# Prediction of Shear Strength of Reinforced Recycled Aggregate Concrete Beams without Stirrups

^{1}

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## Abstract

**:**

_{w}) of 1.16% and 1.81%. It was found that the normalized shear stresses of RAC beams with ρ

_{w}= 1.81% at all levels of replacement percentage were quite similar to those of the NAC counterparts. Moreover, the normalized shear stress of the beam with 100% RCA and ρ

_{w}= 1.16% was only 6% lower than that of the NAC beam. A database of 128 RAC beams without shear reinforcement from literature was analyzed to evaluate the accuracy of the ACI 318-19 shear provisions in predicting the shear strength of the beams. For an RCA replacement ratio of between 50% and 100%, it was proposed to apply a reduction factor of 0.75 to the current ACI code equation to account for the physical variations of RCA, such as replacement percentage, RCA source and quality, density, amount of residual mortar, and physical irregularity.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Materials Properties

#### 2.2. Concrete Mixture Proportions

#### 2.3. Details of Test Beams

_{w}). The first group consisted of five beams reinforced with three 16-mm deformed bars in the tension zone (ρ

_{w}= 1.16%). The second group used longitudinal reinforcement of three 20-mm deformed bars (ρ

_{w}= 1.81%). One third of the beam span did not contain stirrups, in order to induce shear failure in this region. Stirrups were installed on the remaining two-thirds of the beam span to prevent shear failure on this side of the beam.

_{w}= 1.81%). Likewise, RCA25-DB16 indicated that the beam incorporated 25% RCA and three 16-mm longitudinal bars (ρ

_{w}= 1.16%).

#### 2.4. Test Setup and Procedure

## 3. Results and Discussion

#### 3.1. Ultimate Capacity and Failure Behaviour

_{u}, and shear force at failure V

_{test}(i.e., half of P

_{u}). At cracking loads of approximately 40 kN and 50 kN for DB16 and DB20 series, flexural cracks developed at mid-span but these were very small. At ultimate load, an inclined crack suddenly appeared and caused the failure of the beams. The diagonal cracks for all beams were similar. The diagonal cracks of NAC beams were approximately 38 degrees, while crack angles of RAC beams were between 30 to 36 degrees. All of the beams failed in shear when the inclined flexural-shear crack propagated to the beam compression zone. At ultimate load, the lower tip of diagonal crack also penetrated towards the support. The mode of failures of the RAC beams was similar to that of beams tested in previous studies [27,29,31].

#### 3.2. Load-Deflection Responses

_{w}= 1.16% and 1.81%, respectively. Before the first flexural cracks, all beams behaved in a linear elastic manner. Beams in the DB16 series (ρ

_{w}= 1.16%) lost some stiffness at the first cracking loads of approximately 40 kN. For beams in the DB20 series (ρ

_{w}= 1.81%), the first cracking loads were about 50 kN, at which point the beams’ stiffness started to degrade. The deflections of all tested beams were limited and less than 7 mm. These results were similar to tests reported by other researchers [30,32,39], as the beams failed in shear before the yielding of the longitudinal reinforcement. It was also reported that additional deformation due to shear cracks increase the overall deflection of the beam by up to 25% after the formation of shear cracks [44].

_{test}/bd) normalized by the square root of the concrete cylinder strength, f’

_{c}. V

_{test}represents ultimate shear in N, f’

_{c}represents the concrete compressive strength in MPa, b represents the width of beam section (in mm), and d represents effective depth (in mm). These figures allow comparisons of shear strength with different concrete compressive strengths. Figure 6 shows the ratios of normalized shear stress in the RAC and NAC beams. From Figure 4b and Figure 6, the differences in normalized shear stress between the RAC and NAC beams were less than 6% for the beams with ρ

_{w}= 1.16% (DB16 series). It was also observed that the amount of RCA slightly affected the normalized shear stresses of the tested beams. The normalized shear stresses of the beams in this latter series were approximately 0.21. According to ACI 318-14 shear provisions, the normalized shear stress of RC beams is 0.17. It was evident that all RAC beams with ρ

_{w}= 1.16% had normalized shear stress higher than the ACI 318-14 shear equation. From Figure 5b and Figure 6, a similar trend was observed for beams with ρ

_{w}= 1.81% (DB20 series). Normalized shear stresses of the NAC and RAC beams in this series were approximately 0.29, and the amount of RCA barely affected the normalized shear stress of the tested beams, as shown in Figure 6. These results contradicted several previous tests by other researchers [30,31,32,33,34], which reported much lower shear strength in RAC beams compared to NAC beams. However, some researchers reported similar shear strength in RAC and NAC beams [28,29]. To the author’s knowledge, the disagreement of test results may be attributed to the source and quality of concrete waste used to produce RCA. In this study, RCA was obtained by crushing good quality concrete waste with an approximate compressive strength of 30 MPa.

## 4. Prediction of Concrete Shear Strength

_{c}) was investigated. In order to allow for easier comparisons, the partial safety factors for material, as well as load and resistance factors adopted by the different design standards, are not included in the equation below.

#### 4.1. Ultimate Concrete Shear Strength

_{c}is the shear provided by concrete (N), f’

_{c}is the specified compressive strength of concrete cylinder (in MPa), b is the width of cross-section (in mm), and d is the effective depth (in mm). This simplified shear equation has been utilized for several decades and is still being used in shear calculations in some countries. Therefore, the shear strength of the tested beams was also compared to this legacy equation.

