Compressive/Tensile Stresses and Lignified Cells as Resistance Components in Joints between Cladodes of Opuntia laevis (Cactaceae)

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}