JXB Advance Access originally published online on August 14, 2006
Journal of Experimental Botany 2006 57(12):3175-3182; doi:10.1093/jxb/erl079
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© 2006 The Author(s).
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper is available online free of all access charges (see http://jxb.oxfordjournals.org/open_access.html for further details)
RESEARCH PAPER |
Reducing stem bending increases the height growth of tall pines
1Department of Renewable Resources, University of Alberta, Edmonton, Alberta, Canada T6G 2H1
2Department of Natural Resources Management and Engineering, University of Connecticut, 1376 Storrs Road, Storrs, CT 06269, USA
3Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2W2
*To whom correspondence should be sent at Department of Renewable Resources, ESB 4–42, University of Alberta, Edmonton, Alberta, Canada T6G 2E3. E-mail: xianfa{at}ualberta.ca
Received 22 February 2006; Accepted 13 June 2006
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Abstract |
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 Top Abstract IntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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The hypothesis was tested that upper limits to height growth in trees are the result of the increasing bending moment of trees as they grow in height. The increasing bending moment of tall trees demands increased radial growth at the expense of height growth to maintain mechanical stability. In this study, the bending moment of large lodgepole pine (Pinus contorta Dougl. Ex Loud. var. latifolia Engelm.) was reduced by tethering trees at 10 m height to counter the wind load. Average bending moment of tethered trees was reduced to 38% of control trees. Six years of tethering resulted in a 40% increase in height growth relative to the period before tethering. By contrast, control trees showed decreased height growth in the period after tethering treatment. Average radial growth along the bole, relative to height growth, was reduced in tethered trees. This strongly suggests that mechanical constraints play a crucial role in limiting the height growth of tall trees. Analysis of bending moment and basal area increment at both 10 m and 1.3 m showed that the amount of wood added to the stem was closely related to the bending moment produced at these heights, in both control and tethered trees. The tethering treatment also resulted in an increase in the proportion of latewood at the tethering height, relative to 1.3 m height. For untethered control trees, the ratio of bending stresses at 10 m versus 1.3 m height was close to 1 in both 1998 and 2003, suggesting a uniform stress distribution along the outer surface of the bole.
Key words: Bending moment, mechanical constraints, proportion of latewood, tethering, uniform stress, wind load
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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The reason why trees experience a gradual reduction in height growth as they become taller still remains unclear (Pennisi, 2005). It has been hypothesized that hydraulic limitations in tall trees limits water movement (Ryan and Yoder, 1997; Niklas and Spatz, 2004), thereby limiting turgor pressure of leaf cells, stomatal conductance, and CO2 fixation (Koch et al., 2004). However, recent studies testing the hydraulic limitation hypothesis found that hydraulic limitation in large trees is common, but not universal (Ryan et al., 2006). Therefore, there should be other factors limiting height growth in trees (Pennisi, 2005; Ryan et al., 2006). As trees are large, tall perennial plants, it has been proposed that selection pressure would result in stem biomechanics that could efficiently resist the bending moment applied to the tree from the forces of gravity and, especially, wind (Niklas, 1998; Ennos, 1997; Jaffe, 1973; King, 1986; Vogel, 1989; Mattheck, 1991). The basal diameter required for stability of the tree scales exponentially with height (McMahon, 1973; King, 1981, 2005). As a tree increases in height, so does the bending moment. Hence, to maintain the mechanical stability of tall trees, any further increase in height would require trees to invest carbon (C) exponentially into radial growth of the stem. As there is also reduced leaf area and C fixation when trees grow taller and older (Ryan et al., 1997), it is therefore proposed that increasing bending moment will drive tall trees to assign increasingly more of the available C to radial growth relative to height growth; these mechanical constraints will eventually result in trees approaching an upper limit to their height. It has been reported that mechanical perturbation due to wind exposure, shaking, flexing or rubbing resulted in a decrease in height growth of tree seedlings (Larson, 1965; Telewski and Jaffe, 1986a; Telewski and Pruyn, 1998) and medium-sized trees (Valinger, 1992), but the experiment designed to test if reducing the bending moment on large trees which are declining in height growth would result in an increase in height growth is still missing.
