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DYNAMICAL PROPERTIES OF A LARGE GLULAM TRUSS FOR A
TALL TIMBER BUILDING
Pierre Landel1,
1
Andreas Linderholt2, Marie Johansson3
ABSTRACT: When designing a tall timber building, the accelerations due to wind loads are in many cases decisive. The
parameters governing the dynamic behaviour of the building are the structure’s stiffness, damping and mass together with
the loads. The first two parameters are not well-known during the serviceability limit state of timber structures generally
and of timber connections specifically.
In this study, dynamical properties of a large glulam truss, a part of the vertical and horizontal structural system in a
residential six-storey timber building, are estimated from measurements made in the manufacturing plant. The timber
members of the truss are joined with slotted-in steel plates and dowels. Forced vibrational test data are used to extract the
dynamical properties. Finite element (FE) models, supported by the experimental results, were developed and simulations,
to study the influence of the connection stiffnesses on the total behaviour, were performed. The vibration test results of
measurements made on separate structural parts give valuable input to model timber structures and better possibilities to
simulate the dynamic behaviour of tall timber buildings as well as the load distribution in wooden structures in the
serviceability limit state.
KEYWORDS: Vibrational testing, experimental modal analysis, stiffness and damping, timber joints, slotted-in steel
plates with dowels connection
1 INTRODUCTION
Tall Timber Buildings (TTBs) are becoming increasingly
common around the world and their designs generate new
challenges for structural engineers. The horizontal top
floor acceleration due to the dynamic and varying action
of wind is one of the major issue when designing tall
buildings [1-2] and the low density and high flexibility of
wood material actualize the challenge of this issue for
timber buildings at lower heights than for steel and
concrete buildings [3-8]. Depending on the geometry,
stiffness, mass and damping of the building, the
inhabitants might feel uncomfortable or even unsafe at
high levels of wind-induced vibrations. Several tall timber
buildings have been monitored in research projects during
the last decade. The relationship between expected and
measured properties such as natural frequencies, mode
shapes and damping, is not clear but some interesting
features are noticeable [4-7]. Non-structural material
contributes positively to the overall stiffness [9] and
damping [4]. Furthermore, damping depends on the
vibration amplitudes [4]. In principle, TTBs can be
constructed with two systems to handle horizontal loads
and mitigate along-wind accelerations: either using planar
elements such as shear walls (for example CLT or LVL
plates) or using trusses in glulam.
1 Pierre Landel, RISE and Linnaeus University, Sweden, pierre.landel@ri.se
2 Andreas Linderholt, Linnaeus University, Sweden, andreas.linderholt@lnu.se
3 Marie Johansson, RISE, Sweden, marie.johansson@ri.se
Figure 1: 3D-view of the timber structure for the 6-storey
building, with the studied Truss B in blue.
Truss B
In both cases, the stiffness and damping of the
connections are important for the motion of the complete
building. But today, the stiffness properties of timber
joints are not considered when designing a timber
structure. So far, for big timber structures there has not
been any need to consider dynamical issues to fulfil
comfort criteria for people. Nowadays, as the height of
wooden buildings rises, structural designing procedures
might need new input. Large glulam trusses, which must
resist variable loadings, are usually modelled with pin-
joints (free rotation) and sometimes with constrained
joints (no rotation admissible) [10]. Malo et al. argued that
whereas rotational stiffness can be ignored during the
design of slotted-in steel plates with dowel connections
for large glulam frames, axial stiffness must be considered
[3]. Connection models for glulam trusses might have a
major impact on the serviceability limit state design,
specifically on the accelerations due to wind-induced
vibrations. Moreover, connection models taking
stiffnesses into consideration might have an indirect
influence on the load distribution in the structure and
therefore on the ultimate limit state design as well.
In this study, the aim is to evaluate the impact from the
connections on the eigenfrequencies and mode shapes of
a timber structure. To this purpose, forced vibration tests
on a large glulam truss have been performed in
collaboration with Moelven Töreboda AB who has been
developing a system for multi-storey buildings during the
last decade. Their “Trä8-system” offers possibilities to
build high with wood and with spans up to 8 meters and
the investigated large glulam truss is a structural
component from an actual building project, an eight-
storey multi-family house situated in Skövde, Sweden.
