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Based on the experimental estimation of the key dynamic properties of a seven-storey building made entirely of cross-laminated timber (CLT) panels, the finite element (FE) model updating was performed. The dynamic properties were obtained from an input-output full-scale modal testing of the building in operation. The chosen parameters for the FE model updating allowed the consideration of the timber connections in a smeared sense. This approach led to an excellent match between the first six experimental and numerical modes of vibrations, despite spatial aliasing. Moreover, it allowed, together with the sensitivity analysis, to estimate the stiffness (affected by the connections) of the building structural elements. Thus, the study provides an insight into the as-built stiffness and modal properties of tall CLT building. This is valuable because of the currently limited knowledge about the dynamics of tall timber buildings under service loadings, especially because their design is predominantly governed by the wind-generated vibrations.
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Structure and Infrastructure Engineering
Maintenance, Management, Life-Cycle Design and Performance
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Model updating of seven-storey cross-laminated
timber building designed on frequency-response-
functions-based modal testing
Blaž Kurent, Boštjan Brank & Wai Kei Ao
To cite this article: Blaž Kurent, Boštjan Brank & Wai Kei Ao (2021): Model updating of seven-
storey cross-laminated timber building designed on frequency-response-functions-based modal
testing, Structure and Infrastructure Engineering, DOI: 10.1080/15732479.2021.1931893
To link to this article:
© 2021 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Published online: 07 Jun 2021.
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Model updating of seven-storey cross-laminated timber building designed on
frequency-response-functions-based modal testing
z Kurent
stjan Brank
and Wai Kei Ao
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Ljubljana, Slovenia;
College of Engineering, Mathematics and Physical
Sciences, University of Exeter, Exeter, UK
Based on the experimental estimation of the key dynamic properties of a seven-storey building made
entirely of cross-laminated timber (CLT) panels, the finite element (FE) model updating was performed.
The dynamic properties were obtained from an input-output full-scale modal testing of the building in
operation. The chosen parameters for the FE model updating allowed the consideration of the timber
connections in a smeared sense. This approach led to an excellent match between the first six experi-
mental and numerical modes of vibrations, despite spatial aliasing. Moreover, it allowed, together with
the sensitivity analysis, to estimate the stiffness (affected by the connections) of the building structural
elements. Thus, the study provides an insight into the as-built stiffness and modal properties of tall
CLT building. This is valuable because of the currently limited knowledge about the dynamics of tall
timber buildings under service loadings, especially because their design is predominantly governed by
the wind-generated vibrations.
Received 16 February 2021
Revised 16 April 2021
Accepted 17 April 2021
Tall timber building; cross-
laminated timber (CLT);
dynamic service loading;
forced vibration tests;
modal parameters; spatial
aliasing; finite element
model updating
1. Introduction
An evolution in timber building technologies has enabled
construction of tall timber buildings (TTBs) with structural
elements made from cross-laminated timber (CLT). An
example is the seven-storey Yoker building in Glasgow, UK,
see Figure 1, which was the tallest Scottish timber building
when constructed in 2017. In general, TTBs have sufficient
capacity to resist lateral loads for the ultimate limit state
and the design is governed by the wind-generated vibrations
that cause discomfort or annoyance to occupants (e.g.
ar & Lidel
ow, 2017; Johansson, et al., 2016; Reynolds,
Harris, Chang, Bregulla, & Bawcombe, 2015). The amount
of sway/acceleration depends on the mass and stiffness dis-
tribution across the TTB and its ability to dissipate kinetic
energy (e.g. Malo, Abrahamsen, & Bjertnaes, 2016).
Currently, the knowledge on the stiffness and the key
dynamic properties (natural frequencies, mode shapes and
damping) of TTBs is limited, particularly with respect to
connections used (e.g. Abrahamsen et al., 2020), which is
one of the main barriers for further TTBs developments.
Underestimation of the fundamental natural frequency of
up to 50% by a TTB structural model, relative to its experi-
mental counterpart, is common (e.g. Ao & Pavic, 2020).
The modal properties of TTBs are difficult to predict,
however it is possible to learn about the as-built modal
properties of the operational TTBs. Output-only ambient
vibration testing (AVT) was performed for a limited
number of tall CLT buildings (see, Aloisio, Pasca, Tomasi,
& Fragiacomo, 2020; Mugabo, Barbosa, & Riggio, 2019;
Reynolds, Casagrande, & Tomasi, 2016; Reynolds et al.,
2015), where the fundamental vibration modes were identi-
fied and compared with FE results. The AVT methods are
based on measured response due to unmeasured ambient
excitation, which varies with time and produces estimates
that vary from one data block to another. On the other
hand, in the input-output modal testing, both the excitation
force and the corresponding dynamic response are meas-
ured, which allows to estimate FRFs and use them to get a
more reliable estimation of the as-built modal properties
(e.g. Ao & Pavic, 2020). In particular, the properties of
higher modes of vibration are much easier to measure and
investigate using the FRF-based methodology. However,
FRFs have been non-existing in the TTBs studies. One rea-
son is practical difficulties related to forced excitation of a
TTB without damaging it, which can be overcome by using
a refined (best-engineering judgement) FE model before and
during the test. The next reason is complication in measur-
ing responses simultaneously throughout the building,
which can be solved by using synchronised wireless acceler-
ometers (see, Ao & Pavic, 2020).