_{v}< A

_{v,min}), the shear equation is:

_{w}is the ratio of the longitudinal reinforcement area (A

_{s}) to bd and λ

_{s}is the size effect modification factor, defined as:

_{test}/V

_{c}from ACI 318-14 and ACI 318-19 are also shown in column (7) and (9) of Table 5, respectively. It is shown that V

_{test}/V

_{c}in column (7) of Table 5 ranged from 1.22 for the 100% RAC beam to 1.29 for the NAC beam with ρ

_{w}= 1.16%. For the beams with ρ

_{w}= 1.81%, V

_{test}/V

_{c}were 1.73 for the NAC beam and 1.69 for the 100% RAC beam, correspondingly. Figure 7 compares the shear strength from the tests (V

_{test}) with V

_{c}predicted by the ACI 318-14 simplified equation and the ACI 318-19 new shear equation. The shear strength of all tested specimens was higher than the ACI 318 shear prediction. From the graph, it is clear that the V

_{c}predicted by ACI 318-19 is more conservative than ACI 318-14 for ρ

_{w}= 1.16% (DB16 series). However, for ρ

_{w}= 1.81% (DB20 series), the ACI 318-19 shear strength is slightly higher than that given by ACI 318-14. It is also evident that the shear equation in both ACI 318-14 and ACI 318-19 provisions conservatively estimated the shear strength of RAC beams. Furthermore, these values of V

_{test}/V

_{c}shown in the column (7) and (9) in Table 5 indicate a slightly higher margin of safety for NAC over RAC beams.

#### 4.2. Effect of Longitudinal Reinforcement

_{w}in the shear expression, as indicated in Equation (2). The difference between normalized shear stress predicted by ACI 318-14 and ACI 318-19 shear provisions at different longitudinal reinforcement ratios is plotted in Figure 8. It is evident that for ρ

_{w}higher than 1.8%, the shear prediction by ACI 318-14 is lower. However, for low ρ

_{w}, ACI 318-19 yields more conservative predictions. The test results from this study showed higher normalized shear stresses for all tested beams compared to both shear equations.

#### 4.3. Effect of RCA Replacement Ratio

_{test}/V

_{c}predicted by ACI 318-14 and ACI 318-19 for the different RCA replacement percentages and longitudinal reinforcement ratios examined in this study. ACI 318-19 shear provisions consider size effects from the effective depth of beam section, as well as the longitudinal reinforcement ratio (ρ

_{w}). For beams with ρ

_{w}= 1.16% (3DB16), V

_{c}from ACI 318-19 was lower than ACI 318-14. For the beams with ρ

_{w}= 1.81%, V

_{c}from both ACI 318-14 and ACI 318-19 were quite similar. However, higher V

_{c}was expected from ACI 318-19 shear provisions when ρ

_{w}was greater than 1.8, as discussed in the previous section. The decreasing trends in V

_{test}/V

_{c}were observed when the amount of RCA increased, particularly in cases of lower ρ

_{w}(DB16 series)

_{.}However, the decrease rate was low where V

_{test}/V

_{c}of RCA100 was only 6%, and 2.2% lower than that of the NAC beams with ρ

_{w}= 1.16% and 1.81%, respectively.

## 5. Modifications to Code Equation to Allow for the Use of RCA

#### 5.1. Proposed RCA Uncertainty Factor to Existing Design Equation

_{c}), effective depth (d), shear span-to-effective depth ratio (a/d), and longitudinal reinforcement ratio (ρ

_{w}). The shear force at failure in all of the tested beams was denoted V

_{test}. V

_{c}was calculated according to the ACI 318-19 shear provisions, as expressed in Equations (2) and (3).

_{test}/V

_{c}. All unconservative results were from beams with an effective depth below 300 mm. Sixty-nine beams with an effective depth greater than 300 mm yielded conservative shear predictions.

_{test}/V

_{c}. It is obvious that the ratios of shear strength were high for a/d = 1.5, where an arch action played an important role in providing shear resistance. For slender beams where a/d was at least 2.5 or higher, 10 unconservative results were observed out of 109 tests. Figure 10e shows the effect of ρ

_{w}on the ratios of shear strength. The longitudinal reinforcement ratio (ρ

_{w}) has been recently introduced to ACI 318-19 shear provisions. Before 2019, the shear provisions of ACI 318 offered a simplified equation of shear strength, as shown in Equation (1). Using this equation, other studies on the shear strength of RAC beams with a low longitudinal reinforcement ratio (ρ

_{w}< 1%) exhibited 18 unconservative results out of 128 tests [32,36,42], (Figure 11). On the other hand, ACI 318-19 predicted lower shear strength V

_{c}for a low longitudinal reinforcement ratio, thus reducing unconservative V

_{test}/V

_{c}to only four tested beams for ρ

_{w}< 1.0% (Figure 10e).

_{test}/V

_{c}of beams with a/d greater than 2.5, in which ACI 318 shear equations are applicable for slender beams. ACI 318-14 yielded some unconservative results, while ACI 318-19 provided a higher average shear strength ratio.

_{c}from ACI 318-14. They found some unconservative results and recommended a reduction factor to account for the detrimental effect of using RCA. Their suggested modification of the simplified ACI 318-14 shear equation was as follows:

_{c}is the shear strength (in MPa), f’

_{c}is the concrete compressive strength (in MPa), λ

_{d}is the reduction factor for lightweight aggregate, and λ

_{R}is the reduction factor for RCA inclusions. Rahal and Alrefaei [32] recommended λ

_{R}= 0.8 in concrete with RCA and 1.0 in concrete with NCA.

_{r}, is proposed, as discussed in the following section.

#### 5.2. Model Validation and Compared to Existing Test Data

_{r}on the number of unconservative results predicted by ACI 318-19 and ACI 318-14 when a/d is greater than 2.5, which is typical for slender beams. It should be noted that unconservative V

_{test}/V

_{c}values for the ACI 318-14 simplified shear equation come from tested beams with ρ

_{w}less than 1.0%.

