Effect of specimen geometry on axial compressive strength variability in Oriental beech (Fagus orientalis Lipsky) and common hornbeam (Carpinus betulus L.) wood

Abstract

The parallel-to-grain compressive strength of solid wood is significantly influenced by specimen geometry, slenderness ratio (the ratio of specimen length to characteristic cross-sectional dimension), and loading boundary conditions, alongside its heterogeneous and anisotropic structure. In this study, the combined effect of different specimen dimensions and slenderness ratios specified in international standards on the compressive strength of Oriental beech (Fagus orientalis Lipsky) and common hornbeam (Carpinus betulus L.) wood was investigated using a multidisciplinary approach. Experimental data were analysed using Weibull statistics, Bažant’s Size Effect Law (SEL), Carpinteri’s Multifractal Scaling Law (MFSL), and a three-dimensional orthotropic finite element method (FEM). Statistical findings revealed that the species × size interaction was highly significant (p < 0.001) in governing the mechanical response. Hornbeam wood exhibited a consistent loss of strength with increasing specimen volume, displaying a scaling behaviour compatible with Weibull and MFSL approaches. In contrast, beech wood displayed maximum strength at low slenderness ratios, generating a non-linear size effect. Whilst the Bažant SEL model showed a poor fit with the beech data, it failed to yield physically meaningful scaling parameters for hornbeam despite demonstrating a high regression fit. FEM-based stress analyses revealed the three-dimensional stress distribution within the specimens under experimental ultimate loads, enabling a mechanical assessment of the effects of slenderness ratios on stress concentrations and load transfer. Consequently, the findings demonstrate that explaining the compressive strength of solid wood solely through volumetric defect distribution may be insufficient; thus, in reliable engineering designs, the statistical size effect should be evaluated in an integrated manner with geometry- and contact-induced deterministic mechanisms.

Keywords

• Compressive strength
• Fracture mechanics
• Finite element analysis
• Weibull distribution

Doğu kayını (Fagus orientalis Lipsky) ve adi gürgen (Carpinus betulus L.) odunlarında numune geometrisinin basınç dayanımı değişkenliği üzerindeki etkisi

Abstract

Masif odunun liflere paralel basınç dayanımı, heterojen ve anizotropik yapısının yanı sıra numune geometrisi, narinlik oranı (numune uzunluğunun karakteristik kesit boyutuna oranı) ve yükleme sınır koşullarından önemli ölçüde etkilenmektedir. Bu çalışmada, Doğu kayını (Fagus orientalis Lipsky) ve adi gürgen (Carpinus betulus L.) odunlarında uluslararası standartlardaki farklı numune boyutları ve narinlik oranlarının basınç dayanımı üzerindeki birleşik etkisi çok disiplinli bir yaklaşımla araştırılmıştır. Deneysel veriler, Weibull istatistikleri, Bažant’ın Boyut Etkisi Yasası (SEL), Carpinteri’nin Çoklu-Fraktal Ölçekleme Yasası (MFSL) ve üç boyutlu ortotropik sonlu elemanlar yöntemi (FEM) ile analiz edilmiştir. İstatistiksel bulgular, tür × boyut etkileşiminin mekanik özellikler üzerinde son derece belirleyici olduğunu (p < 0,001) göstermiştir. Gürgen odunu, numune hacmi arttıkça istikrarlı bir dayanım kaybı sergileyerek Weibull ve MFSL yaklaşımlarıyla uyumlu bir ölçeklenme davranışı sunmuştur. Buna karşın kayın odunu, düşük narinlik oranlarında maksimum dayanım sergileyerek doğrusal olmayan bir boyut etkisi oluşturmuştur. Bažant SEL modeli kayın verileriyle zayıf bir uyum gösterirken, gürgende yüksek regresyon uyumuna rağmen fiziksel olarak anlamlı ölçekleme katsayıları üretememiştir. FEM analizleri, deneysel nihai yükleme koşullarında numune içerisindeki üç boyutlu gerilme dağılımını ortaya koymuş ve farklı geometrik narinlik oranlarının gerilme yığılmaları ile yük aktarımı üzerindeki etkisinin mekanik olarak değerlendirilmesine olanak sağlamıştır. Sonuç olarak bulgular, masif odunun basınç dayanımının yalnızca hacimsel kusur dağılımıyla açıklanmasının yetersiz kalabileceğini, güvenilir mühendislik tasarımlarında istatistiksel boyut etkisinin, geometri ve temas kaynaklı fiziksel mekanizmalarla entegre biçimde değerlendirilebileceğini göstermektedir.