With the experimental modal properties at hand, an
insight into the distribution of mass and stiffness over the
tested TTB can be gained by performing the FE model
updating (e.g. Mottershead, Link, & Friswell, 2011). The lat-
ter can provide information about the influence of
stjan Brank Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova c. 2, SI-1000 Ljubljana, Slovenia
ß2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (
0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in
any way.
connections/joints on the stiffness of TTBs structural com-
ponents, for example CLT walls and floors. The problem of
choosing the updating parameters is a crucial part of the FE
model updating and can be assisted with the sensitivity ana-
lysis (e.g. Borgonovo & Plischke, 2016; Saltelli et al., 2008).
The latter gives an insight how the FE model responds due
to a change of a parameter value, and it is a great tool for
exploration of a choice for updating parameters. Before the
FE model updating is performed, the FE and experimental
vibration modes must be correlated. When sensors do not
capture enough motion of the structure, the problem of spa-
tial aliasing needs to be overcome (e.g. Fotsch & Ewins,
2001; Yaghoubi & Abrahamsson, 2014).
In this work, the dynamics under service loadings of the
tall CLT building from Figure 1 is studied. Our approach is
in contrast with the previous studies, which were based on
the AVT methods and were using simple FE/analytical mod-
els for correlating experimental results with numerical/ana-
lytical solutions. It is for the first time that the information
about the operational tall CLT building is obtained by the
FE model updating that uses a refined FE model and relies
on FRF-based vibration tests. The chosen updating parame-
ters enabled inclusion of the effects of the connections/joints
in a smeared manner, which led to an excellent match
between the experimental and numerical results. In particu-
lar, the first six vibration modes are matched almost per-
fectly after the FE model updating. This is an excellent
result in comparison with the only (to our best knowledge)
previous study on the model updating of tall CLT building
by Aloisio et al. (2020), where the three vibration modes
were balanced. We note that matching of the higher-order
modes is much more difficult to achieve than matching of
the lower modes, because one needs both reliable (FRF-
based) vibration tests (Ao & Pavic, 2021) and a prudent
choice of updating parameters of a refined FE model. The
results of our FE model updating clearly show how the con-
nections impact the stiffness of the CLT walls and CLT
floors of the considered building.
At the closure of this section let us recall that the import-
ant part of CLT building is steel connections, which are of
various types and use screws or nails. The present study is
adding to the (currently limited) knowledge of how much
the connections contribute to the overall stiffness of a tall
CLT building under service loadings. According to Aloisio et
al. (2020), Gavric, Fragiacomo, and Ceccotti (2015)and
Reynolds et al. (2015), the connections operate far below their
strength at low-amplitude movements and the load transfer
between the panels occurs mainly through the friction and dir-
ect contact, enabling the panels to deform in shear and bend-
ing. In joints with small friction (such as those in CLT floors),
sliding between the CLT panels might occur for service
dynamic loadings. According to the laboratory tests presented
by Brandner et al. (2017), DArenzo, Casagrande, Reynolds,
and Fossetti (2019), Oh et al. (2017) and Yasumura,
Kobayashi, Okabe, Miyake, and Matsumoto (2016), the con-
nections influence the in-plane stiffness of CLT floors and
walls. Moreover, this stiffness is non-trivially dependent on
several other factors, such as panel fabrication, boundary con-
ditions affecting the development of shear mechanism, and the
number and orientation of panels in a composition. Studies by
Ashtari, Haukaas, and Lam (2014)andDArenzo et al. (2019)
concluded that the sliding between the panels is the main fac-
tor contributing to the in-plane flexibility of CLT floors.
As for the shear walls, Yasumura et al. (2016)testedtwo
two-storey CLT structures against lateral load, where the shear
walls of the first and the second structure were composed of
large and small panels, respectively, and for the former case,
the initial stiffness was approximately twofold of the former. A
difference in the initial in-plane shear stiffness was also
reported by Oh et al. (2017) for the three walls made of single,
two and four panels. As for the value of the in-plane shear
modulus for CLT, the study by Brandner et al. (2017)onsin-
gle CLT panels describes their shear mechanism as either
gross-shear or net-shear. According to Brandner et al. (2017),
the narrow-face bonded CLT panels with no cracks develop
the gross-shear and have approximately 50% higher in-plane
Figure 1. Yoker, 7-storey CLT building in Glasgow, UK.
shear modulus than the CLT panels with cracks and/or gaps
(because the narrow faces are not glued) that develop net-
shear. The above-mentioned laboratory results indicate that the
FE modelling of CLT walls and floors in TTBs has to deal
with a large variance in the in-plane shear modulus value of
CLT and uncertainty regarding the influence of connections.
The rest of the paper is organized as follows. In Section
2, the seven-storey CLT building is briefly described, and
Section 3 presents the best-engineering-judgement FE model
of the building. The experimental results are summarized in
Section 4, and the FE model updating is presented in
Section 5. The updating of the FE model that includes foun-
dation is discussed in Section 6, and conclusions are drawn
in Section 7.
2. Building description
The seven-storey residential building has a T-shape with clearly
separated but structurally still connected northern and south-
ern wings, see Figure 1. The structural system of the building
is made completely out of CLT panels, apart from the rein-
forced concrete foundation and ground floor slab, and a few
steel beams and frames that locally reinforce the timber. The
characteristic dimensions of the building are: 31 m by 28 m in
plan, 22 m in height above the ground floor slab, 3745 m
gross floor area, and 550 m
foot print area. Typical floor plan
is shown in Figure 2(a). The facade does not include any sec-
ondary load-bearing elements that could contribute to the
structural stiffness. The soil layer under the building is made
ground. Beneath that is a layer of glacial till, considered as
appropriate foundation bearing material for the multi-storey
building. The foundation is described in Section 6.
