Mechanical Properties and Anatomical Components of Stems of 42 Grass Species

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Mechanical Properties and Anatomical Components of Stems of42 Grass SpeciesAuthor(s): Lance S. Evans, Zella Kahn-Jetter, Chelsea Marks, and Keith R.HarmoneySource: The Journal of the Torrey Botanical Society, 134(4):458-467. 2007.Published By: Torrey Botanical SocietyDOI: http://dx.doi.org/10.3159/07-RA-009.1URL: http://www.bioone.org/doi/full/10.3159/07-RA-009.1

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Mechanical properties and anatomical components of stems of42 grass species

Lance S. Evans1,2

Laboratory of Plant Morphogenesis, Biological Sciences Research Laboratories,Manhattan College, the Bronx, NY 10471

Zella Kahn-JetterDepartment of Mechanical Engineering, Manhattan College, the Bronx, NY 10471

Chelsea MarksLaboratory of Plant Morphogenesis, Biological Sciences Research Laboratories,

Manhattan College, the Bronx, NY 10471

Keith R. HarmoneyKansas State University, Agricultural Research Center, Hays, KS 67601

EVANS, L. S. (Laboratory of Plant Morphogenesis, Biological Sciences Research Laboratories, ManhattanCollege, the Bronx, NY 10471), Z. KAHN-JETTER (Department of Mechanical Engineering, ManhattanCollege, the Bronx, NY 10471), C. MARKS (Laboratory of Plant Morphogenesis, Biological SciencesResearch Laboratories, Manhattan College, the Bronx, NY 10471) AND K. R. HARMONEY (Kansas StateUniversity Agricultural Research Center, Hays, KS 67601). Mechanical properties and anatomicalcomponents of stems of 42 grass species. J. Torrey Bot. Soc. 134: 458–467. 2007.—Stems of grass supportmuch of the world’s food supply during grain maturation. The purpose of this study was to determine themechanical properties of stems and to determine if thick-walled, sclerenchyma cells are the main componentsthat resist stem bending for 42 species of grass plants. During tests, stresses were imposed on grass stemsegments to more than 90% of the maximum elastic load. Anatomical analyses were also performed todetermine relationships between mechanical properties and geometric/anatomical characteristics of grassstems. Data show that more than 59% of all sclerenchyma cells in stems occur in the outer one-fifth radius ofstems. Values of outer diameter, inner diameter, and stem density varied by factors of 10 or more, values ofmodulus of elasticity ranged from 0.1 to 32 GPa (a factor of more than 300 times) and values of maximumbending moment from 0.0005 to 2.0 N-m (a factor of 4000 times). Results of stress tests show that maximumbending moment was highly correlated with section modulus so that maximum bending stress values variedby only a factor of 8. Values of maximum bending stress varied from a low of 1.0E07 to a high of 8.0E07 Paamong the grass species tested with a mean and standard deviation of 3.3 and 2.3E07 Pa, respectively. Dataof this study also showed that maximum bending moments of the 42 species were correlated well (y 5 0.028x+ 0.0001, r2 5 0.64) with the areas of thick-walled sclerenchyma cells in stems. Taken together, these datashow that maximum bending stress values of all 42 grass species were nearly identical and that sclerenchymacells in stems provided the major support for stem integrity at the upper limit of imposed stem stresses. Toour knowledge, this study is the first to compare the geometric, mechanical, and anatomical characteristics ofover forty species of grasses to provide a unifying view of grass stem resistance to mechanical stresses.

Key words: Grasses, modulus of elasticity, Poaceae, sclerenchyma, stem bending moment, stem bendingstress, tissue density, tissues that resist bending.

Grasslands are a major ecosystem type on

most continents. A wide variety of grass

species occupy grasslands and grasses may be

a large component of other ecosystems (Smith

1996). Grass culms (stems) perform all the

functions of stems of plants, which include

providing support for leaves, flowers and

fruits, to store nutrients, and provide nutrients

to roots (Moore et al. 1995). Grass stems must

be able to overcome the mechanical stresses of

the weights of stems, branches, leaves, flowers,

and fruits in harsh environments. For exam-

ple, high winds in prairie environments may

cause lodging. The effects of gibberellins on

growth and lodging (buckling of stems by

excessive growth) of rice plants are well known

(Phinney 1983).

