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Influence of boundary conditions in modal testing on evaluated elastic properties of timber panels

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Abstract and Figures

Cross laminated timber (CLT) has the potential to play a major role in timber construction as floor and wall systems. In order to meet specific design needs and to make the use of CLT more effective, property evaluation of individual CLT panels is desirable. Static tests are time-consuming and therefore costly, and for massive products such as CLT practically impossible to implement. Modal testing offers a fast and more practical tool for the property evaluation of CLT and timber panels in general. This paper presents a comparison of different boundary conditions in modal testing in terms of accuracy, calculation effort and practicality. Single-layer timber panels as well as scaled CLT panels were fabricated. Three elastic properties of the panels were evaluated using modal testing methods with different boundary conditions (BCs). The results were compared with results from static test.
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INFLUENCE OF BOUNDARY CONDITIONS IN MODAL
TESTING ON EVALUATED ELASTIC PROPERTIES OF MASS
TIMBER PANELS
Jan Niederwestberg1, Jianhui Zhou2, Ying Hei Chui3
ABSTRACT: Cross laminated timber (CLT) has the potential to play a major role in timber construction as floor and wall
systems. In order to meet specific design needs and to make the use of CLT more effective, property evaluation of
individual CLT panels is desirable. Static tests are time-consuming and therefore costly, and for massive products such as
CLT hard to implement. Modal testing offers a fast and more practical tool for the property evaluation of CLT and timber
panels in general. Elastic properties of “homogenised” single-layer timber panels and scaled CLT panels were evaluated
using modal testing methods with different boundary conditions (BCs). The results were compared with results from static
test. This paper presents a comparison of different boundary conditions in modal testing in terms of accuracy, calculation
effort and practicality.
KEYWORDS: Cross laminated timber (CLT), Modal testing, Boundary conditions, Elastic properties
1 INTRODUCTION
123
Cross laminated timber (CLT) is an engineered wood
product made from layers of timber pieces. Due to the
layered glue-up with alternating grain directions of
adjacent layers, CLT forms a stiff and strong orthotropic
plate structure. The stiff structure shows high potential in
shear wall and floor applications, construction elements
that are dominated by reinforced concrete in large
structures. CLT has the potential to replace reinforced
concrete in these applications up to a certain point. Unlike
reinforced concrete elements, which are designed based on
the structural needs, CLT elastic properties used for design
purposes are based on the build-up of the panels and on
assumed elastic constants of the component material. The
elastic properties that are mainly needed in CLT design are
the modulus of elasticity parallel to the grain of the outer
layers (E11), the modulus of elasticity perpendicular to the
1
Jan Niederwestberg, Faculty of Forestry and Environmental
Management, University of New Brunswick, 28 Dineen Drive,
Fredericton, NB, Canada. E3B 5A3, Email: j.nwb@unb.ca
2
Jianhui Zhou, Faculty of Forestry and Environmental
Management, University of New Brunswick, 28 Dineen Drive,
Fredericton, NB, Canada, E3B 5A3. Email: jh.zhou@unb.ca
3
Ying Hei Chui, Faculty of Forestry and Environmental
Management, University of New Brunswick, 28 Dineen Drive,
Fredericton, NB, Canada, E3B 5A3. Email: yhc@unb.ca
grain of the outer layers (E22), and the in-plane shear
modulus (G12). The elastic properties of individual CLT
panels can be evaluated by static tests. From these static
test methods only one elastic constant can be evaluated at a
time, for some of them multiple tests are needed, which
makes static tests time-consuming and therefore costly.
Static test methods also have an inherent risk of causing
structural damage within the panel during testing.
Moreover for massive panels, it is difficult in terms of
practicality to test the full-size panels from production
lines, using static test methods. Modal testing methods
show potential to be adopted for non-destructive
evaluation of elastic properties of CLT. In modal testing,
the structure is exposed to a controlled excitation and the
natural frequencies are measured. The natural frequencies
and their order within a response spectrum are influenced
by the dimensions and the density of the structure as well
as the boundary conditions (BCs) and the elastic properties
of the structure. Therefore the elastic constants of a
structure can be evaluated if the structure’s dimensions,
density, the BCs and the response spectrum are known.
