comparison between tensile and compressive young`s modulus of

comparison between tensile and compressive young`s modulus of

COMPARISON BETWEEN TENSILE AND COMPRESSIVE
YOUNG’S MODULUS OF STRUCTURAL SIZE LUMBER
Kwang-Mo Kin1, Kug-Bo Shim2
ABSTRACT: To evaluate MOE of glued laminated timber, usually non-destructive MOE values of lumber were used
as input data. However, as the glulam in under bending load, bending stress of the glulam divided into two loading
mode to the lumber. It is tension and compression stress in the glulam. The tensile modulus is roughly two times greater
than compressive modulus. Therefore, it is important to define the differences and relations with non-destructive MOE
and tensile and compressive modulus. This study was carried out to predict tensile and compressive modulus from
dynamic or static MOE of major softwood lumber in Korea. The measured MOE of the same specimens by various test
methods were slightly different. Especially, the tensile modulus was two times greater than the compressive modulus at
the same specimen. The dynamic MOE or static edgewise and flatwise MOE could be used to predict tensile and
compressive modulus for estimate glulam MOE because of its significant correlation between those MOE and tensile
and compressive modulus.
KEYWORDS: Glulam, Tensile modulus, Compressive modulus, Flatwise MOE, Edgewise MOE, Dynamic MOE
1 INTRODUCTION 1 2
The Korea Forest Research Institute has studied on glued
laminated timber (glulam) to improve its properties for
adding values [1-4]. Kim et al. [3,4] predicted modulus
of elasticity of glulam by transformed section methods.
The predicted MOE of glulam was overestimated about
10 to 30% when dynamic MOE of lumber was chosen as
the imput data.
Shim et al. [5] studied to improve MOE prediction
accuracy of glulam based on neutral axis movement
under bending stress. In this study, the measured tensile
and compressive modulus from actual size structural
lumber showed different values from static or dynamic
MOE of lumber which are used as input data of lumber
to predict MOE of glulam. Especially, the neutal asix
under bending stress shifted to the tension side greater
than predicted movement based on the MOE of lumbers
because tensile modulus of actual size structral lumber
was about two times greater than compressive modulus.
Shim et al. reported that the difference between tensile
and compressive was caused by growing characteristics
of lumber, such as grain deviation near konts or
immature wood. However, measuring tensile and
compressive modulus for using input data of glulam in
plants needs additionally expensive equipment and time
consuming job.
Therefore, this study was carried out to predict tensile
and compressive modulus from dynamic or static MOE
of major softwood lumber in Korea.
2 MATERIALS AND METHODS
2.1 MATERIALS
Six species of major domestic softwoods were chosen to
be tested. Ten lumbers from each species were selected
and dried. The species, size, moisture contents and ovendry density of specimens were shown in Table 1.
Table 1: Specification of test specimen
Size(mm)
M.C.
(%)
Density
(g/cm3)
Korean Red Pine
38ⅹ140ⅹ3,600
8.68
0.44
Korean Larch
33ⅹ152ⅹ3,600
10.47
0.51
Pitch Pine
34ⅹ148ⅹ3,600
9.54
0.50
Korean Pine
39ⅹ150ⅹ3,600
10.62
0.42
Japanese Cedar
30ⅹ120ⅹ3,600
10.95
0.32
Japanese Cypress
30ⅹ149ⅹ3,600
11.79
0.46
Species
1
Kwang-Mo Kim, Div. of Wood Engineering, Dept. of Forest
Resources Utilization, Korea Forest Research Institute, Seoul,
130-712, Korea. Email: [email protected]
2
Kug-Bo Shim, Div. of Wood Engineering, Dept. of Forest
Resources Utilization, Korea Forest Research Institute, Seoul,
130-712, Korea. Email: [email protected]
2.2 MEASUREMENT
2.2.1 Surface images
Digital images of four sides of lumber were taken to
evaluate growing characteristics of lumber prior to
measure MOE. Lumber scanning system and image
merging algirithm were used to get digital images of
3,000mm distance of the middle of lumber [6,7].
which measured loads of 5mm edgewise bending
deflection at the center of lumber. The span length of
edgewise MOE measurement was 3,000mm. To measure
edgewise bending MOE, two opposite edgewise
directions of lumber were tested and the average value of
two directions were taken to calculated edgewise
bending MOE.
2.2.4 Flatwise bending MOE
Flatwise bending MOE was measured by three point
loading method with universal testing machine (Instron
5585, 200kN). The load limitation to measure flatwise
deflection of lumber was 150kgf for 5 species except the
weakest species (Japanese Ceder, 85kgf). As the same as
the edgewise MOE measurement, the average value of
two flatwise direction deflection was taken to calculate
flatwise MOE of lumber. The specimen length for
measuring flatwise MOE was 1,400mm and the span
length was 1,000mm.
Figure 1: Lumber scanning system
2.2.2 Dynamic MOE
Dynamic MOE of lumber was measured at the middle of
lumber in 3,000mm length and 1,000mm length by
ultasonic transmission timber. PUNDIT (CNS Farnell,
UK) was used to measure ultrasonic transmission time,
and MODD was calculated by the equation (1).
