The Cactaceae are a diverse group of plants with a wide variety of morphologies. Many species of Opuntia have segmented stems in which terminal cladodes may be separated from main‐stem cladodes with varying amounts of resistance. From a geometric approach, derivations were used to calculate normal (axial and bending) and shear (transverse force and torque) stresses at joints due to the weight of the cladodes. Normal and shear stresses act perpendicular and parallel to (along) the cross sections of joints, respectively. Normal stress caused by bending was >10 times that of the mean value of any other stress. Analyses were performed to determine the relationship between maximum normal stress and the amount of lignified xylem cells. Such cells had thicker cell walls compared with the various other cells of stem joints that had thin cell walls and that thus would provide the most resistance to normal stresses. An analogy was made between cactus joints and a composite beam with reinforcing rods. In such joints, thin‐walled parenchyma cells might be analogous to concrete that has little resistance to tensile stress, while the thick‐walled, lignified xylem cells would be analogous to reinforcing rods. There were statistically significant relationships between normal stresses (from bending and axial loads) and mean percentage of lignified xylem cells ( \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$r=0.73$$ \end{document} ) and between normal stresses and total areas of lignified xylem cells ( \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$r=0.65$$ \end{document} ) (more stress, more reinforcing xylem cells). Tensile portions of cactus joints had 23% lignified xylem cells, while compressive portions had only 10% lignified xylem cells in joint areas (more tension, more reinforcing xylem cells). In addition, tensile joint tissues had two to three times more thick‐walled, lignified xylem cells in the outer 30% of the radius compared with other joint tissues types (more reinforcing near the surface). To our knowledge, this is the first publication to present mechanical stresses at stem joints of cacti and the first to relate these stresses to characteristics of resisting tissues in the joints of a cactus.

中文翻译：

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压缩/拉伸应力和木质化细胞作为仙人掌（仙人掌科）枝间关节中的阻力成分

仙人掌科植物种类繁多，形态各异。许多仙人掌物种都有分节的茎，其中末端分支可能与主茎分支分开，具有不同程度的阻力。从几何方法中，推导被用来计算由于枝条重量引起的接头处的法向（轴向和弯曲）和剪切（横向力和扭矩）应力。法向应力和剪应力分别垂直和平行于（沿着）接头的横截面作用。由弯曲引起的法向应力大于任何其他应力平均值的 10 倍。进行分析以确定最大法向应力与木质化木质部细胞数量之间的关系。与具有薄细胞壁的干关节的各种其他细胞相比，这些细胞具有更厚的细胞壁，因此对正常压力具有最大的抵抗力。在仙人掌接头和带有钢筋的复合梁之间进行了类比。在这种接缝中，薄壁薄壁组织细胞可能类似于对拉伸应力几乎没有抵抗力的混凝土，而厚壁木质部细胞类似于钢筋。法向应力（来自弯曲和轴向载荷）和木质化木质部细胞的平均百分比（ \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage {mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland, OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty } \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$r=0.65$$ \end{document} ）（更多的压力，更多的强化木质部细胞）。仙人掌关节的拉伸部分有 23% 的木质部细胞，而压缩部分在关节区域只有 10% 的木质部细胞（张力越大，强化木质部细胞越多）。此外，与其他关节组织类型相比，拉伸关节组织在半径外 30% 处的壁厚、木质化木质部细胞是其他关节组织类型的 2 到 3 倍（在表面附近加强）。据我们所知，