It has been proposed that tree stems develop taper to counter the increasing bending moment toward the base of the tree when its crown is subjected to a wind load; bending stress applied at the outer surface of the stem tends to be uniformly distributed along the bole (Metzger, 1893; Dean and Long, 1986). The basic hypothesis is that, to maintain mechanical stability, stem growth at any given height of a tree tends to be related to the bending moment applied at that height (Dean and Long, 1986; Milne and Blackburn, 1989; West et al., 1989; Morgan and Cannell, 1994; Dean, 2004). However, in the past, those testing the uniform stress theory have concentrated either on the comparison of the static bending stress and stem profile (Milne and Blackburn, 1989; West et al., 1989; Morgan and Cannell, 1994), or modelling radial growth based on changes in bending moment during a growth period (Dean, 2004). Some previous guying or staking studies (Jacobs, 1954; Burton and Smith, 1972; Valinger, 1992) have reported stem growth after reducing tree sway, but the relationship of bending moment and stem diameter and height growth has never been quantified.
In addition to the potential impacts on C allocation along the bole, the mechanical perturbation has also been shown to affect the mechanical properties of the wood such as tracheid characteristics (Telewski, 1989), modulus of elasticity (Telewski and Jaffe, 1986a), and wood density (Telewski, 1990), for efficiently resisting the mechanical forces and maintaining the mechanical stability of trees. It has been reported that following addition of sails or thinning treatments, the increased wind loads resulted in an increase in the ratio of high-strength latewood to early wood (Liu et al., 2003). However, there has been also a conflicting report that early wood:latewood ratio is not affected by guying treatment (Burton and Smith, 1972).
In this paper two hypotheses were tested: (i) that reducing bending moment of the bole will result in increased height growth; and (ii) that diameter growth and wood properties of the stem are related to the bending moment applied to that section of the bole.
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Materials and methods |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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Four fire-origin, naturally regenerated, pure, even-aged lodgepole stands across the foothills of Alberta were studied: the Two Creeks site (TC) (54°20' N, 116°23' W) located 50 km west of Whitecourt, the Bighorn site (BI) (51°51' N, 115°22' W) located 50 km west of Sundre (which was later excluded from the analysis as some trees within the plot were found broken by wind at the point of tethering), the Redrock site (RE) (54°32' N, 119°07' W) located 50 km south of Grande Prairie, and the Amundson site (AM) (54°33' N, 118°00' W) located 75 km south east of Grande Prairie. Stands were 50–55-years-old. Height growth of lodgepole in these areas usually peaks at about 15 years (6.3 m in height) and height growth rates decline thereafter (Huang et al., 2001). Lodgepole pine on these sites reach a maximum height of about 24 m at 180 years (Huang et al., 2001). All sites were either near the summit of local hills or west facing, thus exposed to prevailing winds. Ground cover was dominated by feather mosses across the sites. At each site, two plots of similar landform, stem density, and spatial distribution of trees were located within 25 m of each other. Stand density ranges from 3200 stems ha–1 at the TC site to 4400 stems ha–1 at the AM site.
At each site, one of the plots was randomly selected for treatment. To control the bending moment produced by wind drag, in the autumn of 1998, 13–15 trees from treatment plots were tethered together using a 12 mm nylon rope in a web pattern at the height of 9–10 m, about 2/3 of the total tree height. Thus tethered trees were subjected to an external pulling force at the height of the tethering that countered the wind drag acting on the crowns (Fig. 1). Boles were protected from rope abrasion by padded collars. The edge of the web was attached to neighbouring trees at about 6 m in height. Understorey black spruce (Picea mariana (Mill.) BSP) saplings and/or tall shrubs were cleared from the plots to allow ladder access. Clearing was also done in the control plots to duplicate treatment conditions.
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Tree measurements
In the autumn of 2004, the base of all of the trees in the plots and immediately outside of the plot were numbered, mapped, and height, DBH, and height to the base of the live crown were recorded. All trees from both tethered and control plots were destructively harvested. After harvesting, crown size, and leaf area of each tree was carefully measured (Meng et al., 2006). The height increment of the last six years was measured in the field by counting annual whorls. In cases where there was uncertainty of whorl counting, the stem was cut at the base of a questionable internode and rings were counted. Discs, 10–15 cm long at 1.3 m height were cut on each tree. In addition, nine discs were cut at equidistant locations (1/10H) from the bottom to the top of each tree. A thin disc centred on tethering height was cut from the tethered trees. The same thin disc was also cut from control trees at the same relative height (about 10 m height). Therefore, a total of 11 discs were cut from each tree.
