Bending strength and stress wave grading of
(tropical) hardwoods
Dr.ir. J-W.G. van de Kuilen
Faculty of Civil Engineering and Geosciences
Delft University of Technology
ir. G.J.P. Ravenshorst
TNO Building and Construction Research
Workshop
Probabilistic Modeling in Reliability Analysis of
Timber Structures
COST E24 Reliability analysis of timber structures
Joint Committee on Structural Safety
10-11 Oktober 2002 - ETH Zurich
Switzerland
1. Introduction1
Tropical hardwoods are often used in structures that are exposed to direct weathering or soil
conditions where softwood cannot be applied without the use of chemical treatments. A
hardwood species often used in countries like the Netherlands, Belgium, Germany and the
United Kingdom is azobé, also known as ekki (lophira alata). Azobe is used in structures
such as bridges, road decks and sheet pile walls. The material properties of azobé are
reasonably well documented, Blass and Van De Kuilen, [1991], Van der Linden et al. [1994].
However, with the current environmental pressure on harvesting procedures for azobé, new
species, especially from Brazil, have entered the market. These species are often harvested in
accordance with the FSC (Forest Stewardship Council) regulations. Unfortunately, available
strength data for these species is often limited and if there is strength data available, this data
is often acquired from small specimens or the test procedure used is unknown. Also, grading
rules for these species are often not available.
A major setback for these new species is the European standard EN 384. This standard
requires large numbers of tests for the determination of bending strength, modulus of
elasticity and density, before a species can be assigned to a strength class. The theoretical
background for the number of tests required is not very well documented and sampling
procedures for new species that grow over vast areas are not specified.
From a viewpoint of reliability there is a market mechanism that prevents that new species are
used in heavy structures without sufficient knowledge of that species. Before a new species is
introduced on the market in large quantities, small projects will be carried out and designed
on the basis of a few tests on the material that is available for the specific projects. Timber
trader, contractor, designer and future owner closely work together in these stages of the
project, avoiding large mistakes with severe consequences. Following a standard such as EN
384 would prevent the use of new species because of the costs involved. For these small
projects a limited amount of destructive tests in the laboratory can give sufficient information
about the strength of the timber batch, while non-destructive tests are available to determine
modulus of elasticity and density for instance. Knowledge about the species is increased
during small building projects and more tests can be performed when larger projects with
greater risks involved are scheduled.
In order to obtain some basic knowledge about a number of recently introduced species in the
Netherlands a large project was set-up. The main goal of this project was to develop a general
strength model, primarily based on parameters that can be determined non-destructively, that
can be used to safely estimate the strength of new species. 12 new species were selected and
from each species 40 beams (the minimum required according to EN 384 for strength class
assignment). The data of these 12 species would form a database together with the already
existing database of azobé and is used whenever a new species needs to be judged or when
one of the 12 species will be used in large structures. [Van de Kuilen, 1999]. [Van de Kuilen
& Ravenshorst, 2000].
1
This paper and part of this research work was done during a sabbatical leave of J.W.G. van de Kuilen from Delft
University of Technology in 2002. He gratefully acknowledges the Dipartimento di Ingegneria Strutturale of the
Politecnico di Milano, Italy, for their hospitality and cooperation.
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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2. Strength data of azobé
Over the years about 180 tests on azobé beams and boards have been performed. All tests are
performed on structural sizes. Sizes that are used in structures range from 40 mm thick boards
in sheet pile walls to built up beams with individual member sizes of 180 x 180 mm.
In figure 2.1 the relationship between static modulus of elasticity and bending strength (MoR)
is shown, while in figure 2.2 the dynamic modulus of elasticity and bending strength is
Relationship between dynamic modulus of elasticity and bending
strength of azobe
Bending strength (N/mm )
120.00
2
2
Bending strength (N/mm )
Relationship between static modulus of elasticity and bending
strength of azobe
100.00
80.00
60.00
40.00
20.00
0.00
10000 12000
14000
16000
18000
20000
22000
24000
2
120.00
100.00
80.00
60.00
40.00
20.00
0.00
10000
12000
14000
16000
18000
20000
22000
24000
Dynamic modulus of elasticity (N/mm2)
Static modulus of elasticity (N/mm )
Figure 2.1 Static MoE versus MoR
Figure 2.2 Dynamic MoE versus MoR
shown. In both cases the relationship is not very strong.