Keywords

• Basınç dayanımı
• Kırılma mekaniği
• Sonlu elemanlar analizi
• Weibull dağılımı

Ethical Statement

Etik kurul onayı gerekmemektedir.

References

1. Andre, A., Kliger, R., & Asp, L. E. (2014). Compression failure mechanism in small scale timber specimens. Construction and Building Materials, 50, 130–139. https://doi.org/10.1016/j.conbuildmat.2013.09.018
2. Arriaga, F., Wang, X., Íñiguez-González, G., Llana, D. F., Esteban, M., & Niemz, P. (2023). Mechanical properties of wood: A review. Forests, 14(6), 1202. https://doi.org/10.3390/f14061202
3. ASTM D143-25 (2025). Standard test methods for small clear specimens of timber. USA: Annual Book of ASTM Standards.
4. Astrup, T., Clorius, C. O., Damkilde, L., & Hoffmeyer, P. (2007). Size effect of glulam beams in tension perpendicular to grain. Wood Science and Technology, 41, 361–372. https://doi.org/10.1007/s00226-006-0113-6
5. Aydemir, D., Buruc, G., & Bakır, K. (2019). The effect of heat treatment on some properties of Oriental beech and sessile oak wood. Bartın Orman Fakültesi Dergisi, 21, 713–721.
6. Bartolucci, B., De Rosa, A., Bertolin, C., Berto, F., Penta, F., & Siani, A. M. (2020). Mechanical properties of the most common European woods: A literature review. Frattura ed Integrità Strutturale, 14(54), 249–274. https://doi.org/10.3221/IGF-ESIS.54.18
7. Bažant, Z. P. (1984). Size effect in blunt fracture: Concrete, rock, metal. Journal of Engineering Mechanics, 110(4), 518–535. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518)
8. Bažant, Z. P., & Pfeiffer, P. A. (1987). Determination of fracture energy from size effect and brittleness number. ACI Materials Journal, 84(6), 463–480.

