# Evaluation of Yield Improvements in Machine vs. Visual Strength Grading for Softwood Species

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Sampling

#### 2.2. Visual and Mechanical Grading

#### 2.3. Mechanical and Physical Properties

#### 2.4. Indicating Property (IP)

#### 2.5. Derivation of Settings

_{0,mean,EN338}× 0.95, for C strength classes. Then, the characteristic values of GDP were calculated according to EN 384:2016+A2:2019 [20] and EN 14358:2016 [23]. Characteristic values of strength are calculated as ${f}_{k}={k}_{v}{f}_{05}$, being ${f}_{05}$ the 5th percentile of the strength and ${k}_{v}$ the factor that considers the lower variability between subsamples in machine grading with respect to visual grading (EN 384:2016+A2:2019, [20]). ${k}_{v}$ is taken as 1 in the case of portable machines and in-line grading machine from bending tests when ${f}_{m,k}$ > 30 N/mm

^{2}. For the rest of the cases, ${k}_{v}$ is taken as 1.12. Characteristic values of modulus of elasticity are calculated as ${E}_{0,mean}={\overline{E}}_{0}/0.95$, where ${\overline{E}}_{0}$ is the average modulus of elasticity of the sample.

- (1)
- Assigned grades for the sample. The sample is graded from preliminary IP limit values, and the characteristic values are calculated for each assigned strength class and compared with required values, with the condition that a minimum of 20 specimens are allocated in each grade and the number of the rejected specimens is greater than the maximum value between 5 or 0.5% of the total number of specimens.
- (2)
- Assigned grades for the subsample. The sample is divided into the subsamples defined in Table 1 (A, B, C and D) and graded according to the preliminary IP values defined in (1). The characteristic values per subsample are calculated as described in (1) and compared with the required values, which for the case of subsample are calculated as 90%, 95%, and 90% of the required values of the sample for strength, modulus of elasticity and density, respectively.
- (3)
- Optimum grading. In parallel to points (1) and (2), the optimum grading is defined. It consists in assigning the best possible strength class to each specimen while optimizing the yield for the highest strength class. For that, the specimens are sorted from lower to higher values of GDPs. The specimens with the lower values are removed until the characteristic values of the remaining subgroup comply with the required values, which, in this case, are defined directly by the characteristic values of the strength classes (EN 338:2016 [4]).
- (4)
- Size matrix. The size matrix provides the number of specimens in the optimum and assigned grades for the total sample.
- (5)
- Elementary cost matrix. The elementary cost matrix provides a cost of efficiency and safety for each preliminary IP limit values, i.e., wrongly downgrading a specimen leads to an efficiency cost, and wrongly upgrading a specimen leads to a safety cost.
- (6)
- Global cost matrix. The global cost matrix is defined to assess the performance of the grading machine, calculated as the multiplication between the values of the size matrix and elementary cost matrices, and divided by the number of specimens in the assigned grade. The values below the diagonal of the matrix must not exceed 0.4 and trying to minimize the values above the diagonal.

## 3. Results and Discussion

#### 3.1. Physical and Mechanical Properties of the Whole Sample

_{crit}) between the three species for the three GDPs evaluated. In an analysis of variance (ANOVA) between subsamples for each species, it was found that there were significant differences between subsamples for the three species and for the three GDPs.

#### 3.2. Visual Grading

#### 3.3. Machine Grading

#### 3.4. Machine Grading vs. Visual Grading

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Symbol | Description |

N | Number of specimens |

${E}_{0,m}$ | Modulus of elasticity parallel to grain |

${f}_{m}$ | Bending strength |

ρ | Density |

IP | Indicative property |

L | Specimen length |

${f}_{0}$ | Frequency of first longitudinal vibration mode |

CF | Correction factor of wave speed based on moisture content |

${\rho}_{12}$ | Density corrected to a moisture content of 12% |

u | Moisture content |

${E}_{0,mean,E\mathrm{N}338}$ | Modulus of elasticity given by EN338 for a specific strength class |

