Abstract
Although plant stem cross-sections are most often circular, some are square, triangular or elliptic, but these are rare. The advantage of quadratic stems over cylindrical ones, if one exists, is unclear. Here we propose a (bio) mechanical advantage of square-stemmed plants. Our idea is based on the fact that the second moment of inertia I of a stem, depending on the shape of the cross-section, determines the plant’s resistance to bending and torsion deformations induced by wind load and gravitation: a larger I results in greater mechanical resistance. When can a quadratic stem have a larger I than a cylindrical stem of comparable material? We calculated the rotation-invariant I of quadratic and cylindrical hollow stems with the same cross-section area as functions of the quotient k of the inner and outer dimensions, and the quotient Q of the outer dimensions of square and circlular stems. We determined those configurations of the geometric control parameters k and Q for which the I of a quadratic stem is larger than that of a cylindrical one; that is, the former stem is more resistant to mechanical deformations than the latter. This finding provides a clear mechanical benefit of square-stemmed over circle-stemmed plants.
Published Version
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