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In this study, physical and mechanical properties of wheat and barley stems are examined. Transverse sections of the stems are magnified by a microscope and the material structure in the transverse sections are analysed with image processing programs. Geometric properties such as inner, outer radius, stem wall thickness and density variation of the material along the radius are measured and density variations are approximated by a mathematical model. Moment of inertia of the cross-sectional area which plays a vital role in resistance against bending and buckling is calculated approximately. Using the material density variations of the wheat (Triticum sativum L.) stems, new beam/columns are designed. Stress distributions in this new design and conventional designs of equivalent weight are compared using ANSYS program. It is found that stresses are more uniformly distributed in the new design with maximum stresses being lower than the conventional designs.
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Mathematical and Computational Applications, Vol. 15, No. 1, pp. 1-13, 2010.
© Association for Scientific Research
STRENGTH OF WHEAT AND BARLEY STEMS AND DESIGN OF NEW
BEAM/COLUMNS
Gözde Değer
1
, Mehmet Pakdemirli
1*
, Feyza Candan
2
, Selda Akgün
1
and Hakan Boyacı
1
1
Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye,
Manisa, Turkey. mpak@bayar.edu.tr
2
Department of Biology, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
Abstract- In this study, physical and mechanical properties of wheat and barley stems
are examined. Transverse sections of the stems are magnified by a microscope and the
material structure in the transverse sections are analysed with image processing
programs. Geometric properties such as inner, outer radius, stem wall thickness and
density variation of the material along the radius are measured and density variations
are approximated by a mathematical model. Moment of inertia of the cross-sectional
area which plays a vital role in resistance against bending and buckling is calculated
approximately. Using the material density variations of the wheat (Triticum sativum L.)
stems, new beam/columns are designed. Stress distributions in this new design and
conventional designs of equivalent weight are compared using ANSYS program. It is
found that stresses are more uniformly distributed in the new design with maximum
stresses being lower than the conventional designs.
Keywords- Wheat (Triticum sativum L.) Stems, Barley (Hordeum vulgare L.) Stems,
Design of Beam/Columns, Strength
1. INTRODUCTION
Engineers play a vital role in transferring scientific knowledge to technology. In
recent years, with inspirations from natural designs, engineers contributed a lot to the
development of technology by mimicking those designs. Biomimetics is a newly
developed branch of science dealing with such applications. One of the interesting
designs in nature is the stems of wheat and barley. Despite their extra high slenderness,
they possess excellent strength features which enable the plant to bear buckling and
bending forces. The stem length can be 500 times the base diameter of the plant and
despite this high slenderness, extraordinary strength can be achieved.
The aim of this work is to investigate in detail the strength properties of these
stems so that new beam/columns with maximum strength and minimum material can be
designed. Some of the previous literature relevant to our analysis will be briefly
mentioned. Gowin [1] investigated elastic modulus, shear and bending strength of stems
by investigating transverse area and its area moment of inertia. Gibson et al. [2]
examined high performance of micro structures and concluded that bending resistence
of a beam with anisotropic cell structure is better than a solid beam of equivalent
weight. Crook and Ennos, [3] studied wind effects on roots and mechanical properties
of stems of wheat for supported and unsupported plants. They found that unsupported
plants reveal better strength properties.
Niklas [4] investigated the mechanical behaviour of stems subject to twisting
and bending and compared the results with the predictions of elastic stability theory.
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
2
Hornsby et al. [5] examined the micro structure, thermal and mechanical properties of
flax and wheat straw fibers and found that cotton fibers have better strength properties
than the wheat fibers. They suggest using these fibers for additional strength in
thermoplastics.
Cleugh et al. [6] studied wind effects on the growth rates and morphology of the
crops. Kronbergs [7] determined ultimate tensile, shear strength, modulus of elasticity
and shear modulus of wheat stalks experimentally in order to find methods for
mechanical conversion with minimum energy conversion. Hirai et al. [8] measured
horizontal and vertical reaction forces of rice and wheat stalks under five different
loading speeds. They discussed the discrepancies between the analytical and
experimental results. Gibson [9] reviewed the mechanics of a wide range of natural
cellular materials and designed engineered biomaterials with a cellular structure to
replace tissue in the body. Dawson and Gibson [10] investigated cylindrical shells with
compliant cores and presented a more comprehensive analysis by extending the linear-
elastic buckling theory by coupling it with plasticity theory. They performed an optimal
design analysis for cylindrical shells with compliant cores.