Stem discs measurements
As some of the boles of trees were deformed by western gall rust, only discs of the largest five healthy dominant/co-dominant trees were selected from each plot. These five trees were similar in size, spacing, and slenderness coefficient (height/diameter at breast height) between tethered plot and control plot across sites (Table 1). Dominant trees were chosen because they occupied the upper layer of the canopy and were more exposed to wind. All discs of the five dominant trees from each plot were then dried and sanded. On each disc, the longest axis and the axis perpendicular to it were marked on the sanded side, and along each radius, the outer section (containing more then 12 rings) was wetted with glycerol and water and cut smooth using a razor blade. A stage micrometer (Velmex Inc., NY, USA) and dissecting scope was then used to measure the yearly ring width from 1993 to 2004 (to 0.001 mm) along these four radii. The total length of each radius (inside bark) was measured to the nearest 0.001 mm. For the discs cut at 1.3 m height and at the 10 m height, the width of early wood and latewood of each ring from year 1993 to 2004 was also measured on the four radii using the stage micrometer.
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Past growth was reconstructed for each tree by doing stem analysis (annual ring analysis) from each of the stem sections; thus the height growth of the period 1993–1998, and stem volume growth five years before (1993–1997) and after the treatment (1999–2003) were estimated. Height–diameter increment ratio (
H/D) was calculated by dividing the height increment by the mean diameter increment over each of the stem discs along the bole, for both the period 1993–1997 and period 1999–2003. Stem growth for 1998 and 2004 were excluded from radial growth analysis because the latewood ring for these two years were not fully developed when trees were tethered in the autumn of 1998, or when they were harvested in the autumn of 2004. Basal area increments in the period before tethering were calculated by subtraction of the cross-sectional area in 1993 from that in 1997 and after tethering by subtraction of the cross-sectional area in 1999 from that in 2003. Similarly, the mean proportion of latewood prior to treatment (1993–1997) and after treatment (1999–2003) was averaged for the four radii.
Bending moment/stress assessment
The stems of the trees were assumed to act as cantilever beams with one end anchored at the ground. Bending moment (M) produced from wind load was calculated as:
 | (1) |
Because the axial stress caused by gravitation is a small component, it was neglected in the calculation of the total stress (Morgan and Cannell, 1994). The maximum bending stress (
) experienced at the outer edge of the stem was calculated as:
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 | (3) |
 | (4) |
 | (5) |
Similarly, the bending moment, and stress at 1.3 m height for control trees was calculated as:
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The ratio of bending moments, and stresses at those two points was:
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10 and 1.3, it was cancelled out in the calculations, thereby avoiding the difficult problem of accurate estimate of F. Using the same procedure, the ratio of moments/stresses in 1998 was also calculated for each of the five largest control trees. When the moment/stresses were calculated for the year of 1998, it was assumed that the length of the live crown was the same during the periods before and after installation of the roping and hence, bending moments/stress at the 10 m height and 1. 3 m height was calculated accordingly.
Tethered trees were subjected to an external pulling force (P) at the tethering height countering the natural sway of the tree under wind load (Fig. 1b). This force was derived by applying the force method to analyse statically indeterminate structures (Hibbeler, 1999):
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The bending moments and stresses at tethering and 1.3 m height were calculated as follows:
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| (9) |
 | (10) |
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Mean overall bending moment
The mean overall bending moment in 2004 was calculated by averaging the bending moments of each relative height from the base of the stem up to tethering height for each tree.
The bending moments of those relative heights was calculated as:
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 | (13) |
The wind force F (N) was estimated as:
 | (14) |
is the air density (kg m–3), A is the frontal area (m2), and U (m s–1) is the wind speed (Mayhead, 1973). Frontal area was replaced by leaf area in the calculation as it reported that frontal area is proportional to leaf area for lodgepole pine (Dean and Long, 1986). Given that the control plot and the tethered plot in each site had similar landform, stem density, and spatial distribution of trees, it was assumed that Cd, , and U were the same between control and tethered trees in each site. The ratio of mean overall bending moment in 2004 between tethered trees and control trees was calculated by dividing the mean overall bending moment of tethered trees by that of control trees and therefore Cd, , and U cancelled out.
Statistical analysis
This experiment was a randomized complete block design. Sites were treated as the random factor and treatment was treated as a fixed factor. Treatment effects on height increment, basal area increment, and proportion of latewood were analysed using Proc MIXED (SAS Institute, 9.1, Cary, NC). As it was only possible to sample three of the four stands, the experiment had weak statistical power, therefore an 
=0.1 was used for the experiment.
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Results |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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Tethering resulted in a significant increase in height increment (P=0.02) during the six years after tethering, compared with the six years prior to tethering (Table 2). For the tethered trees, the mean ratio of height increment six years after tethering to six years before the tethering was 1.40 compared to a mean of 0.80 for the controls.
