Buckling of Tapered Heavy Columns with Constant Volume

Abstract

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

Mathematical Modelling to Determine the Greatest Height of Trees

“…(25) in Models A, B, and C. In contrast, this function did not satisfy Eq. (25) in Model D. The specific convergence judgement function(25,30) (represented by the single-dotted line in each panel) satisfied Eq. (…”

“…In all models, the calculated values converged as the expansion order increased. However, the convergence of Model D was inferior to the other models that had linear density distributions, i.e., Models A, B, and C. The specific convergence judgement function(20,25) (indicated by the dashed line in each panel) satisfied Eq. (25) in Models A, B, and C. In contrast, this function did not satisfy Eq.…”

Plant strategies for greatest height: tapering or hollowing

“…From a mechanical point of view, this insight leads to the elucidation of the “efficient gravity-resistance mechanism” that plants have retained through evolution while changing their shapes, and the “scaling law of woody plants” that can be applied to the estimation of biomass. Furthermore, this contribution can be applied to design and structural calculations for civil engineering structures because the functionally superior tapered form is widely used in engineering 7 , 27 , 28 . Moreover, it is important and interesting for forest managers, researchers studying plant strategies, and many more to clarify the mechanical stability of woody plants.…”

Mathematical modelling to determine the greatest height of trees

“…The self-buckling problem of columns has been extended to tapered columns, which have recently been actively used in civil engineering structures 25 . A study of tapered columns was initiated by Smith 26 .…”