The effect of plant weight on estimations of stalk lodging resistance

Abstract

Background: Stalk lodging (breaking of agricultural plant stalks prior to harvest) is a multi-billion dollar a year problem. Stalk lodging occurs when bending moments induced by a combination of external loading (e.g. wind) and self-loading (e.g. the plant's own weight) exceed the stalk bending strength of plant stems. Previous studies have investigated external loading and self-loading of plants as separate and independent phenomena. However, these two types of loading are highly interconnected and mutually dependent. The purpose of this paper is twofold: (1) to investigate the combined effect of external loads and plant weight on the flexural response of plant stems, and (2) to provide a generalized framework for accounting for self-weight during mechanical phenotyping experiments used to predict stalk lodging resistance.

Results: A mathematical methodology for properly accounting for the interconnected relationship between self-loading and external loading of plants stems is presented. The method was compared to numerous finite element models of plants stems and found to be highly accurate. The resulting interconnected set of equations from the derivation were used to produce user-friendly applications by presenting (1) simplified self-loading correction factors for common loading configurations of plants, and (2) a generalized Microsoft Excel framework that calculates the influence of self-loading on crop stems. Results indicate that ignoring the effects of self-loading when calculating stalk flexural stiffness is appropriate for large and stiff plants such as maize, bamboo, and sorghum. However, significant errors result when ignoring the effects of self-loading in smaller plants with larger relative grain sizes, such as rice (8% error) and wheat (16% error).

Conclusions: Properly accounting for self-weight can be critical to determining the structural response of plant stems. Equations and tools provided herein enable researchers to properly account for the plant's weight during mechanical phenotyping experiments used to determine stalk lodging resistance.

Keywords: Bending; Flexural; Lodging; Plant; Stalk; Stem; Stiffness; Strength; Weight.

Fig. 1

The loading diagram of a deflected stem, showing two loading locations with all three types of loading (an applied force, an applied moment, and a weight)

Fig. 2

The loading diagrams for two common mechanical phenotyping test protocols used to determine flexural stiffness; a typical maize phenotyping protocol (left), and a typical wheat phenotyping protocol (right)

Fig. 3

A comparison between the closed form solution and the solution of finite element models for stalk flexural stiffness (a) and for stalk bending strength (b), n = 768, as a function of deflection normalized by plant height. Histograms of the error between the closed form solution and the finite element models for stalk flexural stiffness (c) and for stalk bending strength (d), n = 768. a demonstrates that significant errors can occur at very small (near-zero) deflections. A deflection of 2.5% to 20% of the stalk height is recommended to minimize error during stalk flexural stiffness phenotyping experiments

Fig. 4

A comparison between the closed form solution and the finite element model solution (FEM) for very large deflections (i.e., for deflections and loads beyond what would typically be seen in the field). Plots depict the deflection at the tip of the stalk (a) and the maximum moment at the base of the stalk (b); the % error between the finite element model and the closed form calculation of stalk flexural stiffness and stalk bending strength are shown as a function of stalk deflection normalized by stalk height (c)

Fig. 5

An example of the Excel spreadsheet (see Additional file 1), showing loading at three locations, and calculating deflection and induced moments at four locations: the three loading locations and the base of the plant. Note that the error in deflection is not calculated at the base, as deflection at the base is zero regardless of loading condition

Fig. 6

The error of stalk flexural stiffness (left) and stalk bending strength (right), as a function of the ratio between the combined weight of the grain and plant and stalk flexural stiffness