The relation between density and bending strength as is shown in figure 2.3
Relationship between density and bending strength of azobe
Bending strength (N/mm 2)
120.00
100.00
80.00
60.00
40.00
20.00
0.00
800
900
1000
1100
1200
1300
1400
3
Density (kg/m )
Figure 2.3 Density versus MoR
Some beams had severe grain deviations and this was found to be the main strength
determining parameter. On the basis of the test series, azobé has been assigned to strength
class D60 of EN 338 in conformity with EN 384. EC5 allows the use of the following depth
factor:
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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 150 
kh = 

 h 
0 .2
(1)
for depths lower than 150 mm with a maximum value of 1.3. In the Netherlands azobé is
assigned to a strength class with a characteristic bending strength of 70 N/mm2 , (Strength
class K70 according to NEN 5498) but the use of a depth factor is not allowed for strength
classes with a characteristic bending strength higher than 40 N/mm2 .
In figure 2.4 strength data of azobé is shown, as a function of depth and the relationship
between depth and strength is much smaller than is assumed in Eurocode 5. This, naturally, is
caused by the fact that grain deviation does not increase with beam size. It must be recognized
that bridge manufacturers in particular suffer from the depth effect and the corresponding
assignment to strength class D60 it causes. The average strength of azobé was found to be 101
N/mm2 with a standard deviation of 15.1 N/mm2 .
1.8
Eurocode 5/EN384
Azobé
1.6
Depth factor [-]
1.4
1.2
1
0.8
0.6
0.4
0
50
100
Depth [mm]
150
200
250
Figure 2.4 Depth effect in azobé as compared to Eurocode 5.
3. New species
A total of 11 new hardwood species were selected and tested in conformity with EN 384, nine
from (sub)tropical regions and two from Europe. From each species 40 beams were randomly
selected from trade stocks. The species are summarized in table 1.
Based on visual grading of the pieces a general requirement for grain deviation was
determined at 1:10. In addition a maximum knot area of 0.2 was defined, where knot area is
determined as the ratio between the sum of diameters of the knots, measured perpendicular to
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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the longitudinal beam axis, and the circumference of the beam. Although most species do not
have knots at all, a value had to be chosen to avoid the use of beams with large growth
disturbances, which sometimes are knots, but sometimes just appear to be knots. Grain
deviations around these areas often cause very low strength values.
Table 3.1 "New" species
Species
Origin
Latin name
Angelim vermelho
Basralocus
Cumaru
Denya
European oak
Karri
Massaranduba
Nargusta
Piquia
Robinia
Vitex
Dinizia excelsa
Dicorynia guianensis
Dipteryx odorata
Cylicodiscus gabunensis
Quercus robur
Eucalyptus diversicolor
Manilkara bidentata
Terminalia amazonia
Caryocar villosum
Robinia pseudoacacia
Vitex cofassus (spp)
Brazil
Surinam
Brazil
Ghana
Poland
South-Africa
Brazil
Bolivia
Brazil
Hungary
Solomon islands
In figure 3.1 the test results for static modulus of elasticity and bending strength are shown. In
some cases a static modulus of elasticity of more than 30.000 N/mm2 was found. In figure 3.2
and 3.3 the same is done for the dynamic modulus of elasticity and density respectively is
done. The dynamic modulus of elasticity was determined using stress wave analysis
equipment developed at TNO Building and Construction Research.
Strength data of 11 "new" species
160.0
karrie
Bending strength (N/mm 2 )
140.0
European oak
120.0
cumaru
angelim vermelho
100.0
vitex
80.0
massaranduba
nargusta
60.0
piquia
denya
40.0
basralocus
20.0
robinia
0.0
0
5000
10000
15000
20000
25000
30000
2
Static modulus of elasticity (N/mm )
Figure 3.1 Relationship between the static modulus and the bending strength.
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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Strength data of 11 "new" species
karrie
Bending strength (N/mm 2)
160.0
European oak
140.0
cumaru
120.0
angelim vermelho
100.0
vitex
massaranduba
80.0
nargusta
60.0
piquia
40.0
denya
20.0
basralocus
robinia
0.0
0
5000
10000
15000
20000
25000
30000
2
Dynamic modulus of elasticity (N/mm )
Figure 3.2 Relationship between the dynamic modulus of elasticity and the bending strength.
