# Eurocode Shear Design of Coarse Recycled Aggregate Concrete: Reliability Analysis and Partial Factor Calibration

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## Abstract

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## 1. Introduction

#### 1.1. Shear Resistance of Recycled Aggregate Concrete Elements

- At the same time, the mechanical and durability properties of concrete are detrimentally affected by the incorporation of RAs: for the same compressive strength, RAC is typically found to have a smaller Young’s modulus, larger creep and shrinkage and worse durability properties [9,10,11]. Fracture energy and tensile strength are also detrimentally affected, especially when the strength class of concrete is larger [12,13];

- The influence of the incorporation ratio of RAs on shear resistance [21];
- The shear resistance of prestressed RAC beams [22];
- The shear resistance of RAC elements made with RAs that are treated with beneficiation methods [23];
- Meta-analyses that compare the shear resistance of NAC and RAC based on several investigations [24];

- The previous finding is validated by a meta-analysis [24] that compares the model uncertainties (${\theta}_{R}$) [30] of Eurocode shear resistance models for NAC and RAC design. These ${\theta}_{R}$ show that the resistance models of EN1992 [31] and prEN1992 [32] for elements without shear reinforcement overestimate the resistance of RAC in comparison to NAC elements;

- Aggregate interlock is a preponderant mechanism in shear strength mobilisation [39];

#### 1.2. Codified Shear Design of Recycled Aggregate Concrete

- Partial factors ${\gamma}_{G}$ = 1.35 and ${\gamma}_{Q}=1.50$ increase actions. Permanent loads are multiplied by ${\gamma}_{G}$ and variable loads are multiplied by ${\gamma}_{Q}$;
- Partial factors ${\gamma}_{S}$ = 1.15 and ${\gamma}_{C}=1.50$ decrease material properties or resistance (depending on the resistance model). In most cases, the characteristic yield stress of the reinforcement is divided by ${\gamma}_{S}$, while the compressive strength of concrete is divided by ${\gamma}_{C}$;
- ${\gamma}_{C}$ may be modelled as ${\gamma}_{C}={\gamma}_{c}\times {\gamma}_{Rd}$, where ${\gamma}_{c}$ is a partial factor for material variability and ${\gamma}_{Rd}$ is a partial factor that accounts for the uncertainty in geometry and in resistance modelling.

- The behaviour of RAC may be more variable than that of NAC;
- The resistance models used for NAC may not be as representative for RAC.

#### 1.3. Objectives

- Proposal of a resistance format with a specific partial factor for RAC design;
- Reliability analyses for representative cases of design using the stochastic models for ${\theta}_{R}$ proposed in [24];
- Calibration of ${\gamma}_{RAC}$ to be used in the resistance format proposed;
- Sensitivity analyses to understand the robustness of the calibrated ${\gamma}_{RAC}$ for the shear design of elements with shear reinforcement.

## 2. Design Equations of the Eurocode Format

#### 2.1. Design of Members without Shear Reinforcement

- ${\gamma}_{C}$ is the partial factor for concrete;
- $b$ is the width of the web of the beam;
- $d$ is the effective depth of the beam;
- $k=1+\sqrt{\frac{200}{d}}\le 2.0$ accounts for size effects. In this equation, $d$ is in mm;
- ${\rho}_{l}$ is the geometric ratio of the longitudinal tensile reinforcement. In this equation, ${\rho}_{l}\le 2\%$;
- ${f}_{ck}$ is the characteristic compressive strength of concrete and is in MPa;
- ${\nu}_{min}=0.035\times {k}^{3/2}\times \sqrt[2]{{f}_{ck}}$ is the minimum shear stress. This condition is always complied with in this paper and is not mentioned from here on.

- In the case of NAC, ${\gamma}_{C}$ is replaced with ${\gamma}_{NAC}$;
- In the case of RAC, ${\gamma}_{C}$ is replaced with ${\gamma}_{RAC}$.