9. Bažant, Z. P., & Planas, J. (1997). Fracture and size effect in concrete and other quasibrittle materials (Vol. 16). Boca Raton, FL: CRC Press.
10. Binder, E., Kuck, E., Bertram, C., Shehadeh, Z., Schweigler, M., Sandhaas, C., & Bader, T. K. (2026). Stiffness and strength of beech, birch and spruce in compression perpendicular to the grain and rolling shear: Influence of moisture content, annual ring structure, and test method. Construction and Building Materials, 538, 147142. https://doi.org/10.1016/j.conbuildmat.2026.147142
11. Bodig, J., & Jayne, B. A. (1982). Mechanics of wood and wood composites. New York, NY: Van Nostrand Reinhold.
12. Büyüksarı, Ü., As, N., Dündar, T., & Sayan, E. (2017a). Micro-tensile and compression strength of Scots pine wood and comparison with standard-size test results. Drvna Industrija, 68(2), 129–136. https://doi.org/10.5552/drind.2017.1639
13. Büyüksarı, Ü., As, N., Dündar, T., & Korkmaz, O. (2017b). Micro-mechanical properties of oak wood and comparison with standard-sized samples. Maderas. Ciencia y Tecnología, 19(4), 481–494. https://doi.org/10.4067/S0718-221X2017005000801
14. Carpinteri, A. (1994a). Scaling laws and renormalization groups for strength and toughness of disordered materials. International Journal of Solids and Structures, 31(3), 291–302. https://doi.org/10.1016/0020-7683(94)90107-4
15. Carpinteri, A. (1994b). Fractal nature of material microstructure and size effects on apparent mechanical properties. Mechanics of Materials, 18(2), 89–101. https://doi.org/10.1016/0167-6636(94)00008-5
16. Chen, Z., Lu, H., Liao, J., Hu, X., Huang, L., & Song, Y. (2025). Compressive mechanical properties of Mongolian Scots pine: The influence of specimen dimensions. Results in Engineering, 28, 108292. https://doi.org/10.1016/j.rineng.2025.108292
17. DIN 52185 (1976). Testing of wood; compression test parallel to grain. Berlin, Germany: DIN.
18. Ehrhart, T., Steiger, R., Palma, P., Gehri, E., & Frangi, A. (2020). Glulam columns made of European beech timber: Compressive strength and stiffness parallel to the grain, buckling resistance and adaptation of the effective-length method according to Eurocode 5. Materials and Structures, 53(4), 91. https://doi.org/10.1617/s11527-020-01524-6
19. Golovin, Y. I., Gusev, A. A., Golovin, D. Y., Matveev, S. M., & Vasyukova, I. A. (2022). Multiscale mechanical performance of wood: From nano-to macro-scale across structure hierarchy and size effects. Nanomaterials, 12(7), 1139. https://doi.org/10.3390/nano12071139
20. Hu, W., Wan, H., & Guan, H. (2019). Size effect on the elastic mechanical properties of beech and its application in finite element analysis of wood structures. Forests, 10(9), 783. https://doi.org/10.3390/f10090783
21. ISO 13061-1 (2014a). Physical and mechanical properties of wood—Test methods for small clear wood specimens—Part 1: Determination of moisture content for physical and mechanical tests. Geneva, Switzerland: ISO.
22. ISO 13061-2 (2014b). Physical and mechanical properties of wood—Test methods for small clear wood specimens—Part 2: Determination of density for physical and mechanical tests. Geneva, Switzerland: ISO.
23. ISO 13061-17 (2017). Physical and mechanical properties of wood—Test methods for small clear wood specimens—Part 17: Determination of ultimate stress in compression parallel to grain. Geneva, Switzerland: ISO.
24. ISO 3129 (2019). Wood—Sampling methods and general requirements for physical and mechanical testing of small clear wood specimens. Geneva, Switzerland: ISO.
25. Liao, J., Chen, Z., Hu, X., Song, Y., & Lu, H. (2025). Effects of specimen longitudinal dimensions on the compressive mechanical properties of timber: Experimental investigation and quantitative analysis. Case Studies in Construction Materials, 22, e05665. https://doi.org/10.1016/j.cscm.2025.e05665
26. Kiaei, M., Moosavi, V., & Ebadi, S. E. (2019). Effects of altitude on density and biometric properties of hornbeam wood (Carpinus betulus). Forest Systems, 28(2), e011. https://doi.org/10.5424/fs/2019282-14490
27. Lauer, C., Schmier, S., Speck, T., & Nickel, K. G. (2018). Strength-size relationships in two porous biological materials. Acta Biomaterialia, 77, 322–332. https://doi.org/10.1016/j.actbio.2018.07.010
28. Lei, W. S., Qian, G., Yu, Z., & Berto, F. (2019). Statistical size scaling of compressive strength of quasi-brittle materials incorporating specimen length-to-diameter ratio effect. Theoretical and Applied Fracture Mechanics, 104, 102345. https://doi.org/10.1016/j.tafmec.2019.102345