_{test}/V

_{c}predicted by the ACI 318-19 shear equations at different RCA levels. Based on the results in the figure, two β

_{r}were proposed depending on the level of RCA replacement. For RCA replacement levels between 0% and 50%, β

_{r}= 0.9 was proposed, whereas for RCA between 50% and 100% replacement ratio, β

_{r}= 0.75 was recommended so that the ACI 318-19 shear equation did not yield unconservative shear strength ratio. Thus, the ACI 318-19 shear strength equation can be modified as follows:

_{w}is the ratio of longitudinal reinforcement area (A

_{s}) to bd, λ

_{s}is the size effect modification factor defined in Equation (3), λ is the reduction factor for lightweight aggregate, and β

_{r}is the proposed reduction factor for RCA incorporation: β

_{r}= 0.75 for RCA replacement ratios between 50% and 100%, or otherwise β

_{r}= 0.9.

_{r}reduction factor accounts for the (i) physical variations of RCA, such as replacement ratio, source, density, amount of residual mortar, and physical irregularities, as reported by several researchers [5,14,15,16,17,18], and (ii) lower shear strength of RAC beams compared to NAC beams [30,31,32,33,34]. The detailed results of the shear strength of the beams in the database using Equations (4) and (5) is included in Appendix A. Equations (1), (2), (4) and (5) yield an average V

_{test}/V

_{c}equal to 1.27, 1.40, 1.59, and 1.72 respectively. It is evident that the highest V

_{test}/V

_{c}of 1.72 yields the most conservative predictions for all ranges of RCA replacements when using Equation (5), which includes β

_{r}proposed in this study.

_{test}) and the proposed shear strength (V

_{c}), as defined in Equation (5). Mean and standard deviation (SD) values are included in the plot. It can be seen that the proposed modified equation yielded most of the shear strength ratios within the range of the mean ± standard deviation. The proposed shear equation was also conservative (V

_{test}/V

_{c}> 1) for all levels of RCA replacement ratios.

#### 5.3. Design Recommendations

_{r}= 0.75 for RCA replacement ratios between 50% and 100% is suggested for the ACI 318-19 shear equation to yield the best results without an unconservative shear strength ratio. A reduction factor of β

_{r}= 0.9 is suggested for RCA replacement ratios not greater than 50%. Typical aggregate sizes below 25 mm are recommended, as the tested beams in the database used RCA sizes smaller than 25 mm. However, the nature of the shear behavior of reinforced concrete beams is complex, and more tests on RAC beams are required to fully validate these design recommendations.

## 6. Conclusions and Future Works

- For beams with a longitudinal reinforcement ratio of 1.16%, the normalized shear stress of the 100% RAC beam was 6% lower than that of the NAC counterpart.
- The normalized shear stress of RAC and NAC beams with a longitudinal reinforcement ratio of 1.81% had a minimal difference.
- The shear failure modes of RAC and NAC beams were similar. However, the crack inclination angles of NAC beams were slightly higher.
- The current ACI 318-19 shear equation conservatively estimates the shear strength of RAC beams when the replacement percentage is less than 75%.
- For a longitudinal reinforcement ratio less than 1.8%, the ACI 318-19 shear equation yielded lower shear strengths (V
_{c}) than the ACI 318-14 simplified equation, thus increasing the safety factor of shear stress ratios found in previous tests in the literature. - A reduction factor of 0.75 for RCA between 50% and 100% is proposed to the current ACI code provision to account for the physical variations of RCA, such as percentage replacement, source, density, percentage of residual mortar, and physical irregularity.
- The modified ACI equation for predicting the concrete shear strength of RAC beams was calibrated using eight test data carried out by the authors, and then further verified and calibrated against 120 test data from the literature. The use of the modified ACI equation as a design recommendation for predicting the concrete shear strength of RAC beams gives conservative predictions for all levels of RCA up to 100% replacement.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Comparison of concrete shear strength of RCA in concrete beams without shear reinforcement by current ACI codes and modified equations.

Reference | ID | % RCA | f’_{c}(MPa) | b (mm) | d (mm) | a/d | ρ_{w}(%) | V_{test}(kN) | Equation (1) | Equation (2) | Equation (4) | Equation (5) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

This study (2021) | 1 | 25 | 35.7 | 200 | 260 | 3.08 | 1.16 | 67.50 | 52.9 | 46.0 | 42.3 | 41.4 |

2 | 50 | 29.0 | 200 | 260 | 3.08 | 1.16 | 59.50 | 47.6 | 41.4 | 38.1 | 37.3 | |

3 | 75 | 32.9 | 200 | 260 | 3.08 | 1.16 | 62.50 | 50.7 | 44.2 | 40.6 | 33.1 | |

4 | 100 | 31.9 | 200 | 260 | 3.08 | 1.16 | 61.00 | 50.0 | 43.5 | 40.0 | 32.6 | |

5 | 25 | 30.7 | 200 | 260 | 3.08 | 1.81 | 83.85 | 48.9 | 49.4 | 39.2 | 44.5 | |

6 | 50 | 23.0 | 200 | 260 | 3.08 | 1.81 | 72.50 | 42.4 | 42.8 | 33.9 | 38.5 | |

7 | 75 | 34.0 | 200 | 260 | 3.08 | 1.81 | 87.50 | 51.6 | 52.0 | 41.2 | 39.0 | |

8 | 100 | 29.5 | 200 | 260 | 3.08 | 1.81 | 81.15 | 48.0 | 48.5 | 38.4 | 36.3 | |

Wardeh and Ghorbel (2019) [35] | 9 | 100 | 34.5 | 200 | 225 | 1.5 | 1.78 | 130.00 | 44.9 | 45.6 | 35.9 | 34.2 |