Apart from some of the above mentioned studies, where the main concern is
biology or agricultural applications, main aim in this study is to investigate the
mechanical properties and geometry of the transverse area of stems so that the
principles can be applied in designing light beam/columns which can withstand higher
loads. The transverse areas of wheat and barley stems are processed using an image
processing software and material density distributions along the radial direction are
plotted. The plots are approximated by a quadratic function. The elasticity modulus of
the stems is also determined experimentally. The inner and outer radii, area moment of
inertia for the cross section and their variations along the length of the stem are also
plotted. Using the approximate density variation function, a new beam/column is
designed with cellular structure. The new design is contrasted with the conventional
solid and hollow beam designs using ANSYS program. Stress and buckling analysis is
performed using the program. Under same loading conditions with bending and axial
loads, the stress distributions are more uniform in the new design and the maximum
stresses are lower than the others.
2. MATERIALS AND METHODS
In the experimental analysis, wheat (Triticum sativum L.) and barley (Hordeum
vulgare L.) are used.
2.1. Determination of physical properties
30 specimens of newly harvested and undeformed wheat and barley are selected.
Both parts of the stem and spikes of the same specimen are given the same number to
identify collectively the properties of a single specimen. Spikes are weighted with a
precision weight. Internodes are marked to determine the variation of average inner and
outer radii along the length of the stem.
Maximum and minimum diameters are measured by a digital compass. Heights of the
internodal marked points from the ground are also measured.
Strength of Wheat and Barley Stems and Design of New Beam/Columns
3
2.2. Tensile test
To determine the elasticity modulus of stems, from each nodal region of 4 wheat
and 4 barley plant, rectangular cross sectional thin parts are cut. Each internodal region
is marked with letters starting from A, A being the nearest region to ground. For tensile
tests, Shimadzu Autograph tensile test machine with 1 kN load cell is used. Modulus of
elasticity corresponding to each internodal region is measured from the data of the tests.
2.3. Taking stem transverse sections to preparates
To investigate the material structure of transverse sections in a microscope,
specimens are subjected to a number of processes. A fixation liquid composed of 70%
alcohol is used to determine the material amount. After extracting from the fixative, the
specimen is partially dehydrated by immersing in 80%, 90%, 100% alcohol and 2:1
alcohol xylol, 1:1 alcohol xylol, 1:2 alcohol xylol and xylol for a suitable time interval.
After dehydration process, to fill possible gaps formed in the specimens, the gaps are
filled with paraffin. After this process, specimens are placed in paraffin blocks. In a
microtom, transverse sections of 35-50 microns in thickness are taken. To withdraw the
paraffin from the material, the stages containing the transverse sections are heated over
a hot plate. Then they are held in xylol, 2:1 xylol alcohol, 1:1 xylol alcohol, 1:2 xylol
alcohol, pure alcohol, 90% alcohol, 80% alcohol, 70% alcohol and pure water in the
mentioned order for 5 minutes each. The transverse sections are painted by SARTUR
reactive. After this, the transverse sections are held in pure water, 70% alcohol, 80%
alcohol, 90% alcohol, pure alcohol, 2:1 alcohol xylol, 1:1 alcohol xylol, 2:1 xylol
alcohol and xylol for 1-3 seconds. Therefore, the dehydration process is completed.
Preparates are transformed to fixed preparates so that they can be re-used again.
2.4. Microscopic investigation and photographing
Optical microscope is used in investigating the specimens. A camera is
connected to the microscope to transform the images to a computer. Fotographs are
taken in the form of 6-7 pieces from the best appearing transverse sections.
2.5. Inner and outer radius measurements
The transverse sections are elliptic being almost circular. In the measurements,
from a given transverse section, several measurements are taken by Motic Images Plus
2.0 software and average inner and outer radius and wall thickness are calculated. By
combining the data from each labeled transverse sections, variations of these parameters
along the height are determined.