29. Li, J., Yan, J., Zhou, Y., Yang, S., & Singh, A. (2024). Analyzing the effects of size and density on the ultimate compressive strength of structural laminated bamboo parallel to the grain. Journal of Building Engineering, 90, 109481. https://doi.org/10.1016/j.jobe.2024.109481
30. Li, H., Zhang, J., Xu, G., & Li, W. (2025). Compression test and size effect study of defective wood. Wood Material Science & Engineering, 20(5), 1075–1083. https://doi.org/10.1080/17480272.2024.2383747
31. Liu, J., Xu, G., Bai, Y., Lin, Y., & Geng, W. (2024). Effect of wood specimen length on uniaxial stress–strain curve along the grain direction. Forest Products Journal, 74(1), 28–33. https://doi.org/10.13073/FPJ-D-23-00046
32. Mania, P., Hartlieb, K., Mruk, G., & Roszyk, E. (2022). Selected properties of densified hornbeam and paulownia wood plasticised in ammonia solution. Materials, 15(14), 4984. https://doi.org/10.3390/ma15144984
33. MGM. (2025). Resmi iklim istatistikleri. Ankara, Türkiye. https://mgm.gov.tr/veridegerlendirme/il-ve-ilceler-istatistik.aspx
34. Moshtaghin, A. F., Franke, S., Keller, T., & Vassilopoulos, A. P. (2016). Random field-based modeling of size effect on the longitudinal tensile strength of clear timber. Structural Safety, 58, 60–68. https://doi.org/10.1016/j.strusafe.2015.09.002
35. Nasswettrová, A., Šmíra, P., & Křivánková, S. (2016). Effect of microwave heating on compressive strength of beech wood (Fagus sylvatica L.) parallel to grain. Drying Technology, 34(9), 1011–1022. https://doi.org/10.1080/07373937.2015.1077254
36. Oudjene, M., & Khelifa, M. (2009). Finite element modelling of wooden structures at large deformations and brittle failure prediction. Materials & Design, 30(10), 4081–4087. https://doi.org/10.1016/j.matdes.2009.05.024
37. Pedersen, M. U., Clorius, C. O., Damkilde, P., & Hoffmeyer, P. (2003). A simple size effect model for tension perpendicular to grain. Wood Science and Technology, 37(2), 125–140.
38. Safdari, V., Ahmed, M., Palmer, J., & Baig, M. B. (2008). Identification of Iranian commercial wood with hand lens. Pakistan Journal of Botany, 40(5), 1851–1864.
39. Schlotzhauer, P., Nelis, P. A., Bollmus, S., Gellerich, A., Militz, H., & Seim, W. (2017). Effect of size and geometry on strength values and MOE of selected hardwood species. Wood Material Science & Engineering, 12(3), 149–157. https://doi.org/10.1080/17480272.2015.1073175
40. Schneeweiß, G. (1964). Druckfestigkeit und Stempelhärte. Holz als Roh- und Werkstoff, 22(7), 258–264.
41. Senalik, C.A., & Farber, B. (2021). Mechanical properties of wood. In R.J. Ross (Ed.), Wood handbook—Wood as an engineering material (pp. 5-1–5-46). U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. https://doi.org/10.2737/FPL-GTR-282
42. SimScale GmbH. (2026). SimScale. Munich, Germany. https://www.simscale.com/
43. Sinaie, S. (2017). Application of the discrete element method for the simulation of size effects in concrete samples. International Journal of Solids and Structures, 108, 244–253. https://doi.org/10.1016/j.ijsolstr.2016.12.022
44. Skarvelis, M., & Mantanis, G. I. (2013). Physical and mechanical properties of beech wood harvested in the Greek public forests. Wood Research, 58(1), 123–130.
45. Tapia, C., & Aicher, S. (2022). Survival analysis of tensile strength variation and simulated length–size effect along oak boards. Journal of Engineering Mechanics, 148(1), 04021130. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002006
46. Totsuka, M., Jockwer, R., Aoki, K., & Inayama, M. (2021). Experimental study on partial compression parallel to grain of solid timber. Journal of Wood Science, 67(1), 39. https://doi.org/10.1186/s10086-021-01972-w
47. Walley, S. M., & Rogers, S. J. (2022). Is wood a material? Taking the size effect seriously. Materials, 15(15), 5403. https://doi.org/10.3390/ma15155403
48. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293–297.
49. Xiang, S., Chen, H., He, Y., Zhou, C., Li, X., & Gong, M. (2026). Numerical study on structural-scale wood scrimber beams: Modelling, calibration, and size effect. European Journal of Wood and Wood Products, 84(1), 16. https://doi.org/10.1007/s00107-025-02363-4
50. Zauner, M., & Niemz, P. (2014). Uniaxial compression of rotationally symmetric Norway spruce samples: Surface deformation and size effect. Wood Science and Technology, 48(5), 1019–1032. https://doi.org/10.1007/s00226-014-0658-8
51. Zhao, C., Liu, D., Zhang, C., Li, Y., & Wang, Y. (2024). Influence of specimen size on the compressive strength of wood. Buildings, 14(4), 1156. https://doi.org/10.3390/buildings14041156
52. Zhao, P., & Zhang, X. (2019). Size effect of section on ultimate compressive strength parallel to grain of structural bamboo scrimber. Construction and Building Materials, 200, 586–590.