Arboriculture & Urban Forestry 34(2): March 2008 Norway spruce [Picea abies (L.) Karst.], Scots pine (Pinus syl- vestris L.), and birch (Betula spp.). Part of the disparity between tree stress and wood samples can be explained by the fact that stress at the point of failure was based on outside bark diameter. Because bark has a lower MOR than wood, adding bark to the diameter of wood that resists bending underestimates the actual stress. MOR values for wood samples of red and sugar maples in this study were similar to those published in the Wood Handbook (Green et al. 1999), whereas MOR values for Norway maples were less than those from trees sampled in Germany (Hannover and Schaper 2003). It appears that shade tree risk assessment models that use a static pulling test and Hooke’s Law to quantify stem defects (e.g., Brudi and van Wassenaer 2001) may overes- timate bending strength and therefore underestimate the risk of failure because such models use wood properties taken from samples, not entire trees. Prediction of Bending Moment and Stress at the Point of Failure The inverse relationship between stress and diameter cubed ex- plains why diameter at breast height and diameter at breast height cubed were somewhat reliable predictors of stress at the point of failure. The relationships between bending moment at the point of failure and measures of tree size were the result of the fact that bending moment is directly proportional to the fourth power of diameter (Lardner and Archer 1994). The fact that bending moment at the point of failure for codominant fail- ures was not reliably predicted by measures of tree size for codominant failures supports the notion that codominant stems constitute structural defects, although the small sample size may have undermined predictions. This notion is further supported by the fact that stress at the point of failure for codominants was only 45% of the MOR of wood samples. Measures of tree size such as dbh, dbh cubed, and stem volume were excellent pre- dictors of the maximum bending moment for stem failures of forest conifers (Fredericksen et al. 1993; Papesch et al. 1997; Moore 2000; Peltola et al. 2000) with most R2 values greater than 0.90. Coefficients of determination from those studies were much greater than was found for maples in the current study, indicating the importance of defects in causing failure. Slenderness was inversely proportional to the maximum bend- ing moment and stress of forest trees (Petty and Swain 1985; Milne and Blackburn 1989; Fredericksen et al. 1993; Peltola et al. 2000), but was not a reliable predictor of bending moment or stress at the point of failure for maples, regardless of the type of failure. This was likely the result of forest trees from previous studies being noticeably more slender than maples. The least slender trees were tested in New Zealand (height/dbh ≅ 50) (Papesch et al. 1997; Moore 2000), but values are commonly twice as large (Blackburn et al. 1988; Peltola et al. 2000). Typi- cal values of slenderness in windthrow models range from 80 to 120 (Peltola et al. 1999; Ancelin et al. 2004). Comparison to Forest Conifers Most previous studies have reported that root failures were more common than stem failures (Smith et al. 1987; Papesch et al. 1997; Moore 2000; Peltola et al. 2000; Achim et al. 2004), which is attributable in part to the height at which the load was applied. In most cases, it was between one-third and one-half of tree height, less than the height at which a uniform distribution of stress along the trunk would occur (i.e., 80% of tree height) 107 (Wood 1995). When stem failures occurred, however, the vast majority occurred below 10% of tree height (Moore 2000) or closer to the ground (Fredericksen et al. 1993; Peltola et al. 2000). In contrast, although the load was applied, on average, at approximately the same height as previous studies, only two maples failed below 11% of tree height; both were codominant failures. This disparity was presumably attributable, in large part, to the presence of lateral branches. Maples in the current study were noticeably larger than forest trees tested in previous studies, but the maximum bending mo- ment at the point of failure was only marginally greater than the largest bending moments reported for forest trees (e.g., Papesch et al. 1997; Moore 2000). Part of this disparity can be explained by the difference in height of failure; the lever arm from which bending moment was calculated was naturally longer for trees that failed closer to the ground. The maximum bending moment at breast height, however, was more than twice the values from previous studies because maples tested in the current study were larger. This finding further illustrates the importance of defects (i.e., lateral branches and codominant stems) as a source of fail- ure of shade trees. CONCLUSIONS This study was the first to test large shade trees by pulling them to failure, providing much-needed empiric data. In light of po- tential risk associated with failure of large shade trees and their importance to urban and suburban communities, results of this study are integral to developing better techniques to assess the risk of failure of shade trees. Arborists and urban foresters can use the results to quantify risk associated with codominant stems and should cautiously predict tree strength based on MOR of wood samples. It was difficult to predict stress and slightly less difficult to predict bending moment at the point of failure for maples, and extrapolation from forest trees seems to be inappropriate given the importance of defects as points of failure on shade trees. Although species did not appear to influence results, the small sample size made it difficult to draw robust conclusions about the apparent lack of influence. The differences between stem failures and codominant failures merit further investigation. In particular, the importance of included bark as a synergist with codominant stems to weaken the structure of shade trees should be examined as well as investigations to determine the extent to which codominant stems are separate below the point of attachment. Acknowledgments. We gratefully ac- knowledge the following individuals who contributed to this project: Daniel Pepin, Mike Geryk, Charlie Burnham, Alan Snow, Dawn Winkler, Ken Collette, Steve Orlik, Phil Campo, Melanie Joy, Kirk Stephens, Robert Rizzo, and Alex Schreyer. This project was funded in part by a John Z. Duling grant from the TREE Fund. LITERATURE CITED Achim, A., J.-C. Ruel, B.A. Gardiner, G. Laflamme, and S. Meunier. 2004. Modelling the vulnerability of balsam fir forests to wind dam- age. Forest Ecology and Management 204:35–50. Ancelin, P., B. Courbaud, and T. Fourcaud. 2004. Development of an individual tree based mechanical model to predict wind damage within forest stands. Forest Ecology and Management 203:102–121. ©2008 International Society of Arboriculture
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