10 | 100 | 34.5 | 200 | 225 | 1.5 | 1.78 | 150.30 | 44.9 | 45.6 | 35.9 | 34.2 | |

11 | 100 | 34.5 | 200 | 225 | 1.5 | 1.78 | 140.40 | 44.9 | 45.6 | 35.9 | 34.2 | |

12 | 100 | 34.5 | 200 | 225 | 3 | 1.78 | 50.20 | 44.9 | 45.6 | 35.9 | 34.2 | |

13 | 100 | 34.5 | 200 | 225 | 3 | 1.78 | 49.00 | 44.9 | 45.6 | 35.9 | 34.2 | |

Pradhan et al. (2018) [34] | 14 | 100 | 46.7 | 200 | 270 | 2.6 | 1.31 | 92.28 | 62.7 | 56.3 | 50.2 | 42.2 |

15 | 100 | 46.8 | 200 | 270 | 2.6 | 0.75 | 81.29 | 62.8 | 46.8 | 50.2 | 35.1 | |

16 | 100 | 46.5 | 200 | 270 | 2.6 | 0.75 | 81.10 | 62.6 | 46.6 | 50.1 | 35.0 | |

Etman et al. (2018) [33] | 17 | 15 | 22.6 | 150 | 250 | 2 | 2.14 | 55.50 | 30.3 | 32.6 | 24.2 | 29.4 |

18 | 30 | 21.5 | 150 | 250 | 2 | 2.14 | 36.50 | 29.6 | 31.9 | 23.7 | 28.7 | |

19 | 45 | 20.0 | 150 | 250 | 2 | 2.14 | 35.50 | 28.5 | 30.7 | 22.8 | 27.7 | |

20 | 30 | 21.4 | 150 | 250 | 1 | 2.14 | 41.50 | 29.5 | 31.8 | 23.6 | 28.6 | |

21 | 30 | 21.2 | 150 | 250 | 3 | 2.14 | 29.00 | 29.4 | 31.6 | 23.5 | 28.5 | |

22 | 30 | 23.8 | 150 | 250 | 2 | 2.14 | 43.00 | 31.1 | 33.5 | 24.9 | 30.2 | |

23 | 30 | 22.0 | 150 | 250 | 2 | 2.14 | 37.00 | 29.9 | 32.2 | 23.9 | 29.0 | |

Ignjatović et al. (2017) [29] | 24 | 50 | 33.4 | 200 | 235 | 4.2 | 4.09 | 91.75 | 46.2 | 61.8 | 37.0 | 55.6 |

25 | 100 | 34.5 | 200 | 235 | 4.2 | 4.09 | 104.75 | 46.9 | 62.8 | 37.5 | 47.1 | |

Rahal and Alrefaei (2017) [32] | 26 | 10 | 36.6 | 150 | 388 | 3 | 0.79 | 44.50 | 59.9 | 41.0 | 47.9 | 36.9 |

27 | 20 | 35.0 | 150 | 388 | 3 | 0.79 | 40.05 | 58.5 | 40.1 | 46.8 | 36.1 | |

28 | 20 | 35.3 | 150 | 388 | 3 | 0.79 | 48.90 | 58.8 | 40.2 | 47.0 | 36.2 | |

29 | 35 | 35.3 | 150 | 388 | 3 | 0.79 | 45.05 | 58.8 | 40.2 | 47.0 | 36.2 | |

30 | 50 | 38.1 | 150 | 388 | 3 | 0.79 | 46.95 | 61.1 | 41.8 | 48.9 | 37.6 | |

31 | 75 | 36.6 | 150 | 388 | 3 | 0.79 | 47.40 | 59.9 | 41.0 | 47.9 | 30.7 | |

32 | 100 | 35.8 | 150 | 388 | 3 | 0.79 | 42.50 | 59.2 | 40.5 | 47.4 | 30.4 | |

33 | 5 | 37.4 | 150 | 388 | 3 | 0.79 | 56.00 | 60.5 | 41.4 | 48.4 | 37.3 | |

34 | 10 | 34.8 | 150 | 388 | 3 | 0.79 | 52.50 | 58.4 | 40.0 | 46.7 | 36.0 | |

35 | 16 | 35.4 | 150 | 388 | 3 | 0.79 | 54.20 | 58.9 | 40.3 | 47.1 | 36.3 | |

36 | 23 | 34.0 | 150 | 388 | 3 | 0.79 | 47.25 | 57.7 | 39.5 | 46.2 | 35.5 | |

37 | 35 | 35.1 | 150 | 388 | 3 | 0.79 | 42.50 | 58.6 | 40.1 | 46.9 | 36.1 | |

Katkhuda and Shatarat (2016) [39] | 38 | 50 | 25.2 | 206 | 260 | 2 | 1.90 | 58.94 | 45.7 | 46.9 | 36.6 | 42.2 |

39 | 50 | 25.2 | 206 | 260 | 3 | 1.90 | 49.07 | 45.7 | 46.9 | 36.6 | 42.2 | |

40 | 100 | 23.2 | 206 | 260 | 2 | 1.90 | 55.04 | 43.9 | 45.0 | 35.1 | 33.7 | |

41 | 100 | 23.2 | 206 | 260 | 3 | 1.90 | 46.45 | 43.9 | 45.0 | 35.1 | 33.7 | |

Sadati et al. (2016) [38] | 42 | 50 | 32.0 | 305 | 375 | 3.2 | 1.27 | 117.40 | 110.0 | 89.1 | 88.0 | 80.2 |