Five different types of CLT panels were used, varying in
thickness from 100 mm to 140 mm (except for the stair half-
landing with 200 mm CLT panels), having either 3 or 5
layers, see Table 1. As shown in Figure 1(b), the external
walls (as well as some internal walls) consist of large CLT
panels, with pre-cut openings for windows, which have the
height of the storey and the length of the building edge
(except for the last storey, where this is not the case). The
CLT panels in the Yoker building are typically connected
using a combination of angle brackets and wood screws, see
Figure 2. The manufacturer Stora Enso, see Stora Enso
(2019), provides mean material properties for their CLT
panels (made of C24 spruce boards), see Table 2, which also
includes the mean material properties provided by EN-338
for C24 spruce boards.
3. Initial finite element model
This section describes the initial (i.e. the best-engineering-
judgement) FE model that is based on the following
assumptions: (i) the foundation is rigid and fixed, (ii) the
connections do not need to be modelled, and (iii) the floors
are flexible (i.e. the assumption of the rigid-diaphragm is
not used). The model was prepared before the tests were
performed and proved very helpful for test design.
3.1. Modelling with shell finite elements
R(2020) software is applied for the construction of
the FE model. Figure 3 shows the FE mesh. The CLT panels
are modelled by a multi-layer, four-node, shell element with
six degrees of freedom per node (called SHELL181). Each
layer applies the orthotropic material model with six inde-
pendent constants (e.g. Brank & Carrera, 2000), for which
we adopt material properties provided by the CLT manufac-
turer Stora Enso, see Table 2. The mean values are taken for
stiffness and density, which seems a reasonable choice for
undamaged timber. Poissons ratio
is assumed as 0.3 (we
note that various values for
are reported (see Nairn,
2017; Rocco Lahr et al., 2015;St
urzenbecher, Hofstetter, &
Eberhardsteiner, 2010)). The mid-surfaces of the shell finite
elements are placed in accordance with the positions of the
mid-planes of the CLT panels, as shown in Figure 4(b). The
connections between CLT panels are not explicitly modelled
and a perfect bond is assumed. In the bottom horizontal
plane of the FE mesh, which is at the level of the top sur-
face of the reinforced concrete ground floor, all degrees of
freedom are set to zero.
3.2. Modelling the building stiffness and mass
Structural elements that are modelled as entities with stiffness
are: the external and internal load-bearing walls, floors, roof,
and elevator shaft. We neglect the steel beams and frames that
locally reinforce the timber (they add up to less than 1% of
the building elements that are traditionally considered negli-
gible for the overall building stiffness, e.g. non-load-bearing
partition walls (these partition walls account for about 6% of
the total mass of the walls in a storey), stairs, windows, etc.
The mass of the well-documented non-structural building
elements (i.e. facade, insulation, screed, flooring, fireline board,
cladding, and non-load-bearing partition walls) is taken into
account as uniformly distributed area mass over walls and
floors. The sum of masses of non-structural elements attached
to the walls of a particular storey is smeared over the FEs that
model the walls in that storey. The sum of masses of non-
structural elements attached to a particular floor is smeared
over the FEs that model that floor. The mass of all undocu-
mented building elements with uncertain weights (such as win-
dows, doors and steel stairs), documented but unevenly
distributed elements (various steel reinforcements) and uncer-
tain live load (such as furniture, residents, etc.) are combined
into one parameter - uncertain mass - that is estimated to q¼
25 kg/m
. It is distributed over the FEs that model the floors
(it is not distributed over the ground floor and the roof), in
particular over the apartment areas (it is not distributed over
the corridors). The estimated mass of the building (excluding
reinforced concrete foundation and ground floor) is 1270t and
can be assigned to the following contributions: around 515t to
the timber part of the building, around 685t to the well-docu-
mented non-structural elements and around 70t to uncer-
tain mass.
3.3. Convergence analysis
The convergence analysis was performed in order to find an
optimal mesh. To that end, the natural frequencies were
computed by modal analysis for nine different FE meshes.
The results are shown in Figure 5, where the convergence is
presented for the first six natural frequencies in terms of the
relative difference DiðMÞ:The latter is defined for the i-th
natural frequency f
and mesh Mas:
DiðMÞ ¼ fiðMÞ  fiðMfÞ
where Mfdenotes the finest mesh with 2:79 106nodes.
Figure 5 shows that finer meshes lower natural frequencies.
For the subsequent work, we choose mesh Mawith 2:61
105nodes, as a trade-off between accuracy and computa-
tional time. By assuming that the finest mesh Mfyields
converged results, the approximate discretization error
can be computed for the applied mesh Ma:The following
numbers are obtained for the first six natural frequencies:
1.10%, 0.82%, 1.14%, 1.29%, 0.87%, 0.69%.
3.4. Natural frequencies and mode shapes
Table 3 presents the first six mode shapes and the related
natural frequencies. We adopt the ordering based on the
correlation with the experimental modes shown below in
Section 4.2 and Table 4. The first three modes are very
closely spaced in terms of frequencies. The 1
mode is
bending mode in the weaker building direction. Modes 2
and 3 are torsion (almost a mirroring) modes. Mode 4 is a
more complex torsion mode with opposite rotations of the
two building parts (hereinafter denoted as theweband
theflangeof the T-shaped building). Mode 5 is a shear
mode showing, along with modes 4 and 6, in-plane defor-
mations of floor slabs. Mode 6 is a higher-order bend-
ing mode.
4. Experimental results
This section provides a brief description of the FRF-based
modal testing of the Yoker building in operation. In add-
ition, the experimental results are compared with the results
of the initial FE model.
