An evaluation of the uniform stress hypothesis based on stem geometry in select NorthAmerican conifers
Trees - Structure and Function
The uniform stress hypothesis of stem formation was evaluated by comparing stem taper of Abies balsamea, Abies lasiocarpa, Picea rubens, Pinus contorta, Pinus elliottii, Pinus palustris, Pinus ponderosa, Pinus taeda, and Pseudotsuga menziesii to the taper expected if stems develop to uniformly distribute bending stress. The comparison was conducted by regressing stem diameter at height h (D h) against bending moment at h (M h) using the model D h=φ (M h)δ where φ and δ are fitted coefficients, and testing for δ=0.333, the hypothesized value. Twelve curves were fitted with the model. Seven of the fitted values of δ were significantly different from 0.333, but eight of the values were within ±10% of 0.333 and eleven values were within ±15% of 0.333. Where the fitted value of δ was >15% of 0.333, residuals were biased with height. Fit by relative height, values of δ were within ±10% of 0.333 for large portions of these stems. While most of the fitted values of δ support the uniform-stress hypothesis, the values of δ for Pseudotsuga menziesii trees clearly did not. Many of the fitted values of φ were inversely related to the modulus of elasticity (E) of green wood reported for these species. With the exception of Pseudotsuga menziesii, growing conditions appeared to account for extraordinary values of φ. Increases in φ with stem height corresponded with reported decreases in E with height. The covariance between φ and E suggests some regulation of bending curvature by adjustments in cross-sectional area. These results suggest that stems taper to maintain a uniform bending curvature and that when E is relatively constant within and among stems, diameter along the stem or across stems can be predicted from bending moment using a simple power function.
Dean, T.J., S.D. Roberts, D.W. Gilmore, D.A. Maguire, J.N. Long, K.L. O’Hara and R.S. Seymour. 2002. An evaluation of the uniform stress hypothesis based on stem geometry in select North American conifers. Trees - Structure and Function 16(8):559-568.