43 | 50 | 35.5 | 305 | 375 | 3.2 | 2.03 | 111.60 | 115.9 | 109.7 | 92.7 | 98.8 | |

44 | 50 | 32.0 | 305 | 400 | 3 | 2.71 | 151.20 | 117.3 | 120.0 | 93.9 | 108.0 | |

45 | 50 | 35.5 | 305 | 400 | 3 | 1.27 | 148.60 | 123.6 | 98.2 | 98.9 | 88.4 | |

46 | 50 | 32.0 | 305 | 400 | 3 | 2.03 | 171.70 | 117.3 | 109.0 | 93.9 | 98.1 | |

47 | 50 | 35.5 | 305 | 400 | 3 | 2.71 | 168.60 | 123.6 | 126.4 | 98.9 | 113.8 | |

48 | 50 | 30.8 | 305 | 375 | 3.2 | 1.27 | 120.50 | 107.9 | 87.4 | 86.3 | 78.7 | |

49 | 50 | 26.6 | 305 | 375 | 3.2 | 2.03 | 99.90 | 100.3 | 95.0 | 80.2 | 85.5 | |

50 | 50 | 30.8 | 305 | 400 | 3 | 2.71 | 140.80 | 115.1 | 117.7 | 92.1 | 105.9 | |

51 | 50 | 26.6 | 305 | 400 | 3 | 1.27 | 134.60 | 107.0 | 85.0 | 85.6 | 76.5 | |

52 | 50 | 30.8 | 305 | 400 | 3 | 2.03 | 136.30 | 115.1 | 106.9 | 92.1 | 96.2 | |

53 | 50 | 26.6 | 305 | 400 | 3 | 2.71 | 116.80 | 107.0 | 109.4 | 85.6 | 98.5 | |

Arezoumandi (2014 & 2015) [30,31] | 54 | 50 | 32.1 | 300 | 400 | 3 | 1.27 | 117.50 | 115.6 | 91.8 | 92.5 | 82.6 |

55 | 50 | 32.1 | 300 | 375 | 3 | 2.03 | 151.30 | 108.4 | 102.6 | 86.7 | 92.4 | |

56 | 50 | 32.1 | 300 | 375 | 3 | 2.71 | 171.80 | 108.4 | 113.0 | 86.7 | 101.7 | |

57 | 50 | 35.5 | 300 | 400 | 3 | 1.27 | 111.70 | 121.6 | 96.6 | 97.2 | 86.9 | |

58 | 50 | 35.5 | 300 | 375 | 3 | 2.03 | 148.60 | 114.0 | 107.9 | 91.2 | 97.1 | |

59 | 50 | 35.5 | 300 | 375 | 3 | 2.71 | 168.70 | 114.0 | 118.9 | 91.2 | 107.0 | |

60 | 100 | 30.0 | 300 | 400 | 3 | 1.27 | 114.80 | 111.7 | 88.8 | 89.4 | 66.6 | |

61 | 100 | 30.0 | 300 | 375 | 3 | 2.03 | 143.20 | 104.8 | 99.2 | 83.8 | 74.4 | |

62 | 100 | 30.0 | 300 | 375 | 3 | 2.71 | 131.40 | 104.8 | 109.3 | 83.8 | 81.9 | |

63 | 100 | 34.1 | 300 | 400 | 3 | 1.27 | 113.00 | 119.1 | 94.6 | 95.3 | 71.0 | |

64 | 100 | 34.1 | 300 | 375 | 3 | 2.03 | 124.10 | 111.7 | 105.8 | 89.3 | 79.3 | |

65 | 100 | 34.1 | 300 | 375 | 3 | 2.71 | 140.30 | 111.7 | 116.5 | 89.3 | 87.4 | |

Knaack and Kurama (2014) [28] | 66 | 50 | 41.8 | 150 | 200 | 3.875 | 1.34 | 44.00 | 33.0 | 30.4 | 26.4 | 27.4 |

67 | 50 | 41.8 | 150 | 200 | 3.875 | 1.34 | 39.10 | 33.0 | 30.4 | 26.4 | 27.4 | |

68 | 50 | 37.4 | 150 | 200 | 3.875 | 1.34 | 43.70 | 31.2 | 28.8 | 25.0 | 25.9 | |

69 | 50 | 37.4 | 150 | 200 | 3.875 | 1.34 | 41.20 | 31.2 | 28.8 | 25.0 | 25.9 | |

70 | 100 | 39.1 | 150 | 200 | 3.875 | 1.34 | 36.40 | 31.9 | 29.4 | 25.5 | 22.1 | |

71 | 100 | 39.1 | 150 | 200 | 3.875 | 1.34 | 38.00 | 31.9 | 29.4 | 25.5 | 22.1 | |

72 | 100 | 39.2 | 150 | 200 | 3.875 | 1.34 | 39.90 | 31.9 | 29.4 | 25.5 | 22.1 | |

73 | 100 | 39.2 | 150 | 200 | 3.875 | 1.34 | 39.90 | 31.9 | 29.4 | 25.5 | 22.1 | |

Kim et al. (2013) [40] | 74 | 50 | 32.6 | 200 | 300 | 2.5 | 2.85 | 60.60 | 58.2 | 65.9 | 46.6 | 59.3 |

75 | 50 | 32.6 | 200 | 450 | 2.5 | 2.85 | 108.90 | 87.4 | 87.6 | 69.9 | 78.8 | |

76 | 50 | 32.6 | 200 | 600 | 2.5 | 2.85 | 126.10 | 116.5 | 105.9 | 93.2 | 95.3 | |