4.1. FRF-based modal testing
Three synchronised APS Model 400 electrodynamic shakers
with total moving mass of 68.85 kg were installed on the 6
Figure 2. Some details of the Yoker building.
Table 1. Types of CLT panels used.
CLT panel type Thickness [mm] Area [m
Walls Floor/roof
SE-100-L3s/SE-100-C3s 100 1149 525
SE-100-L5s/SE-100-C5s 100 968 /
SE-120-L3s/SE-120-C3s 120 299 /
SE-120-L5s/SE-120-C5s 140 1909 2926
SE-140-L5s/SE-140-C5s 140 1109 190
SE-200-L5s 200 / 49
Table 2. Mean material properties for CLT.
Property Stora Enso EN 338
Elastic modulus E
[MPa] 12 000 11 000
Elastic modulus E
[MPa] by EN 338 370
Shear modulus G12 ¼G13 [MPa] 460 690
Shear modulus G
[MPa] 50 /
Density q[kg/m
] 470 420
Table 3. First six FE mode shapes and respective deformations of the 6
floor (the experimental mode order is adopted).
Mode Frequency Mode shape 6
floor deformation
1 2.85 Hz
2 2.81 Hz
3 2.94 Hz
4 3.98 Hz
5 8.32 Hz
6 8.19 Hz
floor, see Figure 6. Honeywell QA750 and Japan Aviation
Electronics Industry, Limited JA-70SA accelerometers were
used to measure accelerations. Altogether 13 sensor loca-
tions were chosen with 2 sensor locations on each floor (no
sensors were placed on the ground floor) and additional
one on the 6
floor as a reference sensor near the shakers.
Each sensor location measured acceleration in two
horizontal directions, as shown in Figure 7. At the time of
the measurements, the building was operational so installa-
tion of the sensors was limited to the corridors in the core
of the building. Since the measured degrees of freedom do
not give sufficient information about the motion of the
whole building (see modes 4 to 5 in Table 3), some degree
of spatial aliasing is expected.
Two sets of random excitation vibration tests were car-
ried out, one with shakers exciting in the xdirection and
the other in the ydirection (see Figure 7 for the directions).
The average amplitude of the total force was around 500 N
and the location near the shaker had the average structural
Figure 3. Model geometry (left) and detail of the FE mesh (right).
Figure 4. CLT panel (left) and modelling detail (right).
Figure 5. Convergence analysis results.
Table 4. Comparison of initial FE model and experimental results.
Experiment Initial FE model MAC
iFrequency jFrequency
1 2.85 Hz 2 2.85 Hz 0.77
2 2.93 Hz 1 2.81 Hz 0.77
3 3.13 Hz 3 2.94 Hz 0.38
4 3.63 Hz 4 3.98 Hz 0.95
5 6.73 Hz 6 8.32 Hz 0.80
6 8.74 Hz 5 8.19 Hz 0.78
7 9.68 Hz 11 9.39 Hz 0.66
8 11.9 Hz 58 15.3 Hz 0.72
responses of 0.005 m/s
and 0.004 m/s
in the xand ydirec-
tions, respectively. The excitation signal was wide frequency
bandwidth white noise (0 Hz10 Hz). Single-input multiple-
output modal identification method (complex mode indica-
tor function) was used to identify 8 vibration modes.
Typical FRFs of the test point near the electrodynamic
shakers presented in Figure 8 show that the lowest natural
frequencies were clustered. The measured natural frequen-
cies are presented in Table 4 and compared with the FE
results. The experimental mode shapes and the correspond-
ing mode shapes obtained with the initial FE model are
shown below in Table 8.
4.2. Comparison of experimental and numerical results
Modal assurance criterion (MAC) is a commonly used
measure for the correlation between two sets of modes (e.g.
Allemang, 2003), computed as:
, (3)
where wi,eand wj,nare i-th experimental and j-th numerical
mode shapes, respectively, and denotes the conjugation of
complex mode shapes. MAC value 1 suggests a strong simi-
larity between two modes, whereas value 0 suggests no simi-
larity. Commonly, all experimental and numerical mode
shapes are compared pair-by-pair and presented in MAC
matrix, which is ideally a diagonal unit matrix. Figure 9
Figure 6. Test equipment in the 6
Figure 7. Layout of shakers and sensors.
shows that MAC matrix is far from diagonal and there are
quite a few correlated mode shapes. This is a consequence
of spatial aliasing, which can occur not only when too few
sensors are used but also when they are placed so that not
enough features of the mode shapes are captured (e.g.
Allemang, 2003; Liu, Yan, & Guedes Soares, 2018; Yaghoubi
& Abrahamsson, 2014). In our case, poor sensor placement
can be suspected already from the layout presented in
Figure 7. Spatial aliasing can also be confirmed by examin-
ing the Auto-MAC matrices (see Ewins, 2000)inFigure 10,
which display many non-zero off-diagonal terms. However,
the spatial aliasing was inevitable due to limited access to
the building.
With spatial aliasing, additional information is needed to
find matching pairs of modes. Sometimes, a criterion that
combines the MAC value and the frequency is used (e.g.
Petersen & Øiseth, 2017), but in our case, the frequencies in
question are so close that such a criterion does not separate
between a good and a bad mode pair. We used the Auto-
MAC matrices in order to find matching mode pairs. First,
the MAC matrix was compared with the experimental
Auto-MAC matrix, shown in Figure 10(a). It can be seen
that the 1
row of the experimental Auto-MAC matrix
strongly resembles the 2
row of the MAC matrix, but it is
also very similar to the 4
row of the MAC matrix.