- ${d}_{dg}=16+{d}_{max}\le 40\mathrm{mm}$ if ${f}_{c}\le 60\mathrm{MPa};$
- ${d}_{dg}=16+{\left({d}_{max}/{f}_{c}\right)}^{2}\le 40\mathrm{mm}$ if ${f}_{c}>60\mathrm{MPa}$;
- ${a}_{v}=\sqrt{\frac{{a}_{cs}}{4}\times d}$, where ${a}_{cs}=\left|{M}_{cs}/{V}_{cs}\right|\left(\ge d\right)$;
- ${a}_{v}=d$ if ${a}_{cs}>4d$;
- ${V}_{R,c,min}=\left(\frac{10}{{\gamma}_{C}}\right)\times \sqrt[2]{\frac{{f}_{ck}}{{f}_{yk}/{\gamma}_{s}}\times \frac{{d}_{dg}}{d}}$;
- ${f}_{yk}$ is the characteristic yielding stress of the longitudinal reinforcement;
- ${\gamma}_{s}=1.15$ is the partial factor of steel reinforcement;
- ${M}_{cs}$ and ${V}_{cs}$ are the bending moment and shear stress at the control section;
- In this code, no limit on the ${\rho}_{l}$ of EC2 (2004) is imposed.

#### 2.2. Design of Members with Shear Reinforcement

- ${A}_{sw}$ is the shear reinforcement area;
- $s$ is the distance between shear reinforcement;
- ${f}_{yk}$ is the characteristic yield stress of the shear reinforcement;
- ${\gamma}_{S}=1.15$ is the partial factor for reinforcement strength, including geometric and modelling uncertainty;
- $\mathsf{\Omega}$ is the angle of the strut with the longitudinal axis of the element. This angle may be assumed as any value in the region of 21.8 to 45°.

## 3. Reliability Analysis for Partial Factor Calibration

#### 3.1. Calibration Procedure and Reliability Method

- Cases of design are defined;
- The load combination presented in Equation (10) is used to determine ${E}_{d}$;
- An iterative process takes place, beginning with the preliminary proposal of the authors [24] for ${\gamma}_{NAC}$ and ${\gamma}_{RAC}$. For a given ${E}_{d}$, the equation for the design value of resistance is used to design the structural element;
- A reliability analysis takes place, in which a limit state function of the type ${g}_{x}=R-E$ is used to determine $\beta $. $R$ is the random outcome of resistance and $E$ is the random outcome of load-effects. The limit state functions used are presented in Section 3.2 and Section 3.3;
- When $\beta $ is below expectations, a new partial factor is checked and a new iteration (starting at step 3 of this bullet list) takes place;
- The calibration criteria for shear design of elements without shear reinforcement are that:
- In the case of NAC, ${\gamma}_{NAC}$ ensures that the target reliability index (${\beta}_{target}$ = 3.8, since reliability class 2 and a 50-year reference period are considered [44]) is complied with in the majority of cases of design. Moreover, the $\beta $ value should be similar to those obtained in seminal reliability assessments of the Eurocodes [55,56];
- In the case of RAC, the criterion is that ${\gamma}_{RAC}$ results in a similar β value to that obtained when ${\gamma}_{NAC}$ is used for NAC design;

- In the case of the shear design of elements with shear reinforcement, no partial factor for NAC is used and the criterion is that the calibrated ${\gamma}_{RAC}$ leads to a similar $\beta $ value to that when NAC elements are designed.

- The partial factors for shear resistance of elements without shear reinforcement are calibrated for the shear design of slabs;
- The partial factor for shear resistance of elements with shear reinforcement is calibrated for the shear design of beams.

