Structural Analysis of Self-Weight Loading Standing Trees to Determine Its Critical Buckling Height

Abstract

A tree may receive compression and flexure combination, and the structural analysis governed by the building code may be capable of estimating the tree’s safety in the built environment. This study proposed to refer to the building code to check the tree dimension adequacy resisting the load. This study simplified the case by focusing only on the self-weight and ignoring the external loads; therefore, the buckling analysis of a slender tapered round column subjected to compression is advocated. Buckling occurs when the tree’s structure can no longer maintain its original shape. Euler and Ylinen’s buckling stress analysis (Method 1) calculated tree safety with a 95% confidence level. This study also applied the Greenhill formula (Method 2) to determine the critical height of a tree receiving the stem weight, then modified it to include the crown weight (Method 3). The three methods calculated the critical height to determine the safety factor (Sf), that is, the ratio of the actual tree height (H) to the 95% confidence level estimated critical height (Hcr). The safety factors were then categorized as unsafe (Sf < 1.00), safe (1.00 < Sf < 1.645), and very safe (1.645 < Sf). This study demonstrated that Method 1 is the most reliable and applicable among other methods. Method 1 resulted in no unsafe trees, 10 safe trees, and 13 very safe trees among the observed excurrent agathis (Agathis dammara). Meanwhile, among the decurrent rain trees (Samanea saman (Jacq.) Merr), 5, 31, and 14 were unsafe, safe, and very safe, respectively.

Developing a Model for Curve-Fitting a Tree Stem’s Cross-Sectional Shape and Sapwood–Heartwood Transition in a Polar Diagram System Using Nonlinear Regression

“…A tree stem's diameter at the top (D t ) is usually smaller than the diameter at breast height (D bh ). Its three-dimensional shape may resemble a truncated cone [79], sometimes called a conical frustum, as the best-fit idealized standard geometric form. The tree's or log's tapered stem volume equations, empirically proposed by foresters, are Equations ( 30)-( 34) [80].…”

“…The resultant of wind, snow, and unsymmetric crown self-weight generate the non-eccentric compressive load the stem receives. Their combination with the bending moment triggers buckling, severely reducing its load-bearing capacity [79,[81][82][83][84][85]. The buckling generates compressive stress in half of the stem and tensile stress in the other half.…”

Annual Tree-Ring Curve-Fitting for Graphing the Growth Curve and Determining the Increment and Cutting Cycle Period of Sungkai (Peronema canescens)

“…A tree stem may be more similar to truncated cone 3D geometry, a synonym to a conical frustum, than a cylinder [71]; it commonly tappers upward, the bottom diameter is the biggest, and it becomes smaller when nearer to the top. As a product of its evolution, trees commonly have butt swell (bottom thickening), where the stem near the base becomes greatly enlarged to support self-weight loads (i.e., stem and canopy weight) and external loads (i.e., wind and snow mound).…”

Plant strategies for greatest height: tapering or hollowing

“…The validity of this theory was verified by McMahon, who confirmed that it accurately fits trees of various shapes 2 , 3 . Greenhill's scaling law, with its simplicity and applicability, has been used extensively in forest science and ecology 4 – 9 .…”