The dimensions and the BCs can be well controlled for a
test setup. The mass and therefore the density of a full-
scale panel can easily be evaluated without significant
costs or delay of the manufacturing process. In general it is
possible to determine the three main elastic constants (E11,
E22, and G12) of the structure.
While modal testing appears to be a more efficient test
method compared to static testing, especially for massive
elements, research is still required before the modal test
can be adopted widely. One technical challenge is the
choice of the BCs. As mentioned before, BCs affect the
natural frequencies and the response spectrum of a
structure in terms of damping. Also, some BCs offer close-
form solutions for the property evaluation while others
require the use of cumbersome iterative numerical
procedures. Furthermore, different BCs show different
levels of practicality. The objective of this study is to
compare modal testing methods with different BCs in
terms of accuracy of evaluated elastic properties (E11, E22,
and G12), calculation effort and to give a comparative
conclusion on the practicality of applying modal testing to
evaluate full-size CLT panels.
2 METHODS
2.1 SPECIMEN DESCRIPTION AND GENERAL
PROCEDURE
Single-layer panels were produced from conditioned
(moisture content 13%) laminates. The used material was
mainly spruce. Before the manufacturing of the single-
layer panels all laminates were tested in a modal testing
method with free-free BCs by [1, 2]. The laminates were
grouped based on their elastic properties, namely modulus
of elasticity (E) and shear modulus (G), and their growth
ring orientation (flat-sawn, quarter-sawn and about 45°).
Laminates within a group had similar elastic properties (E,
G) and growth ring orientation. The single-layer panels
were formed from these “homogenised” groups. All
laminates within a single-layer were sized to the same
aspect ratio (width to thickness). All single-layers had the
same constant thickness. Three different aspect ratios were
chosen 8:1, 5:1 and 2:1 at a constant thickness of 15.4mm.
The single-layer panels were formed by laminates glued
together over the whole length of the laminates using a
two-component structural polyurethane adhesive. The
order of laminates within a layer was random. To minimize
surface distortion and cupping, the laminates were edge-
glued together with alternating pith location. In case of
changes in the moisture content the alternating pith
location of adjacent laminates led to less surface distortion
and cupping of the single-layer panel and therefore better
dimensional stability. In order to maintain the achieved
moisture content during further processing stages, the
material was stored in a conditioning chamber with a
constant climate.
The three main elastic constants of the single-layer panel,
namely the modulus of elasticity parallel to the grain (E11),
the modulus of elasticity perpendicular to the grain (E22)
and the in-plane shear modulus (G12), have been evaluated
using different test methods. The results of the different
test methods were compared with each other.
The single-layers were face-glued to form 3-layer panels
after the single-layer panel tests were completed. The 3-
layer CLT panels were formed from layers within the same
group, namely the same aspect ratio, and growth ring
orientation. The CLT panels were also formed in a
symmetrical build-up where the outer layers were from
two halves of a full-size single-layer and the centre layer
was from a half of a different full-size panel. The same
glue that was used for the edge-gluing process was used
for the face-gluing. A glue spread rate of 250g/m2 per glue
line and a pressure of 1MPa was applied. Within the
recommended work time of 45 minutes four 3-layer CLT
panels were produced at the same time. The pressure was
maintained for the first 3 hours of the curing process. After
the pressure release the CLT panels were stored in the
conditioning chamber for at least another 12 hours before
further processing. The elastic constants, namely the
modulus of elasticity parallel to the grain of the outer
layers (E11), the modulus of elasticity perpendicular to the
grain of the outer layers (E22), and the in-plane shear
modulus (G12), of the CLT panels were evaluated using the
same test methods previously used for the single-layer
panels. The results of the different test methods are
compared and discussed below.
2.2 MODAL TESTING METHODS
The elastic properties of the single-layer panels and the
CLT panels were evaluated using modal testing methods
with different BCs. In modal testing, the frequency
response function (FRF) of each pair of impact and
response locations was calculated using data measured by
an accelerometer and an instrumented impact hammer.
Signals from these sensors were recorded by a spectrum
analyser with a built-in analysis software to calculate FRF.
The natural frequencies and the corresponding mode shape
information can be extracted manually from the various
FRF’s calculated from different locations on the surface of
a plate specimen. More details on modal testing can be
found in [3].