The two first storeys of the building have a structure of
prefabricated concrete elements and the six storeys above
are made of a glulam post-and-beam structure with
prefabricated LVL-glulam rib-floor elements. The lateral
bracing system is a hybrid structure composed of one
concrete stair-and-elevator-shaft centrally placed in the
building and collaborating with three cantilever glulam
trusses. The six-storey high trusses (18.5 m) are clamped
to the concrete at the 2nd floor and have overall widths up
to 5.0 m. One of them, truss B, have been used for this
study and participate to the stabilization of the building
against wind loads and to carry some of the gravitational
loads. Figure 1 illustrates the building and its structure.
The next section describes the characteristics and the
properties of this truss. Section 3 presents the different
FE- analyses which were developed to model the truss.
Section 4 describes the procedure of FVT performed at
the plant and shows the results. Before the conclusion,
section 6 suggests discussion points based on the
comparison of the experimental and numerical results
presented in section 5.
Figure 2: Section and elevation of the glulam truss B
with dimensions in mm, element IDs and placements of
accelerometers (orange ).
18 465
pc 80
b107-6
pc52 + pc53 + pc81
b107-5
b107-1
b107-3
b107-2
b107-4
4 321
Y
Z
X
2 THE LARGE GLULAM TRUSS
INVESTIGATED
The truss B is made of glulam of quality GL30c according
to [11]. Figure 2 presents a section and an elevation with
overall dimensions and the identification numbers (IDs)
of the glulam members.
The short elements, diagonals and beams, have
rectangular cross-sections of 215 x 360 mm. The right
column, pc80, has a rectangular cross-section of 215 x 540
mm. The left column is composed of a similar cross-
section glued with 90 x 215 members on each side to form
a T-shaped cross-section. The glulam members are
connected with 8 mm thick slotted-in steel plates, two
plates at each joint, and numerous of ø 12 mm smooth
dowels and some ø 12 mm threaded dowels with washers
and nuts, see Figure 3. Both steel plates and the dowels
are made of S355JO steel quality.
Figure 3: Detail drawings of two different connection types
with slotted in steel plates and dowels.
After CNC cutting, each glulam element as well as the
steel elements were weighted, geometrical dimensions as
the length and the cross-sectional dimensions of the
members were measured. The density were calculated
and the moisture content of the members were recorded.
Moreover, impact testing with an impulse hammer and a
single-axial accelerometer, was performed on some
rectangular beams (b107-1, b107-2, b107-3, b107-4 and
b107-5) and on the column pc80. The moduli of elasticity
were estimated from the test data. The short-sledge
impulse hammer (model 086D20 from PCB Piezotronics)
has a sensitivity of 0.23 mV/N (+/- 15%) and the ceramic
shear accelerometer (model T333B30 from PCB
Piezotronics) has a sensitivity of 100 mV/g (+/- 10%). The
glulam members hanged at their gravity centre from an
overhead crane. The impulse and the axial acceleration
were measured at one end of the structural element. The
acquired data were analysed with the software Signal Calc
ACE to estimate the natural axial frequencies . The
ambient climate conditions were 20.6 ºC and 45 %
relative humidity the first day and 19.9 ºC and 42 %
relative humidity the second day.
To calculate the modulus of elasticity from the first
natural frequencies, the assumption of Euler-Bernouilli
beams was adopted. From the equation of motion and the
boundary conditions of a free-free beam, the undamped
circular natural frequency for the th axial mode at
frequency is derived, see Equation (1).
=
(1)
Thus, the modulus of elasticity corresponding to the th
axial mode is:
=
(2)
The moduli of elasticity of the un-tested members were
directly correlated to the density, with pc80 taken as the
reference. From the experimental modal analysis (EMA),
the data for element b107-1 and b107-5 showed only one
axial natural frequency within the frequency range tested.
Table 1: Measured properties of the glulam members (values in italic are correlated to pc80).