Comparing also the frequencies of those modes, it can be
concluded that the 1
experimental mode matches the 2
FE mode. In a similar fashion, we connected the 2
mental to the 1
FE mode, the 4
experimental to the 4
FE mode, the 5
experimental to the 6
FE mode, and the
experimental to the 5
FE mode. This leaves us with the
only reasonable connection left between the 3
tal and the 3
FE mode. The pairs can also be confirmed
by comparing the columns of the FE Auto-MAC matrix in
Figure 10(b) with the columns of the MAC matrix.
How well (in terms of natural frequencies and MAC
ues) the modes match is shown in Figure 11 using the plot
of frequency scaled modal assurance criterion (FMAC)
introduced by Fotsch and Ewins (2000,2001). MAC
defined as the MAC value of i
matching pair, i¼1, ...,8
(the order coincides with the order of experimental modes),
and the relative error of the numerical frequency is defined
fi,exp fi,FEM
Let us note that although some MAC values in Table 4
are not sufficiently high and the frequency differences are
too large for a clear pairing of modes, we match them for
the purpose of model updating and later comparison.
5. Model updating
In this section, we explain the choice of parameters for the
FE model updating and interpret the results of sensitivity
analysis and model updating.
5.1. Parameter selection
After the initial screening sensitivity analysis, we can con-
clude that the following parameters are important: elastic
modulus E
, in-plane shear modulus G
, timber density q,
and uncertain mass q. These parameters significantly affect
the natural frequencies and mode shapes. We could also
Figure 8. Typical FRFs.
Figure 9. MAC matrix for the initial FE model.
conclude that elastic modulus E
, out-of-plane shear moduli
and G
), and Poissons ratio
have little influence
on the results. Moreover, timber density has a similar effect
as uncertain mass q. On this basis, six parameters from
Table 5 are chosen for more detailed sensitivity analysis and
FE model updating. From Table 5 it can be seen that there
are three and two parameters associated with major elastic
modulus and in-plane shear modulus, respectively. This
way, we want to accommodate for the effects of connections
in a smeared sense. We know in advance that after the
updating most of the parameters from Table 5 will not rep-
resent the material properties because they will bepolluted
with the modelling error. The chosen ranges of the parame-
ters reflect not only the information on the material data,
see Table 2, but also allow capturing the stiffness reduction
of walls and floors due to the connections. The range for
mass parameter accommodates for uncertain weights of
structural and non-structural building elements and
live loads.
5.2. Shear wall stiffness reduction due to the wall-
floor joint
The wall-floor joint shown in Figure 2(b) reduces the stiff-
ness of the shear wall. The initial FE model does not con-
sider this reduction, because it models the wall-floor joint as
shown in Figure 4(b). We expect that the parameter e
take this effect into account in a smeared sense. The effect
of the wall-floor joint on the vertical axial stiffness of the
shear wall can be explained as shown in Figure 12. For illus-
tration purposes only, we assume that a unit depth of one
storey of the shear wall, consisting of vertical and horizontal
CLT panels denoted as A and B, respectively, is supported
at the bottom and imposed to unit axial displacement at the
top. It is discretized with either (i) two bar FEs with elastic
moduli E
and E90 ¼E2for elements A and B, or (ii)
one bar FE with effective elastic modulus lE0:Equating the
forces that produce unit displacement gives the value for l.
Figure 13 shows las a function of c, which takes into
account the effective width of the floor CLT, and as a func-
tion of afor different configurations of CLT panels from
Table 1 used for the walls, a0:6, 0:7:It can be seen that
this simple analysis gives l0:5, 0:7Þfor c1, 2:
5.3. In-plane stiffness of CLT walls and floors
On each storey, the shear walls of the Yoker building are
composed of large CLT panels with pre-cut openings, the
lengths of which equal the lengths of the building edges, see
Figure 1. These panels, which are constrained on their top
and bottom with CLT floors, are under axial compression
(due to gravity) producing large friction in the wall-floor
joints. On the other hand, the floors are composed of a
number of CLT panels, as can be observed from Figure
2(a), with small friction between the panels. Furthermore,
theweband theflangeof the building are connected
only by a narrow strip, which defines the specific geometry
of the CLT floors and influences their in-plane behaviour.
These differences in geometry and panel layouts suggest that
the in-plane shear stiffness for the CLT shear walls and CLT
floors may differ considerably. To account for this, the
parameters g
and g
were introduced. Moreover, another
parameter, e
, was introduced to capture the effect of the
floor connections in a smeared sense (besides g
5.4. Sensitivity analysis
Sensitivity analysis was performed in order to analyse the
influence of the parameters from Table 5 on natural fre-
quencies and MAC values. Variance-based sensitivity ana-
lysis was carried out by computing first-order and total
effect sensitivity indices. This method is sometimes referred
to as Sobolmethod or Sobolvariance decomposition (e.g.
Borgonovo & Plischke, 2016; Saltelli et al., 2008). The first-
order sensitivity index tells us what fraction of total variance
V(Y) of response Ycan be attributed to parameter X
computed through the expected value EXiðYjXi¼x
response Yover all parameters except X
at fixed value Xi¼
i:Large variance of this expected value VXiðEXiðYjXiÞÞ
over the parameter space of X
implies a high influence of
parameter X
on response Y. The first-order sensitivity index
is computed as a ratio between conditional and total vari-
Another measure of importance is the total effect term.
