PLANT BIOPHYSICS - Y. I. Posudin - 2004

I. PHYSICAL PROPERTIES OF PLANT CELLS AND TISSUES

1. MECHANICAL PROPERTIES

1.3. MEASUREMENT OF YOUNG'S MODULUS

For a rod of circular cross-section with a radius R, fixed at one end (Fig. 1.2), Young's modulus is determined by the formula:

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where l is the length of the rod, F = mg is the force applied to the rod, m is the mass of the load, g is the acceleration due to gravity, and λ is The amount of rod deflection ("deflection sag").

In the case of a tubular cross-section, Young's modulus of a rod fixed at one end is determined as follows:

where R1 and R2 are the outer and inner radii of the tube, respectively.

Fig. 1.2. Determination of Young's modulus for a rod of circular cross-section with radius R, fixed at one end.

If the rod is supported at both ends, the proportionality coefficient 3 in the denominators of the last two formulas is replaced by 48.

Young's modulus E of a rod with a rectangular cross-section can be determined by measuring the rod deflection (Fig. 1.3) using the formula:

where l is the length of the rod, a and b are the width and thickness of the rod, F = mg is the force applied to the rod, m is the mass of the load, g is the acceleration due to gravity, and λ is the amount of rod deflection ("deflection sag").

Fig. 1.3. Determination of Young's modulus for a rectangular cross-section rod supported at both ends by measuring its deflection.

A plant Cell is surrounded by an elastic Cell wall of Cellulose-pectin composition. Plant Cell Walls exhibit elastic properties that enable them to stretch under external loads. Young's modulus, which characterizes the Elastic properties of Materials, is 108 N·m-2 for pure cellulose, which is about 5% of Young's modulus for steel. Because The Cell wall contains various components In addition to cellulose, its Young's modulus is lower than that of pure cellulose. For instance, Young's modulus of the cell wall in the alga Nitella is 7·108 N·m-2 [Nobel, 1973]. Young's modulus for woody plants ranges from (0.35-1.93)·1010 N·m-2 [Haygreen, Bowyer, 1989].

Example. Determine Young's modulus of the wood from which a beam with dimensions a = b = 5 cm and l = 70 cm is made, if under the action of a force F = 6860 N, the deflection λ of the rod is 0.7 cm.

Solution. Substituting the numerical values into equation (1.9):



Last update: 07/08/2026

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