Strength data of 11 "new" species
karrie
Bending strength (N/mm 2)
160.0
European oak
140.0
cumaru
120.0
angelim vermelho
100.0
vitex
massaranduba
80.0
nargusta
60.0
piquia
40.0
denya
20.0
basralocus
0.0
500
robinia
700
900
1100
1300
Density (N/mm2)
Figure 3.3 Relationship between the density and the bending strength.
The average values for the species are summarized in table 3.2. The values given for the
bending strength are the values as obtained from the tests. Thus, no correction factors for
depth, moisture content or sample size as specified by EN 384 have been applied to the given
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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data. The depth of the beams in the test was always around 150 mm and the tests were
performed as four-point bending in accordance with EN 408.
Table 3.2 Average values of 11 “new” species.
Species
Bending strength
Static modulus of
elasticity
[N/mm2 ] (cov)
[N/mm2 ] (cov)
Angelim vermelho
Basralocus
Cumaru
Denya
European oak
Karri
Massaranduba
Nargusta
Piquia
Robinia
Vitex
78.8
58.0
102
75.7
42.0
62.0
110
73.9
63.0
66.0
58.0
(21%)
(33%)
(21%)
(16%)
(16%)
(20%)
(14%)
(22%)
(14%)
(24%)
(18%)
16000
17200
18300
17000
9300
15500
24700
19900
18600
15200
13100
(11%)
(30%)
(16%)
(30%)
(18%)
(17%)
(35%)
(22%)
(31%)
(13%)
(16%)
Density
[kg/m3 ] (cov)
1086 (5%)
939 (11%)
1078 (5%)
991 (8%)
885 (7%)
924 (8%)
1100 (4%)
742 (9%)
940 (5%)
740 (6%)
908 (10%)
A typical failure mode for a tropical hardwood is shown in figure 3.4. This is failure of a
massaranduba beam on the left and a piquia beam on the right. The piquia beam shows a
combination of compression wrinkles and tensile failure.
Figure 3.4 Failure of a massaranduba (right) and a piquia (left) beam.
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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Figure 3.5 Failure in compression of a karri beam.
4. Prediction of bending strength using stress wave analysis
Multiple regression analysis was used to determine a “general” strength model for new
species. In the following table the correlation coefficients are given for the "all data" dataset.
Parameter
Edyn
rho
Estat
f stat
Edyn
1.0000000
0.4347751
0.6558195
0.7438121
?
Estat
f stat
1.0000000
0.2241474
0.4111260
1.0000000
0.5913608
1.0000000
The linear multiple regression equation reads:
f m = 0.038 Edyn + 0.0008 Estat + 0.0223ρ − 28.2675 with R2 = 0.582 (r = 0.764)
(2)
A slightly better prediction is obtained when also the logarithm of Estat and Edyn is used as well
as ?2 :
f m = 0.0079Edyn − 84.2096log( Edyn ) − 0.0008Estat + 36.6253log( Estat) − 0.3038ρ + 0.0002ρ 2 + 538.0231
with R2 = 0.615 (r = 0.784)
(3)
The abovementioned species were used to derive a general regression equation. Regression
equations were derived with the database minus the data of one species and the bending
strength of this species was then predicted. In this way the model was optimized using all
datasets and the sensitivity could be determined to judge the strength of a new unknown
species. Predicted strength is calculated on the basis of a regression equation including static
and dynamic modulus of elasticity, as obtained with the TNO apparatus and density. In
addition, all the data of the species azobé was added to the database. It is outside the scope of
this paper but the system in practice uses a larger database, including some softwood data, as
well as several modification factors for the determination of the actual strength class. The
status of the overall model before it was applied for the first time in practice was even better
than presented here (R = 0.85). The relationship between regressed strength and actual
strength is shown in figure 4.1.
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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Figure 4.1. The regressed bending strength on the basis of the general strength model.
In figure 4.2 the relative mistake is shown on the average bending strength. The ratio given is
the predicted strength divided by the measured strength. Consequently, a value above 1.0 is
an overestimation, while a value lower than one is an underestimation of the strength. The
same is done in figure 4.3 for the characteristic value. These modification factors included
moisture content, depth effect, samples size. The values presented here are just the rough data
from which the characteristic value is determined as m-1.64s, where m is the sample mean
and s the sample standard deviation.