The modal testing method described in [4] was initially
developed for the determination of the orthotropic elastic
constants of plywood boards. The elastic modulus in face
grain direction (E11), the elastic modulus perpendicular to
the face grain direction (E22), and the in-plane shear
modulus (G12) are determined simultaneously by the
determination of three natural frequencies. In the method,
the plate-shaped specimen is vertically erected. The panel
is simply supported along the bottom edge while the other
edges have free BCs (FFFS). Simple support BC was
achieved by clamping the specimen edge with two steel
pipes. The test setup can be seen in Figure 1.
Figure 1: Test setup for modal tests in FFFS BCs
The elastic properties were calculated using the equations
given in [4] for the three selected natural frequencies. In
this study the natural frequencies f11, f12 and f31 were
selected. In theory, any 3 natural frequencies can be used.
However the sensitivity of calculated results is dependent
on values of the elastic properties and specimen geometry.
The natural frequencies used in the calculation were
selected based on a sensitivity study. A total of 55 single-
layer panels were tested with the FFFS BCs.
The method by [5] is based on free-free BCs (FFFF). The
approach has no closed form solution. FFFF BCs were
achieved by suspending the plate from a rigid structure
with springs in a vertical position. The natural frequencies
and the related mode shapes of the panels were
determined. The test setup for a single-layer panel can be
seen in Figure 2.
Figure 2: Test setup for modal tests in FFFF BCs
In this method the elastic constants E11, E22 and G12 are
determined in an iterative process using finite element (FE)
analysis. In the process, the three elastic constants were
adjusted successively until experimental and analytical
natural frequencies and related mode shapes (f1,1, f2,0, f0,2)
matched. A FE model of the test setup used was
developed. The panel was modelled as a shell element, the
FFFF BCs were achieved by two supports at the locations
of the springs. The supports allow movement in direction 2
(minor axis) and 3 (out-of-plane) but restrain the in-plane
movement in direction 1. The FE model for a single-layer
panel can be seen in Figure 3.
Figure 3: Finite element model for test setup in FFFF BCs
In the iterative process within the FE analysis the material
properties E11, E22, G12 and G13 were adjusted until the
experimental and analytical natural frequencies and related
mode shapes matched. The material properties G12 and G13,
and ν12 and ν13 were assumed to be equal. For the density
of the panel the values determined during the laboratory
tests were used for the corresponding panel. For the
material properties E33, G23, ν12, ν13, and ν23 constant values
for all panels were chosen. A sensitivity study has shown
that these values, as well as G13 show only minor influence
on the natural frequencies. Table 1 shows the selected
values for the material properties E33, G23, ν12, ν13, and ν23.
Table 1: Material properties used for iterative FE process
E33
[MPa]
G23
[MPa]
ν12
ν13
500
50
0.48
0.48
In this series of tests using methods proposed in [4] and
[5], a total of 55 single-layer panels and nine 3-layer CLT
panels have been tested with the FFFF BCs.
A second series of modal tests was conducted to
investigate additional BCs using a subset of 10 panels. In
2
1
3
2
1
1
2
3
this series modal tests with BCs of two simply supported
opposite edges and the other edges free were undertaken.
Tests were performed for the two directions separately,
with the span parallel to the grain of the single-layer of the
outer layer of the CLT panel (SFSF), and with the span
perpendicular to the grain of the single-layer or other layer
of the CLT panel (FSFS). In both cases the panels were
supported on round steel pipes. The panels were clamped
on to the supports by additional pipes to assure a constant
contact of the supports and the panels during the tests. The
span was 595mm in the SFSF test setup and 578 mm in the
FSFS test setup, respectively. Based on [6], natural
frequencies and mode shapes were determined and the
elastic constants E11 and E22 were evaluated from the two
test setups using only the fundamental natural frequencies.
G12 could not be determined from this approach. The test
setup of a SFSF test and a detail of the clamping situation
at the supports can be seen in Figure 4. The same ten
panels were evaluated further using modal tests with BCs
of all four edges simply supported (SSSS). For the SSSS
BCs a closed form solution exists. For these BCs the three
elastic constants, E11, E22 and G12, can be calculated
directly from three experimentally determined natural
frequencies as stated in [6, 7]. A total of ten single-layer
panels were tested using these BCs.
