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617
WOOD RESE ARCH
58 (4): 2013
617-626
EFFECT OF KNOTS ON THE BENDING STRENGTH AND
THE MODULUS OF ELASTICITY OF WOOD
S K, S F, J A, R T
U W H
I W S
S, H
(R M )
ABSTRACT
The utilization of wood materials is limited signif icantly by wood defects. This is especially
valid for knots - as the most important wood defect - which can decrease the density as much as
40-50 % or in some cases even more. This is the biggest problem of the wood architecture, where
the softwoods are the most commonly used materials. Hungary has shortage in good quality
materials due to its forestry structure (85 % hardwoods, 15 % softwoods). This is why substituting
the softwoods with hardwoods is a recurrent subject for wood industry experts. In Hungary the
most important raw materials for the mass production of wooden items (boxes, pallets, board
products) are the poplars. Due to its density and other physical properties they can be considered
as the replacement of softwoods.
The main obstacle of utilization of poplars is the knots. The aim of this study is to examine
the effect of knots on elasticity, strength and modulus of elasticity in case of hybrid poplars and
softwoods.
KEY WORDS: Knot diameter ratio, bending strength, modulus of elasticity, hybrid poplar, Scots
pine, SEM test of knot.
INTRODUCTION
The utilization of wood materials is limited signif icantly by wood defects like knots, wavy
and distorted grain, etc. In terms of structural (load bearing) wood, knots are considered to be
the most critical type of defect that are especially limiting the technical properties. It has the
most adverse effect. Usually increasing the diameter of rough timbers has a positive effect on the
quantity of good quality raw materials. But at the same time increasing the diameter of rough
timbers may cause the increase of the effect of knots in quality measurements, for example in
case of poplars (Danilovic 2011). Therefore, increasing knot area ratios and knot diameter ratios
result in a signif icant decrease of bending strength (MOR) and modulus of elasticity (MOE)
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WOOD R ESEARC H
values. Sometimes the reduction may be as much as 40 to 50 %. In softwoods, knots of 25 and
75 mm in diameter cause 18 and 50 % decrease in bending strength, respectively (Panshin and
deZeeuw 1964). The location or position of knots is an important factor in bending, sometimes
more important than their size (Falk et al. 2003). Therefore there is an interest in making a survey
of the position of knots nowadays as well (Que-ju et al. 2013). Similarly, expressing the effect of
knots in knot area ratio (KAR) or knot diameter ratio (KDR) is also effective (Lam et al. 2005).
If the projected knot area (PKA) is more than 50 %, the MOR value is about half as much as in
the case of a PKA values under 20 % (Zhou and Smith 1991). Divos (1997) examined the effect
of knot diameter ratio on Picea and Pinus species. In his study, the modified concentrated knot
diameter ratio (CKDRm) was found to correlate well with bending strength, with a correlation
coefficient of 0.608.
The anatomical structure of wood affects the strength properties of different species
groups to a varying degree. The structure of ring-porous woods typically affects the technical
characteristics more than that of more homogeneous softwoods (Oliver-Villanueva et al. 1996).
The structure of knots differs from that of normal wood. Because k not structure varies in different
species groups, the negative effect of knots is usually different in softwoods and diffuse porous
species (e.g. poplars). The observations of some industrial users seem to confirm this statement.
Poplars and softwoods are important in the Hungarian forest management and wood
industries. Based on some of their properties, both groups may be used in similar areas, e.g. as
structural materials. The purpose of our research was to reveal the differences in the effect of
knots on softwoods and poplars, and to trace the relationship between the knottiness and the
strength and elastic properties by studying the material characteristics of these two species.
The wood of various poplars and poplar hybrids is considered to be inferior compared to various
softwoods. This depends on many factors like loose grain and low density, etc. Some poplar
clones, however, exhibit reliably higher densities, in excess of 0.400 g.cm-3. Thus, they may be
considered for structural applications. The question is how knots affect the material properties as
compared to softwoods.
MATERIAL AND METHODS
Because poplars are very important in Hungary (their share in the forest area and the gross
harvest is 10.3 and 16 %, respectively), two clones were chosen for the investigations, namely
Populus x euramaricana cv. ’I-214 ’ and Populus x euramericana cv. ’Pannonia’. The density of the
‘I-214 ’ variety is usually less than or barely over the 0.400 g.cm-3 limit, but its significance in
Hungar y is such that it has to be used as control. From the soft wood group, Pinus sylvestris L.
was chosen for the study. The two poplar varieties and the Scots pine trees were harvested from
similar sites to reduce the effect of external factors. The dimensions of the bending specimens
were 1200x140x21 mm, which is the same as those of the top element of a pallet. The moisture
content of the specimens was very high, above the fibre saturation point. Because we couldn’t dry
them, specimen moisture content was equalised at 45 %. The sample number was 40 for each
species/varieties.
