## 3 Test Results and Analysis  
### Crack Morphology  
Figure 15 shows the crack morphology of the Group A irregular concrete deep beam specimens at failure. In the figure, C\({}_{\text{r1}}\), C\({}_{\text{r2}}\), and C\({}_{\text{r3}}\) was the sequence of crack initiation in the specimen. When the load at the top of the beam specimens in this group passed around the opening on both sides and was transferred to the two end supports, because the loading point was closer to the left support the stress on the left side of the force transfer path was relatively higher. The test phenomenon of the plain concrete specimen A-01 is shown in Figure 15a. The cracks C\({}_{\text{r1}}\) and C\({}_{\text{r2}}\) were the fracture cracks at the failure of the specimen, and the other cracks were those generated during the collision and removal of the specimens after fracture. According to the failure pattern, the weak regions of the specimens in this group were the region between the upper part of the opening and the loading point as well as the region between the lower left corner of the opening and the left support. Because the stress was concentrated at the corners of the opening and the loading point, along with the proximity of the loading point to the upper left corner of the opening, the concrete between the upper left corner of the specimen and the loading point cracked first, i.e., crack C\({}_{\text{r1}}\) was generated. When the loading effect became large, the diagonal crack C\({}_{\text{r2}}\) was formed between the lower left corner of the opening and the left support, and crack C\({}_{\text{r3}}\) was generated due to the cracking at the bottom of the beam under tension. In the STM A-02 of this specimen, there are only two horizontal ties (rebars) limiting the propagation of crack C\({}_{\text{r1}}\), while there are no corresponding orthogonal bar members (rebars) to limit cracks C\({}_{\text{r2}}\) and C\({}_{\text{r3}}\). Eventually, specimen A-02 failed in shear along crack C\({}_{\text{r1}}\), as shown in Figure 15b. \begin{table}
\begin{tabular}{c c c c} \hline
**Diameter (mm)** & **Yield Strength \(f_{y,m}\) (MPa)** & **Ultimate Strength \(f_{u,m}\) (MPa)** & **Yield Strain \(\epsilon_{y,m}\) (10\({}^{-6}\))** \\ \hline
8 & 332 & 420 & 1661 \\
10 & 340 & 511 & 1701 \\
12 & 497 & 626 & 2483 \\ \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of rebars. It can be seen from the STM A-03 that there is no tie placed at the bottom of specimen A-03. Therefore, the concrete first cracked at the bottom of the beam at the midspan, and the crack propagated upward along the tie (rebar) on the right side of the opening until reaching the left side of the opening, i.e., generating crack C\({}_{\text{r1}}\). Subsequently, crack C\({}_{\text{r2}}\) was created at the upper right corner of the opening. Due to the restriction of the tie (rebar) at the upper right corner of the opening, crack C\({}_{\text{r2}}\) did not continue to grow. When the loading effect became large, the vertical crack C\({}_{\text{r3}}\) was created between the lower right corner of the opening and the bottom of the beam at the midspan, and the width of this crack increased rapidly. Eventually, specimen A-03 failed due to the fracture of the concrete at cracks C\({}_{\text{r1}}\) and C\({}_{\text{r3}}\), as shown in Figure 15c. In the STM A-04 the bar members are sparsely arranged and ties (rebars) are provided at the bottom of the specimen, the upper part of the opening, and the lower left corner of the opening to limit or delay the generation of cracks. A diagonal crack C\({}_{\text{r1}}\) was first formed in the specimen between the upper left corner of the opening and the loading point. As the diagonal crack C\({}_{\text{r1}}\) propagated continuously, cracks C\({}_{\text{r2}}\) and C\({}_{\text{r3}}\) were formed in the upper right part of specimen A-04, which eventually failed in shear along crack C\({}_{\text{r1}}\). Its failure pattern was similar to that of specimen A-02, as shown in Figure 15d.