Knots and their effect on the tensile strength of lumber: A case study

Abstract

When assessing the strength of sawn lumber for use in engineering applications, the sizes and locations of knots are an important consideration. Knots are the most common visual characteristics of lumber, that result from the growth of tree branches. Large individual knots, as well as clusters of distinct knots, are known to have strength-reducing effects. However, industry grading rules that govern knots are informed by subjective judgment to some extent, particularly the spatial interaction of knots and their relationship with lumber strength. This case study reports the results of an experiment that investigated and modeled the strength-reducing effects of knots on a sample of Douglas Fir lumber. Experimental data were obtained by taking scans of lumber surfaces and applying tensile strength testing. The modeling approach presented incorporates all relevant knot information in a Bayesian framework, thereby contributing a more refined way of managing the quality of manufactured lumber.

Keywords:

• Bayesian predictive model
• quality control
• strength-reducing characteristics
• structural lumber testing
• visual stress grading
• wood products

Acknowledgements

The authors thank Conroy Lum, along with FPInnovations and its technical support staff, for facilitating the experimental work that was done to produce the data used in this case study. Thanks also to Conroy for his expertise and assistance in helping the authors understand better the complexities involved in grading lumber and providing constructive comments on the manuscript. Finally, the work profited from the comments of members of the Forest Products Stochastic Modelling Group, centered at the University of British Columbia.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The code and data that support the results of this study are provided in the supplementary .zip file.

Additional information

Funding

The work reported in this case study was partially funded by FPInnovations and grants from the Natural Science and Engineering Research Council of Canada.

Notes on contributors

Shuxian Fan

Shuxian Fan is a PhD candidate at the University of Washington, with research interests in integrating information theory in designing efficient data strategies. Shuxian received her Bachelor’s and Master’s degrees from the University of British Columbia. Her research focuses on applying stochastic modeling to forest products and deriving data strategies for verbal autopsy data for the study of under-five child mortality using Bayes inference, Bayes active learning, and imprecise probabilities.

Samuel W. K. Wong

Samuel W. K. Wong is an Associate Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. He received his PhD in Statistics from Harvard University in 2013. His research focuses on developing analytical methods to tackle data-driven problems arising in scientific domains that include protein bioinformatics, dynamic systems, and quality assessment of forest products.

James V. Zidek

James V. Zidek is Professor Emeriti of Statistics at the University of British Columbia. He is an expert in the area of environmetrics about which he has co-authored a book with Dr Nhu Le that was published in 2006 and a second with Gavin Shaddick on spatio-temporal modelling in environmental epidemiology published in 2015. His research has involved the design of networks for monitoring environmental hazards as well as methods for modelling and analyzing the data these networks produce. He has taught courses and short courses on a variety of topics associated with spatial and temporal modelling. Currently he is consultant for the National Lumber Grading Association of Canada. His achievements have been recognized by his appointments as a Fellow in the Royal Soc of Canada and an Officer in the Order of Canada.