Anatomical characteristics of grass stems of

annual crops such as wheat, barley, and rye

have been described (Hayward 1938, Esau

1 Author for correspondence. E-mail: [email protected]

2 The authors thank the excellent technicalassistance of Patricia M. Evans for her efforts withmechanical testing of samples in Florida and in themid-western states. The authors appreciate financialsupport of The Catherine and Robert FENTONEndowed Chair to LSE.

Received for publication May 15, 2007, and inrevised form October 9, 2007.

Journal of the Torrey Botanical Society 134(4), 2007, pp. 458–467

458

1964, Fahn 1967, Spatz and Speck 1994, Spatz

et al. 1997). Hayward (1938), Esau (1964),

Fahn (1967), and Li et al. (1994) have shown

that vascular bundles are scattered within the

ground parenchyma in stems of Triticum

aestivum, Zea mays, and three species of

Bambusa. Stems of Triticum aestivum and

Hordeum vulgare, and many other annual

grasses have hollow stems with epidermal

cells, (mechanical) sclerenchyma cells (Hay-

ward 1938), vascular tissues, and many thin-

walled parenchyma cells (Hayward 1938, Esau

1964). In contrast to the stems of annual

crops, stems of perennial grasses like bamboo

have more sclerenchyma (sclerified parenchy-

ma) cells (Li et al. 1994). Sclerenchyma cells

appear to provide most of the mechanical

resistance to bending in bamboo stems

(Hsiung et al. 1980). Li et al. (1994) stated

that bamboo culms may have tensile strength

values as high as 530 MPa, equal to the tensile

strength of steel. In many regions of the world,

bamboo stems are used in the construction of

buildings and other structures.

Many engineering and construction materials

have a uniform composition throughout. In

contrast, most living materials are composites

of many cell types (Hayward 1938, Esau 1964,

Fahn 1967, Silk et al. 1982, Niklas 1992, Spatz

and Speck 1994). In addition to being a

composite material, grass stems do not have a

uniform cross sectional geometry, and they also

have nodes. Because all the above apply to grass

stems, it is recognized that mechanical principles

of uniform materials cannot be used effectively

to characterize grass stems or any other

composite material. Thus, values for second

moment of area (I) and modulus of elasticity (E)

generated herein are approximations.

The purpose of this research is to under-

stand the mechanical properties of stems of

grass species and relate these mechanical

properties to anatomical characteristics. Spe-

cifically, among 42 grass species, we tested the

following hypotheses: (1) The largest percent-

ages of sclerenchyma cells are located near the

external stem surfaces for grass species, (2)

Maximum bending stress values are relatively

constant among grass species, and (3) Maxi-

mum bending moments are positively related

to amounts of sclerenchyma cells in stems for

grass species.

Materials and Methods. PLANT SPECIES

TESTED. The inclusion of each grass species

selected for study was based upon availability

of at least 15 healthy, green, growing stems

and the ability to positively identify the species

(Table 1). Plants of Hakonechloa macra var.

aureoa, Dactylis glomerata, Bambusa multiplex

(synonym 5 Bambusa glaucescens), Phragmites

australis, Miscanthus sinensis var. zebrinus,

Miscanthus sinensis var. gracilimus, Pennisetum

alopecuroides, and Echinochloa crus–galli, were

obtained from sites from the Bronx, NY or

from Tarrytown, NY. Plants of Hordeum

vulgare, Triticum aestivum, Saccharum offici-

narum, and Zea mays were obtained from

plants grown in the Manhattan College green-

house. Plants of Z. mays, T. aestivum and H.