Glulam
id
Cross-section
Area (mm
2
)
Length
(mm)
Density
(kg/m3)
MC
(%)
f
1x
(Hz)
f
2x
(Hz)
f
3x
(Hz)
f
4x
(Hz)
f
5x
(Hz)
E
m
(MPa)
b102
76 826
4 110
435.6
14.6
-
-
-
-
-
11 210
b103
76 826
4 222
414.9
12.6
-
-
-
-
-
10 677
b104
76 826
4 223
421.7
15.2
-
-
-
-
-
10 851
b105
76 826
4 223
452.4
13.8
-
-
-
-
-
11 640
b106
76 826
4 223
433.0
12.7
-
-
-
-
-
11 141
b107-1
76 826
3 226
427.8
15.6
820.4
-
-
-
-
11 006
b107-2
76 826
3 227
413.6
13.3
794.0
1592.5
-
-
-
10 693
b107-3
76 826
3 226
414.8
13.2
805.8
1589.3
-
-
-
10 859
b107-4
76 826
3 227
432.9
15.2
797.5
1579.5
-
-
-
11 153
b107-5
76 826
3 226
433.0
14.4
830.0
-
-
-
-
11 141
b107-6
76 826
3 226
426.5
14.8
-
-
-
-
-
10 974
b108
76 826
4 246
402.2
12.5
-
-
-
-
-
10 349
pc52
18 939
18 242
430.0
14.8
-
-
-
-
-
11 064
pc53
18 939
18 242
430.5
14.5
-
-
-
-
-
11 077
pc80
115 453
18 248
434.8
14.8
138.8
276.3
424.1
557.2
692.0
11 188
pc81
114 970
18 245
424.9
14.4
-
-
-
-
-
10 933
Mean value
426.8
14.1
10 997
Their moduli of elasticity were also estimated
proportional to the density. The properties stemming from
the measurements of the glulam members are summarized
in Table 1. It should be noticed that the different CNC-
cutting, the 10 mm slots and the holes for the dowels, are
not considered in the calculation of the modulus of
elasticity according to Equation (2).
The glulam members were assembled together with the
slotted steel plates and the dowels at the manufacturing
plant. The overall weight of the glulam truss including the
steel elements is 4 284 kg.
3 THE FE MODELS DEVELOPED
MSC Nastran, an FE solver, and SimXpert, a pre- and
postprocessing software, were used to model and analyse
the Truss B with one-dimensional FE elements. Three
different models were developed to study the impact of
the connection on the dynamical properties of the glulam
truss. The properties of the beam elements for all three
models were settled according to the previous section and
the principles of the connection models are presented in
Figure 4. An isotropic material model was selected for the
glulam beams. A Poisson’s ratio of 9, to keep a similar
relationship between the shear modulus and the modulus
of elasticity for GL30c glulam, according to [11], was
chosen.
Firstly, the model A1 with constrained connections was
established with beam elements for the glulam members
and massless rigid elements to link the beams at the joints.
Secondly, the beam model A2 was developed with pin-
joints at the connecting nodes. Instead of rigid massless
elements, massless beam elements were used with one
pin-end node to allow rotation around the X-axis.
Finally, the beam model A3 was developed with spring
joints placed at each centre of dowel groups. For this
purpose, CBUSH elements from Nastran were used, see
[13]. Such elements link two different coincident nodes
with different translational and rotational spring
properties in the X-, Y- and Z-directions.
nodes beam element (CBAR) rigid element (RBAR)
weightless beam element with a pin-end (CBAR) spring connection (CBUSH)
Figure 4: Principle for the connection models: top left clamped-joint (model A1), top right pin-joint (model A2) and bottom left and
right spring joint (model A3), inspired from [12].
Z
Y
X
The spring values , were calculated according to
the equation for slip modulus for dowels from the Table
7.1 of the Eurocode 5 [14]. This value is valid per shear
plane between two wood members with density based
on the measured density and a dowel diameter d in mm.
, =
(3)
Considering that for a steel to timber connection
, is multiplied by two. Then the translational
stiffness of the studied connection with dowels
and two plates is:
= 8 ,
(4)
The rotational stiffness , of the studied connection
with dowels situated at a distance from the
geometrical centre of the group of dowels is:
, =8 ,,
(5)
The translational spring acts in the Y- and Z-directions
and the rotational spring acts around the X-axis.
For example, the connections between pc80 and b107-4,
see also the bottom right sketch in Figure 4, were
modelled with the following stiffness values:
a) for the group of dowels at the end of the beam b107-4,
= 375.9 kN/mm and , = 2 480 kNm/rad,
b) for the group of dowels in the column pc80, =
378.4 kN/mm and , = 5 449 kNm/rad.
The steel elements contribute, in these models, only with
their masses and they were modelled as concentrated mass
elements placed at the connection nodes, with some
eccentricity. For the boundary conditions, the elasticity of
the lifting straps used during the test were modelled with
two spring elements each with an axial stiffness of 8 372
N/mm to match the natural frequency of the global
bouncing mode in the Y-direction between the
experimental results and the model A3. Table 2
summarizes the type and the number of elements used in
each model.