#### 3.2. Limit State Function for Slabs without Shear Reinforcement

#### 3.3. Limit State Function for Beams with Shear Reinforcement

## 4. Cases of Design and Modelling

#### 4.1. Cases of Design

- The uncertainty in the outcome of resistance of this type of design is virtually lognormally distributed and reliability is predominantly dependent on the moments of ${\theta}_{R}$ and ${f}_{y}$, which do not depend on the case of design. This occurs because Equation (13) has a multiplicative nature, is mainly composed of lognormal distributions, and depends mostly on ${\theta}_{R}$ and ${f}_{y}$;
- The uncertainty in the outcome of load-effects depends on ${\theta}_{E}$, $P$, and $Q$ only. Since the statistics of ${\theta}_{E}$ are fixed for all cases of design, loads are given by $P$+$Q$ and the variability of $P$ and $Q$ are defined in terms of their coefficient of variation (CoV), different cases of design lead to similar uncertainty in the outcome of load-effects.

#### 4.2. Deterministic and Stochastic Modelling

- Assumption 1, in which the statistics of NAC are those presented in fib Bulletin 80 [79] for ${\rho}_{w}$ ∙${f}_{yd}$ between 1 and 2 MPa. Concerning RAC, this case assumes that the mean value of ${\theta}_{R}$ is unaffected by the incorporation of RAs, but the standard deviation increases as the RA incorporation ratio increases;
- Assumption 2, in which the statistics of NAC are those presented in fib Bulletin 80 [79] for ${\rho}_{w}$ ∙${f}_{yd}$ between 1 and 2 MPa and pessimistic expectations for the influence of RAs on the mean value and standard deviation of ${\theta}_{R}$ are assumed.

## 5. Results

#### 5.1. Slabs without Shear Reinforcement

#### 5.1.1. Design with prEN1992

#### 5.1.2. Design with EN1992

#### 5.2. Beams with Shear Reinforcement

- For Assumption 1 and χ = 50%, the beam made with RAC100 has a 50-year $\beta $ of 3.75. Assumption 1 models ${\theta}_{R}$ with a mean of 1.25;
- If the mean of ${\theta}_{R}$ is 1.20 instead of 1.25, the actual 50-year $\beta $ would correspond to roughly:

#### 5.3. Recommendations for Design

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## List of Acronyms and Symbols

CDW | construction and demolition waste |

CoV | coefficient of variation |

NA | coarse natural aggregate |

RA | coarse recycled aggregate |

RAC | concrete with partial or total incorporation of coarse recycled aggregate concrete |

RAC50 | recycled aggregate concrete elements with 50% incorporation of coarse recycled aggregates |

RAC100 | recycled aggregate concrete elements with full incorporation of coarse recycled aggregates |

${A}_{s}$ | cross-sectional area of the reinforcement |

${A}_{sw}$ | area of shear reinforcement |

$E$ | random outcome of load-effects |

${E}_{d}$ | design value of load-effects |

${E}_{s}$ | Young’s modulus of reinforcement |

${F}_{2}$ | conversion of delivered strength measured on standard specimens to the strength within structural elements |

$H$ | height of the beam |

${M}_{cs}$ | bending moment at the control section |

$P$ | random outcome of permanent loading |

${P}_{k}$ | characteristic value of permanent loading |

$Q$ | random outcome of variable loading |

${Q}_{k}$ | characteristic value of variable loading |

$R$ | random outcome of resistance |

${V}_{cs}$ | shear stress at the control section |

${V}_{Rd}$ | design value of shear resistance |

${V}_{Rd,cmin}$ | design value of the minimum shear resistance of elements without shear reinforcement |

${V}_{Rd,strut}$ | design value of the shear resistance of the compression struts of the resistance model of beams with shear reinforcement |

${V}_{Rd,tie}$ | design value of the shear resistance of the ties of the resistance model of beams with shear reinforcement |

$b$ | width of the web of the beam |

$c$ | concrete cover |

$d$ | effective depth of the beam |

${d}_{max}$ | maximum aggregate diameter |

${f}_{c}$ | random outcome of the compressive strength of concrete |

${f}_{ck}$ | characteristic value of the compressive strength of concrete |

${f}_{y}$ | random outcome of the yield stress of the reinforcement |

${f}_{yd}$ | design value of the yield stress of the reinforcement |

${f}_{yk}$ | characteristic yield stress of the reinforcement |

${g}_{x}$ | limit state function |

$s$ | distance between reinforcement |

$\Delta B$ | uncertainty in the width of the beam |

${\Phi}_{Asl}$ | diameter of longitudinal reinforcement |

$\mathsf{\Omega}$ | angle of the compression strut with the longitudinal axis used in the resistance model of elements with shear reinforcement |

