## 3 Experimental Results
### Shear Behavior
#### 3.4.3 Size Effects on Shear Behavior  
The shear strength of the RC beams increased with increases in the beam width and/or effective depth. However, the increase in the shear strength was not proportional to the increase in the beam size, even though the shear span-to-effective depth ratio was constant, as shown in Table 5, which presents the experimental data of the shear strength test of the RC beam, without shear reinforcement, using a natural aggregate ([PERSON] [23]). The beam size doubled by maintaining a shear span-to-effective depth ratio (_a/d_) of 3.0 and a reinforcement ratio (\(\rho\)) of 1.35%. [PERSON] reported that the average shear stress of the half-sized beams increased by a factor of 1.14 or 1.21, compared to that of the original beams. In contrast, the current experimental results indicated that the average shear stress of the small beams was 1.7 times higher than that of the large beams, regardless of the recycled aggregate quality. Dowel action contribution with the different \(\rho\) might have caused a difference of the shear strength between the small and large beams. The ultimate shear strength increased as the beam size increased. However, the shear stress calculated by Equation (2) was almost identical. In addition, the \(v_{u}\) of the small specimens was typically higher than that of the large specimens. In the JIS, the ultimate shear strength of the RC beam due to diagonal shear failure was calculated using Equation (3). \[v_{u}=\frac{V_{u}}{b_{w}d} \tag{2}\]  
\[V_{u}=0.2f_{c}^{1/3}(100p_{w})^{1/3}(\frac{10^{3}}{d})^{1/4}(0.75+\frac{1.4d}{ a})b_{w}d \tag{3}\]  
where \(v_{u}\) was the ultimate shear stress (MPa), \(V_{u}\) was the ultimate shear strength due to diagonal shear failure (N),\(f_{c}^{r}\) was the compressive strength of concrete (MPa), \(p_{w}=A_{s}/b_{w}d\) was the longitudinal tensile reinforcement ratio, \(d\) and \(b_{w}\) were the effective depth and width of the rectangular cross-section beam (mm), respectively, and \(a\) was the shear span (mm). Figure 20: Shear strength of the RC beams and material properties of the concrete. Table 6 shows the experimental results of the shear strength of the RC beams, using a natural and recycled coarse aggregate concrete, without the shear reinforcement. The effective depth of the large beams was two times larger than that of the small beams. However, the large and small beams had the same cross-sectional area of reinforcement, resulting in half the reinforcement ratios for large beams, at 1.32%, versus 2.65% for the small beams. The shear strengths obtained experimentally were typically smaller than the estimated values, which ranged from 0.85 to 1.27. For the large beams, the ultimate shear strength was consistent with the compressive strength of concrete, regardless of the effect of the recycled aggregate quality. However, the current estimation equation appeared to overestimate the shear strength of the large beam for all types of aggregate. Although the specimens had enough anchorage length and the local rebar slip at the anchorage region was not observed during the loading test, the splitting cracks as shown in Figure 16, might have affected the shear strength. For the small beams, the ultimate shear strength of the natural aggregate increased from 46.39 to 51.55 kN, whereas the shear strength of all specimens made of recycled aggregate decreased to 43.90, 36.30, and 37.35 kN, for the high-, medium-, and low-quality recycled aggregate, respectively, irrespective of the compressive strength. The effects of the recycled aggregate quality could be clearly observed among the small beams. The aggregate interlocking mechanism had a greater influence on the shear strength of the smaller beam sizes. Similarly, the shear strength of the RC beams with different specimen sizes, shear span-to-effective depth ratios, and recycled aggregate types, found in the literature, are shown in Table 7. The recycled aggregate used in each experiment was classified, based on its density and water absorption, using the JIS.