69 While a sigmoid function for jabon Equation 6 was fitted R
2
= 0.975 to the experimental values for modelling purposes:
� � � = . +
. +
− . ��−
.
…………. 6 where MOE MOE in MPa is deduced from segmented ring
� in radius from pith mm.
MOE of veneer would influence MOE of LVL. Therefore, the MOE solid wood evolution from pith to bark was important in our model.
Figure 43 The average of solid wood MOE of sengon left and jabon right
based on segmented ring
5.1.1.3 Specific Modulus of Elasticity of sengon and jabon LVL
Several researchers have used specific modulus of rupture SMOR and specific modulus of elasticity SMOE to evaluate MOE and MOR results by
taking into account the effect of density on flexural properties Bao et al. 2001; Bal and Bektaş 2012. SMOE were directly obtained by dividing MOE with
density. The above relationships will enable us to obtain the specific modulus of elasticity according to the radial position in the log.
5.2 Model building
The model was developed using Wolfram Mathematica Software 2015. The model consists of four different phases Figure 44 Girardon et al. 2016.
The phases are : 1 to determine the modulus of elasticity along veneer length using the equations above developed by Girardon et al. 2016; 2 to divide
veneers into two groups, “juvenile” and “mature”. The width of 500 mm is used, based on Rahayu et al. 2015. The demarcation points between juvenile and
mature were based on fiber length trait taken from Chapter 2. The demarcation point of 5 years old sengon and jabon were after 7 years old. Each veneer is
virtually subdivided into subsamples of 20 mm thickness the final thickness of the LVL samples; 3 for each LVL samples the veneers are assembled into
layers to represent a LVL panel of 20 mm thickness. The number of veneer layers depends on the thickness of the veneers. Seven layers of 3 mm and four layers of
5.25 mm were produced. It is assumed that veneers are selected randomly in each category in accordance with Rahayu et al. 2015; and 4 to cut 20 mm thickness
Jabon Sengon
70 LVL samples. The specific modulus of elasticity of each LVL sample is
calculated from each layer’s properties as described below.
Figure 44 Virtual peeling and assembly process shades of grey correspond to
local cambial age of veneer Girardon et al. 2016
5.2.1 Virtual peeling
The first step is to determine the maximum veneer length depending on the log diameter. In cross-section, the peeling process corresponds to following a
spiral curve Figure 44. The equation of a spiral in polar coordinates is given by Equation 7, where
s
is the spiral radius mm with respect to the angle θ in rad,
� is the initial log radius in mm and t is the peeling thickness in mm. � =
�
− .
�
……………………..7
The length of this curve can be calculated by the integration of Equation 10, which corresponds to the veneer length. Second-order length is neglected due to
linear variations in radius with respect to the angle. Thus the veneer length is determined by the following Equation 8:
�
, , = ∫ √ ′ � +
� �
�� �
�� �
………….8
Specific MOE SMOE were calculated from each layer of LVL samplesoduction
SMOE
e
and SMOE
f