77 | 50 | 32.6 | 300 | 450 | 2.5 | 3.02 | 154.20 | 131.0 | 133.9 | 104.8 | 120.5 | |

78 | 50 | 32.6 | 400 | 600 | 2.5 | 2.85 | 261.50 | 233.0 | 211.9 | 186.4 | 190.7 | |

79 | 100 | 34.9 | 200 | 300 | 2.5 | 2.85 | 72.90 | 60.3 | 68.1 | 48.2 | 51.1 | |

80 | 100 | 34.9 | 200 | 450 | 2.5 | 2.85 | 96.40 | 90.4 | 90.6 | 72.3 | 67.9 | |

81 | 100 | 34.9 | 200 | 600 | 2.5 | 2.85 | 125.10 | 120.5 | 109.6 | 96.4 | 82.2 | |

82 | 100 | 34.9 | 300 | 450 | 2.5 | 3.02 | 159.80 | 135.6 | 138.5 | 108.5 | 103.9 | |

83 | 100 | 34.9 | 400 | 600 | 2.5 | 2.85 | 256.60 | 241.0 | 219.2 | 192.8 | 164.4 | |

Fathifazl et al. (2011) [22] | 84 | 63.5 | 41.6 | 200 | 300 | 1.5 | 1.00 | 186.70 | 65.8 | 52.5 | 52.6 | 39.4 |

85 | 63.5 | 41.6 | 200 | 300 | 2 | 1.50 | 169.50 | 65.8 | 60.1 | 52.6 | 45.0 | |

86 | 63.5 | 41.6 | 200 | 309 | 2.59 | 1.62 | 103.90 | 67.8 | 63.0 | 54.2 | 47.2 | |

87 | 63.5 | 41.6 | 200 | 201 | 5.69 | 1.99 | 89.30 | 44.1 | 46.4 | 35.3 | 34.8 | |

88 | 63.5 | 41.6 | 200 | 305 | 3.93 | 2.46 | 83.20 | 66.9 | 71.7 | 53.5 | 53.8 | |

89 | 63.5 | 41.6 | 200 | 381 | 2.73 | 1.83 | 99.50 | 83.6 | 76.1 | 66.8 | 57.1 | |

Choi et al. (2010) [41] | 90 | 30 | 24.5 | 200 | 360 | 1.5 | 1.61 | 161.70 | 60.6 | 53.8 | 48.5 | 48.4 |

91 | 30 | 24.5 | 200 | 360 | 2.5 | 1.61 | 81.34 | 60.6 | 53.8 | 48.5 | 48.4 | |

92 | 30 | 24.5 | 200 | 360 | 3.25 | 1.61 | 56.70 | 60.6 | 53.8 | 48.5 | 48.4 | |

93 | 30 | 24.5 | 200 | 360 | 2.5 | 0.53 | 56.70 | 60.6 | 37.1 | 48.5 | 33.4 | |

94 | 30 | 24.5 | 200 | 360 | 2.5 | 0.83 | 78.40 | 60.6 | 43.1 | 48.5 | 38.8 | |

95 | 50 | 24.2 | 200 | 360 | 1.5 | 1.61 | 152.88 | 60.2 | 53.4 | 48.1 | 48.1 | |

96 | 50 | 24.2 | 200 | 360 | 2.5 | 1.61 | 87.90 | 60.2 | 53.4 | 48.1 | 48.1 | |

97 | 50 | 24.2 | 200 | 360 | 3.25 | 1.61 | 71.54 | 60.2 | 53.4 | 48.1 | 48.1 | |

98 | 50 | 24.2 | 200 | 360 | 2.5 | 0.53 | 57.82 | 60.2 | 36.9 | 48.1 | 33.2 | |

99 | 50 | 24.2 | 200 | 360 | 2.5 | 0.83 | 67.13 | 60.2 | 42.8 | 48.1 | 38.5 | |

100 | 100 | 22.6 | 200 | 360 | 1.5 | 1.61 | 107.80 | 58.1 | 51.6 | 46.5 | 38.7 | |

101 | 100 | 22.6 | 200 | 360 | 2.5 | 1.61 | 84.77 | 58.1 | 51.6 | 46.5 | 38.7 | |

102 | 100 | 22.6 | 200 | 360 | 3.25 | 1.61 | 57.77 | 58.1 | 51.6 | 46.5 | 38.7 | |

103 | 100 | 22.6 | 200 | 360 | 2.5 | 0.53 | 59.78 | 58.1 | 35.6 | 46.5 | 26.7 | |

104 | 100 | 22.6 | 200 | 360 | 2.5 | 0.83 | 70.07 | 58.1 | 41.4 | 46.5 | 31.0 | |

González-Fonteboa and Martínez-Abella (2007) [27] | 105 | 100 | 39.7 | 200 | 303 | 3.3 | 2.98 | 90.64 | 64.9 | 74.2 | 51.9 | 55.7 |

Etxeberria et al. (2007) [26] | 106 | 25 | 42.4 | 200 | 303 | 3.3 | 2.98 | 104.00 | 67.1 | 76.8 | 53.7 | 69.1 |

107 | 50 | 41.3 | 200 | 303 | 3.3 | 2.98 | 89.00 | 66.2 | 75.8 | 53.0 | 68.2 | |

108 | 100 | 39.8 | 200 | 303 | 3.3 | 2.98 | 84.00 | 65.0 | 74.3 | 52.0 | 55.8 | |

Sato et al. (2007) [42] | 109 | 100 | 46.5 | 150 | 160 | 4.4 | 1.06 | 21.00 | 27.8 | 23.7 | 22.3 | 17.8 |

