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AOBPreview published online on July 24, 2006
Annals of Botany, doi:10.1093/aob/mcl161
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© The Author 2006. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received March 23, 2006
Revised May 10, 2006
Accepted June 2, 2006

Article

Modelling Environmental Variation in Young's Modulus for Pinus radiata and Implications for Determination of Critical Buckling Height

MICHAEL S. WATT 1 *, JOHN R. MOORE 2, JEAN-PHILIPPE FAÇON 3, GEOFF M. DOWNES 4, PETER W. CLINTON 1, GRAHAM COKER 1, MURRAY R. DAVIS 1, ROBYN SIMCOCK 5, ROGER L. PARFITT 6, JOHN DANDO 6, EUAN G. MASON 7, and HORACIO E. BOWN 7

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
7 School of Forestry, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

* To whom correspondence should be addressed.
MICHAEL S. WATT, E-mail: michael.watt{at}ensisjv.com


  Abstract

• Background and Aims Although density-specific stiffness, E/{rho}, (where E is Young's modulus and {rho} 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/{rho} 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/{rho} scaled positively with D, the exponent of 0·95 between Hcrit and D exceeded the assumed value of 0·67 under constant E/{rho}. 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/{rho} 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/{rho} and Hcrit across environmental gradients.

Keywords: Air temperature, environment, Euler buckling, Pinus radiata, safety factor, stem slenderness, taper, Young's modulus.
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