AOBPreview originally published online on July 24, 2006
Annals of Botany 2006 98(4):765-775; doi:10.1093/aob/mcl161
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Modelling Environmental Variation in Young's Modulus for Pinus radiata and Implications for Determination of Critical Buckling Height
1 Ensis, PO Box 29237, Christchurch, New Zealand, 2 Centre for Timber Engineering, Napier University, Merchiston Campus, Edinburgh, UK, 3 Ecole Polytechnique, 91128 Palaiseau, Cedex, France, 4 CSIRO Forestry and Forest Products, Private Bag 12, Hobart, Australia, 5 Landcare Research, Private Bag 92170, Auckland, New Zealand, 6 Landcare Research, Private Bag 11052, Palmerston North, New Zealand and 7 School of Forestry, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
* For correspondence. E-mail michael.watt{at}ensisjv.com
Received: 23 March 2006 Returned for revision: 10 May 2006 Accepted: 2 June 2006 Published electronically: 24 July 2006
• Background and Aims Although density-specific stiffness, E/
, (where E is Young's modulus and is wood density) is often assumed constant by the elastic similarity model, and in determination of critical buckling height (Hcrit), few studies have tested this assumption within species. Here this assumption is tested for Pinus radiata growing across an environmental gradient, and theory is combined with data to develop a model of Young's modulus.
• Methods Analyses use an extensive series of environmental plots covering the range of climatic and edaphic conditions over which P. radiata is grown in New Zealand. Reduced major axis regression was used to determine scaling exponents between log–log plots of Hcrit vs. groundline diameter (D), and E/ vs. D. Path analysis was used to identify significant direct and indirect (through stem slenderness) edaphic and climatic influences on E.
• Key Results Density-specific stiffness exhibited 3-fold variation. As E/ scaled positively with D, the exponent of 0·95 between Hcrit and D exceeded the assumed value of 0·67 under constant E/. The final path analysis model included mean air temperature in early autumn (Taut) and slenderness as significant (P < 0·05) positive direct influences on E. Tree leaf area index and Taut were indirectly associated with E through their significant (P < 0·05) positive direct relationship with stem slenderness. Young's modulus was most sensitive to Taut, followed by stem slenderness then leaf area index, and the final model explained 76 % of the variance in E.
• Conclusions The findings suggest that within species E/ variation may influence Hcrit and the scaling exponent between D and Hcrit so important in assumptions regarding allometric relationships. The model presented may provide a useful means of determining variation in E, E/ and Hcrit across environmental gradients.
Key words: Air temperature, environment, Euler buckling, Pinus radiata, safety factor, stem slenderness, taper, Young's modulus