This includes all higher-order terms that also capture inter-
actions between the parameters. The total effect sensitivity
index S
is defined as:
The expected value of response Yover parameter X
computed by fixing all but parameter X
and finding its
variance over all parameters except X
. If the values of S
and S
are close to zero, parameter X
does not have much
influence on response Y. The higher the values of S
and S
the greater the influence of parameter X
on response Y.If
the values of S
and S
are similar, there is little interaction
of parameter X
with other parameters. Also, if the sum of
all terms S
is equal to 1, the model is said to be additive
and there is little interaction between the parameters.
The total number of runs of the FE model in this method
is defined as Nðkþ2Þ, where Nis called base sample (usu-
ally chosen around 500-1000) and kis the number of
parameters. N¼500 was chosen, which for k¼6 results in
4000 total runs of the FE model. Open source python
library SAlib (Herman & Usher, 2017) was used to carry
out the sensitivity analysis. Results are presented in Figure
14. Comparing the sensitivity plots from Figure 14(a) and
(c), it can be concluded that the parameters influence the
first six natural frequencies fairly independently. Indeed,
indices S
are very close to S
. Parameter g
has a strong
influence on all but the 5
natural frequency. On the other
hand, g
strongly influences the 5
, but has a negligible
effect on the first three frequencies. Parameter e
effects the
first natural frequency. It has also a minor impact on the
other frequencies, except on the 5
. Parameter e
has a neg-
ligible effect on all natural frequencies. The same can be
said for parameter e
for the first three frequencies, while e
has a small impact on the last three frequencies. Lastly, q
has a moderate effect on all natural frequencies. There is
high interaction between the parameters in the effect on
values. Figure 14(b) and (d) show that the total-effect
indices S
are much higher than the first-order indices S
This means that the effect of one parameter on the response
will depend on the values of other parameters.
5.5. Model updating
Two measures of the difference between the computed and
measured response were applied. One relates to the similar-
ity of the mode shapes:
ð1MACiÞ2, (7)
and the other relates to the difference in natural frequen-
dfreq ¼X
fi,exp fi,FEM
, (8)
where fi,exp and fi,FEM are the experimental and numerical
natural frequencies of the i-th matching mode pair, respect-
ively. As can be noticed from (7) and (8), only the first six
correlated vibration modes are used in the objective func-
tions. Modes 7 and 8 are not considered. Instead, it will be
checked after the updating how much they are improved
(or worsened) without taking part in the process
of updating.
The optimization was performed by using optimization
tools incorporated in Ansys, in particular, the multi-object-
ive genetic algorithm with 200 initial samples, 15 maximum
iterations, and with 100 samples per iteration. The max-
imum allowable Pareto percentage is set at 70%, and the
convergence stability percentage is set at 1%. The measures
(7) and (8) were used as two equally important minimiza-
tion objective functions. The algorithm converged in 11 iter-
ations, with 1% Pareto percentage and 0.59% stability
percentage, giving three candidate points (CP) shown in
Table 6. They give us fairly close parameter values (within
3.3% range) so the choice for further observation is some-
what arbitrary. We advance with CP1 as it gives the lowest
and d
The results of the FE model updating are shown in
Tables 7 and 8, together with the results of the initial FE
model and experimental data. The results are also presented
with FMAC plot in Figure 15, which can be compared to
the FMAC plot of the initial model in Figure 11. It is appar-
ent that all six modes that are included in the objective
function have improved compared to the initial model. The
most significant improvement is for the mode shape of the
mode and the natural frequencies of the 4
and the 5
modes. The remaining two modes that are not included in
the objective function (i.e. 7
and 8
mode) are shown
Figure 10. Auto-MAC matrices.
Figure 11. FMAC plot for the initial FE model.
here as a simple validation that the solution of model updat-
ing is reasonable and not overfitting the results. It is also
worth noting that the differences in natural frequencies are
comparable to the discretization error estimated in Section
3.3. From the MAC matrix in Figure 16, one can see that
the updating also improved the order of the numerical
modes. By excluding the 6
to 9
numerical modes of the
new MAC matrix (with emphasized local deformations), it
has a strong resemblance to experimental Auto-MAC matrix
from Figure 10(a), even in non-diagonal terms, which is a
supporting indication that the problem of spatial aliasing
was successfully tackled.
5.6. Updated values of parameters
Parameter e
is updated to 50:9%of the initial value. As
expected, e
captures the effect of the wall-floor joint
explained in Section 5.2. With this in mind, the updated
value for e
seems a reasonable solution. Parameter e
4:6%higher than what the CLT manufacturer claims for E
and the difference can be attributed to the uncertainty of
this material property. Let us note, however, that the sensi-
tivity analysis (see Figure 14) showed that the frequencies
and MAC
values are almost unaffected by the change of the
Table 5. Parameters used in sensitivity analysis and model updating.
Parameter Range Property Application
6 to 12 GPa E
Used for CLT panels in walls. Only for layers with fibres in vertical direction.
10 to 13 GPa E
Used for CLT panels in walls. Only for layers with fibres in horizontal direction.
6 to 12 GPa E
Used for CLT panels in floor slabs. All layers.
400 to 750 MPa G
Used for CLT panels in walls. All layers.
200 to 500 MPa G
Used for CLT panels in floor slabs. All layers.
q5 to 100 kg m
Mass Additional distributed mass over all the floors.
Figure 12. Effective axial vertical stiffness of the shear wall due to the wall-floor joint (note that E
and E90 ¼E2).
Figure 13. Domain of values for factor lfrom Figure 12.
value for e
(thus the updated result for e
may not be very
trustworthy). Parameter e
is 26:2%lower than the initial
value, because it captures the in-plane flexibility of the
floors due to connections discussed in Sections 5.3 and 1.