α | direction cosine of a stochastic variable |

β | reliability index |

${\beta}_{target}$ | target reliability index |

${\gamma}_{C}$ | partial factor for the strength of concrete |

${\gamma}_{c}$ | partial factor for the variability of the strength of concrete |

${\gamma}_{G}$ | partial factor for permanent loads |

${\gamma}_{Q}$ | partial factor for variable loads |

${\gamma}_{NAC}$ | partial factor for shear design of natural aggregate concrete elements without shear reinforcement |

${\gamma}_{RAC}$ | partial factor for shear design of recycled aggregate concrete elements |

${\gamma}_{RAC}$ | partial factor for shear design of recycled aggregate concrete elements with 50% incorporation of coarse recycled aggregates |

${\gamma}_{RAC100}$ | partial factor for shear design of recycled aggregate concrete elements with full incorporation of coarse recycled aggregates |

${\gamma}_{Rd}$ | partial factor for the uncertainty in geometry and in resistance modelling |

${\gamma}_{S}$ | partial factor for the yield stress of the reinforcement |

${\theta}_{E}$ | model uncertainty of load-effect modelling |

${\theta}_{R}$ | model uncertainty of the resistance model |

$\lambda $ | stochastic model for the conversion of specified to delivered strength |

${\rho}_{l}$ | geometric ratio of longitudinal tensile reinforcement |

${\rho}_{w}$ | geometric ratio of shear reinforcement |

${\nu}_{min}$ | minimum shear stress of the resistance model of elements without shear reinforcement |

$\chi $ | ratio of the design value of the variable loading to the total design value of loading |

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**Figure 2.**χ vs. $\beta $ for shear resistance design of NAC slabs without shear reinforcement. prEN1992 [32]. ${\gamma}_{NAC}=1.40$.

**Figure 4.**${\alpha}^{2}$ for $\chi =0$ and Slab 1 and the preliminary partial factors for shear design of elements without stirrups presented in Part 3. prEN1992 [32]. ${\gamma}_{NAC}=1.40$; ${\gamma}_{C,V,RAC50}=1.60;{\gamma}_{C,V,RAC50}=1.70$.

**Figure 5.**β vs. χ of Slab 1 for NAC and RAC. prEN1992 [32]. ${\gamma}_{NAC}=1.40$ and ${\gamma}_{CRAC50}=1.50,{\gamma}_{RAC100}=1.60$ (after calibration).

**Figure 6.**χ vs. $\beta $ for shear resistance design of NAC slabs without shear reinforcement. EN1992 [31]. ${\gamma}_{NAC}=1.45$; ${\gamma}_{RAC50}=1.55;{\gamma}_{RAC100}=1.60$ (no calibration needed).

**Figure 7.**${\alpha}^{2}$ for $\chi =0$ and Slab 1. Slabs without shear reinforcement. EN1992 [31]. ${\gamma}_{NAC}=1.45$ and ${\gamma}_{CRAC50}=1.55,{\gamma}_{RAC100}=1.60$ (no calibration needed).