A third series of tests was then conducted. In this series
simultaneous measurement of E11, E22 and G12 based on the
Rayleigh solution of SFSF was also conducted by using
three sensitive natural frequencies identified from modal
testing. The frequency equations were adopted from the
approximate expressions proposed by [8]. The elastic
constants were obtained by minimizing the differences
between measured and calculated frequencies to less than
1.0 % by an iteration algorithm. The same ten single-layer
panels and nine 3-layer CLT panels were tested with this
method.
The single-layer panels were tested using the modal testing
methods by [4-8]. For the modal test using methods [4, 5],
the single-layer panels had a length of 1220mm, a width of
588mm and a thickness of 15.4mm. After the completion
of these tests each panel was cut in two halves for process
reasons. They were then tested using methods [6-7].
Nine 3-layer CLT panels were fabricated from the square
single-layer panels. These 3-layer CLT panels were tested
using the modal test method by [5]. The 3-layer CLT
panels had a length and a width of 570mm and a thickness
of 46mm. The 3-layer CLT was modelled as a solid cross-
section in the FE analysis. The elastic constants of E11, E22,
G12, and G13 were adjusted in an iterative process until
natural frequencies and related mode shapes (f1,1, f2,0, f0,2)
from laboratory tests and FE analysis matched.
Figure 4: Test setup and clamping detail for SFSF test
2.3 STATIC TESTING METHODS
Static tests were performed to evaluate the elastic constants
E11, E22 and G12 of the single-layer panels and E11 and E22
of the 3-layer CLT panels. The elastic constants E11 and
E22 were evaluated by single-span three-point bending tests
based on [9]. In both test setups the specimens were
supported over the full width by supports that allowed free
rotation. The load was applied at mid-span and distributed
over the full width of the specimen by a squared hollow
aluminium section. The deflection was measured by two
linear variable differential transformers (LVDTs), located
at the centre of the span and 100mm in from the edges.
The two measurements from the LVDTs were averaged for
the calculation of the E values. The E11 values were
measured using a span of 1100mm and a displacement rate
of 8mm/min. After the completion of these tests each
single-layer panel was cut into two halves to perform the
E22 value evaluation. The tests were performed using a
span of 500mm and a displacement rate of 0.75mm/min.
Figure 5 shows the test setup for the evaluation of the E11
values of a single-layer panel.
Figure 5: Bending test setup for E11 value evaluation
2
1
The test procedure for the evaluation of the in-plane shear
modulus G12 was based on [10]. In the test setup the square
panel was supported on two diagonally opposite corners by
ball bearings and were loaded on the other two diagonally
opposite corners. The span of the supports was 800mm and
the distance between the loading points was 800mm. The
tests were performed at a displacement rate of 3mm/min.
According to [10] the deflection of the quarter points of the
diagonals between support or load points shall be
measured with respect to the centre point. Therefore the
deflections at the centre of the panel and at the quarter
points of the diagonal between support or load points were
measured by two LVDTs. After a test, the LVDT at a
quarter point was moved to another quarter point and the
test was repeated until the deflection of all four quarter
points have been measured. The relative deflection of the
quarter points to the centre of the panel was determined.
The deflections of the quarter points were averaged and
used for the determination of the G12 values. The test setup
for the twisting test can be seen in Figure 6. The elastic
properties evaluated in static tests were used as reference
values in the comparison of those measured using modal
test methods under different BCs.
Figure 6: Twisting test setup for G12 value evaluation
The single-layer plate specimens were tested to
determinate their elastic parameters using static tests based
on [9, 10]. A total of 55 single-layer panels were tested in
static bending. Static twisting tests in accordance to [10]
were performed on 18 single-layers to evaluate the in-
plane shear modulus G12.
The 3-layer CLT panels were tested using three-point
bending tests in accordance to [9]. The specimen size for
the modal tests was 570mm (length and width) and 46mm
thick. The tests were performed at a span of 500mm and a
displacement rate of 0.5mm/min. A total of nine 3-layer
CLT panels were tested in static bending. At the time of
writing this paper no static twisting tests in accordance to
[10] have been performed. Therefore no values for the in-
plane shear modulus G12 of the 3-layer CLT panels are
included in this paper.