2.6. Determination of material density variations
Investigating the images of the transverse sections, it is found that the light gray
parts correspond to the cell and the dark black parts correspond to cell walls. Inner parts
of cell are assumed to be empty and the dark parts are materials. The material density
variation along the radial direction is determined by Motic Images Plus 2.0 software.
In the density variation measurements, only transverse sections of wheat are
used because the wall thicknesses of wheat are larger than the barley cross sections and
variations can be determined with better precision. Rectangular areas are selected over
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
4
pieces of the transverse sections and each material density within the region is recorded.
A dimensionless wall thickness parameter is defined
i
i
rr
rr
t
=
0
(1)
where r is the radial distance from the center, r
i
and r
0
are the inner and outer radius
respectively. The material density variations are recorded with respect to this
dimensionless thickness parameter for universality of results. From the average
measured density points (mid points of each rectangular areas) an approximate curve is
drawn. An optimum parabolic function is used to approximate the density variations.
2.7. Area moment of inertia
Area moment of inertia is effective in resisting to buckling and bending forces.
For the calculation of area moment of inertia, the integral
=
d
i
r
r
rdrrrI
πρ
2)(
2
(2)
is evaluated. The transverse section area is assumed to be circular with average inner
and outer radius. ρ(r) is the density variation along the radial direction. The approximate
parabolic function is employed in the calculations. Variation of area moment of inertia
with height from the ground is given in the figures.
3. RESULTS AND DISCUSSION
In this section, first the measurement results of the plants will be given. Then,
based on the density variations of the cross section, a new beam/column design will be
proposed and tested using ANSYS program. Comparisons of the new design with
conventional designs will be made.
3.1. Measurements
To determine the static loads of wheat and barleys, spike weights are measured.
The average weight of spikes for wheat is 1.45 g and for barley it is 3.57 g.
Average outer diameter of wheat and barley corresponding to different heights
from the gound are given in Figure 1. The average outer diameter increases some
amount with the height and then decreases. Under the effect of aerodynamical forces to
the spike, the bending moment will be maximum in the region close to the root. It
should be expected that the outer diameter be maximum close to the root. As seen from
the figure, it is not the case. One explanation is that, in the measurements, the leaves of
the plants are removed and the leaves are wrapped more to the stem close to the root
and provide additional strength.
Strength of Wheat and Barley Stems and Design of New Beam/Columns
5
Figure 1. Average outer diameters vs. average heights for (a) Wheat (Triticum sativum
L.) stems (b) Barley (Hordeum vulgare L.) stems
The tensile tests are conducted to determine the elasticity modulus of the
specimens. An average value of 6799 MPa is found for wheat stems and 11064 MPa for
barley stems. Barley spikes are heavier and therefore the modulus of elasticity to bear
higher loads should be greater. Kronbergs [7] reported a higher value of 13100 MPa for
wheat stems. Several reasons may cause the discrepancy between the data. First of all,
the species are not exactly the same and regional raising conditions have direct effect on
the mechanical strength.
In Figure 2, part of a typical transverse section of wheat is shown. Sclerenchyma
is the outer tissue which is harder than the inner tissue. Parenchyma is the cellular tissue
with larger cells between the inner and outer radius. Since it is of cellular nature, its
contribution to strength is less compared to Sclerenchyma. The vascular bundles located
nearer to the outer radius contribute much to the strength because they are denser.
The distribution and geometry of the cells are interesting. Cells have hexagonal
structure. This structure is found extensively in nature. It is mathematically proven that
minimum line length is achieved if a plane is divided into equal hexagonal areas.
Minimal line length of course means minimum material. See [2,10] for detailed
discussion of hexagonal structures in nature. As a general rule, the cells in the inner
parts are larger whereas those in the outer parts are smaller and denser. These plants are
subject to high bending moments and to reduce the stresses, the area moment of inertia
should be higher. To make the area inertia higher, the cells are located denser near to the
outer parts.