110 | 100 | 32.9 | 150 | 160 | 4.4 | 1.06 | 21.70 | 23.4 | 20.0 | 18.7 | 15.0 | |

111 | 100 | 46.6 | 150 | 160 | 4.4 | 1.06 | 21.40 | 27.9 | 23.8 | 22.3 | 17.8 | |

112 | 100 | 30.4 | 150 | 160 | 4.4 | 0.59 | 12.10 | 22.5 | 15.8 | 18.0 | 11.8 | |

113 | 100 | 28.4 | 150 | 160 | 4.4 | 0.59 | 12.60 | 21.7 | 15.3 | 17.4 | 11.4 | |

114 | 100 | 34.5 | 150 | 160 | 4.4 | 0.59 | 13.20 | 24.0 | 16.8 | 19.2 | 12.6 | |

115 | 100 | 31.8 | 150 | 160 | 4.4 | 0.59 | 13.50 | 23.0 | 16.1 | 18.4 | 12.1 | |

116 | 100 | 30.4 | 150 | 160 | 4.4 | 1.06 | 19.70 | 22.5 | 19.2 | 18.0 | 14.4 | |

117 | 100 | 28.4 | 150 | 160 | 4.4 | 1.06 | 20.00 | 21.7 | 18.5 | 17.4 | 13.9 | |

118 | 100 | 34.5 | 150 | 160 | 4.4 | 1.06 | 20.00 | 24.0 | 20.4 | 19.2 | 15.3 | |

119 | 100 | 31.8 | 150 | 160 | 4.4 | 1.06 | 21.40 | 23.0 | 19.6 | 18.4 | 14.7 | |

120 | 100 | 30.4 | 150 | 160 | 4.4 | 1.65 | 27.30 | 22.5 | 22.2 | 18.0 | 16.7 | |

121 | 100 | 28.4 | 150 | 160 | 4.4 | 1.65 | 27.70 | 21.7 | 21.5 | 17.4 | 16.1 | |

122 | 100 | 34.5 | 150 | 160 | 4.4 | 1.65 | 28.30 | 24.0 | 23.7 | 19.2 | 17.8 | |

123 | 100 | 31.8 | 150 | 160 | 4.4 | 1.65 | 31.10 | 23.0 | 22.7 | 18.4 | 17.1 | |

Han et al. (2001) [46] | 124 | 100 | 39.6 | 170 | 270 | 1.5 | 1.10 | 83.50 | 49.1 | 41.6 | 39.3 | 31.2 |

125 | 100 | 30.6 | 170 | 270 | 2 | 1.10 | 65.20 | 43.2 | 36.6 | 34.5 | 27.4 | |

126 | 100 | 32.6 | 170 | 270 | 2 | 1.10 | 60.60 | 44.6 | 37.7 | 35.6 | 28.3 | |

127 | 100 | 31.2 | 170 | 270 | 3 | 1.10 | 42.70 | 43.6 | 36.9 | 34.9 | 27.7 | |

128 | 100 | 31.9 | 170 | 270 | 4 | 1.10 | 31.70 | 44.1 | 37.3 | 35.3 | 28.0 |

_{w}= longitudinal reinforcement ratio.

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**Figure 1.**(

**a**) Concrete cylinder waste (

**b**) Custom-made crushing machine (

**c**) Coarse aggregate sieving test results, and (

**d**) View of recycled coarse aggregate (RCA).

**Figure 4.**(

**a**) Load-deflection curve for beams with reinforcement ratio, ρ

_{w}= 1.16%, and (

**b**) Normalized shear stress vs. deflection for beams with reinforcement ratio, ρ

_{w}= 1.16%.

**Figure 5.**(

**a**) Load-deflection curve for beams with reinforcement ratio, ρw = 1.81%, and (

**b**) Normalized shear stress vs. deflection for beams with longitudinal reinforcement ratio, ρ

_{w}= 1.81%.

**Figure 6.**The ratio of normalized shear stress between RAC and NAC beams with different amounts of RCA.

**Figure 9.**Ratios between ultimate shear from test and concrete shear prediction from ACI318 shear provisions.

**Figure 10.**Comparison between V

_{test}/V

_{c}using ACI 318-19 shear provisions for different parameters (

**a**) V

_{test}/V

_{c}vs. % RCA (

**b**) V

_{test}/V

_{c}vs. f’

_{c}(

**c**) V

_{test}/V

_{c}vs. d (

**d**) V

_{test}/V

_{c}vs. a/d (

**e**) V

_{test}/V

_{c}vs. ρ

_{w}.

**Figure 12.**The proposed reduction factor for RCA to shear strength predicted by ACI 318-19 shear equation.

Properties | FA | NCA | RCA |
---|---|---|---|

Bulk Specific Gravity (SSD) | 2.6 | 2.7 | 2.43 |

Unit Weight (kg/m^{3}) | 1730 | 1397 | |

Water Absorption (%) | 1.05 | 0.28 | 4.59 |

Moisture (%) | 1.35 | 0.61 | 2.24 |

Fineness Modulus | 2.7 | ||

Max. size (mm) | 4.76 | 19.1 | 18.6 |

Impact value (%) | 10.15 | 13.4 | |

Crushing value (%) | 21.77 | 23.12 | |

Residual mortar (%) | 32.5 |

Nominal Size (mm) | Yield Stress (MPa) | Ultimate Stress (MPa) | Elongation (%) |
---|---|---|---|