3 RESULTS AND DISCUSSION
Single-layer plate modal tests with different BCs, FFFS,
FFFF, SFSF, FSFS and SSSS, have been conducted and
the elastic properties evaluated. E11 and E22 of the single-
layer panels have been evaluated in static tests as well as
G12 of some of the single-layer panels. The 3-layer CLT
panels have been tested with two BCs of FFFF and SFSF.
The E11 and E22 values of the CLT panels have been
evaluated using static bending tests. The modal test
methods and its corresponding boundary conditions are
listed in Table 2.
Table 2: Modal test methods and corresponding
information
Modal
test
methods
Boundary
conditions
Elastic constants
calculation method
Note
1
FFFS
Closed-form
frequency equation
[4]
2
FFFF
FE modelling and
iteration [5]
3
SFSF
Self-developed
algorithm based on
Rayleigh frequency
solution [8]
4
SFSF&FSFS
&SSSS
Three fundamental
frequency equations
[6]
Three
single
tests
3.1 SINGLE-LAYER PANEL RESULTS
E11, E22 and G12 of the single-layer panel were evaluated
using modal tests with different BCs (E11,modal, E22,modal,
G12,modal). The values are compared with the corresponding
E11, E22 and G12 values measured from static tests (E11,static,
E22,static, G12,static). Figure 7 shows a comparison of the
results measured from static and modal tests. The black
lines are the 45 degree lines. Table 3 gives an overview of
the maximum, average, and minimum deviation of the
modal test values from the static values in percent.
Figure 7 a) shows that E11 results from modal tests with
both modal test method 1 and 2 (FFFS and FFFF) are in
good agreement in general, with the latter giving slightly
higher values than the former. It can be seen that the
results from modal test method 2 are close to the static test
results but the modal test method 1 results are slightly
lower than static results. As it can be seen in Table 3 the
E11 values determined using modal test method 1 lie within
a range of -14.1% to +4.5%, the average being -5.7% of
the static test values. The average difference of E11 values
from modal test method 2 is about -0.3%. Only a few
samples show a significantly higher difference. The values
lie within a range of -3.0% and +8.0% of the static values.
E22 values in Figure 7 b) show a much larger deviation
than the E11 results. In both BCs the modal tests generally
lead to an overestimation of E22, but the modal test method
2 results are closer to the static results than the modal test
method 1 results. Table 3 shows that the E22 values from
the modal test method 1 are within the range of -47.1% and
+114.9% of the static values with an average difference of
about +22.4%. The average difference between the modal
E22 values from modal test method 2 and static E22 is about
+11.9%, with a range of -35.2% and +54.5%.
From the G12 value graph (Figure 7 c)) and from Table 3 it
can be seen that values determined by modal test method 1
show over- and underestimations within a range of -14.4%
to +10.9% in this test setup. The modal test method 1
values have an average deviation of about +0.6. The results
from modal test method 2 compared to the results from
static tests are all underestimated within a range of -20.1%
and -0.6%. The average is about -10.9%.
Figure 7: Comparison of single-lay panel properties
measured using static tests and modal test method 1 and 2
Table 3: Average and extreme values of single-layer panel
property deviation results shown in Figure 7
Property
BCs
Max
Average
Min
[%]
[%]
[%]
E11
FFFS
4.4
-5.7
-14.1
FFFF
8.0
-0.3
-3.0
E22
FFFS
114.9
22.4
-47.1
FFFF
54.5
11.9
-35.2
G12
FFFS
10.9
0.6
-14.4
FFFF
-0.6
-10.9
-20.1
In modal test method 3 (SFSF) and 4 (evaluation based on
a combination of SFSF&FSFS&SSSS) a total of ten
single-layer specimens were tested. These ten specimens
were part of the 55 samples tested in modal test method 1
and 2. For comparison reasons the results from modal test
method 1 and 2 of these ten single-layer panels are here
presented again. Figure 8 shows the difference of E11,modal
and E22,modal values of these ten single-layer panels
compared to the corresponding results from static tests. For
two of these ten panels comparable data for the G12 value
exist. The black markers indicate the E11,static, E22,static and
G12,static values, respectively of the corresponding panel.