vulgare were grown from seed obtained from

Carolina Biological Co. (Burlington, North

Carolina). Plants of S. officinarum were grown

from stem segments obtained from a commer-

cial cane grower in Maui, Hawaii. For plants

grown in the greenhouse, only single plants

were grown in plastic pots that contained a

minimum of two liters of soil. Plants were

watered daily as necessary. Pots were spaced

more than one meter from all other pots so that

plants would not be light limited. Plants of

Calamagrostis acutiflora, Sporobolus asper,

Sporobolus cryptandrus, Bouteloua gracilis,

Pascopyrum smithi, Andropogon gerardii, Bo-

thriochloa bladhii, Bothriochloa ischaemum,

Bothriochloa saccharoides, Schizachyrium sco-

parium, Sorghum halepense, Sorghastrum nu-

tans, Cenchrus longispinus, Digitaria ischae-

mum, Digitaria sanguinalis, Panicum virgatum,

Eriochloa contracta, Pennisetum setaceum, Se-

taria lutescens, and Setaria viridis were ob-

tained from various locations in the vicinity of

Hays, Kansas. Plants of Eragrostis curvula,

Chasmanthium laxum (synonym 5 Uniola

laxa), Panicum repens, Paspalum notatum, and

Stenotaphrum secundatum were used from

locations in the vicinity of New Smyrna Beach,

Florida. Plants of Elymus repens were obtained

near Clear Lake, Iowa. Plants of Hordeum

jubatum and Phalaris arundinacea were ob-

tained near Bismarck, North Dakota. Plants of

Bromus inermis were obtained near Pierre,

South Dakota, and plants of Elymus trachy-

caulus subsp. subsecundus were obtained near

St Cloud, Minnesota. Herbarium specimens

were made of each plant species that could not

be immediately identified. Plants from New

York were sampled in June through August of

2003 and June through August of 2004. Plants

from Florida were sampled in January 2005.

2007] EVANS ET AL.: MECHANICAL PROPERTIES AND ANATOMY OF GRASS STEMS 459

Table 1. Grass species collected and grouped by sub-family and tribe, outer and inner stem diameters oftested samples along with photosynthetic pathway.

Subfamily Tribe Species

Outerdiameter

(mm)Inner diameter

(mm)Photosynthetic

pathway

Festucoideae Agrostideae Calamagrostisacutiflora

1.9 1.1 C3

Festucoideae Agrostideae Sporobolus asper 2.7 1.2 C4Festucoideae Agrostideae Sporobolus

cryptandrus1.1 0.8 C4

Festucoideae Bambuseae Bambusa multiplex 13.1 7.6 C3Festucoideae Chlorideae Bouteloua gracilis 1.2 0.2 C4Festucoideae Festuceae Bromus inermis 1.7 1.0 C3Festucoideae Festuceae Dactylis glomerata 1.9 0.2 C3Festucoideae Festuceae Eragrostis curvula 1.9 1.0 C4Festucoideae Festuceae Hakonechloa macra

var. aureola1.5 0.6 C3

Festucoideae Festuceae Phragmites australis 11.1 8.5 C3Festucoideae Festuceae Chasmanthium

laxum1.7 0.4 C3

Festucoideae Hordeae Elymus repens 2.0 1.7 C3Festucoideae Hordeae Pascopyrum smithii 1.1 0.5 C3Festucoideae Hordeae Elymus trachycaulus

subsp.subsecundus

1.2 0.8 C3

Festucoideae Hordeae Hordeum jubatum 0.5 0.4 C3Festucoideae Hordeae Hordeum vulgare 2.3 0.9 C3Festucoideae Hordeae Triticum aestivum 2.1 0.9 C3Festucoideae Phalarideae Phalaris arundinacea 3.3 2.2 C3Panicoideae Andropogoneae Andropogon gerardii 4.6 1.8 C4Panicoideae Andropogoneae Bothriochloa bladhii 1.9 1.1 C4Panicoideae Andropogoneae Bothriochloa

ischaemum1.6 0.0 C4

Panicoideae Andropogoneae Bothriochloasaccharoides

2.1 1.1 C4

Panicoideae Andropogoneae Miscanthus sinensisvar. graicillimus

2.4 0.0 C4

Panicoideae Andropogoneae Miscanthus sinensisvar. zebrinus

3.9 0.0 C4

Panicoideae Andropogoneae Saccharumofficinarum

16.4 3.9 C4

Panicoideae Andropogoneae Schizachyriumscoparium

1.9 0.0 C4

Panicoideae Andropogoneae Sorghastrum nutans 3.6 1.6 C4Panicoideae Andropogoneae Sorghum halepense 3.2 2.2 C4Panicoideae Paniceae Cenchrus longispinus 1.5 1.3 C4Panicoideae Paniceae Digitaria ischaemum 0.8 0.4 C4Panicoideae Paniceae Digitaria sanguinalis 1.2 1.1 C4Panicoideae Paniceae Echinochloa

