# Crack Propagation Law of Reinforced Concrete Beams
## 2 Comparison of Finite Element Model and Experiment Results
### Comparison of the Experimental and Finite Element Modeling of Strains  
The load-strain curves of the bottom longitudinal reinforcement in the test are compared with the finite element simulation results, as shown in Figure 8, and the test results are in good agreement with the finite element simulation structure. It can be seen that for the RC beams with different shear-to-span ratios, the load-strain curves of the bottom longitudinal reinforcement are close to the linear relationship without inflection points, indicating that the longitudinal reinforcement at the bottom of the reinforced concrete beams has not yet reached the yield state. The error of finite element simulation in predicting the strain-load curve of the longitudinal reinforcement, compared to the test, is reflected in the specimen JL-2.5-8-200, which is 9.83%.  
Based on the data from both the test and the finite element simulation, as shown in Figure 9, it is evident that the JL-2.5-8-200 test beam enters the elastic-plastic state earlier than the test beams with shear span to effective depth ratios of 1.5 and 2.0. When the load reaches approximately 70 kN, the test beam transitions into the elastic-plastic state, which aligns well with the test results. Throughout the entire loading process, the test beam exhibits a complete elastic-elastic-plastic damage progression. Initially, before the test beam develops cracks (elastic stage), the deflection increases linearly with the applied load. Once cracking initiates (elastic-plastic stage), the rate of deflection increase accelerates. As the load continues to increase (failure stage), the deflection grows rapidly.  
The load-stirrup strain curve shows that in the stage of slight damage, before the concrete cracks, the shear force in this stage is mainly borne by the concrete and the shear force borne by the stirrup is very weak; thus, the stirrup strain of the test beam is extremely small and fluctuates around 0.  
As the beam transitions into the stage of stable damage growth, the shear force is gradually transferred from the concrete to the stirrup, particularly when the bending shear inclined crack appears. As a result of the shear stress, the stirrup strain increases gradually. With the continued increase in shear force, multiple abdominal shear oblique cracks appear and their widths continue to expand. The shear force borne by the stirrup increases significantly and reaches a second inflection point where the stirrup strain increases rapidly. Figure 10 indicates that the strain at stirrup-1 agrees well with the test results; whereas, the strain growth rate at stirrup-2 is lower than the test results in the comparison between the original test and finite element simulation results but the trend remains the same.  
The longitudinal strain-load curve, stirrup strain-load curve, and deflection curve are in good agreement with those obtained by Abaqus finite element analysis; however, the interaction and slip between concrete and steel bars are not considered, resulting in a small strain and the calculated deflection of steel bars, that is, a large calculated stiffness.  
Figure 7: Abaqus mesh model.  
Figure 8: Load–strain comparison curve between test and finite element. (**a**) \(\lambda=1.5\); (**b**) \(\lambda=2.0\); (**c**) \(\lambda=2.5\).