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
6
Figure 2. Transverse section of wheat (Triticum sativum L)
In all wheat and barley specimens, inner radius, outer radius and their difference
are calculated. Barley diameters are generally higher than the wheat diameters. Reasons
for this may be that barley spikes are heavier and barley stems are longer than those of
wheat.
In Figure 3, average outer and inner radius values corresponding to height are
plotted. Initially, both inner and outer radius values increase a small amount with height
and then a sharper decrease is observed. In Figure 4, the average difference between the
radii which is the stem wall thickness is presented. The stem wall thickness attains
higher values close to the root.
Figure 3. Outer and inner radii vs. height (a) Wheat (Triticum sativum L.) Stems (b)
Barley (Hordeum vulgare L.) Stems (Solid outer radius, dashed inner radius)
Strength of Wheat and Barley Stems and Design of New Beam/Columns
7
(a) (b)
Figure 4. Stem wall thickness vs. height (a) Wheat (Triticum sativum L.) (b) Barley
(Hordeum vulgare L.)
The material density along the radial direction is presented in Figure 5 for wheat.
As pointed earlier, a dimensionless stem wall thickness coordinate defined in equation
(1) is used for convenience. An optimum parabolic curve is also drawn as an
approximation. Transverse section of internodal point A which is the closest point to the
root is used.
(a) (b)
Figure 5. Density variation vs. dimensionless thickness for wheat (Triticum sativum L.).
Transverse section of internodal point A is used (a) piece #1 (b) piece #2 (Dashed
measurements, solid parabolic approximation)
Many different specimens are investigated and common features in density variations
are observed. Near to the inner radius, there is a small decline observed in density. After
a minimal value, density increases sharply attaining 100% value at the outer radius. The
small increase in density in the inner wall may aid in strengthening the stem against
local inner wall buckling.
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
8
Using the approximate parabolic distribution, area moment of inertia along the
height is also calculated. As height increases, moment of inertia has a peak first and
then decreases sharply.
Figure 6. Area moment of inertia vs. height for wheat (Triticum sativum L.)
Bending moments are higher near to the root. To resist bending and buckling
forces in this region, the area moment of inertia is designed to be higher. Note that since
the leaves wrapped around the stem are removed in the measurements, their additional
contribution to strength can not be depicted.
3.2. Design of new beam/columns
Using the data of the previous section (i.e. inner, outer radius, density variations)
new beam/column design is proposed. The new design mimics the inner and outer
radius ratios and density variations of wheat (Transverse section A). It has a cellular
structure but simplifications in geometry are made so that production can be easier.
SolidWorks software is used in the drawings. To compare the efficiency of this design,
a solid beam/column and a hollow beam/column with equal outer diameter are also
drawn. All beams have the same cross-sectional areas. Geometrical dimensions of the
beams are given in Table 1.
In Figure 7, the new beam design is generated based on the geometric properties
of piece 1 whereas in Figure 8, geometric propereties of piece 2 is employed.
Table 1. Dimensions of design, solid and hollow beams
Piece # of
Transverse
Section A
Solid
Beam
Radius
(mm)
Hollow
Beam
Inner
Radius
(mm)
Hollow
Beam
Outer
Radius
(mm)
Desing
Beam
Inner
Radius
(mm)
Desing
Beam
Outer
Radius
(mm)
Length of
Beam
(mm)
1 144.52 178.93 230 100 230 1000
2 145.63 178.02 230 100 230 1000
Strength of Wheat and Barley Stems and Design of New Beam/Columns
9
Figure 7- Solid, hollow and design beam cross-sections and image of piece 1 used as a
reference in the design.
Figure 8- Solid, hollow and design beam cross-sections and image of piece 2 used as a
reference in the design.
3.3. Buckling and stress analysis using ANSYS
In this section, buckling and stress analysis of solid, hollow and design
beam/columns are done using ANSYS. All beams are assigned the same material. One
ends of the beams are fixed and the other ends free. Three different loading conditions
are tested: i) Axial compressive force of 1000 N applied to the free end. ii) Shear force
of 1000 N applied to the free end. iii) A combination of both forces. Critical buckling
forces, maximum and minimum stress values are determined for all loading conditions.
Results for reference piece 1 and piece 2 are given in Tables 2 and 3 respectively.