**Table 1.**Cases of design for shear design of NAC slabs without shear reinforcement using prEN1992 [32].

Slab | ${\mathit{f}}_{\mathit{c}\mathit{k}}$ (MPa) | ${\mathit{d}}_{\mathit{m}\mathit{a}\mathit{x}}$ (mm) | $\mathit{H}$ (mm) | $\mathit{c}$ (mm) | $\mathit{L}$ (m) | $\mathit{a}/\mathit{d}$ | ${\mathit{\Phi}}_{\mathit{A}\mathit{s}\mathit{l}}$ (mm) | $\mathit{s}$ (mm) | ${\mathit{\rho}}_{\mathit{l}}$ | ${\mathit{V}}_{\mathit{R}\mathit{d}}$ (kN) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 25 | 20 | 170 | 25 | 5.0 | 2.5 | 12 | 100 | 0.81% | 122.1 |

2 | 25 | 20 | 140 | 25 | 5.0 | 2.5 | 16 | 100 | 1.88% | 135.5 |

3 | 25 | 20 | 210 | 25 | 5.0 | 2.5 | 16 | 150 | 0.76% | 140.0 |

4 | 40 | 20 | 170 | 25 | 6.5 | 2.5 | 16 | 150 | 0.97% | 150.4 |

5 | 40 | 20 | 145 | 25 | 6.5 | 2.5 | 16 | 75 | 2.39% | 177.1 |

**Table 2.**Partial factors for elements without shear reinforcement used in the first iteration of the calibration procedures [24].

Code | ${\mathit{\gamma}}_{\mathit{N}\mathit{A}\mathit{C}}$ | ${\mathit{\gamma}}_{\mathit{R}\mathit{A}\mathit{C}\mathbf{50}}$ | ${\mathit{\gamma}}_{\mathit{R}\mathit{A}\mathit{C}\mathbf{100}}$ |
---|---|---|---|

EN1992 [32] | 1.45 | 1.55 | 1.60 |

prEN1992 [31] | 1.40 | 1.60 | 1.70 |

**Table 3.**Cases of design for shear design of NAC slabs without shear reinforcement using EN1992 [31].

Slab | ${\mathit{f}}_{\mathit{c}\mathit{k}}$ (MPa) | $\mathit{H}$ (mm) | $\mathit{c}$ (mm) | $\mathit{L}$ (m) | $\mathit{a}/\mathit{d}$ | ${\mathit{\Phi}}_{\mathit{A}\mathit{s}\mathit{l}}$ (mm) | $\mathit{s}$ (mm) | ${\mathit{\rho}}_{\mathit{l}}$ | ${\mathit{V}}_{\mathit{R}\mathit{d}}$ (kN) |
---|---|---|---|---|---|---|---|---|---|

1 | 25 | 190 | 25 | 5.0 | 2.5 | 16 | 104.1 | 1.23% | 122.1 |

2 | 25 | 190 | 25 | 5.0 | 2.5 | 16 | 86.2 | 1.49% | 135.5 |

3 | 25 | 215 | 25 | 5.0 | 2.5 | 16 | 100 | 1.10% | 140.0 |

4 | 40 | 175 | 25 | 6.5 | 2.5 | 16 | 73 | 1.94% | 150.4 |

5 | 40 | 200 | 25 | 6.5 | 2.5 | 20 | 94.2 | 2.02% | 177.1 |

**Table 4.**Case of design for reliability analysis of shear design of NAC beam with shear reinforcement.

${\mathit{f}}_{\mathit{c}\mathit{k}}$ (MPa) | $\mathit{b}$ (mm) | $\mathit{H}$ (mm) | $\mathit{c}$ (mm) | $\mathit{d}$ (mm) | ${\mathit{\Phi}}_{\mathit{A}\mathit{s}\mathit{l}}$ (mm) | ${\mathit{\Phi}}_{\mathit{A}\mathit{s}\mathit{w}}$ (mm) | $\mathit{s}$ (mm) | ${\mathit{A}}_{\mathit{s}\mathit{v}}/\mathit{s}$ (cm ^{2}/mm) | ${\mathit{\rho}}_{\mathit{w}}$ | ${\mathit{\rho}}_{\mathit{w}}$$\xb7{\mathit{f}}_{\mathit{y}\mathit{k}/{\mathit{\gamma}}_{\mathit{S}}}$ (MPa) | Ω | ${\mathit{V}}_{\mathit{R}\mathit{d}}$ (kN) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

