# Crack Propagation Law of Reinforced Concrete Beams
###### Abstract  
During the process of the shear and bending failure of reinforced concrete beams, the cracks generated on the side of the beam are mostly type I-II composite cracks. Considering the material nonlinearity and geometric irregularity of reinforced concrete, it is of great significance to study the dynamic evolution law of crack propagation in reinforced concrete members. Crack propagation consists of the elongation of the crack length at the surface of the concrete material, as well as the widening of the crack width. In this paper, a finite element model of simply supported reinforced concrete beams is established by considering material nonlinearity and geometric nonlinearity and considering the damage of the concrete. Comparing the experimental results, the finite element model can accurately reflect the strain changes of longitudinal reinforcement and stirrups with a maximum error within 10%. The crack development of concrete is basically consistent with the experimental results. It shows the accuracy of the finite element analysis. On this basis, a beam-column joint is analyzed and its crack propagation under reciprocating load is investigated. An important contribution is made to the preliminary analysis of the actual crack control project. The nonlinear finite element results show that the compressive damage to the concrete of the joint is insignificant at 0.1. but the tensile damage is significant at 0.96. The cracks in the connection between the frame and the floor slab mainly show bending cracks and the concrete damage in the floor slab is higher than that in the beam. reinforced concrete beam; crack; damage propagation; finite element analysis 2024 1409. 1409. 1  
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essential to thoroughly investigate the propagation of cracks during the failure process of reinforced concrete beams. [PERSON] [10] performed numerical and continuum media mechanics simulations of flexural shear crack propagation in concrete beams without transverse reinforcement. The study involved using numerical and continuum media mechanics simulations to investigate flexural shear crack propagation in concrete beams without transverse reinforcement. The researchers utilized concrete damage plastic material modeling to develop the model, incorporating the crack propagation method and the diffuse cracking method. By comparing the crack patterns observed in actual beam tests with the results obtained from different finite element models, the study aimed to gain insights into crack propagation and internal force redistribution within concrete members. Crack width, interface roughness between cracks, and concrete strength have an effect on the shear transfer capacity of the cracked interface [11; 12]. [PERSON] [13] conducted an experimental study on the shear performance of continuous beams of lightweight aggregate concrete and fitted a discount factor for the shear capacity, which was related to the maximum aggregate particle size, density, and splitting tensile strength of lightweight aggregate concrete. [PERSON] [14] derived an expression for crack propagation resistance in ordinary three-point bending concrete specimens and investigated the influence of the span/height ratio on the fracture process of three-point bending concrete beams. The findings indicate that the crack propagation resistance curve exhibits an increase with crack propagation and both the curve and the fracture process zone curve are unaffected by the span/height ratio. However, they do demonstrate an increase with the specimen height. [PERSON] [15] presents an analytical method for determining the resistance curve to crack extension in concrete. It is assumed that crack extension starts when the difference between the stress intensity factor due to external force and the stress intensity factor due to cohesive force in the fracture process zone is equal to the initial crack toughness.