From Table 2, in all loading conditions, maximum and minimum stresses attain
the lowest values in the design beam. This means that stresses are more uniformly
distributed in the design beam than the others. Stress concentrations which initiate
failure in beams will be lower in the new design. In the case of critical buckling forces,
results vary with respect to loading conditions. In the axial and combined loading cases,
the design beam has intermediate values whereas in the shear loading, buckling force is
the least in the design beam. Note that local wall bucklings are more important in such
slender elements compared to global bucklings. Since the local bucklings are associated
with stress concentrations, it is expected that the design beam will perform best in wall
bucklings.
Similar results can be deducted from Table 3, which is calculated based on the
design beam of piece 2.
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
10
Table 2. Maximum, minimum stresses and critical buckling forces of solid, hollow and
design beams (Piece 1)
Loading
Condition
Results Solid
Hollow Design
Equivalent Maximum
Stress (Pa) 20091 18299 17226
Equivalent Minimum
Stress (Pa) 7645.6 7207.8 5036
Axial
compressive
force of 1000
N Critical Buckling
Force (N) 1.6715e+8 5.4242e+8 5.0856e+8
Equivalent Maximum
Stress (Pa) 4.1879e+5 1.9951e5 1.8359e+5
Equivalent Minimum
Stress (Pa) 4064 5023.6 1252.5
Shear force
of 1000 N
Critical Buckling
Force (N) 2.3268e+8 2.8942e+8 2.0063e+8
Equivalent Maximum
Stress (Pa) 4.1952e+5 2.1722e+5 1.9767e+5
Equivalent Minimum
Stress (Pa) 6973.2 4549.5 2064.4
Combined
loading of
axial and
shear forces
of 1000 N
each
Critical Buckling
Force (N) 1.2427e+8 2.547e+8 1.941e+8
Table 3. Maximum, minimum stresses and critical buckling forces of solid, hollow and
design beams (Piece 2)
Loading
Condition
Results Solid
Hollow Design
Equivalent Maximum
Stress (Pa) 19810 18027 17539
Equivalent Minimum
Stress (Pa) 7523.3 7107.8 4937.3
Axial
compressive
force of 1000
N Critical Buckling
Force (N) 1.7232e+8 5.5069e+8 5.1466e+8
Equivalent Maximum
Stress (Pa) 4.0955e+5 1.9676e+5 1.8098e+5
Equivalent Minimum
Stress (Pa) 3799.2 4994.4 2119.9
Shear force
of 1000 N
Critical Buckling
Force (N) 2.3982e+8 2.9941e+8 2.0156e+8
Equivalent Maximum
Stress (Pa) 4.1011e+5 2.142e+5 1.9563e+5
Equivalent Minimum
Stress (Pa) 6640.1 4327.7 1583.5
Combined
loading of
axial and
shear forces
of 1000 N
each
Critical Buckling
Force (N) 1.3995e+8 2.9138e+8 1.8744e+8
Strength of Wheat and Barley Stems and Design of New Beam/Columns
11
ANSYS results of stress distributions are given for axial loading (Figure 9),
shear loading (Figure 10) and combined loading (Figure 11). As can be seen from the
figures, the distributions are more uniform and the maximum stresses are lowest in the
design beam.
Figure 9- Comparison of stress distributions of solid, hollow and design beams for axial
load of 1000 N with geometric properties taken from piece 1.
Figure 10- Comparison of stress distributions of solid, hollow and design beams for
shear force of 1000 N with geometric properties taken from piece 1.
G. Değer, M. Pakdemirli, F. Candan, S. Akgün and H. Boyacı
12
Figure 11- Comparison of stress distributions of solid, hollow and design beams for
combined axial and shear load of 1000 N with geometric properties taken from piece 1.
Acknowledgment- This work is supported by The Scientific and Technological
Research Council of Turkey (TUBITAK) under project number 107T581.
4. REFERENCES
1. J. Gowin, Methods for determining geometry of cereal stalk cross-section, 6th
International Conference on Agrophysics, Lubnin, Poland, 1977.