crus–galli3.2 1.3 C4

Panicoideae Paniceae Eriochloa contracta 1.2 1.1 C4Panicoideae Paniceae Panicum repens 1.5 1.0 C4Panicoideae Paniceae Panicum virgatum 2.1 1.3 C4Panicoideae Paniceae Paspalum notatum 1.4 0.0 C4Panicoideae Paniceae Pennisetum

alopecuroides1.9 1.1 C4

Panicoideae Paniceae Pennisetumsetaceum

1.5 0.0 C4

Panicoideae Paniceae Setaria lutescens 1.4 1.3 C4Panicoideae Paniceae Setaria viridis 1.2 0.0 C4Panicoideae Paniceae Stenotaphrum

secundatum3.3 1.5 C4

Panicoideae Tripsaceae Zea mays 7.8 0.0 C4

460 JOURNAL OF THE TORREY BOTANICAL SOCIETY [VOL. 134

Plants from Kansas, Iowa, North Dakota,

South Dakota and Minnesota were sampled in

July and August 2005. Plant species were

identified by the authors or personnel at the

New York Botanical Garden, Bronx, NY.

Species were grouped in sub-families and tribes

using the classification proposed by Hitchcock

(1971) while current species names were deter-

mined using the USDA NRCS PLANTS

Database (2006).

MECHANICAL TESTING. For each plant spe-

cies, at least 15 stems were placed into the

apparatus to determine mechanical properties.

All stem samples of this study were green with

only green leaves present at harvest. Stems

used for testing were harvested and tested

within two hours of sampling. From harvest to

testing, the bottoms of cut stems were kept in

water so that stems and leaves would not

desiccate. For most species, stem samples were

processed so that all mechanical tests were

completed within 40 minutes. For each stem

sample tested, all leaf sheaths were removed

from stem segments tested and segments were

placed in a device that simulated a simply-

supported beam with a concentrated load at

midspan (Fig. 1). The distance between the

two supporting loops was varied among

species from 4.1 cm up to 26.1 cm. Stem

segments were always placed on the two

supporting loops so that internodes were

always tested. In other words, no nodes were

ever tested (located between the supports).

This was important since Niklas (1989), Li et

al. (1994), and Spatz and Speck (1994) showed

that nodal areas had different anatomical and

mechanical characteristics than internodal

areas. Stems were rested in the supporting

loops, but the ends of the stems could move

slightly from side to side as weights were

added at the mid-span. This was necessary in

order to prevent lateral stresses (stresses along

the stem’s length). Deflection distances were

measured from the mid-point on the stem for

all measurements with a caliper (catalog # 14-

648-17, Fisher Scientific Co.). For each stem

sample tested, the time between the addition of

the first weight and removal of all weights was

less than five minutes. After each weight was

added, the deflection distance was measured.

For each stem, deflection measurements were

made to the nearest 0.1 mm. The total

deflection of all stems was always less than

10% of the distance between the two support-

ing loops. At least three weights were added to

the midspan of each stem tested. The distance

was measured before weights were added. The

weights (Precision Analytical and Reference

Weights Cat. No. 02-225-059) used were

calibrated on two balances, which themselves

were verified using separate weight standards.

Before the actual testing that yielded the

results described herein, we added weights to

at least four preliminary stem samples. For

this preliminary stem testing the diameter of

each sample and the weight necessary to cause

permanent deformation (buckling) was deter-

mined. Thus, for each species, we made a

rough relationship between stem diameter and

weight necessary of failure. Based upon these

preliminary tests, we feel that the total weight

added during actual testing (when stems

returned to their original condition after all

weights were removed) were more than 90% of

the maximum elastic load. Overall, we believe

that additional loads would have caused the

stem to exceed its elastic limit (cause a

permanent deflection). The span (between

supporting loops)-to-stem diameter values for

FIG. 1. Diagram of the apparatus to test mechanical properties of grass stems. L is the length betweensupports, P is the applied load, Y is the deflection when the load is applied.


the largest diameter samples of each species

were always above 10. With these relatively

high values, shearing stresses were not ac-

counted for since they would have been

negligible compared with bending stresses.