Table 4 gives the maximum, average and minimum values
from the modal tests undertaken with modal test method 1-
4. The table shows the relative values for the evaluated E11,
E22 and G12 in percent in comparison with the
corresponding static values. Since only two of the
specimens that were used in this paper were tested in static
twisting tests in accordance to [10] only two data sets are
available for comparison. Therefore the maximum and
minimum G12 values of the data for the different BCs
presented in Table 4 are equal to the results from the test
specimens.
The E11 results (Figure 8 a) and Table 4) show that modal
test method 1 based values are underestimated in general.
Here the average is -8.0%, the values lie within a range of -
9.4% and -4.1%. Modal test method 2 based values show
much better correlation with an average difference of
+1.0%. The results are within the range -1.6% and +8.0%.
Values based on modal test method 3 lie within a range of
-13.1% and +5.1% with an average of -3.5%. The values
determined by modal test method 4 show an
overestimation in all tests within the range of +6.5% -
+26.0%, and an average of +13.7%.
The E22 results (Figure 8 b) and Table 4) show that modal
test method 1 based values are overestimated in general.
The range of results is -24.1% and +125.1%. The average
is +40.0%. Modal test method 2 based values show only
overestimated values within +1.4% and +33.0%, with an
average difference of +18.6%. Values based on modal test
method 3 are within -23.0% and +18.2% and have an
average of -3.7%. The values determined by modal test
6
8
10
12
14
16
6 8 10 12 14 16
x103 E11,modal [MPa]
x103 E11,static [MPa]
a) Comparison of E11,modal to E11,static
FFFS
FFFF
100
150
200
250
300
350
400
450
500
100 200 300 400 500
E22,modal [MPa]
E22,static [MPa]
b) Comparison of E22,modal to E22,static
FFFS
FFFF
600
650
700
750
800
850
900
950
1000
600 650 700 750 800 850 900 950 1000
G12,modal [MPa]
G12,static [MPa]
c) Comparison of G12,modal to G12,static
FFFS
FFFF
method 4 show an overestimation in all tests within a range
of +50.4% - +96.3%, and an average of +71.7%.
The G12 results (Figure 8 c) and Table 4) only contain
values from two specimens, nevertheless the graph
suggests certain trends. Modal test method 1 based values
are overestimated, and the two values are quite close to
each other (+9.8% and +10.9%). The modal test method 2
based values are slightly underestimated (-4.4% and -
3.4%). Values based on modal test method 3 are
overestimated (+5.2% and +11.3%). The values
determined by modal test method 4 show an
underestimation for both panels (-30.6% and -16.2%). The
results from this approach show the highest difference
from the static measurements.
Figure 8: Deviation of modal test results for single-layer
panels using modal test method 1-4 and static test results
Table 4: Average and extreme values of single-layer panel
property deviation results shown in Figure 8
Property
BCs
Max
Averag
e
Min
[%]
[%]
[%]
E11
FFFS
-4.1
-8.0
-9.4
FFFF
8.0
1.0
-1.6
SFSF
5.1
-3.5
-13.1
SFSF &
FSFS
& SSSS
26.0
13.7
6.5
E22
FFFS
125.1
40.0
-24.1
FFFF
33.0
18.6
1.4
SFSF
18.2
-3.7
-23.0
SFSF &
FSFS
& SSSS
96.2
71.7
50.4
G12
FFFS
10.9
10.3
9.8
FFFF
-3.4
-3.9
-4.3
SFSF
11.3
8.2
5.2
SFSF &
FSFS
& SSSS
-16.2
-23.4
-30.6
3.2 3-LAYER CLT PANEL RESULTS
E11 and E22 of the 3-layer CLT panels were evaluated from
modal tests with different BCs (E11,modal, E22,modal). The
values were compared with the corresponding E11 and E22
values evaluated from static tests (E11,static, E22,static).
