applicability of the proposed SDR and its correlation with load and stiffness are verified through load tests on rectangular beams with different reinforcement ratios using Cervenka’s test. Parameter analysis has shown that the section modulus, concrete strength, reinforcement arrangement, and ratios significantly influence how beam stiffness varies with SDR. The presented simulation model for concrete crack evolution, combined with the synthetic parameter of crack characteristics, and the correlation analysis, provide a valuable approach for the safety evaluation of concrete beams during their service life.