Relative resistance of hollow, septate internodes to twisting and bending

Abstract

The aim of this paper was to examine the mechanical behaviour of hollow internodes with transverse nodal septa subjected to bending and twisting and to determine the extent to which this behaviour agreed with predictions made by the theory of elastic stability treating thin walled tubes or 'shells'. This theory determined the experimental protocol used in this study because it required the empirical determination of two important material properties of stem tissues (i.e. the Young's elastic modulus, E, and the critical shear stress, τ) and required the use of a dimensionless grouping of variables as a descriptor of internodal shape (i.e. l2/2tR, where l is internodal length, t is wall thickness, and R is external radius). All of these variables were measured for a total of 92 internodes (removed from the stems of field grown plants from a total of six species) followed by correlation analyses to determine whether the ability of internodes to resist twisting relative to bending (summarized by the quotient τ/E) correlated with the shape descriptor l2/2tR. Analyses of the data indicated that: (1) the extent to which nodal septa influenced internodal bending stiffness declined as internodal length increased relative to wall thickness or external radius; and (2) the ability to resist torsion relative to the ability to resist bending declined as internodal length increased relative to wall thickness or external radius. Both of these trends agreed well with the theory of elastic stability. Also, as theory predicts, the mechanical behaviour of internodes was correlated better with the shape descriptor l2/2tR than with any measure of absolute internodal size (e.g. l or t). Thus, internodal shape (in part defined by the spacing of nodal septa which influences l) largely dictates the mechanical behaviour of stems subjected to twisting or bending.