Parameter g
captures even more the in-plane flexibility of
the floors because it settles at 47:6%of the initial value. It is
worth recalling that g
significantly affects the 5
mode, as
well as the 4
and the 6
modes, but it affects negligibly
the first three modes, see Figure 14. In other words, the first
three modes are almost unaffected by the change of the
value for g
. Large in-plane flexibility of the floors for higher
modes may also be partly attributed to the specific floor
plan of the Yoker building (see Figures 2 and 7).
A large 61:7%discrepancy between the increased updated
value and the initial value can be seen for g
. In this con-
text, let us note that the uncertainty in the material param-
eter G
is large, see Table 2 and research by Brandner,
Flatscher, Ringhofer, Schickhofer, and Thiel (2016) and
Shahnewaz, Tannert, Alam, and Popovski (2017). With this
in mind, one can notice that the updated value for g
only 7:8%higher than the value given for G
in EN-338,
and 14:5%higher than G12 ¼650MPa reported by
(Brandner et al., 2016) for CLT with narrow face bonding
(this is the type of CLT produced by Stora Enso). The above
suggests that the updated result for g
may be attributed to
a large extent to the stochastic nature of G
, and partly to
capturing the neglected contributions to the in-plane shear
stiffness of the shear walls in the Yoker building. The
change of the uncertain mass parameter qcontributes to
2.59% increase of the estimated initial mass of the building,
which was 1270t. It can be concluded that the updated val-
ues for the parameters from Table 6, except the one for e
include the effects of the modelling error. Thus, the updated
values for e1,e3,g1and g
are not material properties. The
modelling error is most pronounced for e
(due to the wall-
floor joints) and for g
(due to the large in-plane flexibility
of the floors that may be attributed to the connections and
specific floor plan). Large in-plane flexibility of the floors is
Figure 14. First order and total sensitivity indices.
captured also by e
. It might be that parameter g
includes some modelling error due to the stiffness of non-
load-bearing building elements not included in the model.
6. Inclusion of foundation in the model
In the above presented FE models, the foundation was not
considered. In this section, the initial FE model is changed
to take into account the flexibility of the foundation and its
interaction with the soil. By performing updating of the ini-
tial model improved in this way, the effect of the foundation
on the dynamic response of the building will be checked.
The foundation of the Yoker building consists of several
parts. Beneath the reinforced concrete ground floor slab
with a thickness of 175 mm, there is a system of short rein-
forced concrete walls with a height of 850 mm and a thick-
ness of 215 mm (140 mm on the edges), see Figure 17. The
walls are connected at their bottom to the reinforced con-
crete horizontal frame with the square cross-section of
600 mm 600 mm. Underneath the frame, there are 135
reinforced concrete piles with a diameter of 250 mm and a
length of approximately 9 m.
6.1. Foundation modelling
The ground floor slab and the walls below are modelled
with shell finite elements and the horizontal frame with
beam finite elements. The data for the reinforced concrete
are: density q¼2300 kg m
, modulus of elasticity E¼32
MPa and Poissons ratio m¼0:18:The effects of the pile
and the pile-soil interaction were accounted for by three
orthogonal springs located at the point where the pile is
attached to the horizontal frame. The stiffnesses of the hori-
zontal and vertical spring are denoted as k
and k
respectively. Moreover, the interaction between the founda-
tion wall system (and frame) and the soil is accounted for
by the horizontal area spring with stiffness k
. The founda-
tion part of the FE model is illustrated in Figure 17.
Stiffness values for the springs are very uncertain, but
estimates can be made based on the geometrical and mater-
ial properties of the piles and estimated elastic modulus of
the soil (e.g. Stewart et al., 2012). The elastic modulus of the
soil was estimated from twelve quick undrained triaxial
compression tests at various locations under the building,
which yielded values ranging from 0.9 MPa to 21.1 MPa
with an average of 6.1 MPa. Using these values in the equa-
tions from a technical report by Stewart et al. (2012) gives
from 1.9 10
to 2.3 10
for k
from 7.9 10
to 1.4 10
for k
Another estimate for the vertical stiffness of the pile is
obtained by simply treating the pile as a bar and obtaining
Lp¼1:67 105Nmm
from elastic moduli, cross-
section area and pile length.
6.2. Updating of the model with foundation
The FE model updating is repeated for the initial model
that takes into account the foundation. The stiffness of the
springs, k
and k
, are added to the six parameters from
Table 5. To be able to choose the range of the three newly
introduced parameters and gain some further insights into
these parameters, a linear (one-at-a-time) sensitivity analysis
was carried out (by using the updated model from Section
5.5). For each parameter, a threshold value was found,
above which the FE model behaves as if the corresponding
degrees of freedom (either vertical or horizontal) are fixed,
see Figure 18. This threshold is chosen to be the upper
bound of the parameter range for the second model updat-
ing. The sensitivity analysis also suggests that lowering the
Table 6. Values of parameters and objective functions for initial model and for three candidate points representing updated model.
Parameter Initial model CP1 CP2 CP3
Value % of initial Value % of initial Value % of initial
[GPa] 12 6.11 50.9% 6.23 51.9% 6.24 52.0%
[GPa] 12 12.55 104.6% 12.45 103.8% 12.57 104.8%
[GPa] 12 8.85 73.8% 8.98 74.8% 8.98 74.8%
[MPa] 460 744.1 161.7% 748.0 162.6% 747.8 162.6%
[MPa] 460 219.0 47.6% 216.1 47.0% 212.0 46.1%
q[kg m
] 25 36.63 þ2.59%
36.88 þ2.64%
36.37 þ2.53%
[103] 74.9 1.87 1.90 1.92
[102] 58.1 4.53 4.83 4.87
Difference from initial model presented as a percentage of estimated initial mass of the building.