Table 2: Number of elements used in each model.
Type of elements
Model
A1
Model
A2
Model
A3
CBAR (beam)
224
248
224
CONM2 (concentrated
mass)
14
14
14
CELAS1 (spring)
2
2
2
RBAR (rigid bar)
24
2
32
CBUSH (spring
connection)
-
-
37
Dynamic analyses were performed for the three
undamped models to determine the natural frequencies
and the associated mode shapes up to 125 Hz. The results
characterize the basic dynamic behavior of the truss and
give indications on how it will respond to dynamic
loadings like an impulse from an impact hammer or wind.
The truss is according to the design assumed to be acting
as a 2D-structure with motion only in the YZ-plane. Only
the eigenmodes of interest, i.e. with motion in the YZ-
plane, were therefore studied.
4 THE EXPERIMENTAL MODAL
ANALYSIS PERFORMED
When the truss was assembled, forced vibrations tests
(FVT) were performed at the factory. With overhead
cranes, the truss was lifted from the ground with lift straps
placed close to the centre of gravity of the truss, see Figure
5. Excitations were induced in different directions on and
close to the steel foot of column pc80 (bottom end) with
an impulse hammer, the same as for the single
components testing. Figure 6 shows excitation during an
FVT with impacts in the X-direction.
Figure 5: Truss B hanging above the ground under an FVT at
the factory.
During the tests, fourteen tri-axial piezo electrical
accelerometers at the centre of each truss connection and
twelve single axial accelerometers on the middle of the
short glulam elements were used, see Figure 2. The
accelerometers were glued on one side of the glulam
members. The data were recorded with an LMS data
acquisition system with 54 input channels that measured:
- 51 accelerations in the X- Y- or Z-directions,
- the excitation force from the impulse hammer.
Figure 6: Excitation with a modal hammer in the X-direction
near the steel foot of column pc80.
Z
Y
X
The measured data were then analysed with LMS
Test.Lab. The ambient climate conditions during the FVT
were: 19.8 ºC and 31 % relative humidity.
5 RESULTS
From the FE analyses, the normal modes up to 125 Hz
showing motion in the YZ-plane are gathered. In total,
there are 21 such modes for model A1, 28 modes for
model A2 and 26 modes for model A3. The experimental
data from the impact tests on the steel foot of column pc80
with excitation in the Y-direction show valuable results
and are further used for this study. They are analysed and
compared to the numerical results from the FE analyses.
Comparing natural frequencies from the experiments with
their analytical counterparts is a straightforward task.
However, comparing mode shapes of a structure with
many degrees-of-freedom (DOF) is a more complex task
and the Modal Assurance Criterion (MAC) can be used
for this purpose.
The MAC, value is calculated according to Equation (6)
and it evaluates the degree of correlation between two
mode shapes, and , see [15]. A value close to 0
means that the mode shapes are completely different or
orthogonal. A value close to 1 means that the mode shapes
are similar or consistent.
,=
(6)
After calculating the MAC values between the 75
different analytical mode shapes and the five
experimental mode shapes, the main analytical modes, the
ones with a MAC value above 0.75, are presented in Table
3.
Table 3: Experimental and analytical natural frequencies with percentage difference in brackets, the corresponding MAC values in
respect to the experimental results and visualization of the mode shape from the FVTs and from the FE-model A3. Here, ζr is the
relative critical viscous damping of mode r stemming from the experimental tests.