Significant correlation has been found between dynamic and static methods during modulus
of elasticity measurements of wooden material which can even signif icantly decrease due to
the knottiness (Hossein et al. 2011). The modulus of elasticity was determined using several
different methods including nondestructive and destructive techniques like dynamic longitudinal
vibrations, dynamic bending vibrations and static bending thanks to the development of
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the nondestructive methods in the past few years (Bodig and Jane 1982) and they are still
continuously improving.
During the measurement of the longitudinal dynamic modulus of elasticity (MOEdyn.long)
the the vibration was induced at the end of the specimen using an impact hammer. The signal was
detected by a microphone at the opposite side and analysed by a Fast Fourier Transform analyser.
Eq. 1 was used for modulus of elasticity determination:
(1)
where: ρ - density,
L - specimen length,
flong - longitudinal vibration frequency.
During the measurement of the dynamic bending vibration (MOEdyn.bend) the first free
bending vibration mode was used for the measurement where the length of the overhang is 0.224 l.
Vibration was induced between the supports. The signal was detected at the same location by
a microphone, and evaluated by an FFT analyser. The Timoshenko theory was used for the
determination of MOEdyn.bend because the specimens were prismatic in shape (Timoshenko and
Young 1954). Since the effect of shear deformation is negligible, correction was unnecessary and
the formula derived from the Euler Eq. 2 could be used:
(2)
where: f - bending vibration frequency (mode no. 1), γ=3.561 (mode no. 1),
m - mass,
l - specimen length,
I - inertia moment.
Two methods, three- and four-point bending were used for static bending modulus of
elasticity determination (EN 408: 2003). The modulus of elasticity value measured by three-point
bending (MOEstat. 3p) is affected by the shear deformation between the supports. The modulus
of elasticity determined by four-point bending (MOEstat.4p) is unaffected by shear deformation,
because there is no shear load between the two loading points.
Eqs. 3 and 4 were used for MOE determination in three and four-point bending, respectively:
(3)
(4)
where: ΔF - applied load,
L1 - span (3), and gauge length (4),
A - distance between the loading point and nearest support,
I - inertia moment,
Δw - deflection.
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WOOD R ESEARC H
The determination of MOEstat.3p and MOEstat.4p allows the calculation of shear modulus
as well (Eq. 5):
(5)
where: K=1.2 in beams of rectangular cross section,
H - specimen depth.
Bending strength was determined by using four-point bending measurement. Eq. 6 was used
for MOR calculation:
(6)
where: Fmax - ultimate load,
B - specimen width.
The effect of knots was examined according to the Japanese Agricultural Standard for
Structural Softwood Lumber (JAS 1991), using the knot diameter ratio (KDR). Several methods
may be used for calculating KDR, whereby the location of knots is taken into consideration. In
our investigations, the knot diameter ratio was calculated on the wide face of the specimen, on
the tensile side (KDRwide,tensile=d2/b), and in the tensile zone on the narrow face (side) of the
specimen (KDRedge,tensile=d1/h), see Fig. 1.
Fig. 1: The parameters used for knot diameter ratio determination.
In several cases, the knots were clustered in the specimen. The concentrated knot diameter
ratio (CKDR) is used for the evaluation of the effect of clusters. An earlier study (Divos and
Tanaka 1997) demonstrated the importance of the modified concentrated knot diameter ratio
(CKDRm) that allows for the stress distribution in wood under load (Eq. 7).
(7)
Various statistical methods were used for the analysis of measurement results. Descriptive
statistical parameters were calculated for the general characterisation of the measurement data
series. The significance of the differences between the values of various parameters was evaluated
using the analysis of variance (ANOVA). Regression analysis is most useful for detecting
correlation and investigating the effect of influencing factors.
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Vol. 58 (4): 2013
In case of knotty wood materials, practical experiences are implying that breakages are
located around the knot at the edge between the knot and xylem since xylem’s anatomical
structure differs from knot’s structure. For testing how the knot and the surrounding tissue are
bonded, scanning electron microscopic pictures were taken on the margin surface of knots with
different type and size.