Figure 9 shows the difference of E11,modal and E22,modal
values of nine 3-layer CLT panels relative to E11,static and
E22,static. At the time preparing this paper, no G12 values of
any 3-layer CLT panel were evaluated in static testing,
therefore no G12 value comparison is presented. The E11
and E22 values were measured using modal test method 2
and 3. The results from the SFSF tests were evaluated with
a Rayleigh solution. The black markers indicate the E11,static
and E22,static values, respectively of the corresponding CLT
panel. Table 5 gives the maximum, average and minimum
values from the modal tests method 2 and 3. The table
shows the values for the evaluated E11, E22 and G12 values
relative to the static results in percent.
It is interesting to note that while the E11 values from
modal test method 3 are in better agreement with static
values than modal test method 2, the opposite is true for
the E22 results. In the graph showing E11 data (Figure 9 a))
and from Table 5, it can be seen that the modal test results
from the modal test method 2 show a difference of
between +37.0% and +49.5% compared with the static test
results, with an average of about +43.0%. The results from
the modal test method 3 show a difference between -10.0%
and -20.9%, with an average deviation of -16.8%.
0
2
4
6
8
10
12
-20
-15
-10
-5
0
5
10
15
20
25
30
x103 E11,static [MPa]
Difference [%]
a) Difference of E11, modal to E11,static
FFFS FFFF SFSF SFSF & FSFS & SSSS
0
50
100
150
200
250
300
350
-40
-20
0
20
40
60
80
100
120
140
E22,static [MPa]
Differene [%]
b) Difference of E22, modal to E22,static
SFFF FFFF SFSF SFSF & FSFS & SSSS
900
905
910
915
920
925
930
935
940
945
950
-40
-30
-20
-10
0
10
20
G12,static [MPa]
Difference [%]
c) Difference of G12, modal to G12,static
FFFS FFFF SFSF SFSF & FSFS & SSSS
For the E22 results (Figure 9 b) and Table 5), it can be seen
that the results from the modal test method 2 show a
difference of between +15.6% and +34.0% from the static
test results, with an average of +27.1%. The results from
the modal test method 3 show a difference between -28.3%
and -50.1%, and an average deviation of -36.3%.
The large difference between the modal and static test
results can be explained by the short span in the static tests
and the large influence of shear deformation in three-point
bending tests with a low span-to-thickness ratio (L/h). The
L/h ratio during the static tests was about 10. For CLT
panels with L/h ratios of around 10 a shear deformation of
about 50% can be expected. The influence of shear
deformation has to be evaluated. When accounting for the
shear deformation in the bending test, the actual difference
between modal and static tests should be considerably less
than those shown in Figure 9 and Table 5. Further static
tests with proper accounting of shear deformation have
been planned to clarify this issue.
Figure 9: Deviation of modal test results for CLT panels
using modal test method 2 and 3 and static test results
Table 5: Average and extreme values of single-layer panel
property deviation results shown in Figure 9
Property
BCs
Max
Averag
e
Min
[%]
[%]
[%]
E11
FFFF
49.5
43.0
37.0
SFSF
-10.0
-16.8
-20.9
E22
FFFF
34.0
27.1
15.6
SFSF
-28.3
-36.3
-50.1
3.3 INFLUENCE OF BCs ON PROPERTY
EVALUATION OF MASSIVE PANELS
Here an overview of the feasibility and the calculation
efforts in measuring elastic properties of mass timber
panels is presented. Modal test method 1 seems to be
feasible for larger panels and do not demand a large area as
the test panel is oriented vertically. However, there are
concerns related the need to develop a stabilisation setup
for the vertically erected panel that will ensure safety
during operation while having minimal influence on the
measured natural frequencies. The three natural
frequencies can be determined in a single test if the range
of the desired frequencies is known. The evaluation is
based on simple equations, so the calculation effort is
small.
Modal test method 2 seems also feasible for larger panels
and do not demand a large area. A crane-like setup that
provides vertical support and allows mounting and
dismounting of the panel, as well as panel fixtures for the
suspension are needed. The three necessary natural
frequencies can be determined in a single test if the range
of the desired frequencies is known. The evaluation is
based on a tedious iterative method, but the development
of an algorithm could reduce calculation efforts.
Modal test method 3 works well for thin plate based on the
Rayleigh frequency solution. This method is feasible for
panel products of both small and large dimensions such as
full size CLT panels. It has great potential for online
testing in the production line. With a well-developed
algorithm, the sensitive frequencies can be easily identified
from a few frequency spectra up to three. However, for
thick panel products, the algorithm should be modified
based on thick plate theory considering the effects of shear
deformation and rotatory inertia.
