In most structural systems, initial imperfections, such as initial deflection, is an unavoidable challenge, and it significantly influences buckling. This study aimed to theoretically explain the effect of initial deflection and initial slope on self-buckling characteristics of heavy columns subjected to self-weight. Specifically, we examined cantilevers composed of isotropic material with a constant cross-section. Accounting for both self-weight and axial compression load, we developed a formula characterizing the self-buckling problem for some simplified cases such as sin-curve, hypergeometric curve, and straight line (initial slope). Consequently, we established the relationship between the self-buckling characteristics and the level of initial imperfections. We discovered that the greatest height for self-weight buckling is proportional to the 2/3 power of radius, regardless of the initial imperfection. Moreover, our findings suggest the potential to predict the height of tree-like natural structures using the greatest height formula and considering initial imperfections.

在大多数结构系统中，初始缺陷（例如初始挠度）是不可避免的挑战，它会显着影响屈曲。本研究旨在从理论上解释初始挠度和初始坡度对自重重柱自屈曲特性的影响。具体来说，我们检查了由具有恒定横截面的各向同性材料组成的悬臂。考虑到自重和轴向压缩载荷，我们开发了一个公式来描述一些简化情况的自屈曲问题，例如正弦曲线、超几何曲线和直线（初始斜率）。因此，我们建立了自屈曲特性与初始缺陷水平之间的关系。我们发现，无论初始缺陷如何，自重屈曲的最大高度与半径的 2/3 次方成正比。此外，我们的研究结果表明，使用最大高度公式并考虑初始缺陷来预测树状自然结构的高度是有潜力的。