RESULTS AND DISCUSSION
Examination of strength and elasticity properties
The investigation of the two poplar clones and Scots pine provided a conclusive result
concerning the effect of knots. Tab. 1 shows the results of the statistical evaluation of the measured
data. Significant correlation has been found between dynamic and static methods during modulus
of elasticity measurements of wooden material (Hossein et al. 2011). On average, nondestructive
MOE measurements yield higher values than the static method. The difference varies between
2-15 %. Dynamic MOE measurement results indicated significant differences between the
species/clones. The ‘Pannonia’ clone yielded the highest value (approx. 10 MPa), while Scots pine’s
values were the lowest (approx. 7.8 MPa). The results of static testing were less straightforward.
The MOE of the ‘I-214 ’ clone and Scots pine was similar, according to Duncan’s test. Since
there is a tight correlation between MOE and MOR, bending measurements provided similar
results, i.e. the strength of knotty Scots pine (31.2 MPa) is less than that of poplars (37-38 MPa).
There is no significant difference between the shear modulus of different species, although the
standard deviation of the data sets is very different. The variation of the ‘Pannonia’ clone is the
most favourable (smallest).
Tab. 1: Statistical evaluation of the measurement data.
Species Ex amined character istics Descriptive statistics AN OVA 2
Min Max. Avg.1Std . dev. α
Pinus
sylvestris
MOEdyn.lon g (GPa) 4.5 13.6 7.9 2.1 < 0.001
MOEdyn.bend (GPa) 4.5 11.8 7. 6 1.9 < 0.001
MOEstat.3p (GPa) 3.9 12.8 7.5* 2.1 0.137
MOEstat.4p (GPa) 4.7 13.4 7.8 * 2.4 < 0.001
MOR4p (MPa) 18.7 47. 5 31.2 6.8 < 0.001
G(MPa) 50.1 7746.5 834.0* 1389.4 0.260
’Pannonia’
MOEdyn.lon g (GPa) 5.7 15.4 10.1 1.4 < 0.001
MOEdyn.bend (GPa) 5.3 15.2 9.8 1.5 < 0.001
MOEstat.3p (GPa) 4.0 13.1 8.4* 1.4 0.137
MOEstat.4p (GPa) 4.0 21.9 10.1 3.7 < 0.001
MOR4p (MPa) 16.0 68.1 38.4* 10.8 < 0.001
G(MPa) 4 7.4 954.5 780.4* 15.7 0.260
’I-214 ’
MOEdyn.long (G Pa) 5.1 13.0 8.8 1.7 < 0.001
MOEdyn.bend (GPa) 5.0 16.0 8 .9 2.0 < 0.001
MOEstat.3p (GPa) 3.7 13.8 8.0* 1.8 0.137
MOEstat.4p (GPa) 5.6 15.4 8.6* 2.0 < 0.001
MOR4p (MPa) 16.5 69.8 37. 8* 9.1 < 0.001
G(MPa) 36.5 4929.1 584.6* 846.3 0.260
1 Resu lts of Dunc an’s test. Hom ogeneou s groups a re marke d by aster isks
2 One-way A NOVA compari sons of the sp ecies/var ieties ba sed on the given pa rameter. There i s a signi fica nt diffe rence bet ween the spec ies
if α< 0.05.
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WOOD R ESEARC H
Several factors influence bending strength. Johansson and Kliger (2002) found that the
largest inf luence on bending strength were modulus of elasticity, knot area ratio and grain angle.
Two of these factors, MOE and knots, were investigated experimentally. The best predictor of
lumber strenght is the MOE (Divos and Tanaka 1997). The effect of the modulus of elasticity
determined by various methods and that of other influencing factors is best described by the
correlation coefficient (Tab. 2).
Tab. 2: Correlation coefficients of the factors influencing bending strength.
Predictor Bending strength
Pinus sylvestris ‘Pannonia’ ‘ I-214 ’
MOEdyn.long 0.658 0.715 0.809
MOEdyn.bend 0 .672 0.736 0.806
MOEstat.3p 0.645 0.708 0.7 14
MOEstat.4p 0.672 0.732 0.753
KDRwide.tensi le -0.532 -0.188 -0.596
KDRedg e.tensile -0.716 -0.117 -0.432
CKDRm -0.142 -0.201 -0.402
There is evidently a close relationship between the modulus of elasticity and bending
strength. The nondestructively determined MOE values provided the best results. Fig. 2 shows
the relationship between the modulus of elasticity measured by dynamic bending vibrations
(MOEdyn.bend) and bending strength. The relationship is tighter for the two poplar varieties than
in the case of Scots pine.
