72 In accordance with Figure 45: Z
= Distance from the neutral axis to an arbitrary reference
; �0= Distance from the i
th
layer netral axis to an arbitrary reference
; ��= Distance from the i
th
layer netral axis to the global neutral axis
Figure 45 Geometrical and mechanical properties of LVL in a specimen cross- section
Thus, the distance between each layer’s neutral axis and the global neutral axis, ��
is deduced by Equation 12: �
�
= �
,�
− � ………. 12 Then the specific modulus of elasticity can be determined by the following
Equation 13: �� � =
∑ �
� �
+�
�
�
� ��
�= � �
……………………13 Where: SMO
�� = Specific modulus of elasticity of the i
th
layer � ; �� =
Inertia of the i
th
layer
4
; � = �
� ℎ ℎ �
4
; �� =
Section of the i
th
layer
2
; �� = Distance from the i
th
layer neutral axis to the neutral axis
; and ρt = density of the i
th
layer kg m
-3
5.2.3 Stochastic approach
Since in virtual peeling process the layout is based on a randomized assembly process, the process is repeated a thousand times to identify and enhance
a tendency. Indeed, the peeling process always gives the same veneer for a given thickness value, but there are several combinations of veneer arrangements after
the primary cutting. These combinations are high due to the possibility to turn each veneer upside-down. The veneer position influences the flatwise SMOE
whereas it does not impact the edgewise SMOE. Consequently, a great number of processes have to be performed to obtain results close to experimental conditions.
The number of possible combinations for a single
layer LVL is given by Equation 14 :
=
� ��
…………… 14 Where,
is the number of possible combinations and is the number of
layers. Symmetric cases are considered in the number of combinations; therefore the number is divided by two.
73 According to the log size used in this study, the total amount of sengon and
jabon veneer sheets were 147 and 133 veneer sheets respectively for juvenile group. Due to the numerous ways to choose sheets from a set of 147 and 133
veneer sheets, a stochastic approach is chosen in order to obtain results within a reasonable computing time. The number of possible combinations is determined
with binomial coefficients, which gives the following results Equation 15 for the studied cases 4 layers of 5.25 mm thickness and 7 layers of 3 mm thickness over
a total number of veneer sheets of 147 and 133:
≈ . ≈ .
≈ . ≈ .
………………….15
5.3 Results and discussion
The model can be used to predict the specific modulus of elasticity of a parameterized LVL sample. It could be used with different scenarios but requires
validation through a comparison with experimental data, which is done in the following
.
Table 17 Specific MOE � .
3
.
−1
LVL of sengon and jabon based on experimental data Chapter 4 from pith to bark
Segment Sengon
Jabon 1 pith
15.33 + 0.84 14.25 + 0.12
2 15.56 + 1.82
14.54 + 1.91 3
15.78 + 0.34 14.25 + 1.16
4 15.58 + 1.87
16.04 + 1.16 5
15.57 + 0.37 15.86 + 1.16
6 15.39 + 1.28
16.37 + 1.89 7 bark
16.74 + 0.02 18.37 + 5.56
Average 15.71 + 2.53
15.67 + 1.85
5.3.1 Experimental results
A summary of the results from Chapter 4 is shown in Table 17. Specific MOE were resulted from destructive testing by INSTRON in flatwise direction.
Moreover, the sengon and jabon LVL were made of 3 mm veneers. The same with MOE solid wood, the specific MOE of LVL tended to increase from pith to
bark.
5.3.2 Model results
Our model was computed based on parameters Chapter 3 : initial log radius: 280 mm; kernel log radius: 60 mm; veneer thicknesses: 3 and 5.25 mm;
veneer length: 500 mm; LVL sample width: 20 mm. The model is based on the assumption that all sengon and jabon behaved in the same way in terms of growth,
MFA variation and juvenile – mature transition