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Tethered trees had decreased basal area increment at 1.3 m height (BAI1.3 m) six years after tethering relative to six years before tethering compared to control trees (P=0.05, Table 2). This was opposite to the values at 10 m height, where tethered trees had increased BAI10m after tethering (P=0.06; Table 2). Along the bole, for all of the sites, the tethered trees added more wood higher up the stem in the period after tethering than in the period before tethering, compared with the control trees (Fig. 2). At 0.8 relative height, the tethered trees had a 20–65% gain in basal area after tethering compared with the period before tethering (Fig. 2). At 0.1 relative height, basal area increment of the tethered trees decreased between 25% and 30% relative to the period before tethering. By contrast, the control trees showed no consistent change in allocation with height, before and after the period of tethering.
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Tethering increased height growth in relation to average diameter growth along the stem
H/D (P=0.04, Table 2) compared with the control trees (Table 2). Tethered trees tended to have an increase in stem volume growth after tethering, but it was not statistically significant (P=0.12; Table 2). Tethering treatment produced a higher proportion of latewood at tethering height (10 m) relative to the proportion of latewood at 1.3 m height, six years after tethering (P=0.01; Table 2). For the control trees, the proportion of latewood at 10 m height was 31% less than that at 1.3 m. By comparison, six years after the time of tethering, the proportion of latewood for the tethered trees was 2.6% greater at the tethering height than at 1.3 m height.
The ratio of bending stresses at 1.3 m versus 10 m height was greatly affected by the tethering treatment (Table 3). For the control plots, the ratios were near 1 in both 1998 and 2003. By contrast, because the tethered trees received an extra pulling force at the tethering height to counter the wind force, the mean ratio of the stresses at 1.3 m versus 10 m height, across all of the sites, was reduced to around 0.340 in 1998 at the time of tethering to 0.260 by 2003. The mean overall bending moment of tethered trees was reduced to 38% of the control trees across the three sites. The ratio of BAI1.3m and BAI10m was also affected by the tethering treatment (Table 3). The average ratio of the BAI1.3m:BAI10m was 0.667 on tethered trees, compared with 1.190 for control trees.
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Discussion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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The results of this study show that tall trees that are declining in height growth will increase their height growth rates when the overall bending moment of the trees is reduced by tethering (Table 2). This strongly suggests that mechanical constraints play a crucial role in limiting height growth when trees grow taller. In spite of the increased bending moment at the tethering height relative to 1.3 m height, the mean overall bending moment of the tethered trees was only 38% of control trees. The reduced overall bending moment apparently eased the need for lateral stem growth to maintain the stability of the tree during wind, resulting in increased height growth relative to radial growth along the bole (Table 2). Increased height growth may also have been related to increased stem elongation (Telewski and Jaffe, 1981, 1986a) and reduced C allocation to structural root growth anchoring the stem (Urban et al., 1994; Stokes et al., 1995, 1997; Henry and Thomas, 2002) when the bending moment acting on the stem was reduced. The fact, that trees growing in windy areas are shorter than those from sheltered areas (Ennos, 1997), provides additional support for the hypothesis that increased bending moment limits height growth.
For both control and tethered trees, this study shows the allocation of wood along the bole of large, dominant lodgepole pine trees is strongly related to bending moment. Tethering resulted in decreased bending moment at the base of the trees and increased bending moment at the point of tethering and above (Table 3). This resulted in a corresponding increase in wood allocation to the upper part of the trees (Table 2; Fig. 2), similar to reports by Jacobs (1954) and Burton and Smith (1972). The quantitative analysis of the ratio of bending moments at 1.3 m versus 10 m and the corresponding ratio of BAI at those two points on both control stems and tethered stems indicates that C allocation along the bole was very closely related to the bending moments applied to the bole (Table 3). If wood properties were also considered in the analysis (Table 2), there would probably be an even closer relationship between wood growth/strength and lateral force applied. At the tethering height, tethered trees grew wood with a higher percentage of latewood than at the same height of the control trees (Table 2), clearly indicating a response to counteract the change in the location of bending moment by a change in both the amount and type of wood laid down along the stem. The mechanisms by which the bending moment influences cell growth and division of the cambium were reported to be related with changes in ethylene production (Telewski and Jaffe, 1986b). The fact that the bending stress was relatively uniform at 1.3 m, and 10 m up the bole in the control trees (Table 3) lends strong support to the uniform stress hypothesis for allocation of wood in trees (Dean and Long, 1986). It is demonstrated, however, if the bending stress along the bole is changed experimentally, allocation of wood changes accordingly.
