Size Effect on the Elastic Mechanical Properties of Beech and Its Application in Finite Element Analysis of Wood Structures
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials and Equipment
2.2. Specimens Preparation
2.3. Testing Methods
2.3.1. Physical Properties of European Beech Wood
2.3.2. Proportional Limit Stress and Elastic Constants
2.3.3. Load Capacity of Chair
2.4. Modeling
3. Results and Discussion
3.1. Physical Properties of European Beech Wood
3.2. Size Effect on Proportional Limit Stresses of European Beech
3.3. Size Effect on Elastic Constants of Beech
3.4. Load Capacity of Chair and Failure Mode
3.5. Comparison and Analysis
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Specimen Types | Dimensions | Number | ||||
---|---|---|---|---|---|---|
Cross-Sectional Area (mm2) | Height (mm) | Elastic Constants | Proportional Limit Stress | Total | ||
Width (mm) | Length (mm) | |||||
1 | 10 | 10 | 10 | 30 | 30 | 60 |
2 | 10 | 10 | 20 | 30 | 30 | 60 |
3 | 10 | 10 | 30 | 30 | 30 | 60 |
4 | 20 | 20 | 30 | 30 | 30 | 60 |
5 | 30 | 30 | 30 | 30 | 30 | 60 |
Monitor Factor | Sum of Squares | Degree of Freedom | Mean Squares | Fisher’s F-Test | Significance |
---|---|---|---|---|---|
Intercept | 17,851.842 | 1 | 17,851.842 | 6394.165 | p < 0.01 |
Height (a) | 219.444 | 2 | 109.722 | 39.300 | p < 0.01 |
Cross-sectional Area (b) | 181.119 | 2 | 90.559 | 32.437 | p < 0.01 |
a × b | 0 | 0 | |||
Error | 167.514 | 60 | 2.792 |
Specimen Type | EL (MPa) | ER (MPa) | ET (MPa) | μLR | μLT | μRT | GL (MPa) | GR (MPa) | GT (MPa) |
---|---|---|---|---|---|---|---|---|---|
1 | 13449 | 1027 | 764 | 0.697 | 0.720 | 0.444 | 527 | 399 | 173 |
COV (%) | 4.8 | 5.8 | 4.5 | 1.0 | 9.4 | 0.8 | 6.4 | 2.7 | 10.3 |
2 | 15284 | 1161 | 863 | 0.643 | 0.549 | 0.644 | 729 | 462 | 265 |
COV (%) | 0.3 | 2.7 | 0.7 | 3.0 | 1.3 | 3.5 | 1.0 | 5.5 | 13.1 |
3 | 17980 | 1537 | 1041 | 0.398 | 0.625 | 0.515 | 945 | 499 | 373 |
COV (%) | 2.4 | 6.8 | 2.0 | 1.9 | 0.5 | 2.8 | 1.5 | 14.4 | 4.5 |
4 | 14075 | 1482 | 707 | 0.710 | 0.338 | 0.465 | 832 | 444 | 259 |
COV (%) | 1.1 | 2.8 | 4.7 | 7.7 | 14.1 | 2.8 | 3.0 | 7.8 | 1.3 |
5 | 12617 | 1337 | 642 | 0.408 | 0.368 | 0.588 | 828 | 398 | 169 |
COV (%) | 1.9 | 3.1 | 6.8 | 0.9 | 10.1 | 0.3 | 10.4 | 3.8 | 18.6 |
Monitored Factor | Dependent Variable | Sum of Squares | Degree of Freedom | Mean Squares | Fisher’s F-Test | Significance |
---|---|---|---|---|---|---|
Cross-sectional Area × Height | EL | 176,983,729.639 | 4 | 44,245,932.410 | 237.704 | p < 0.01 |
ER | 899,669.479 | 4 | 224,917.370 | 39.344 | p < 0.01 | |
ET | 195,869.174 | 4 | 48,967.294 | 30.436 | p < 0.01 | |
νLR | 0.293 | 4 | 0.073 | 51.594 | p < 0.01 | |
νLT | 0.318 | 4 | 0.079 | 24.222 | p < 0.01 | |
νRT | 0.082 | 4 | 0.021 | 65.324 | p < 0.01 | |
GLR | 293,182.023 | 4 | 73,295.506 | 19.698 | p < 0.01 | |
GLT | 21,512.839 | 4 | 5378.210 | 6.430 | p < 0.01 | |
GRT | 84,329.602 | 4 | 21,082.400 | 19.736 | p < 0.01 |
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Hu, W.; Wan, H.; Guan, H. Size Effect on the Elastic Mechanical Properties of Beech and Its Application in Finite Element Analysis of Wood Structures. Forests 2019, 10, 783. https://doi.org/10.3390/f10090783
Hu W, Wan H, Guan H. Size Effect on the Elastic Mechanical Properties of Beech and Its Application in Finite Element Analysis of Wood Structures. Forests. 2019; 10(9):783. https://doi.org/10.3390/f10090783
Chicago/Turabian StyleHu, Wengang, Hui Wan, and Huiyuan Guan. 2019. "Size Effect on the Elastic Mechanical Properties of Beech and Its Application in Finite Element Analysis of Wood Structures" Forests 10, no. 9: 783. https://doi.org/10.3390/f10090783