Calibrating wood products for load duration and rate: a statistical look at three damage models

Abstract

Lumber and wood-based products are versatile construction materials that are susceptible to weakening as a result of applied stresses. To assess the effects of load duration and rate, experiments have been carried out by applying preset load profiles to sample specimens. This paper studies these effects via a damage modeling approach, by considering three models in the literature: the Gerhards and Foschi accumulated damage models, and a degradation model based on the gamma process. A statistical framework is presented for fitting these models to failure time data generated by a combination of ramp and constant load settings, and it is shown how estimation uncertainty can be quantified. The models and methods are illustrated and compared via a novel analysis of a Hemlock lumber dataset. Practical usage of the fitted damage models is demonstrated with an application to long-term reliability prediction under stochastic future loadings.

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References

  1. Agnew DC (1992) The time-domain behavior of power-law noises. Geophys Res Lett 19(4):333–336

    Article  Google Scholar 

  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723

    Article  Google Scholar 

  3. American Wood Council (2018) National design specification (NDS) for wood construction. American National Standards Institute/American Wood Council (ANSI/AWC), Leesburg

  4. ASTM Standard D4761 (2005) Standard test methods for mechanical properties of lumber and wood-base structural material. Technical Report https://doi.org/10.1520/D4761-05, ASTM International, West Conshohocken, PA

  5. Bartlett F, Hong H, Zhou W (2003) Load factor calibration for the proposed 2005 edition of the national building code of Canada: Statistics of loads and load effects. Can J Civ Eng 30(2):429–439

    Article  Google Scholar 

  6. Botev ZI, Grotowski JF, Kroese DP et al (2010) Kernel density estimation via diffusion. Ann Stat 38(5):2916–2957

    Article  Google Scholar 

  7. Ellingwood B, Rosowsky D (1991) Duration of load effects in LRFD for wood construction. J Struct Eng 117(2):584–599

    Article  Google Scholar 

  8. Foschi RO, Barrett JD (1982) Load-duration effects in western hemlock lumber. J Struct Division 108(7):1494–1510

    Google Scholar 

  9. Foschi RO, Folz B, Yao F (1989) Reliability-based design of wood structures, vol 34, Department of Civil Engineering, University of British Columbia

  10. Foschi RO, Yao Z (1986) Another look at three duration of load models. IUFRO Wood Engineering Group Meeting, Florence, Italy

  11. Gerhards C (1979) Time-related effects of loading on wood strength: a linear cumulative damage theory. Wood Sci 11(3):139–144

    Google Scholar 

  12. Gerhards C, Link C (1987) A cumulative damage model to predict load duration characteristics of lumber. Wood Fiber Sci 19(2):147–164

    Google Scholar 

  13. Gilbert BP, Zhang H, Bailleres H (2019) Reliability of laminated veneer lumber (LVL) beams manufactured from early to mid-rotation subtropical hardwood plantation logs. Struct Saf 78:88–99

    Article  Google Scholar 

  14. Hoffmeyer P, Sørensen JD (2007) Duration of load revisited. Wood Sci Technol 41(8):687–711

    CAS  Article  Google Scholar 

  15. Karacabeyli E, Barrett J (1993) Rate of loading effects on strength of lumber. Forest Prod J 43(5):28

    Google Scholar 

  16. Karacabeyli E, Lum C (1994) Failure rate and strength degradation in lumber under constant load. IUFRO S5.02 Timber Engineering Meeting, Sydney, Australia

  17. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90(430):773–795

    Article  Google Scholar 

  18. Köhler J, Svensson S (2011) Probabilistic representation of duration of load effects in timber structures. Eng Struct 33(2):462–467

    Article  Google Scholar 

  19. Li Y, Lam F (2016) Reliability analysis and duration-of-load strength adjustment factor of the rolling shear strength of cross laminated timber. J Wood Sci 62(6):492–502

    Article  Google Scholar 

  20. Liska J (1950) Effect of rapid loading on the compressive and flexural strength of wood. United States Forest Products Laboratory, Report No. R1767

  21. Madsen B, Johns K (1982) Duration of load effects in lumber. Part II: experimental data. Can J Civ Eng 9(3):515–525

    Article  Google Scholar 

  22. Madsen HO, Krenk S, Lind NC (2006) Methods of structural safety. Courier Corporation

  23. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  Google Scholar 

  24. Wang JB, Lam F, Foschi RO (2012) Duration-of-load and creep effects in strand-based wood composite: experimental research. Wood Sci Technol 46(1–3):361–373

    CAS  Article  Google Scholar 

  25. Wang Z, Yang N (2019) Parameter-based applicability analysis of Gerhards cumulative damage model in residual strength and life prediction of wood in bending. Wood Sci Technol 53(6):1255–1277

    CAS  Article  Google Scholar 

  26. Wong SW, Zidek JV (2018) Dimensional and statistical foundations for accumulated damage models. Wood Sci Technol 52(1):45–65

    CAS  Article  Google Scholar 

  27. Wong SW, Zidek JV (2019) The duration of load effect in lumber as stochastic degradation. IEEE Trans Reliab 68(2):410–419

    Article  Google Scholar 

  28. Wood L (1951) Relation of strength of wood to duration of load. US Forest Products Laboratory, Madison, Wisc., USA, Report No. R1916

  29. Yang C-H, Zidek JV, Wong SW (2019) Bayesian analysis of accumulated damage models in lumber reliability. Technometrics 61(2):233–245

    Article  Google Scholar 

Download references

Acknowledgements

The work reported in this paper was partially supported by FPInnovations and a CRD grant from the Natural Sciences and Engineering Research Council of Canada. The author is greatly indebted to Conroy Lum and Erol Karacabeyli from FPInnovations for introducing the author to this important area of research, sharing extensive advice during the conduct of this study, and providing the Forintek dataset analyzed herein. The author also thanks James V Zidek for helpful discussions during the preparation of the manuscript.

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Correspondence to Samuel W. K. Wong.

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Wong, S.W.K. Calibrating wood products for load duration and rate: a statistical look at three damage models. Wood Sci Technol 54, 1511–1528 (2020). https://doi.org/10.1007/s00226-020-01227-9

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