Studies have suggested that C allocation to height growth relative to radial growth is mainly affected by: competition (Weiner et al., 1990; Weiner and Thomas, 1992), competition plus vertical foliage profile of an individual plant (Yokozawa and Hara, 1995), or internal plant variables such as nutrient status in foliage and stem (Thornley, 1999). In this study, the light reaching the canopy of the trees was not affected by the tethering treatment, thus competition for light was unchanged before and after tethering, similar to studies by Telewski (1990) and Valinger (1992). Hence the shift of C allocation along the bole and the increased height growth of the tethered trees were a result of the altered bending moment caused by tethering. While others have attempted to separate the role of light competition and wind pressure on stem allometry (Holbrook and Putz, 1989), only Mitchell (2003) and Henry and Thomas (2002) developed studies where shading and mechanical stimulation were not confounded. Mitchell reported that shading did not have a strong effect on stem allometry comparing with the bending effect on Douglas-fir seedlings grown for one summer. By contrast, Henry and Thomas found that light competition takes a dominant role influencing height–diameter allometry of an annual herbaceous plant. This study cannot assess to what degree competition for light affects the stem allometry of tall trees, it does, however, demonstrate that bending moment has a strong effect on the C allocation along the bole of trees.
This study indicates that allocation of resources to height and diameter growth along the stems of lodgepole pine trees can be explained by the wind forces applied to the various heights of the bole, providing empirical support for the uniform stress hypothesis (Dean and Long, 1986), and the authors' hypothesis that the upper height that a tree can reach is affected by mechanical constraints. As there was little difference in the height of tethered and control trees in this study, and no significant difference in hydraulic conductivity of stem segments collected at the tether point (
10 m; data not presented), stem hydraulics as a limitation to height growth (Ryan and Yoder, 1997; Koch et al., 2004; Niklas and Spatz, 2004), was not a factor in this study. When the bending moment was manipulated by tethering the trees at 10 m height, thereby countering the wind force, the tethered trees added wood to the bole approximately in proportion to the bending moment along the bole after the tethering was applied. The overall reduction in bending moment of the tethered tree reduced the demands on the tree's resources to grow laterally to maintain mechanical stability, thereby allowing resources to be allocated to further height growth.
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Appendix I |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix IReferences |
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Derivation of pulling force (P) at the tethering point under the wind load, using the force method (Hibbeler, 1999)
To derive the pulling force caused by the wind load, the principle of superposition was applied, which states that the total displacement in a structure subjected to several external loadings can be determined by adding together the displacements caused by each of the external loads acting separately (Hibbeler, 1999). This was done by choosing the pulling force as ‘redundant’ and temporarily removing its effect on the stem so that the stem then becomes statically determinate and stable. As a result, the wind force F will cause the stem to be potentially displaced a1 at the tethering height (Fig. 3A). By superposition, however, the unknown pulling force P causes the stem at the tethering height to be potentially displaced a2 which is opposite to a1 (Fig. 3B). The potential displacement of a1 and a2 were calculated as:
 | (15) |
 | (16) |
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As the tethered trees were held firmly at the tethering height, it was assumed that there was no displacement incurred at that point; therefore, the pulling force can be obtained by relating the following equation: a1+a2=0.
 | (17) |
 | (18) |
It was observed that, in spite of the tight tethering, the tethered trees still had slight displacement during the gusty winds. If this displacement was set as k, then based on the principle of superposition, a1+a2=k.
 | (19) |
With E being set as 7.4 GPa for lodgepole pine (Dean et al., 2002), and k being set as 20 cm, it was calculated that, when F varied from 50 N to 200 N, the average pulling force, P1, was reduced by less then 5% when compared with P which had no displacement. Therefore, slight displacement had only a minor impact on the estimation of the bending stress and bending moment.
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Acknowledgements |
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Research was funded from the Natural Sciences and Engineering Research Council of Canada (NSERC), West Fraser, Weyerhaeuser, Millar Western, CanFor, and the NCE-SFM. The authors thank Sarah Lieffers, Anna Brown, Erin Smith, Xiaodong Liu, Anna Mühlhuber, and Tobias Diwischek for field assistance.
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Footnotes |
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Present address: Centre for Northern Forest Ecosystem Research, Ontario Ministry of Natural Resources, Lakehead University Campus, 955 Oliver Road, Thunder Bay, ON, Canada P7B 5E1. 
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