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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

ν23

500

50

0.48

0.48

0.455

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.

REFERENCES

[1] Chui Y. H., Smith I.: Influence of Rotatory Inertia,

Shear Deformation and Support Condition on Natural

Frequencies of Wooden Beams. Wood and Fibre

Science: Journal of the Society of Wood Science and

Technology. 24:233-245, 1990

[2] Chui Y. H.: Simultaneous Evaluation of Bending and

Shear Moduli of Wood and the Influence of Knots on

these Parameters. Wood and Fibre Science: Journal of

the Society of Wood Science and Technology. 25:125-

134, 1991

[3] Ewins, D. J.: Modal testing: Theory, practice, and

application. Baldock, Hertfordshire, England:

Research Studies Press. 2000

[4] Sobue N., Katoh A.: Simultaneous Determination of

Orthotropic Elastic Constants of Standard Full-Size

Plywoods by Vibration Method. Japan Wood Research

Society, 1992. Internet resource.

[5] Larsson, D.: Using Modal Analysis for Estimation of

Anisotropic Material Constants. Journal of

Engineering Mechanics. 123:222-229, 1997

[6] Leissa. A. W.: Vibration of plates. U.S. National

Aeronautics and Space Administration Washington,

D.C., 1969.

[7] Hearmon, R. F. S.: The Fundamental Frequency of

Vibration of Rectangular Wood and Plywood Plates.

Proceedings of the Physical Society. 58(1):78, 1946.

[8] Kim, C. S., Dickinson, S. M.: Improved approximate

expressions for the natural frequencies of isotropic and

orthotropic rectangular plates. Journal of Sound and

Vibration, 103(1):142-149, 1985

[9] ASTM: Standard Test Methods of Static Tests of

Lumber in Structural Sizes. Designation D198. West

Conshohocken, Pa: ASTM International, 2010

[10] ASTM: Standard Test Method for Shear Modulus of

Wood-Based Structural Panels. Designation D3044.

West Conshohocken, Pa: ASTM International, 2006