Once all testing was completed for a sample,

the inside diameters (for hollow samples) and

outside diameters were determined with cali-

per to the nearest 0.01 mm at each stem end

and at positions J, K and L distance along

the stem tested. The length and weight of each

sample was obtained within 5 minutes after

testing. Stem segments were weighed with an

analytical balance (Denver Instruments, model

number XE100) to the nearest 0.01 g. Stan-

dard weights were used to calibrate the

balance before each use. Tissue volumes were

calculated for each stem sample from data of

internal radius (for hollow stems), external

radius and length of the segments. Tissue

densities were calculated for each sample

based upon values of tissue mass and tissue

volume, expressed as kg m23.

By knowing the applied load and the

geometry of the stem, and measuring the

deflection, the modulus of elasticity (E), in

Pascals, was calculated according to the

following formula

E ~PL3

48Iyð1Þ

where:

P is the load in Newtons,

L is the length of the grass stem between

supports in meters,

I is the second moment of area or moment

of inertia in m4 (the calculated values are for

all tissues of the stem and is equal top(r4

o { r4i )

4, where ro and ri are the outer and

inner radii of the stem), and, y is the deflection

under the load, in meters (Beer and Johnston

1992). Even though Equation (1) is derived for

an isotropic material with a uniform cross

section throughout the length of the ‘beam’,

this equation would provide an ‘effective’

modulus of elasticity in this study. The

modulus of elasticity of a material is an

indication of its stiffness, i.e., ability to bend

under a given load and go back to its original

geometry when the load is removed.

We also realize that the stems were tapered

with smaller diameters for apical ends and

larger diameters for acropetal ends. In all

cases, the diameters of the apical end of a stem

segment were within 95% of the acropetal end.

Therefore, the modulus values presented and

discussed in this paper can only be used for

comparative purposes for the species studied

and are not meant to present true grass

modulus values.

The bending moment, M, in units of N-m,

for a simply-supported beam with a concen-

trated mid-span load is given as

M ~PL

2ð2Þ

The maximum bending stress, s, in units of Pa

was determined from

s ~Mc

Ið3Þ

where c is the outside radius. Equation (3) can

be rewritten as

s ~M

Sð4Þ

where S is the section modulus, defined as I/c.

HISTOLOGICAL SAMPLES. Two, 2 cm long

stem pieces from at least seven randomly

selected stem segments from the mechanically

tested samples were taken for histology.

Histological samples were fixed in FAA

(Jensen 1962) within 15 min after the mechan-

ical testing. Tissues were left in fixative for at

least 24 h and stored in 70% ethanol until

further processing could occur. Tissues were

processed through a tertiary butanol series to

paraffin. During each solution change, plant

samples were placed in a container and a

vacuum pump was used to facilitate solution

infiltration into the tissues. After at least two

changes of paraffin, samples were embedded

in paraffin (Sass 1958) and cut at 25 to 30 mm

with a rotary microtome. Tissues were stained

with either the safranin - fast green procedure

of Sass (1958) or the six-dye staining proce-

dure of Shellhorn and Hull (1961).

EVALUATION OF HISTOLOGICAL TISSUE SAM-

PLES. Our histological analysis was aimed at

determining the areas of sclerenchyma cells

(Fig. 82.1 from Fahn 1967; Fig. 51 from

Hayward 1938) or the so-called ‘mechanical’

tissues (Figs. 24 and 25 from Hayward 1938)

within stems since these tissues were hypoth-

esized to provide the greatest resistance to

stem bending (Li et al. 1994). Mauseth (1998)

categorized sclerenchyma into two groups, the


mechanical sclerenchyma composed of sclere-

ids and fibers and the conducting sclerenchy-

ma composed of tracheids and vessel elements.

Specifically, our analysis was aimed at deter-

mining all areas of sclerenchyma cells and all

areas of non-sclerenchyma (thin-walled) cells

within cross sections of stems. The sum of

these two areas always equaled the entire stem

cross sectional area.