2. L. J. Gibson, M. F. Ashby, G. N. Karam, U. Wegst and H. R. Shercliff, The
mechanical properties of natural materials. II. Microstructures for mechanical
efficiency, Proc. R. Soc. Lond. A 450,141-162, 1995.
3. M. J. Crook and A. R. Ennos, Mechanical differences between free-standing and
supported wheat plants, Triticum aestivum L., Annals of Botany 77, 197-202, 1996.
4. K. J. Niklas, Relative resistance of hollow, septate internodes to twisting and
bending, Annals of Botany 80, 275-287, 1997.
5. P. R. Hornsby, E. Hinrichsen and K. Tarverdi, Preparation and properties of
polyropylene composites reinforces with wheat and flax straw fibres: Part I Fibre
characterization, Journal of Materials Science 32, 443-449, 1997.
6. H. A. Cleugh, J. M. Miller and M. Bohm, Direct mechanical effects of wind on crops,
Agroforestry Systems 41, 85-112, 1998.
7. E. Kronbergs, Mechanical strength testing of stalk materials and compacting energy
evaluation, Industrial Crops and Products 11, 211-216, 2000.
Strength of Wheat and Barley Stems and Design of New Beam/Columns
13
8. Y. Hirai, E. Inoue and K. Mori, Application of a quasi-static stalk bending analysis to
dynamic response of rice and wheat stalks gathered by a combine harvester reel,
Biosystems Engineering 88 (3), 281–294, 2004.
9. L. J. Gibson, Biomechanics of cellular solids, Journal of Biomechanics, 38, 377-399,
2005.
10. M. A. Dawson and L. J. Gibson, Optimization of cylindrical shells with compliant
cores, International Journal of Solids and Structures 44, 1145-1160, 2007.
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... The xylem is responsible for the conduction of raw sap from the roots to the vegetative parts. This structure also plays the role of a supporting element (Deger et al., 2010). On the other hand, the phloem ensures the conduction of elaborated sap (Déjardin et al., 2010). ...
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... Le xylème permet la circulation de la sève brute des racines jusqu'aux parties végétatives. Cette structure joue aussi un rôle de soutien [18]. Le phloème, quant à lui, assure la circulation de la sève élaborée [19]. ...
... The results [14] wm.ŵ 0.25 ,ŵ 0.5 , ANDŵ 0. 75 ARE THE FIRST QUARTILE, MEDIAN, AND THIRD QUARTILE OF THE ESTIMATES WITHIN A GIVEN FIELD, RESPECTIVELY. SEE TABLE I FOR A DESCRIPTION OF THE FIELDS AND THE CROP TYPES [36], [37], [38]: ...
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Flax (Linum usitatissimum L.) is a plant with multiple interests. Its stem provides fibers, which have long been used in the textile industry. The economic potential of flax explains its varietal selection, aiming at developing varieties exhibiting higher fiber yields as well as greater resistance toward diseases and lodging. More recently, flax fibers have been dedicated to the reinforcement of composite materials due to their outstanding mechanical and morphological properties. These singular characteristics are related to fiber development and functions within the stem. Thus, the present work offers a multi-scale characterization of flax, from the stem to the fiber cell wall, in order to understand the link between plant growth parameters, the development of its fibers and their properties. The general architecture of a flax stem is investigated, as well as the impact of the varietal selection on this structure and on fiber performances. Moreover, changes in mechanical properties of fiber cell walls over plant growth and retting process are characterized. In addition, the fiber contribution to the stem stiffness is highlighted, as well as the fiber role in the resistance of the stem to buckling. The influence of culture conditions on stem architecture and fiber features is also studied through cultivations in greenhouse and by simulating a lodging event. This original approach emphasizes the uncommon characteristics of flax, which make this plant an instructive model toward future bioinspired composite materials.
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The microstructure, thermal and mechanical properties of flax and wheat straw fibres have been examined with a view to using these natural fibres as reinforcing additives for thermoplastics. In this regard, the fibres were characterized prior to incorporation into the polymer, using a range of techniques, including SEM, image analysis, thermogravimetric analysis and micro-mechanical tensile testing, at room and elevated temperatures. The thermal and mechanical properties obtained have been discussed in relation to the measured composition and structural form of the fibres.
