Skip to main content

Official Journal of the Japan Wood Research Society

Strain analysis of lumber containing a knot during tensile failure


We analyzed the strain distribution of lumber containing a knot under a tensile load. The local tensile strain near the knot was measured using the digital image correlation method. Fracture often initiated near the knot where the fiber orientation changed in a three-dimensional manner. The fiber direction in this zone was different from that in the clear part, coinciding with the thickness direction and not with the longitudinal direction of the specimen. Our results disagree with those of previous models that assumed the longitudinal direction of lumber as the direction of crack propagation. Strain analysis showed that a nonlinear region existed around the knot just before ultimate fracture occurred. The results indicated that nonlinear characterization is necessary to determine the failure mechanism of lumber containing a knot, despite the brittleness fracture at the macroscopic scale.


  1. Oh JK, Shim K, Kim KM, Lee JJ (2009) Quantification of knots in dimension lumber using a single-pass X-ray radiation. J Wood Sci 55:264–272

    Article  Google Scholar 

  2. Oh JK, Kim KM, Lee JJ (2010) Use of adjacent knot data in predicting bending strength of dimension lumber by X-ray. Wood Fiber Sci 42:10–20

    CAS  Google Scholar 

  3. Sasaki H, Maku T (1962) On the strain distribution and failure of wood plates with a round knot under tensile load (in Japanese). Wood Res 28:1–23

    Google Scholar 

  4. Takahashi A (1966) Strain determination of wood by using photoelastic coating technique VI — On the strain distribution of board with a loose knot subjected to tensile load (in Japanese). Mokuzai Gakkaishi 12:63–66

    Google Scholar 

  5. Cramer SM, Goodman JR (1983) Model for stress analysis and strength prediction of lumber. Wood Fiber Sci 15:338–349

    Google Scholar 

  6. Zandbergs JG, Smith FW (1988) Finite element fracture prediction for wood with knots and cross grain. Wood Fiber Sci 20:97–106

    Google Scholar 

  7. Cramer SM, Fohrell WB (1990) Method for simulating tension performance of lumber members. J Struct Eng 116:2729–2746

    Article  Google Scholar 

  8. Itagaki N, Mihashi H, Ninomiya S, Yoshida N, Esashi T (1999) Influence of knots on tensile strength of sugi lamina (in Japanese). Mokuzai Gakkaishi 45:367–374

    Google Scholar 

  9. Jeong GY, Zink-Sharp A, Hindman DP (2009) Tensile properties of earlywood and latewood from loblolly pine (Pinus taeda) using digital image correlation. Wood Fiber Sci 41:51–63

    CAS  Google Scholar 

  10. Murata K, Masuda M, Ukyo S (2005) Analysis of strain distribution of wood using digital image correlation method — Four-point bending test of timber including knots (in Japanese). Trans Vis Soc Jpn 25:267–273

    Google Scholar 

  11. Ljungdahl J, Berglund LA, Burman M (2006) Transverse anisotropy of compressive failure in European oak — A digital speckle photography study. Holzforschung 60:190–195

    Article  CAS  Google Scholar 

  12. Shipsha A, Berglund LA (2007) Shear coupling effects on stress and strain distributions in wood subjected to transverse compression. Compos Sci Tech 67:1362–1369

    Article  Google Scholar 

  13. Murata K, Masuda M, Ichimaru M (1999) Analysis of radial compression behavior of wood using digital image correlation method (in Japanese). Mokuzai Gakkaishi 45:375–381

    Google Scholar 

  14. Ministry of Land, Infrastructure, Transport and Tourism (2001) Ministerial announcement No. 1024. (in Japanese)

  15. Shigo AL (1985) How trees are attached to trunks. Can J Bot 63:1391–1401

    Article  Google Scholar 

  16. Miyauchi K, Murata K (2007) Strain-softening behavior of wood under tension perpendicular to the grain. J Wood Sci 53:463–469

    Article  Google Scholar 

  17. Vasic S, Smith I, Landis E (2002) Fracture zone characterization — micro-mechanical study. Wood Fiber Sci 34:42–56

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Hiroaki Nagai.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nagai, H., Murata, K. & Nakano, T. Strain analysis of lumber containing a knot during tensile failure. J Wood Sci 57, 114–118 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words

  • Strain distribution analysis
  • Knot
  • Digital image correlation