Mode nr. and
description
Data set
Mode 1
Bouncing in Y-
direction
Mode 2
One column-
end moving in
Y-direction
Mode 3
First global bending
mode around X
Mode 4
Second global
bending mode
around X
Mode 5
Third global
bending mode
around X
Experimental
results
8.96 Hz
ζ1 = 1.67 %
25.25 Hz
ζ2 = 0.88 %
42.65 Hz
ζ3 = 1.00 %
61.57 Hz
ζ4 = 0.57 %
92.78 Hz
ζ5 = 0.75 %
FE model A1
(clamped-joints)
9.19 Hz
(+2.6 %)
MAC = 0.997
26.32 Hz
(+4.2 %)
MAC = 0.994
47.86 Hz
(+12.2 %)
MAC = 0.979
69.99 Hz
(+13.7 %)
MAC = 0.934
105.91 Hz
(+14.2 %)
MAC = 0.759
FE model A2
(pinned-joints)
9.14 Hz
(+2 %)
MAC = 0.996
22.65 Hz
(-10.3 %)
MAC = 0.992
50.30 Hz
(+17.9 %)
MAC = 0.966
55.24 Hz
(+29.5 %)
MAC = 0.862
75.18 Hz
(+22.1 %)
MAC = 0.574
92.61 Hz
(-0.2 %)
MAC = 0.763
FE model A3
(spring-joints)
8.96 Hz
(0 %)
MAC = 0.997
24.22 Hz
(-4.1 %)
MAC = 0.997
42.09 Hz
(-1.3 %)
MAC = 0.987
59.98 Hz
(-2.6 %)
MAC = 0.792
84.66 Hz
(-8.8 %)
MAC = 0.918
Y
Z
X
6 DISCUSSIONS
FE models are usually good to assess distribution of static
loads and deformations in a complex structure. To
evaluate their usefulness when studying the dynamical
properties, it is interesting to compare them to vibrational
tests on real structures. For this purpose, a modal test and
three numerical analyses of a large glulam truss have been
performed according to the previous sections of this
article.
The results presented in Table 3 show that 15 numerical
eigenmodes are consistent to five experimental
eigenmodes at a MAC level > 0.75. At the same time,
several numerical eigenmodes among the 75 modes
gathered, have eigenfrequencies very close to the natural
frequencies of the experimental modes but low mode
shape consistencies, i.e. MAC-values < 0.75. These
modes are therefore not listed in Table 3.
All three numerical models have at least one mode shape
consistent to each of the experimental modes, except
model A2 for the second global bending mode around X
with a MAC = 0.574. This experimental second bending
mode, mode 3, seems to have less similarities with the
numerical results in general, either the natural frequency
or the mode shape deviates. When comparing the global
bending modes, mode 3, 4 and 5, it is interesting to notice
that both model A1 and model A2 have higher natural
frequencies than model A3. In another term, the joint
models with either constrained or pinned connections
used here, create a stiffer truss than the joint model with
translational and rotational springs.
After an overall observation of the results, it is obvious
that the FE model A3, with spring connections, best
matches the experimental results with eigenfrequencies
deviating with less than 10 %, except for the second
bending mode around X. This comment shows that the
value for the slip modulus for dowels from [14] is useful
for estimation of the stiffness in a large glulam truss.
In the case of tall structures sensitive to wind-induced
sway, building codes recommend, in the first hand, to
mitigate the horizontal acceleration due to the first global
eigenmode, see [16-17]. The results from this study gives
an indication that rotational and translational stiffnesses
in the joints of a timber structures should be considered
when designing comfort in tall timber structures with
respect to wind-induced vibrations.
The experimental results are stemming from mean values
of sequences of five impacts. The place and the direction
of the impulse might differ between the five impact tests
done by hand.
The occurrence of small gaps between the dowels and the
glulam or the steel plate might then affect the results since
different excitation amplitude can involve different
numbers of dowels which influence the connection
stiffness and leads to non-linear structural dynamic
behaviour.
The numerical models do not take consideration of a
measured shear modulus for the glulam elements.
Transversal beam vibrations due to shear stiffness might
have an influence on the eigenmodes of the truss in plane.
Furthermore, the accelerometers were glued on one side
of the glulam member but the mode shapes from the
numerical models were obtained from nodes situated on
the symmetry axis of the beams. This thickness difference
is 107 mm, which affects the mode shapes.
7 CONCLUSION
There is still limited knowledge on the stiffness and
damping of real timber connections for dynamic loads.
This study is contributing with stiffness data measured on
a real large structure which can be used for development
of models for complete tall timber buildings. Connection
models with spring values according to the Table 7.1 in
Eurocode 5 [14] give better dynamical results than models
with either constrained or pinned joints. Further studies on
damping properties in timber structures must be
performed to better evaluate the dissipation of energy.
ACKNOWLEDGEMENT
We would like to express our thanks to Moelven Töreboda
AB for the opportunity and the help to measure in their
factory while manufacturing had to run with tight
schedule for the building project. The authors gratefully
acknowledge the funding for the project “Tall Timber
Buildings – concept studies” from Formas the Swedish
Research Council for Environment, Agricultural Science
and Spatial Planning [Dnr: 942-2015-115].
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