25 | 250 | 450 | 25 | 407 | 16 | 8 | 150 | 6.7 | 0.27% | 1.17 | 30° | 185.9 |

Parameter | Deterministic Model | Stochastic Model | Reference | ||||
---|---|---|---|---|---|---|---|

Symbol | Fractile | Symbol | Mean | Standard Deviation (σ) | Probability Distribution | ||

Permanent load | ${P}_{k}$ | 50 % | $P$ | ${P}_{k}$ | 0.10 × $P$ | Normal | [44] |

Maximum variable load (50 years) | ${Q}_{k}$ | * | $Q$ | 0.60 $\times {Q}_{k}$ | 0.35 $\times Q$ | Gumbel | [65,66,67,68,69,70] |

Model uncertainty of load-effects | Absent from deterministic modelling | ${\theta}_{E}$ | 1.00 | 0.05 | Lognormal | [55,71] | |

Compressive strength | ${f}_{ck}$ | 5% fractile | ${f}_{c}$ | ${f}_{c}=\lambda \times {F}_{2}\times {f}_{ck}$, with ${f}_{ck}$ assumed deterministic | [63,64] | ||

Specified to delivered strength | Absent from deterministic modelling | $\lambda $ | 1.20 | 0.17 | Lognormal | ||

Standard to strength-in-structures | Absent from deterministic modelling | ${F}_{2}$ | 0.95 | 0.13 | Lognormal | ||

Yield stress of the reinforcement | ${f}_{yd}$ | 5% fractile | ${f}_{y}$ | ${f}_{yd}+2\sigma $ | 30 MPa | Lognormal | [55,56,62,72]; |

Young’s modulus of the reinforcement | ${E}_{s}$ = 200 GPa assumed as deterministic | ||||||

Cross-sectional area of the reinforcement | ${A}_{s}$ assumed as deterministic | ||||||

Height of the cross-section | H assumed as deterministic | ||||||

Concrete cover (vertical) | $cy$ | Nominal value | $cy+\Delta cy$ | $\Delta cy$: 5 mm (slabs) $\Delta cy$: −5 mm (beams) | $\Delta cy$: 5 mm (slabs) $\Delta cy$: −5 mm (beams) | $\Delta cy$: Normal $cy$ is deterministic | [13,62] |

${\mathit{\theta}}_{\mathit{R}}$ | Incorporation Ratio of RAs | Mean Value | Standard Deviation (σ) | Probability Distribution |
---|---|---|---|---|

EN 1992 [31] | NAC | 1.03 | 0.113 | Lognormal |

RAC50 | 1.00 | 0.120 | Lognormal | |

RAC100 | 0.95 | 0.114 | Lognormal | |

prEN 1992 [32] | NAC | 0.98 | 0.088 | Lognormal |

RAC50 | 0.93 | 0.102 | Lognormal | |

RAC100 | 0.93 | 0.121 | Lognormal |

${\mathit{\theta}}_{\mathit{R}}$ | Incorporation Ratio of RA | Mean | Standard Deviation (σ) | Probability Distribution | Source |
---|---|---|---|---|---|

Assumption 1 | NAC | 1.25 | 0.312 (CoV = 25.0%) | Lognormal | NAC: fib Bulletin 80 [79] RAC: Same mean value as NAC; pessimistic expectation of the CoV |

RAC50 | 1.25 | 0.343 (CoV = 27.5%) | Lognormal | ||

RAC100 | 1.25 | 0.375 (CoV = 30.0%) | Lognormal | ||

Assumption 2 | NAC | 1.25 | 0.312 (CoV = 25.0%) | Lognormal | NAC: fib Bulletin 80 [79] RAC: Pessimistic expectation of the mean value and CoV |

RAC50 | 1.21 | 0.333 (CoV = 27.5%) | Lognormal | ||

RAC100 | 1.17 | 0.351 (CoV = 30.0%) | Lognormal |

**Table 8.**Ratio $\beta $ RAC/$\beta $ NAC of slabs. prEN1992 [32]. ${\gamma}_{NAC}=1.40$ and ${\gamma}_{CRAC50}=1.50;{\gamma}_{RAC100}=1.60$ (after calibration).