For each stem segment processed, the most

representative tissue sections with the least

amount of microtome knife damage were

photographed. About J of each stem cross-

section was photographed to make a compos-

ite. A composite usually consisted of three to

six individual (each individual photograph was

approximately 11 cm by 15 cm) photographs

(Kahn-Jetter et al. 2000, 2001). For each

composite, five concentric arcs were drawn.

Each incremental arc was made 1/5 the

distance from the inner radius to the outer

radius for hollow and 1/5 the distance along

the radius for solid (non-hollow) stem tissue

sections. After the arcs were drawn on the

composite, all areas of sclerenchyma cells were

also marked. The total area of all sclerenchy-

ma cells in each arc and the total area of

each arc were determined with a planimeter

(Model L10, Los Angeles Scientific Instru-

ment Co. Inc., Los Angeles, CA). The total

area of all sclerenchyma cells for all arcs

was determined. Sclerenchyma cell area was

calculated as a percentage of the total area of

stem tissue for each of the five arcs. As a

result, the sum of all five percentages of

sclerenchyma cells areas for the five arcs

equaled 100%. This same procedure was used

previously (Kahn-Jetter et al. 2000, 2001). The

planimeter was calibrated for accuracy with

known areas before each use. All planimeter

areas were corrected for areas in tissue

samples.

STATISTICAL ANALYSIS. Several statistical

analyses were performed. To determine if

percentages of sclerenchyma cells were differ-

ent among the arcs, values for the five tissue

arcs were subjected to analysis of variance

(ANOVA) followed by a multiple range test

with SYSTAT 10 (SPSS 1997). Before per-

forming statistical analyses with percentage

values, all percentages were converted to

arcsine values. Regression analysis was also

performed using several parameters with

Microsoft Excel (Excel 97, Microsoft Corp.).

For each relationship an equation of the line

and a coefficient of determination were

provided by the program. To determine if

parameters differed among various taxonomic

groups or photosynthetic pathways, analysis

of variance (SYSTAT 10 SPSS 1997) or t-tests

(Excel 97) were used to establish statistical

significance. For t-tests, all values in a

category were grouped for analysis.

Results. BASIC ANATOMY OF GRASSES. Our

histological samples were identical to those

already published. Specifically, for grass

stems, vascular bundles are dispersed and are

not arranged in a circular pattern on the inside

of the cortex and outside the pith like that of

dicotyledonous plants, likewise reported by

Fahn (1967) and Hayward (1938). In stems of

this study the thick-walled sclerenchyma cells

toward the outer portions of stems, identified,

as ‘mechanical tissues’ of many species, were

identical to those showed in Figs. 24 and 73 of

Hayward (1938). Moreover, for some species

like Phragmites australis and Bambusa multi-

plex, stems had large amounts of sclerenchyma

in a distinct band near the outer surface of

young stems (Hsiung et al. 1980, Mohmod et

al. 1993, Li et al. 1994). Since the anatomies of

many grass species have been well described,

no photographs of stem segments are present-

ed here.

Data from the 42 species show that the

mean outer and mean inner diameters were 3.1

and 1.2 mm, respectively. Using these mean

values, the calculated area percentages of the

five arcs (from inside to outside) were 13, 17,

20, 23, and 27% of the total, respectively.

These percentages are shown in Table 2. In

contrast, percentages of sclerenchyma cells in

the five arcs were quite different from the

percentage of total stem tissue area of each

arc. For example, 59% of the total scleren-

chyma cell area was present in the outer arc of

stems while the total area of the arc was only

27% of the entire stem area. In contrast, only

9% of the total sclerenchyma cell area was

present in the two-innermost arcs of stems.

Overall, a disproportionately large area of

sclerenchyma cells is found in the outer arc

while a disproportionately small area of

sclerenchyma cells is found in the two-

innermost arcs. These results are consistent

with the hypothesis that sclerenchyma cells are

most responsible for resistance to bending in

these species.


Stems of Bambusa multiplex and Phragmites

australis have relatively large diameters and

showed a preponderance of sclerenchyma cells

in the outer portions of stems (Hsiung et al.

1980, Mohmod et al. 1993, Li et al. 1994) while

stems of smaller diameter annual grasses

(Hayward 1938) appear to have a more

random arrangement of sclerenchyma cells

associated with vascular bundles. Therefore,

we tested the relationship between stem

diameter and percentages of sclerenchyma

cells area in the five stem arcs. For the 42

grass species, there was no statistical difference

between percentage of sclerenchyma area in

stem arcs and stem diameter.

