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.