Modal test method 4 necessitates three separate tests and
setups, which is feasible for small and thin panels. Only
three fundamental natural frequencies are needed for
simple calculation. Also there is no need to draw mode
shapes and identify frequencies. However, the accuracy of
this method is not as good as the other BCs, especially for
E22 and G12. Therefore, this method is only recommended
for getting approximate values of a panel.
0
1
2
3
4
5
6
7
8
-30
-20
-10
0
10
20
30
40
50
60
x103 E11,static [MPa]
Difference [%]
a) Difference of E11, modal to E11,static
FFFF SFSF Rayleigh
0
100
200
300
400
500
600
700
800
900
-60
-40
-20
0
20
40
E22,static [MPa]
Difference [%]
b) Difference of E22, modal to E22,static
FFFF SFSF Rayleigh
4 CONCLUSIONS
Modal test method 1 was only used for the evaluation of
E11, E22 and G12 values of single-layer plates. In general
these BCs lead to an underestimation of E11 values, but
overestimations can occur. The results lie within a
reasonable range. The results of the E22 evaluation show a
wide range of over- and underestimations. The G12 results
show over- and underestimations within a similar range to
the one for E11. Modal test method 1 appears to be useful
as a rough estimation of E11 and G12 values. With the
selected arrangement, an E22 value evaluation with modal
test method 1 is not recommended. An evaluation using
different natural frequencies might help to increase the
precision of the E22 evaluation. The test setup seems
feasible for bigger panels. The required three natural
frequencies can be determined simultaneously if their
range is known. The calculation procedure is based on use
of simple equations.
Modal test method 2 was used for the evaluation of E11, E22
and G12 values of the single-layer panels and for the 3-
layer CLT panels. In general these BCs lead to an
underestimation of E11 values, but overestimations can
occur. The results are within a fairly close range. The
results of the E22 evaluation show a wide range and tend to
be overestimated. In general the G12 value related results
show underestimations of up to -20%. Modal test method 2
appears to be useful for the evaluation of E11 values and
rough estimation of G12 values. The range for E22 values is
closer than for modal test method 1, but still fairly wide.
An evaluation using different natural frequencies might
help to increase the precision of the E22 and G12 evaluation.
The test setup seems feasible for bigger panels. The
required three natural frequencies can be determined
simultaneously if their range is known. The evaluation is
based on a tedious iterative method, but an algorithm could
lead to a lower calculation efforts.
Modal test method 3 was used for the evaluation of E11, E22
and G12 values of the single-layer panels as well as for the
small size 3-layer CLT. With the algorithm developed by
the authors, the accuracy for single-layer panels is fairly
good. But for small size CLT in this study, due to its
width/ thickness ratio, the accuracy is not as good as modal
test method 2. In the authors’ other tests not reported
herein, this method worked well for full size CLT panels.
More attentions will be paid to small size CLT panels
which should be considered as thick plates.
Modal test method 4 was used for the evaluation of E11, E22
and G12 values of single-layer plates. In general, it leads to
overestimations of all three values to different extent. The
method is only feasible for approximate evaluation of
elastic constants.
5 FURTHER RESEARCH
Further modal and static tests on 3- and 5-layer
CLT panels will be undertaken in order to
evaluate the applicability of different BCs for the
evaluation of the elastic properties of CLT panels.
Further bending tests are needed to obtain the true
E11 values of the CLT panels and to determine the
influence of shear deformation on the obtained
results.
Static tests for the evaluation of G12 values will be
undertaken in order to compare the applicability
of the different BCs.
Modal test method 3 shows great potential for
online testing, especially for massive time panel
products. Future research will focus on accuracy
improvement and frequency identification. Thick
plate theory will be adapted for thick panel
products to improve its feasibility and to measure
transvers shear modulus as well.
ACKNOWLEDGEMENTS
This research was supported through funding by Natural
Sciences and Engineering Research Council of Canada
(NSERC) to the Strategic Network on Innovative Wood
Products and Building Systems. The authors would like to
thank Dr. Lin Hu, FPInnovations for her technical
guidance.
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