GEOMETRIC AND MECHANICAL PROPERTIES

OF STEMS. Data in Table 1 show that outer

diameters of stems among the 42 species tested

varied from 0.53 to 16.4 mm and densities

varied from 101 to 997 kg m23. However, stem

densities were normally distributed (Fig. 2).

Values of modulus of elasticity ranged from

0.1 to 31 GPa (a factor of more than 300

times) with a mean of 7.7 and a standard

deviation of 6.0 GPa. Values of maximum

bending moment ranged from 5.0 3 1024 to

2.0 N-m (a factor of 4000 times) with a mean

of 0.15 and a standard deviation of 0.43 N-m.

Values of rigidity (E*I) varied from 7.54 to 21

N-m2, a factor of 2.8 3 105.

Data in Fig. 3 show that values of maxi-

mum bending moment were correlated with

section modulus. The relationship was char-

acterized by y 5 2.0 3 107x + 0.0006 with a

coefficient of determination of 0.48. The slope

of this relationship is maximum bending stress

since maximum bending stress is calculated as

Table 2. Percentages of total sclerenchyma cell area within stem portions of 42 species of grasses.Percentages with a different superscript are significantly different from each other. (P , 0.05)

Arc Percentage of total tissue area in arcPercentage of total sclerenchyma cell area in arc

(mean 6 SD)

Outer arc 27 58.9a (6 18.1)Second outer arc 23 22.6b (6 8.5)Third outer arc 20 9.6c (6 7.4)Fourth outer arc 17 6.4c (6 8.1)Inner arc 13 2.5c (6 5.3)

FIG. 2. Frequency distribution of densities (kg m23) of stems of 42 grass species. The densities werecalculated including the hollow stems of some species. Frequency is the number of species in each category.Overall, the mean and standard deviation values were 441 and 207 kg m23, respectively.


s 5 M/S (see equation 4 above). Maximum

bending stress values for the 42 species varied

from 1 to 8E07 Pa with a mean of 3.3 and

standard deviation of 2.3E07 Pa. Thus the 42

species showed remarkably similar maximum

bending stresses. Overall, even though many

geometric characteristics among the species

differed markedly, all 42 species of grasses had

similar maximum bending stresses.

Data in Fig. 4 show grasses with higher

bending moments had more total sclerenchy-

ma cell area than species with lower bending

moments. The equation of the relationship

was y 5 0.028x + 0.0001 with a coefficient of

determination of 0.65. These data strongly

support the idea that sclerenchyma cells in

stems were responsible for resisting the bend-

ing moment. An analysis was also performed

in which the five species with the largest values

of maximum bending moment and total

sclerenchyma cell area were removed. After

these five values were removed, the same

equation of the line with the same coefficient

of determination was obtained.

Groups of grasses were tested to determine if

differences in mechanical properties existed

(refer to Table 1 for the groups). No statisti-

cally significant differences between members

of the Festucoideae and the Panicoideae

families were found. Within the Festucoideae,

maximum bending stress levels were signifi-

cantly different among the Agrostideae, Festu-

ceae, and Hordeae tribes. However, since no

other significant differences in any other

property were found, we do not know the

general significance of these differences. No

statistically significant differences between the

Andropogoneae and Paniceae tribes within the

Panicoideae family were present. A t-test

performed between the 28 C4 species and the

14 C3 species showed no statistically significant

differences. The lack of any statistically signif-

icant and consistently different pattern between

any plant groupings supports the general thesis

of this study, that all 42 species of grass showed

remarkably similar stem bending properties.

Discussion. The anatomies of grass stems

have been described well (Hayward 1938, Esau

1964, Fahn 1967, Hsiung et al. 1980, Mohmod

et al. 1993, Li et al. 1994). Past research has

also centered on the structural aspects of

grasses. Some research has been focused on

buckling of stems of grasses since buckling

could decrease seed yield of plants (Phinney

1983, Ennos 1993, Spatz and Speck 1994,

FIG. 3. Relationship between maximum bending moment (N-m) as a function of section modulus (m3)of grass stems exposed to external stresses. Each data point is one grass species. This relationship is expressedas y 5 2E07x + 0.0006 (r2 5 0.48).