20 | 519 | 668 | 18 |

16 | 561 | 658 | 21 |

6 | 424 | 639 | 28 |

Mix Type | Cement | FA | NCA | RCA | Water | SP |

NCA | 357 | 719 | 1069 | 190 | 1.07 | |

25% RCA | 357 | 750 | 802 | 216 | 190 | 1.07 |

50% RCA | 357 | 780 | 535 | 432 | 190 | 1.07 |

75% RCA | 357 | 810 | 267 | 648 | 190 | 1.07 |

100% RCA | 357 | 840 | 864 | 190 | 1.07 |

Specimen ID | f’_{c}(MPa) | ρ_{w}(%) | P_{u}(kN) | ∆_{u} (mm) | Shear Crack Inclination Angle (Degree) | V_{test} (kN) | v_{test} = V_{test}/bd(MPa) | ${v}_{\mathit{test}}/\sqrt{{f}_{c}^{\prime}}$ |
---|---|---|---|---|---|---|---|---|

RCA0-DB16 | 29.9 | 1.16 | 125 | 5.9 | 38 | 62.5 | 1.20 | 0.220 |

RCA25-DB16 | 35.7 | 1.16 | 135 | 6.5 | 31 | 67.5 | 1.29 | 0.217 |

RCA50-DB16 | 29.0 | 1.16 | 119 | 6.2 | 31 | 59.5 | 1.14 | 0.212 |

RCA75-DB16 | 32.9 | 1.16 | 125 | 5.8 | 31 | 62.5 | 1.20 | 0.209 |

RCA100-DB16 | 31.9 | 1.16 | 122 | 5.9 | 36 | 61.0 | 1.17 | 0.208 |

RCA0-DB20 | 29.7 | 1.81 | 166.6 | 6.8 | 38 | 83.3 | 1.60 | 0.294 |

RCA25-DB20 | 30.7 | 1.81 | 167.8 | 6.2 | 32 | 83.9 | 1.61 | 0.291 |

RCA50-DB20 | 23.1 | 1.81 | 145 | 5.5 | 31 | 72.5 | 1.39 | 0.290 |

RCA75-DB20 | 34.1 | 1.81 | 175 | 6.5 | 31 | 87.5 | 1.68 | 0.289 |

RCA100-DB20 | 29.5 | 1.81 | 162.4 | 6.3 | 30 | 81.2 | 1.56 | 0.287 |

Specimen ID | f’_{c}(MPa) | ρ_{w} (%) | Ultimate Load P_{u} (kN) | V_{test} (kN) | V_{c} (kN) ACI 318-14 | V_{test}/V_{c}ACI 318-14 | V_{c} (kN) ACI 318-19 | V_{test}/V_{c}ACI 318-19 |
---|---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) |

RCA0-DB16 | 29.9 | 1.16 | 125 | 62.5 | 48.35 | 1.29 | 42.07 | 1.49 |

RCA25-DB16 | 35.7 | 1.16 | 135 | 67.5 | 52.85 | 1.28 | 45.99 | 1.47 |

RCA50-DB16 | 29.0 | 1.16 | 119 | 59.5 | 47.60 | 1.25 | 41.42 | 1.44 |

RCA75-DB16 | 32.9 | 1.16 | 125 | 62.5 | 50.74 | 1.23 | 44.15 | 1.42 |

RCA100-DB16 | 31.9 | 1.16 | 122 | 61.0 | 49.95 | 1.22 | 43.46 | 1.40 |

RCA0-DB20 | 29.7 | 1.81 | 166.6 | 83.3 | 48.19 | 1.73 | 48.65 | 1.71 |

RCA25-DB20 | 30.7 | 1.81 | 167.8 | 83.9 | 48.94 | 1.71 | 49.41 | 1.70 |

RCA50-DB20 | 23.1 | 1.81 | 145 | 72.5 | 42.49 | 1.71 | 42.89 | 1.69 |

RCA75-DB20 | 34.1 | 1.81 | 175 | 87.5 | 51.55 | 1.70 | 52.04 | 1.68 |

RCA100-DB20 | 29.5 | 1.81 | 162.4 | 81.2 | 48.01 | 1.69 | 48.47 | 1.67 |

Code Provision | Ratios of V_{test}/V_{c} | ||
---|---|---|---|

Average | Least Conservative Value | COV | |

ACI 318-14 | 1.15 | 0.54 | 0.25 |

ACI 318-19 | 1.28 | 0.77 | 0.30 |

β_{r} | Number of Unconservative (V_{test}/V_{c}) by Modified ACI 318-19 | Number of Unconservative (V_{test}/V_{c})by ACI 318-14 |
---|---|---|

0.90 | 6 | 7 |

0.85 | 4 | 7 |

0.80 | 2 | 7 |

0.75 | 0 | 4 |

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**MDPI and ACS Style**

Setkit, M.; Leelatanon, S.; Imjai, T.; Garcia, R.; Limkatanyu, S.
Prediction of Shear Strength of Reinforced Recycled Aggregate Concrete Beams without Stirrups. *Buildings* **2021**, *11*, 402.
https://doi.org/10.3390/buildings11090402

**AMA Style**

Setkit M, Leelatanon S, Imjai T, Garcia R, Limkatanyu S.
Prediction of Shear Strength of Reinforced Recycled Aggregate Concrete Beams without Stirrups. *Buildings*. 2021; 11(9):402.
https://doi.org/10.3390/buildings11090402

**Chicago/Turabian Style**

Setkit, Monthian, Satjapan Leelatanon, Thanongsak Imjai, Reyes Garcia, and Suchart Limkatanyu.
2021. "Prediction of Shear Strength of Reinforced Recycled Aggregate Concrete Beams without Stirrups" *Buildings* 11, no. 9: 402.
https://doi.org/10.3390/buildings11090402