Linear regression was used for the assessment of the effect of knots as well (Tab. 2). The
correlation coefficients show clearly that the modified concentrated knot diameter ratio did
not provide good results. On the other hand, the other two diameter ratios, KDRwide.tensile and
KDRedge.tensile correlated well with bending strength. The location or position of knots is an
important factor in bending (Falk et al. 2003). The strength reduction resulting from knots
running out to the face is signif icant (Fig. 3). The ‘Pannonia’ variety, where the correlation
coefficient indicates a poor relationship, is an exception. This holds true for the other two knot
diameter ratios as well. This indicates that the overall effect of knots on the ‘Pannonia’ clone is not
very substantial. The KDRedge.tensile parameter provided an especially interesting result. Knots
running to the edge in the tensile zone decrease the bending strength significantly.
The examination of the effect of knots was extended to the modulus of elasticity and rigidity
as well. Based on the correlation coefficients, neither knot diameter ratio has any notable effect
on either mechanical parameter of ‘Pannonia’ poplar (Fig. 4). The correlation coeff icient for
bending strength and for static modulus of elasticity is approx 0.1-0.2, i.e. the correlation is
negligible. Although the coeff icient is somewhat higher for the relationship of the dynamic MOE
and KDRwide.tensile, its value (0.3-0.35) is still rather low. On the other hand, the correlation
coefficients indicate a tighter relationship in the case of the ‘I-214 ’ variety, which shows that this
clone is more sensitive to the presence of knots (Fig. 5). For the various moduli of elasticity, the
correlation coefficient approaches 0.4, especially in the case of the two knot diameter ratios. The
effect of KDRedge.tensile on bending strength is signif icant; the correlation coefficient is close to
0.6. Knots running to the side of the specimen cause significant strength loss. The effect on the
modulus of rigidity is, again, negligible.
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Fig. 2: The relationship between the modulus of
elasticity and bending strength.
Fig. 3: The relationship bet ween KDRwide,ten sile
and bending strength.
Fig. 4: The effect of k nots on the various parameter s
of the ‘Pannonia’ poplar clone.
Fig. 5: The effect of knots o n the various parameters
of the ‘I-214’ poplar clone.
Based on the measurement results, the effect of knots on Scots pine is the highest of the
three species and varieties examined (Fig. 6). The correlation coeff icients between KDRwide,tensile
and MOE approach and, in one case, even surpass the value of 0.4. With respect to bending
strength, this value is over 0.5. The effect on shear modulus is very small again.
Fig. 6: The effect of knots on the various parameters of Scots pine.
The correlation between KDRedge.tensile and various material properties is much stronger
(R = 0.65-0.85) than in the case of KDRwide.tensile. This indicates that Scots pine’s properties are
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WOOD R ESEARC H
very dependent on the side knots. In general, Scots pine’s correlation coefficients are clearly much
higher compared to the poplar varieties, especially in the case of side knots.
Examination of anatomical structure
Examination of the technical characteristics shows that different anatomical structure of the
different species may have a strong influence on the strength reducing effect of knots.
The aim of the examination of the knots and the xylem around them by Scanning Electron
Microscope was to give an explanation for the ruptures at the borderlines of the knots - which
were detected during mechanical examination - by analysing the anatomical structure.
Considering the different types of knots it can be stated that in case of poplar wood materials
less partially encased or fallen out knots may appear. Resin-ring and rough spots on the surface of
the knots are frequent occurrences between the knots and the bark in softwoods (Fig. 7).
Fig. 7: Resin-ring at the borderline of the knot
and the xylem (Pinus sylvestris).
Fig. 8: The borderline between the knot and
xylem.
According to this, stronger bond can be assumed between knots and xylem in case of poplars.
The gradation zone appears in a different way in case of poplars and Scots pine. There is a
wide gradation area in the xylem around the knot in case of poplars (Fig. 8). On the other hand,
in case of Scots pine the gradation zone is narrow and sharp at the borderline of knot (Fig. 9).
The examination of how knots are connected to xylem could give an explanation why Scots
pine is more sensible of knottiness than poplar. In case of softwoods the narrow gradation zone
between the knot and xylem, the lack of proper connection among the xylem elements is the
reason of the frequent rupture around the knot. Additionally there is a huge difference between
the anatomical properties (density, strength).
Fig. 9: The gradation zone between the knot and the xylem.
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Vol. 58 (4): 2013
Due to the smooth gradation zone between the xylem and the knot in poplars, the two
different anatomical sections join to each other along a relatively wider path. Accordingly, the
negative strength reducing effect of knots is thought to be significantly decreased compared to
pines.
ACKNOWLEDGMENT
This research – as part of the development of Student Talent Fostering at WHU, TAMOP
4.2.2 B-10/1-2010-0018 project – was sponsored by the EU/European Social Foundation. The
financial support is gratefully acknowledged.
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S K, S F, J A, R T
U W H
I W S
H- S
B Z. S. .
H
Corresponding author: komansz@fmk.nym
