# Crack Propagation Law of Reinforced Concrete Beams
## 2 Comparison of Finite Element Model and Experiment Results  
### Overview of the Test  
To validate the accuracy of the finite element modeling, an Abaqus model is created based on the experimental investigation of crack propagation patterns in reinforced concrete simply supported beams documented in the literature [19]. The test beams have cross-sectional dimensions of 150 mm \(\times\) 250 mm, a total length of 1800 mm, and a calculated span of 1500 mm. The pads used in the experiment have cross-sectional dimensions of 150 mm \(\times\) 60 mm \(\times\) 20 mm. The reinforcement details are provided in Table 1 and the dimensions and reinforcement arrangement of the test beams can be seen in Figure 1, based on the results of the experimental study. Table 2 shows the reinforced concrete beams of different sizes. The effective spans are all 1500 mm but the shear span to effective depth ratios and the stirrup ratio are different. Taking JL-1.5-6-150 as an example, it indicates that the shear span to effective depth ratio is 1.5, the stirrup diameter is 6 mm, and the stirrup spacing is 150 mm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Diameter/mm** & **Material** & **Yield Strength/MPa** \\ \hline Longitudinal & 22 & HRB335 & 379.35 \\ Strut & 12 & HPB300 & 312.55 \\ Stirrup & 6/8 & HPB300 & 312.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties. Figure 1: Schematic diagram of the simply supported beam test. It should be noted that the experimental designs all used over-reinforced beams. The failure mode of concrete beams under bending is ductile; however, shear failure, if it occurs, tends to be brittle [20]. Shear failure poses a significantly higher risk compared to bending failure as it often lacks clear warning signs [21]. In practical projects, controlling the shear-to-span ratio and stirrup ratio helps mitigate the occurrence of shear failure in the inclined section of concrete beams. To elucidate the evolution of crack propagation in shear beams, it becomes necessary to conduct experimental studies on beams regarding more dangerous \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Species** & **Effective** & **Shear Span to** & **Concentrated** & & & \\
**Span/mm** & **Effective Depth Ratio** & **Load Span/mm** & & & \\ \hline JL-1-5-6-150 & 1500 & 1.5 & 338 & 6@150 & 0.25 \\ JL-1-5-8-200 & 1500 & 1.5 & 338 & 8@200 & 0.36 \\ JL-1-5-8-150 & 1500 & 1.5 & 338 & 8@150 & 0.45 \\ JL-2-0-6-150 & 1500 & 2.0 & 450 & 6@150 & 0.25 \\ JL-2-0-8-200 & 1500 & 2.0 & 450 & 8@200 & 0.36 \\ JL-2-0-8-150 & 1500 & 2.0 & 450 & 8@150 & 0.45 \\ JL-2-5-6-150 & 1500 & 2.5 & 563 & 6@150 & 0.25 \\ JL-2-5-8-200 & 1500 & 2.5 & 563 & 8@200 & 0.36 \\ JL-2-5-8-150 & 1500 & 2.5 & 563 & 8@150 & 0.45 \\ \hline \hline \end{tabular}  
* The Z-1 strain gauges were arranged in the bottom longitudinal reinforcement and the strain gauges L-1, L-2, R-1, and R-2 were arranged in the left and right shear-bend section hoops. The location of the stirrup strain gauge is illustrated in Figure 2, where stirrup-1 is situated near the loading point and stirrup-2 is positioned closer to the support end. The strain gauge is located at the point where the connection between the loading point and support end intersects with the stirrup-1 and stirrup-2 positions. The setup for the test is shown in Figure 3.  
\end{table} 
Table 2: Parameters of reinforced concrete beams. Figure 3: Reinforced concrete beam loading test device from reference [19]. Figure 2: Test beam stirrup strain gauge position. shear failure. Consequently, the tests use different shear-to-span ratios and stirrup ratios, employing an over-reinforced beam design. By doing so, it can be ensured that the concrete beam would not experience bending failure but rather shear-compression failure. As shown in Figure 4, each test beam was damaged in shear-compression damage.