RA | Slab | χ | ||||||
---|---|---|---|---|---|---|---|---|

0% | 10% | 30% | 50% | 70% | 90% | 100% | ||

RAC50 | Slab 1 | 98% | 98% | 99% | 101% | 101% | 102% | 102% |

Slab 2 | 98% | 98% | 99% | 101% | 101% | 102% | 102% | |

Slab 3 | 98% | 98% | 100% | 101% | 102% | 102% | 102% | |

Slab 4 | 98% | 98% | 99% | 101% | 103% | 103% | 102% | |

Slab 5 | 100% | 102% | 103% | 104% | 104% | 104% | 104% | |

RAC100 | Slab 1 | 96% | 96% | 98% | 100% | 101% | 102% | 102% |

Slab 2 | 93% | 92% | 96% | 99% | 101% | 102% | 102% | |

Slab 3 | 94% | 93% | 100% | 97% | 102% | 102% | 103% | |

Slab 4 | 94% | 93% | 96% | 100% | 101% | 102% | 102% | |

Slab 5 | 94% | 93% | 96% | 99% | 101% | 102% | 102% |

**Table 9.**Ratio $\beta $ RAC/$\beta $ NAC of slabs. EN1992 [31]. ${\gamma}_{NAC}=1.45$; ${\gamma}_{RAC50}=1.55;{\gamma}_{RAC100}=1.60$ (no calibration needed).

RA | Slab | χ | ||||||
---|---|---|---|---|---|---|---|---|

0% | 10% | 30% | 50% | 70% | 90% | 100% | ||

RAC50 | Slab 1 | 100% | 100% | 100% | 101% | 101% | 100% | 102% |

Slab 2 | 100% | 100% | 100% | 101% | 101% | 102% | 102% | |

Slab 3 | 102% | 100% | 101% | 101% | 101% | 101% | 102% | |

Slab 4 | 100% | 101% | 100% | 101% | 101% | 102% | 102% | |

Slab 5 | 101% | 100% | 100% | 101% | 101% | 102% | 102% | |

RAC100 | Slab 1 | 98% | 98% | 99% | 100% | 100% | 98% | 100% |

Slab 2 | 98% | 97% | 98% | 99% | 100% | 100% | 100% | |

Slab 3 | 101% | 101% | 98% | 97% | 101% | 100% | 99% | |

Slab 4 | 98% | 98% | 99% | 99% | 100% | 100% | 100% | |

Slab 5 | 98% | 97% | 98% | 99% | 100% | 100% | 100% |

Elasticity (%) | NAC | RAC50 Assumption 1 | RAC100 Assumption 1 | RAC50 Assumption 2 | RAC100 Assumption 2 |
---|---|---|---|---|---|

Mean | 2.01 | 2.04 | 1.99 | 1.97 | 1.94 |

Standard deviation | −0.86 | −0.88 | −0.89 | −0.89 | −0.91 |

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**MDPI and ACS Style**

Pacheco, J.; de Brito, J.; Chastre, C.; Evangelista, L.
Eurocode Shear Design of Coarse Recycled Aggregate Concrete: Reliability Analysis and Partial Factor Calibration. *Materials* **2021**, *14*, 4081.
https://doi.org/10.3390/ma14154081

**AMA Style**

Pacheco J, de Brito J, Chastre C, Evangelista L.
Eurocode Shear Design of Coarse Recycled Aggregate Concrete: Reliability Analysis and Partial Factor Calibration. *Materials*. 2021; 14(15):4081.
https://doi.org/10.3390/ma14154081

**Chicago/Turabian Style**

Pacheco, João, Jorge de Brito, Carlos Chastre, and Luís Evangelista.
2021. "Eurocode Shear Design of Coarse Recycled Aggregate Concrete: Reliability Analysis and Partial Factor Calibration" *Materials* 14, no. 15: 4081.
https://doi.org/10.3390/ma14154081