Critical Height for Self-Weight Buckling in Tapered Trees

Kanahama, Tohya; Fujimura, Takanori; Sato, Motohiro

doi:10.2208/jscejam.77.1_62

“…( 4 ) is independent of the hollow ratio . Because it has the same formula as the volume correction factor in the truncated cone model, we can consider as a function that only varies with and is independent of 17 .…”

Section: Methodsmentioning

confidence: 99%

“…( 12 ) are exactly the same as those in the solid truncated cone model, except for the definition of . Therefore, as in the formulation of a solid tapered column 17 , the following conditional expression for can be obtained using the boundary conditions on the fixed-end side: …”

Section: Calculationmentioning

confidence: 99%

“…However, in many studies, the theoretical scaling law that links the tapered form and greatest height for self-buckling has not been clarified because the calculation model was limited, and the finite element method was used as an analytical method 7 , 15 , 16 . Previously, we extended the calculation model from a cylinder to a truncated cone, which was arbitrarily tapered to deeply consider the effect of this form, and derived the greatest height for self-weight buckling 17 . In the study, we formulate a new scaling law for the degree of taper and determine the greatest height, in addition to a scaling law for the radius, which is the same as Greenhill's law.…”

Section: Introductionmentioning

confidence: 99%

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Plant strategies for greatest height: tapering or hollowing

Kanahama,

Sato

2023

Sci Rep

1

0

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The tapered form and hollow cross-section of the stem and trunk of wild plants are rational mechanical approaches because they facilitate the plant simultaneously growing taller for photosynthesis and supporting its own weight. The purpose of this study is to clarify the advantages and disadvantages of tapering and hollowing from the perspective of the greatest probable height before self-buckling. We modelled woody plants using tapering or hollow cantilevers, formulated the greatest height before self-buckling, and derived a theoretical formula for the greatest probable height considering tapering and hollowing. This formula theoretically explains why almost all plants exhibit a tapered form: it allows for a greater height at an earlier growth stage than a hollow cross-section.

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“…Previously, we theoretically derived a simple scaling law for a heavy tapered column for the first time 37 with the aim of applications in engineering as well as in ecology and forest science. We found that the critical height of a linearly tapered column is inversely proportional to the 1/6 power of the ratio of the radius of the free end to the radius of the fixed end.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling to determine the greatest height of trees

Kanahama

¹

,

Sato

²

2022

Sci Rep

Self Cite

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This study aimed to analyse the critical height of a column whose weight varies vertically in order to obtain a simple scaling law for a tree where the weight distribution considered. We modelled trees as cantilevers that were fixed to the ground and formulated a self-buckling problem for various weight distributions. A formula for calculating the critical height was derived in a simple form that did not include special functions. We obtained a theoretical clarification of the effect of the weight distribution of heavy columns on the buckling behaviour. A widely applicable scaling law for trees was obtained. We found that an actual tree manages to distribute the weight of its trunk and branches along its vertical extent in a manner that adequately secures its critical height. The method and findings of this study are applicable to a wide range of fields, such as the simplification of complicated buckling problems and the study of tree shape quantification.

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“…Previously, we theoretically derived a simple scaling law for a heavy tapered column for the first time [34] with the aim of applications in engineering as well as in ecology and forest science. We found that the critical height of a linearly tapered column is inversely proportional to the 1/6 power of the ratio of the radius of the free end to the radius of the fixed end.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling to Determine the Greatest Height of Trees

Kanahama

¹

,

Sato

²

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

This study aimed to analyse the critical height of a column whose weight varies vertically in order to obtain a simple scaling law for a tree where the weight distribution considered. We modelled trees as cantilevers that were fixed to the ground and formulated a self-buckling problem for various weight distributions. A formula for calculating the critical height was derived in a simple form that did not include special functions. We obtained a theoretical clarification of the effect of the weight distribution of heavy columns on the buckling behaviour. A widely applicable scaling law for trees was obtained. We found that an actual tree manages to distribute the weight of its trunk and branches along its vertical extent in a manner that adequately secures its critical height. The method and findings of this study are applicable to a wide range of fields, such as the simplification of complicated buckling problems and the study of tree shape quantification.

show abstract

Critical Height for Self-Weight Buckling in Tapered Trees

Cited by 7 publications

References 12 publications

Plant strategies for greatest height: tapering or hollowing

Plant strategies for greatest height: tapering or hollowing

Mathematical modelling to determine the greatest height of trees

Mathematical Modelling to Determine the Greatest Height of Trees

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