## 2 Experimental Design
### STM Model Construction  
The optimal STM should fully reflect the load transfer mechanism of a structural member. To determine the load transfer path in an irregular concrete deep beam and understand the corresponding stress distribution and diffusion, a two-dimensional planar FEM was developed of the two groups of irregular concrete deep beam examples using ANSYS software. The analysis results are shown in Figures 2 and 3.  
It can be seen from Figure 2 that in the Group A irregular concrete deep beams, the principal tensile stress is high at the bottom of the beam midspan, the middle of the top of the opening, and the lower left corner of the opening. The tensile stress at the middle of the top of the opening is transferred diagonally to the upper left corner and to the upper right corner. The principal compressive stress at the loading point is transferred around the opening and diagonally toward the two end supports, the compressive stress is larger along the transfer path on the left side of the opening, and the compressive stress is concentrated at the corners of the opening, the concave corners of the variable cross sections, and the supports.  
It can be seen from Figure 3 that, in the Group B irregular concrete deep beams, the tensile stress is high at the bottom of the beam and at the upper right and lower left corners of the opening, the tensile stress at the upper right corner of the opening diffuses diagonally to the left upper part and to the right support, and the tensile stress at the lower left corner of the opening is transferred to the left support and the bottom of the beam at the lower right of the opening. When the load at the top of the beam is transferred to both end supports, most of the compressive stress is transferred diagonally to the right support. As a result, the compressive stress is high at the loading point and at the right support. It is also relatively high on the left side and at the lower right corner of the opening.  
To accurately and reasonably obtain the optimal STM, the BESO method was used to optimize the topology of each group of irregular concrete deep beams based on the aforementioned FE analysis [21; 22]. The corresponding optimal topologies were obtained, as shown in Figure 4. Figures 5 and 6 show the stress contour plots of the two groups of irregular concrete deep beams with optimal topologies.  
Based on the FE analysis results and the stress contour plots of the two groups of irregular concrete deep beams with optimal topology, the optimal STMs constructed in this study are shown in Figure 7 and are designated as STM A-04 and the STM B-04. In the figure, the solid line is the tie, the dashed line is the strut, and the circle is the joint.  
Figure 4: Optimal topology of the irregular concrete deep beams: (**a**) Group A beam; (**b**) Group B beam.  
Figure 5: Stress contour plots of the Group A irregular concrete deep beams with optimal topology: (**a**) principal tensile stress; (**b**) principal compressive stress.  
Several other researchers have also proposed their own optimal STMs for the two groups of irregular concrete deep beams investigated in this study and used those STMs to guide the reinforcement design. To facilitate a comparative analysis in this study, the two optimal STMs proposed by [PERSON] et al. [23] for the Group A irregular concrete deep beams were selected, as shown in Figure 8. They are designated as STM A-02 and STM A-03, with the joints in the models omitted. The two optimal STMs proposed by [PERSON] and [PERSON] [24] for the Group B irregular concrete deep beams were selected, as shown in Figure 9, and are designated as STM B-02 and STM B-03, with the joints in this model also omitted.  
Figure 8: Optimal STMs proposed by [PERSON] et al.: (**a**) STM A-02; (**b**) STM A-03.  
Figure 6: Stress contour plots of the Group B irregular concrete deep beams with optimal topology: (**a**) Principal tensile stress; (**b**) Principal compressive stress.  
Figure 7: Optimal STMs proposed in this study: (**a**) STM A-04 and (**b**) STM B-04.