MOED = C 2 × ρ
(1)
2.2.5 Tensile modulus
Tensile modulus was measured by acutual size tension
testing machine (Kyoung Sung Testing Machine Co.,
Ltd, Korea, 1,000kN) for 3,000mm specimen length and
600mm grip distance at each end. The displacement of
specimen at 4tonf tension load for 5 species except the
weakest species (Japanese Cedar, 2.5tonf) was measrued
by LVDT in two wide sides and 1,000mm distance at the
center of specimen. The displacements were averaged in
two wide surfaces.
Dynamic MOE were measured in three different
transducer locations at the end of lumber. Ultrasonic
transmission velocity, c, was calculated by the average
transmission time divided by the specimen length. Mass
density, ρ, was measured by the weight and size of
lumber.
2.2.3 Edgewise bending MOE
Figure 3: Acutual size tension testing machine
Figure 2: Edgewise bending testing machine
Edgewise bending MOE was measured by continuous
MOE measuring equipment. The edgewise bending
MOE was calculated by three point loading method
2.2.6 Compressive modulus
Universal testing machine (Instron 5585, 200kN) was
used for testing compressive modulus of lumber.
Additional plates were designed and attached to prevent
buckling of specimen under compressive load. The
specimen length was 1,000mm and compressive
displacement was measured from cross-head movement.
The maximum slope of 200 kgf load increase was
selected from the load-displacement curve and used to
calculate compressive modulus.
2.3 MEASUREMENT PROCEDURE
The test procedure was described in table 2 and figure 4.
Table 2: Measurement procedure and corresponding
specimen length
Measurements
①
Edgewise
bending MOE
②
Surface image
③
Dynamic MOE
④
Tensile modulus
⑤
Flatwise
bending MOE
⑥
Dynamic MOE
Length(mm)
Note
3,600
(3,000)*
2.2.3
2.2.1
2.2.2
3,000
2.2.5
1,400
(1,000)
2.2.4
2.2.2
1,000
Compressive
modulus
* ( ) : Span length for bending test
2.2.6
⑦
Figure 4: Cutting length for each measurement procedure
3 RESULTS AND DISCUSSIONS
3.1 VARIATION OF MOE BY TEST METHODS
The average MOE values by different test methods were
shown in table 3. However, 3 specimens of Korean Pine
were broken under edgewise bending load and 2
specimens of Korean Red Pine and Korean Pine were
failed under tensile load because of unexpectedly great
knot of knot clusters (figure 5).
Korean Larch and Japanese Cypress had higher MOE
values and Pitch pine and Japanese Cedar had lower
MOE values, respectively. However, due to the sample
sizes, it is difficult to define that the MOE values in table
3 were representative values of those species. The
Japanese Cypress showed higher values and Pitch Pine
showed lower values than its density order with other
specimens, relatively.
The dynamic MOE was the greatest and tensile modulus,
flatwise bending MOE, edgewise bending MOE and
compressive modulus was followed in order. In the case
of dynamic MOE values, the longer specimen
(3,000mm) showed 5% lower value than shorter
specimen (1,000mm). This might be the energy reducing
effect of ultrasonic transmission caused by the length of
specimen. The differences of dynamic MOE in long and
short specimens of low grade lumber (low MOE
specimen) were greater than high grade lumber (high
MOE specimen) because low grade lumbers had more
defects to reduce ultrasonic transmission energy
Edgewise bending MOE value was 10% lower than
flatwise bending MOE. It is because of the location and
size effect of growing characteristics in the edgewise
bending which are reducing strength of lumber.
Additionally, shear effect of edgewise specimen were
greater than flatwise specimen because of span to depth
ratio during bending test.
The value of tensile and compressive modulus of Korean
Larch and Pitch pine was greater than the results in Shim
et al. reported [5], but there was the same tendency
which the tensile modulus was about two times greater
than compressive modulus. The tendency of modulus
differences between tensile and compressive modulus of
actual size lumber was because of low compressive
modulus due to the grain deviation near defects.
The value of bending MOE was nearly the same as the
average values of the tensile and compressive modulus.
As a lumber resists against bending stress, tensoin and
compression stress acts at the same time in the opposite
side of lumber. The correlation between average value of
tensile and compressive modulus and edgewise bending
MOE showed that the formar had 6% higher than the
latter and the correlation coefficient (R2) was 0.905
(figure 6).
Table 3: Average MOE of each species by loading modes (N/mm2)
Bending
Dynamic
Tensile
Compressive
8,660
11,230
6,130
9,700
9,920
13,010
6,900
9,970
6,590
6,820
8,320
4,620
10,630
10,890
6,260
8,040
9,270
4,810
Japanese Cedar
8,500
8,810
6,490
7,050
8,800
4,610
Japanese Cypress
13,170
13,790
9,660
10,710
13,280
7,050
11,150
11,680
7,890
8,560
10,810
5,730
Species
3,000mm
1,000mm
Edgewise
Flatwise
Korean Red Pine
12,160
12,420
8,160
Korean Larch
13,420
14,000
Pitch Pine
8,890
Korean Pine
Average
(a) Korean pine
(b) Korean red pine
Figure 5: Examples of surface images of specimens damaged during tensile test
3.2 PREDICTION OF TENSILE AND
COMPRESSIVE MODULUS
Figure 6: Relationship between edgewise bending MOE
and the average of tensile and compressive MOE for
each specimen
When a lumber was under bending load, the neutral axis
moved to tension side because of the tensile and
compressive modulus difference. To consider this effect,
edgewise bending MOE was estimated with tensile and
compressive modulus by transformed section method.