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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, wherelis internodal length,tis wall thickness, andRis 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 descriptorl2/2tR. 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 descriptorl2/2tRthan with any measure of absolute internodal size (e.g.lort). Thus, internodal shape (in part defined by the spacing of nodal septa which influencesl) largely dictates the mechanical behaviour of stems subjected to twisting or bending.
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The effect of wind sway on the mechanical characteristics of the anchorage roots and the stem was investigated in mature winter wheat ( Triticum aestivum L., cv. Hereward). Wheat plants were field-grown, either supported by a frame, which prevented wind sway, or unsupported (free-standing) and the morphology and mechanical properties of the stems and the anchorage, ‘coronal ’, roots were measured. Wind sway had little influence on either the stem height or ear weight of the plants but did affect the mechanical properties of the stem. Stems of supported plants were weaker and more flexible than the stems of free-standing plants. There were also differences in the anchorage systems between the treatments: supported plants had just under half as many ‘coronal ’ anchorage roots as the free-standing plants. This reduced the anchorage strength of supported plants by a third. These differences in mechanical structure meant that the free-standing plants were more resistant to stem buckling and more resistant to anchorage failure. However, considering the difference in the need for mechanical strength in plants from the two regimes, these differences were small. This suggests that wheat has inherent mechanical integrity and, as a monocotyledon with no secondary thickening, it differs little structurally between environments.
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Thin-walled, cylindrical structures are found extensively in both engineering components and in nature. The weight to load bearing ratio is a critical element of design of such structures in a variety of engineering applications, including space shuttle fuel tanks, aircraft fuselages, and offshore oil platforms. In nature, thin-walled cylindrical structures are often supported by a honeycomb- or foam-like cellular core, as for example, in plant stems, porcupine quills, or hedgehog spines. Previous studies have suggested that a compliant core increases the buckling resistance of a cylindrical shell over that of a hollow cylinder of the same weight. In this paper, we extend the linear-elastic buckling theory by coupling it with basic plasticity theory to provide a more comprehensive analysis of isotropic, cylindrical shells with compliant cores. We examine the optimal design of a thin-walled cylinder with a compliant core, of given radius and specified materials, for a prescribed load bearing capacity in axial compression. The analysis gives the values of the shell thickness, the core thickness, and the core density that maximize the load bearing capacity of the shell with a compliant core over an equivalent weight hollow shell. The analysis also identifies the optimum ratio of the core modulus to the shell modulus and is supported by a Lagrangian optimization technique. The analysis further discusses the selection of materials in the design of a cylinder with a compliant core, identifying the most suitable material combinations. The performance of a cylinder with a compliant core is compared with competing designs (optimized hat-stiffened shell and optimized sandwich-wall shell). Finally, the challenges associated with achieving the optimal design in practice are discussed, and the potential for practical implementation is explored.
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Many natural materials have exceptionally high values of the mechanical performance indices described in the previous, companion paper. For beams and plates of a given stiffness or strength, or for a column of a given buckling resistance, woods, palms and bamboo are among the most efficient materials available. Their mechanical efficiency arises from their combination of composite and cellular microstructures. In this paper we analyse the microstructures which give rise to exceptional performance, describe the fabrication and testing of model materials with those microstructures and discuss the implications for design of mechanically efficient engineering materials.
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The great potential of cereal lignocelluloses for use as energy or as an industrial raw material source determines the necessity to investigate the mechanical properties of stalks, as the main parts of any herbaceous material. Annual world production of cereal straw is approximately of the same amount (around 2 billion tons) as wood material production. Latvia as a country with more than 2000 lakes has wide areas, covered with reeds, which are also an important stalk material resource. Stalk cross section and structural studies show that it is a complicated structure. Special test piece preparation and clamping methods, measuring devices, testing procedure for stalk material strength testing have been worked out. Ultimate tensile (118.7±8.63 N/mm2) and shear (8.47±0.56 N/mm2) strength, modulus of elasticity (13.1±1.34 GPa) and shear modulus (0.643±0.043 GPa) had been experimentally determined for wheat stalks in order to find methods for mechanical conversion with minimum energy consumption. Stalk biomass compacting methods and energy requirement for that are analysed on the basis of the results from the experiments. It has been stated, that energy for wheat straw pressing (≈40 kJ/kg up to pressure 160 MPa) is one order of magnitude less than that for heating of the same mass up to 200°C in the briquetting process (≈360 kJ/kg), if solid material has to be obtained. Depending on the target goals for usage, different energy saving compacting technologies can be developed. Thus the analysis of mechanical and physical properties of the stalk materials determines the profit of biomass usage.