Speck 1994, Bodega et al. 1996). Vincent’s

(1982) analysis of ryegrass leaves shows that

90 to 95% of leaf stiffness is accounted for by

fibrous cells. However, our research did not

center on stem buckling.

The purpose of our research was to

understand the anatomy of grass stems in

relation to resistance to stem bending, not

stem buckling. We hypothesized that more

sclerenchyma cells would be near the outside of

stems where bending stresses are highest (Beer

and Johnston 1992). Data from this study

support that hypothesis. Data of Li et al.

(1994) showed that (1) tensile and flexural

strengths are highest near the outer surface and

(2) fiber volume fraction (bast, sclerenchyma

cells) was highest near the external surface for

three species of bamboo. Our data extend the

results of Li et al. (1994) with data of 42 grass

species even though these species have a wide

variety of internal characteristics, geometric

properties, and mechanical properties.

Li et al. (1994) showed that species of

bamboo with larger stems had proportionally

more sclerenchyma than species of bamboo

with smaller stems. Our data from 42 grass

species show that the proportion of stem area

attributed to sclerenchyma cells was not

correlated with stem diameter. Our results

suggest that no mechanical properties were

related to grass stem diameters.

Li et al. (1994) reported modulus of

elasticity values between 4 and 29 GPa for

Bambusa glaucescens. These values were very

similar to our effective modulus values of 0.1

to 31 GPa among the 42 grass species studied.

Moreover Li et al. (1994) reported densities

from 0.1 to 1.0 g cm23 (equivalent to 100 to

1000 kg m23) for B. glaucescens. The density

values of the 42 species tested ranged from 101

to 1000 kg m23, values identical to those

reported by Li et al. (1994).

Grass stems have a conspicuous diaphragm

at each node (Li et al. 1994). For our

experiments, no nodes were present in stem

segments between the support loops during

testing. This knowledge is important since Li

et al. (1994) showed that nodal areas had

different mechanical characteristics than inter-

nodal areas for bamboo. Moreover, Niklas

(1989) showed that diaphragms of Equisetum

hyemale increased stem stiffness between 16 to

20% while only adding 2% to stem mass.

Although Li et al. (1994) demonstrated that

(1) tensile strength was highest near the outer

surface, (2) tensile modulus was highest near

FIG. 4. Relationship between maximum bending moment (N-m) as a function of the area ofsclerenchyma cells (mm2) in grass stems exposed to external stresses. Each data point is one grass species.This relationship is expressed as y 5 0.028x + 0.0001 (r2 5 0.65).


the outer surface, (3) sclerenchyma fiber

volume was highest near the outer surface,

and (4) tensile strength was positively related

to fiber volume in stems of bamboo, very little

additional research has been performed to

understand the mechanical properties of grass

stems and relate these mechanical properties to

anatomical characteristics. In general, the

same characteristics developed by Li et al.

(1994) are extended here for 42 species of grass

species. We have extended the results of Li et

al. (1994) since we imposed external stresses on

stems. Our data showed 59% of the total

sclerenchyma cell area in stems occurred in the

outer one-fifth of stems. Stem densities,

modulus of elasticity and maximum bending

moments were normally distributed. Results of

stress tests show that maximum bending

moment was highly correlated with section

modulus so that maximum bending stress

values were between 1.0E07 and 8.0E07 Pa

among the grass species tested. These values

were relatively constant with a mean of 3.3E07

Pa. Moreover, data of this study also show that

maximum bending moments of the 42 species

were strongly related to (y 5 0.028x + 0.0001,

r25 0.64) the areas of sclerenchyma cells.

Taken together, these data show that all grass

species studied had nearly identical mechanical

properties and that sclerenchyma cells in stems

provide the major support for stem integrity at

the upper limit of imposed stem stresses. To

our knowledge, this study is the first to

compare the geometric, mechanical, and ana-

tomical characteristics of over forty species of

grasses to provide a unifying view of grass stem

resistance to mechanical stresses.

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Mechanical Properties and Anatomical Components of Stems of 42 Grass Species