The result showed that the compressive area was about
57.7% of lumber cross-section and the correlation
coefficient between estimated and measured edgewise
bending MOE was improved to 0.927.
The linear correlations between MOE measurement
methods were analized, and the results shown in table 4
and figure 7. It is certain that there were dependent
relationships in the MOEs measured by different test
methods becuase the coefficients were very high.
Especially, the case of including compressive modulus
showed the highest correlation coefficients.
Generally, the dynamic and static bending MOE were
used as input data for predicting mechanical properties
of lumber or glulam because it is easy to measure. Many
commercial equipments to measure dynamic and static
bending MOE have been developed. However,
measuring tensile and compressive modulus was not
easy, and the measuring equipment of tensile and
compressive modulus for structural lumber was not
being developed for commercial purposes. Therefore, the
bending MOE of lumber was suggested in most research
results as representative MOE of the lumber species.
Based on the results of this study, there were high
correlations between tensile and compressive modulus
and the other MOE values. Therefore, predicting MOE
of engineered wood based on the tensile and
compressive modulus is possible because of high
correlation between tensile and compressive modulus
and other MOE values.
Table 4: Correlation coefficients between different MOE measuring methods
Bending
Dynamic
Tensile
Compressive
0.834
0.805
0.876
0.865
0.824
0.806
0.893
0.865
1
0.833
0.841
0.949
0.834
0.824
0.833
1
0.812
0.878
Tensile
0.805
0.806
0.841
0.812
1
0.879
Compressive
0.876
0.893
0.949
0.878
0.879
1
Dynamic
Bending
3,000mm
1,000mm
Edgewise
Flatwise
3,000mm
1
0.921
0.827
1,000mm
0.921
1
Edgewise
0.827
Flatwise
Figure 7: Linear correlation between MOE measurement methods
Figure 7: Linear correlation between MOE measurement methods (Continue)
Table 5: Prediction equations of tensile and compressive MOE based on edgewise bending MOE
Tensile MOE
A
*
b
Compressive MOE
**
R
2
a
*
b**
R2
Korean Red Pine
1.674
-2,431
0.711
0.571
1,206
0.961
Korean Larch
1.698
-3,465
0.833
0.716
-54
0.782
Pitch Pine
1.399
-903
0.642
0.780
-527
0.678
Korean Pine
1.307
1,071
0.926
0.521
1,392
0.749
Japanese Cedar
1.343
85
0.706
0.729
-117
0.838
Japanese Cypress
0.674
6,771
0.610
0.589
1,360
0.934
-208
0.841
0.712
17
0.951
Total
1.383
2
* a: Gradient, ** b: y-axis intercept, R : Coefficient of determination
significant. Therefore, considering the applicability, and
The linear regression coefficients for predicting tensile
equation constructed from all species base could be used
and compressive modulus for each species from
for predicting tensile and compressive modulus of
edgewise MOE of lumber were shown in table 5.
lumber. The comparison results between predicted
However, there is possibility to predict tensile and
modulus from all species base and measured modulus
compressive modulus from flatwise MOE or dynamic
were shown in figure 9.
MOE.
The root mean square error (RMSE) of predicted and
4 CONCLUSIONS
measured MOE was calculated by equation (2) and
This study was carried out to predict tensile and
shown in figure 8. The prediction equation was
compressive modulus from dynamic or static MOE of
constructed from the coefficients in table 4 for each
major softwood lumber in Korea.
species basis and all species base values.
RMSE =
∑ ( MOE
predicted
− MOEmeasred )
Number ⋅ of ⋅ specimen
2
(2)
The RMSE of tensile modulus was about 800N/mm2. On
the other hand, RMSE of compressive modulus was
lower than 400N/mm2. The RMSE of high MOE species
such as Korean Larch had higher value but low MOE
species such as Korean Pine had low RMSE value,
relatively.
The RMSE calculated from all species base value
showed greater than the RMSE calculated from each
species base value but the differences were not
(a) Tensile MOE
The conclusions are as followed:
A. The measured MOE of the same specimens by
various tes methods were slightly different.
Especially, the tensile modulus was two times grater
than the compressive modulus at the same specimen.
B. The dynamic MOE or static edgewise and flatwise
MOE could be used to predict tensile and
compressive modulus for estimate glulam MOE
because of its significant correlation between those
MOE and tensile and compressive modulus.
(b) Compressive MOE
Figure 8: RMSE’s of predicted MOE for each species (N/mm2). Prediction equations derivated for each species and for
total specimen were compared
(a) Tensile MOE
(b) Compressive MOE
Figure 9: Prediction accuracy of tensile and compressive MOE based on edgewise bending MOE
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