1.4
Ratio predicted / measured
1.2
1
0.8
0.6
0.4
0.2
Ro
bin
ia
Ba
sra
loc
us
De
ny
a
Pi
qu
ia
Na
rgu
sta
Vi
Ma
tex
ss
ara
nd
ub
a
ve
rm
elh
o
Cu
m
ar
u
An
ge
lim
oa
k
Eu
rop
an
Ka
rri
0
Figure 4.2 Prediction of the average bending strength
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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2.2
Ratio predicted / measured
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Ro
bin
ia
Ba
sra
loc
us
De
ny
a
Pi
qu
ia
Na
rg
us
ta
Vi
M
tex
as
sa
ran
du
ba
Cu
An
m
ge
ar
lim
u
ve
rm
elh
o
oa
k
Eu
rop
an
Ka
rri
0
Figure 4.3 Prediction of the characteristic value of the bending strength
From figures 4.2 and 4.3 it can be concluded that the characteristic bending strength for
nearly all species can be determined with an accuracy of +/- 20%. At the strength class levels
of most of these hardwoods, generally around D40, D50 of D60, this 20% is about one step in
strength class. Consequently, when the characteristic bending strength class is determined on
the basis of this model, the species could be assigned to a strength class one lower than
predicted and this would be a safe approximation for most species. The one species that
stands out from a negative point if view is basralocus. The sample tested had a very large
scatter as can be seen from table 3.2 and figure 3.3. The cause of this scatter is unknown,
since no specific growth details could be determined visually other than knots. In figure 4.4
the influence of the knot area on the bending strength is shown. Although the bending
strength decreases due to the knots, the knot area is most cases was still relatively small.
2
Bending strength (N/mm )
Knot area and bending strength of Basralocus
100
80
60
40
20
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Knot area [-]
Figure 4.4 Influence of knot area on the bending strength of basralocus
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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As a result of this, the general strength model takes into account model and prediction
uncertainties, sample sizes and the required safety level in structural applications.
5. Conclusions and practical application
Based on a large dataset of 12 species a prediction model for the strength of new "unkown"
species has been developed. The model is able to predict the strength class using static and
dynamic modulus of elasticity and density. The system is currently being used for analysis of
batches of timber from one of the 12 species that are to be used in heavy structural
applications. The first trial was for a batch of cumaru to be used in a sluice door. In figure 5.1
the large beams are analysed on the timberyard. In figure 5.2 the beams already form part of
the frame of the sluice door.
Figure 5.1 Testing of large dimension cumaru
beams.
Figure 5.2 Beams in a sluice door frame
In figure 5.3 and 5.4 the sluice doors are placed in position. The doors are 4.5 meters wide
and 6.6 meters high. The two largest member sizes that were machine graded were 7 meter
long with a cross section of 0.42 x 0.42 meters. The second largest members were seven
beams of 5 meters long with a cross section of 0.4 by 0.4 meters. Although the whole batch
was acquired as 'cumaru', two distinct colors could be distinguished, one yellowish and one
brownish and questions were raised whether they were indeed all of the species 'cumaru'. The
stress wave grading, however, showed no differences in strength between these members.
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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Figure 5.3. Sluice door hoisted into position.
Figure 5.4 Sluice door in its final position
The system is in trial state to be used whenever a batch of a new species enters the market.
The non-destructive testing method can be used to specify a safe characteristic bending
strength value for structural applications of a batch of that particular "unknown" species.
Literature
Blass, H.J., Van de Kuilen, J-W.G., The characteristic strength of azobe, TNO Report B-911124, 1991.
Van der Linden, M.L.R., Van de Kuilen, J-W.G., Blass, H.J., Application of the Hoffman
Yield Criterion for load sharing in timber sheet pile walls. Pacific Timber Engineering
Conference pp. 1994
Van de Kuilen, J-W.G. Development of a general determination method for the strength of
timber. Phase 1. TNO Reports 1999-LBC-R7027 / R7028/2 / R7029 / R7030/2. (in Dutch)
Van de Kuilen, J-W.G., Ravenshorst, G.J.P. Development of a general determination method
for the strength of timber Phase 2. TNO Reports 2000-CHT-R101 / R102 / R156 / R157 /
R158 / R172 / R173 / R174 / R178 / R179 (in Dutch).
J-W.G. van de Kuilen, G.J.P. Ravenshorst
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