Arboriculture & Urban Forestry 39(5): September 2013 METHODS Data Base The data analyzed for this communication are taken from the catalogs of Jessome (1977), Lavers (1983), and Kretschmann (2010). With one exception, all entries were included where the mechanical properties of green wood were listed. The exception was the entry for Mgongo in the Lavers catalog, where the species was not clearly identifiable. The analysis represents 306 different species and subspecies. Some species/ subspecies were listed in two or even all three catalogs; how- ever, they were treated separately in this analysis. This led to a total of 393 entries for species and subspecies, and in some cases for the same species/subspecies from different regions. Definitions In the Jessome catalog (1977) and the USDA Wood Handbook (Kretschmann 2010) the density of wood is given as “weight when oven dry over volume when green.” This is a workable but somewhat unrealistic definition. However, Lavers (1983), who showed that the mechanical properties of wood change lit- tle above a moisture content of 50%, gives the density of green wood at 50% moisture content (which does not imply that all measurements were conducted at this moisture content). Adopt- ing Lavers’ definition, the entries in the other two catalogs were multiplied by a factor of 1.5 to obtain realistic reference values. Two definitions of strength are used in the literature, either the maximum in the stress-strain relation for a given material or the stress at the deviation from linearity (yield stress) in the stress- strain relation. Reported here are data for the maximal stress in bending, compression, and shear. The relation between maxi- mum stress and yield stress in bending will be discussed later. Statistics Three different protocols were applied: (1) a linear ordi- nary least squares (OLS) regression including the origin (y = a • x), (2) a linear OLS regression not including the origin (y = b • x + c), and (3) an OLS fit with a power function (y = b • xa ). In order to establish a functional relationship reduced mayor axes (RMA) regression is appropriate (Niklas and Spatz 2012a). For this the scaling exponent aRMA was calculated using the formula aRMA = aOLS/R, where R is the correlation coefficient (see Niklas and Spatz 2012b, section 10.4, and the literature cited there for a more detailed discussion of the differ- ences and merits of RMA versus OLS analyses). RESULTS The modulus of elasticity (MOE) of green wood from conifers and deciduous trees is plotted against the density in Figure 1. Irrespective of whether the samples tested originate from conifers or deciduous trees, or whether from trees grown in tropical zones or temperate regions, the data can be represented by a common trend line. Figure 1. The modulus of elasticity as function of green wood density for conifers from temperate zones (triangles), and deciduous trees from temperate zones (diamonds) and tropical zones (squares). The trend-line drawn is an OLS fit to a power function (y = 18.6 • x0.94 ). ©2013 International Society of Arboriculture 219 The correlations between MOE and density are given in the Appendix. Clearly, density is a reasonable predictor, although deviations from the common trend line exist. As pointed out by Lavers (1983), these reflect differences between in- dividual trees even within the same stand, soil conditions, and climatic differences. For large sample sizes, the differ- ences may average out to a certain degree; however, particu- larly for tropical trees, the sample sizes were often limited. A similar correlation between mechanical properties and density is seen in Figure 2, Figure 3, and Figure 4. Again the data can be represented by common trend-lines, although the compression strength of deciduous trees from temper- ate zones seems to be somewhat lower than for those from tropical zones. In bending strength, compression strength and shear strength the deviations from the trend-lines are smaller than in case of the modulus of elasticity (Figure1). A detailed statistical analysis is presented in the Appendix. The formula used in Protocol 1 predicts a simple proportionality (e.g., linear relation) between mechanical property and density of green wood. From a physics per- spective, this is more reasonable than the formula used in Protocol 2, which allows for a finite intercept c, since at den- sity zero the modulus of elasticity and the strengths should also diminish. It should be noted that the coefficient of determination R2 is not very different for the two pro- tocols. The authors have therefore not listed the results obtained using Protocol 2 in the Appendix. Appling Protocol 3, which serves primarily as a test for linearity, leads to a relation between the modulus of elasticity and green wood density with a weighted average of the scaling exponent of aOLS of 0.98. The relations between strength proper- ties and green wood density are characterized by a weight- ed average of the scaling exponent of aOLS of 1.11, both weighted by the coefficient of determination R2 (Appendix). Quite good agreement between the data from the three cata- logs is found, especially if the results of the statistical analysis according to Protocol 1 are compared (Appendix). This supports the notion that the three catalogs mutually support each other.
September 2013
| Title Name |
Pages |
Delete |
Url |
| Empty |
Search Text Block
Page #page_num
#doc_title
Hi $receivername|$receiveremail,
$sendername|$senderemail wrote these comments for you:
$message
$sendername|$senderemail would like for you to view the following digital edition.
Please click on the page below to be directed to the digital edition:
$thumbnail$pagenum
$link$pagenum
Your form submission was a success. You will be contacted by Washington Gas with follow-up information regarding your request.
This process might take longer please wait