${f}_{k}$ | Characteristic strength of a sample |

${k}_{v}$ | Factor considering the variability between subsamples, given by EN384 |

${f}_{05}$ | 5th percentile of the strength |

${f}_{m,k}$ | Characteristic bending strength of a sample |

$\overline{{E}_{0}}$ | Average modulus of elasticity of a sample |

${\rho}_{mean}$ | Average density of a sample |

${\rho}_{k}$ | Characteristic density of a sample |

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**Figure 1.**Residential building in Cornellá and Green Impulse Building in Lugo, build using GLT and CLT of Radiata pine (Source: Ref. [16]).

**Figure 2.**Distribution of maritime, radiata, and Scots pine in Spain [17].

**Figure 3.**Identification of subsamples by species: (

**a**) maritime pine; (

**b**) radiata pine; and (

**c**) Scots pine.

**Figure 6.**Yields (%) obtained for in-line grading machines by strength class per each species. Note: Empty columns reflect that the strength class combination did not provide a better yield with respect to the immediately higher strength class combination.

**Figure 7.**Yields (%) obtained for handheld grading machines by strength class by species. Note: Empty columns reflect that the strength class combination did not provide a better yield with respect to the immediately higher strength class combination.

Species | Subsample A | Subsample B | Subsample C | Subsample D | Total | ||||
---|---|---|---|---|---|---|---|---|---|

Origin | N | Origin | N | Origin | N | Origin | N | N | |

Maritime pine (ssp. atlantica) | Galicia North and Asturias | 122 | Galicia West | 121 | Galicia Interior | 129 | Basque Country | 111 | 483 |

Radiata pine | Asturias | 109 | Galicia | 116 | Gipuzkoa-Basque Country | 145 | Biscay-Basque Country | 125 | 495 |

Scots pine | Segovia- Castile and Leon | 147 | Soria- Castile and Leon | 165 | Cuenca- Castile La Mancha | 119 | Navarre | 128 | 559 |

Property | Subsample | Total | |||||
---|---|---|---|---|---|---|---|

A | B | C | D | ||||

Galicia North & Asturias | Galicia West | Galicia Interior | Basque Country (BC) | ||||

Specimens | 122 | 121 | 129 | 111 | 483 | ||

Moisture content | % | 11.9 | 12.2 | 12.4 | 12.0 | 12.1 | |

CoV | % | 6 | 17 | 16 | 26 | 17 | |

Strength | ${f}_{m}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 48.7 | 42.0 | 38.3 | 47.0 | 43.9 |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 19.0 | 16.1 | 16.2 | 17.7 | 16.9 | |

CoV | % | 37 | 46 | 45 | 40 | 17 | |

Modulus of elasticity | ${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 12.1 | 10.8 | 11.7 | 13.3 | 12.0 |

CoV | % | 30 | 38 | 32 | 29 | 33 | |

Density | ${\rho}_{mean}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 575 | 540 | 540 | 569 | 556 |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 489 | 447 | 446 | 482 | 457 | |

CoV | % | 9 | 13 | 13 | 11 | 12 |

Property | Subsample | Total | |||||
---|---|---|---|---|---|---|---|

A | B | C | D | ||||

Asturias | Galicia | Gipuzkoa-BC | Biscay-BC | ||||

Specimens | 109 | 116 | 145 | 125 | 495 | ||

Moisture content | % | 14.9 | 13.6 | 10.6 | 12.2 | 12.7 | |

CoV | % | 8 | 10 | 16 | 23 | 20 | |

Strength | ${f}_{m}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 28.7 | 47.6 | 36.3 | 38.4 | 37.8 |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 12.1 | 22.1 | 16.7 | 18.5 | 15.2 | |

CoV | % | 44 | 25 | 36 | 35 | 38 | |

Modulus of elasticity | ${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 7.65 | 10.2 | 12.1 | 12.4 | 10.8 |