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This review describes those mechanisms by which wind directly affects crop growth rates and hence yields. Wind-induced plant movement is capable of altering growth rates and leaf morphology, although this is unlikely to be a major cause of growth differences between sheltered and unsheltered crops grown outdoors. The wind's force can tear leaves or strip them from the plant. Dense plant canopies may suffer abrasion through intermittent or constant rubbing. Soil particles lifted into suspension by the wind have the potential to abrade and damage plant tissue. The wind's force can physically knock plants over, making crops difficult to harvest. Each of these mechanisms operates at a particular time of the growing season. Recovery, and hence final yield, depends on the growth stage and soil/plant moisture status when the damage occurred, the particular species and variety as well as the preceding and subsequent weather. The fact that damage effects are so dependent on the crop and the past weather makes modelling and any simple synthesis of direct wind effects difficult. The most common forms of damage likely in Australia's agricultural regions are from sandblasting and lodging. These damage events will be intermittent – their frequency depending on the local climate. Leaf tearing is likely in broad-leafed horticultural crops, and growth effects are also likely in any windy location. It is not possible to predict what the impact of this damage, and other direct effects, will be on final yields, Based on the results in the literature, protection from damage offered by windbreaks may have as large an effect on yields as incremental microclimate benefits.
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Horizontal and vertical reaction forces of rice and wheat stalks gathered by a combine harvester reel were measured by the experiment system, newly developed in order to clarify dynamic response of the crop stalks related to the gathering performance and to discuss the application of a quasi-static stalk bending analysis to the determination of the reaction force of crop stalks under dynamic loading conditions. The experiment was conducted under five different loading speeds, and the effect of the loading speed on the reaction force was investigated. As the loading speed increased, the horizontal force had a large positive peak value, while the vertical force involved the change in the force direction and had a negative peak value, depending on the initial deflection shape of crop stalks. Thus, the results simulated by the stalk bending analysis involved a large amount of error, and limitations of the analytical method were identified. The experimental results were examined in terms of acceleration at the loading point during the gathering operation. The location of a positive peak in the horizontal reaction force and a negative peak in the vertical one coincided with that of the negative peak in the horizontal acceleration and the positive peak in the vertical one, respectively. These results indicated that the peak values under high loading speeds were due to the effect of the inertial force of the crop stalks. Further, the error in the simulated results under high loading speeds was investigated in terms of the direction of the acceleration force determined by the difference between the simulated and measured values. The direction of the acceleration force coincided with the loading direction during the gathering operation, and the error was shown to be the force required for the accelerated motion.
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Accuracy of determining mechanical properties of the stalk depends, to a large extent, on the accuracy of determining characteristics of the sample cross-sectional geometry. Accurate calculations are very difficult due to geometrically complex shape of this cross-section. Generally, the cross-section is assumed to be shaped like a filled hollow or hollow ellipse and the stalk material to be homogeneous and mechanically isotropic. The paper presents two new, more accurate methods for determining cross-sectional area and the moment of inertia of the stalk cross-section. The first method is an application of a measuring microscope, the second one an application of a PC image analysis programme.
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Materials with a cellular structure are widespread in nature and include wood, cork, plant parenchyma and trabecular bone. Natural cellular materials are often mechanically efficient: the honeycomb-like microstructure of wood, for instance, gives it an exceptionally high performance index for resisting bending and buckling. Here we review the mechanics of a wide range of natural cellular materials and examine their role in lightweight natural sandwich structures (e.g. iris leaves) and natural tubular structures (e.g. plant stems or animal quills). We also describe two examples of engineered biomaterials with a cellular structure, designed to replace or regenerate tissue in the body.