CoV | % | 38 | 23 | 22 | 21 | 30 | |

Density | ${\rho}_{mean}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 479 | 545 | 488 | 501 | 503 |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 417 | 459 | 401 | 409 | 413 | |

CoV | % | 9 | 11 | 11 | 12 | 12 |

Property | Subsample | Total | |||||
---|---|---|---|---|---|---|---|

A | B | C | D | ||||

Segovia– Castile Leon | Soria– Castile Leon | Cuenca–Castile La Mancha | Navarra | ||||

Specimens | 147 | 165 | 119 | 128 | 559 | ||

Moisture content | % | 14.3 | 13.6 | 13.6 | 9.1 | 12.8 | |

CoV | % | 10 | 15 | 15 | 8 | 20 | |

Strength | ${f}_{m}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 35.1 | 37.1 | 39.8 | 45.4 | 39.1 |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 17.6 | 19.4 | 17.7 | 19.2 | 18.4 | |

CoV | % | 32 | 28 | 37 | 41 | 20 | |

Modulus of elasticity | ${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 10.8 | 11.5 | 10.7 | 12.2 | 11.3 |

CoV | % | 19 | 20 | 22 | 23 | 22 | |

Density | ${\rho}_{mean}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 526 | 531 | 482 | 595 | 534 |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 450 | 464 | 397 | 517 | 441 | |

CoV | % | 10 | 8 | 11 | 9 | 12 |

Species | GDPs | Visual Grades | |||
---|---|---|---|---|---|

ME-1 | ME-2 | R | |||

Maritime pine | n | 72 | 270 | 141 | |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 25.3 | 16.7 | 14.8 | |

CoV | % | 32 | 41 | 51 | |

${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 14.4 | 11.7 | 10.9 | |

CoV | % | 30 | 34 | 33 | |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 517 | 448 | 446 | |

CoV | % | 9 | 12 | 11 | |

Strength class (SC) | C24 | C16 | C14 | ||

SC EN1912 | C24 | C18 | R | ||

Radiata pine | n | 68 | 106 | 51 | |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 23.1 | 12.3 | 9.2 | |

CoV | % | 23 | 40 | 61 | |

${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 11.6 | 9.74 | 7.68 | |

CoV | % | 24 | 35 | 44 | |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 449 | 414 | 404 | |

CoV | % | 11 | 12 | 13 | |

Strength class (SC) | C22 | - | - | ||

SC EN1912 | C24 | C18 | R | ||

Scots pine | n | 134 | 307 | 118 | |

${f}_{m,k}$ | $\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 24.5 | 19.5 | 14.4 | |

CoV | % | 33 | 32 | 43 | |

${E}_{0,mean}$ | $\mathrm{k}\mathrm{N}/\mathrm{m}{\mathrm{m}}^{2}$ | 12.7 | 11.0 | 10.4 | |

CoV | % | 22 | 20 | 30 | |

${\rho}_{k}$ | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | 422 | 406 | 387 | |

CoV | % | 13 | 14 | 14 | |

Strength class (SC) | C24 | C18 | C14 | ||

SC EN1912 | C27 | C18 | R |

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## Share and Cite

**MDPI and ACS Style**

Moltini, G.; Íñiguez-González, G.; Cabrera, G.; Baño, V.
Evaluation of Yield Improvements in Machine vs. Visual Strength Grading for Softwood Species. *Forests* **2022**, *13*, 2021.
https://doi.org/10.3390/f13122021

**AMA Style**

Moltini G, Íñiguez-González G, Cabrera G, Baño V.
Evaluation of Yield Improvements in Machine vs. Visual Strength Grading for Softwood Species. *Forests*. 2022; 13(12):2021.
https://doi.org/10.3390/f13122021

**Chicago/Turabian Style**

Moltini, Gonzalo, Guillermo Íñiguez-González, Gonzalo Cabrera, and Vanesa Baño.
2022. "Evaluation of Yield Improvements in Machine vs. Visual Strength Grading for Softwood Species" *Forests* 13, no. 12: 2021.
https://doi.org/10.3390/f13122021