Table 7. Comparison of initial and updated model with experimental data.
Experiments Initial model Updated model
Frequency Frequency Deviation MAC
Frequency Deviation MAC
2.85 Hz 2.85 Hz 0.11% 0.77 2.84 Hz 0.41% 0.83
2.93 Hz 2.81 Hz 4.10% 0.77 2.95Hz 0.72% 0.99
3.13 Hz 2.94 Hz 6.07% 0.38 3.08Hz 1.54% 0.97
3.63 Hz 3.98 Hz 9.64% 0.95 3.77 Hz 3.75% 0.96
6.73 Hz 8.32 Hz 23.6% 0.80 6.70 Hz 0.46% 0.95
8.74 Hz 8.19 Hz 6.64% 0.78 8.64 Hz 1.16% 0.90
9.68 Hz 9.39 Hz 3.05% 0.66 9.38 Hz 3.11% 0.78
11.9 Hz 15.3 Hz 28.6% 0.72 12.4 Hz 4.30% 0.56
Table 8. Graphical comparison of initial and updated model with experimental data.
Experiments Initial model Updated model
stiffness of parameters k
and k
worsens the results
obtained by the first updating from Section 5.5, while the
value of parameter k
below the threshold slightly improves
the mode shapes obtained by that updating.
The ranges for the three new parameters are given in
Table 9. For the remaining six parameters from Table 5 the
ranges did not change, except for the uncertain mass q, the
range of which is now from 50 to 100 kg m
. A negative
value for parameter qwould mean a reduction in the esti-
mated initial mass of the building, which would also com-
pensate for the variance in the timber density and the
discrepancy of the weight of non-structural elements from
the documented values.
As in the model updating in Section 5.5, a multi-object-
ive genetic algorithm was selected for the optimization in
Ansys. Due to longer computation times, the number of
samples per iteration was 75 with the limit of 12 iterations.
The maximum allowable Pareto percentage was 70%, and
the convergence stability percentage was 1%. Objective func-
tions from Equations (7) and (8) remain the same as for the
first updating. The algorithm converged in 9 iterations with
1.33% Pareto percentage and 0.65% stability percentage
giving three candidate points shown in Table 6. CP1 is
selected as it gives the lowest d
, see Table 10.
6.3. Results of the second updating
The resulting values of the old parameters are close to those
from the first model updating (compare CP1 in Tables 6 and
10). There is a change for e
, where the previously updated result
(50.9%) changed to 59.8% of the initial value, which is still a rea-
sonable solution according to the discussion in Section 5.6.
Differences in other stiffness parameters are either not very sig-
nificant (within 5% from the first updating for parameters e
and g
) or they are around the mean value of the material par-
ameter (5.2% less than the initial value for e
). It can be con-
cluded that for the parameter values for e1,e2,e3,g1and g
Table 10, the observations made in Section 5.6 still hold and that
the values from the second updating are reasonable. The uncer-
tain mass parameter qsettles at a value of 2.95 kg m
in effect, reduces the estimated initial mass of the building by
6.22%. Compared to the result of the first updating, the second
updating suggests that the total mass of the building (without
ground floor slab and foundation) is 91% of the total mass
resulting from the first updating. This is still within the reason-
able bounds for the timber building, having in mind that even
the mean value for the C24 spruce density varies by more than
10% between relevant documents, see Table 2.
The newly introduced parameters provide insight into
how the foundation might behave under small amplitude
and low frequency range dynamic excitations. The two hori-
zontal spring stiffness parameters (k
and k
) settled on
Figure 15. FMAC plot of the updated model.
Figure 16. MAC matrix of updated model.
Figure 17. Modelling of the foundation.
values near the upper bound, where the horizontal motion
is almost completely restrained. Thus, the second FE model
updating suggests that the horizontal motions of the foun-
dation system are negligible. In contrast, vertical spring stiff-
ness parameter k
settles to a value that allows some
movement according to the sensitivity analysis in Figure 18.
The remaining results of the second updating, i.e. the nat-
ural frequencies and MAC values, are presented in Figures
19 and 20. They are compared with the results of the first
updating in Table 11. For this comparison see also MAC
matrices from Figures 16 and 19 and FMAC plots from
Figures 15 and 20. The results show that by adding founda-
tions to the FE model, matching with the experiments has
not improved. In the terms of the mode shapes, there is
slightly better matching with the first, but worse matching
Figure 18. One-at-a-time sensitivity analysis for the spring stiffness parameters. Parameter range for the second model updating is shaded in red. The updated
value is presented with red line.
Table 10. Values of parameters and objective functions of the initial model and of three candidate points representing the solution of the second
model updating.
Parameter Initial model CP1 CP2 CP3
Value % of initial Value % of initial Value % of initial
[GPa] 12 7.17 59.8% 8.52 71.0% 7.16 59.7%
[GPa] 12 11.38 94.8% 10.87 90.6% 10.34 86.2%
[GPa] 12 8.42 70.2% 6.76 56.3% 7.77 64.8%
[MPa] 460 726.1 157.8% 741.5 161.2% 704.8 153.2%
[MPa] 460 213.0 46.3% 210.7 45.8% 213.0 46.3%
q[kg m
]252.95 6.22%
6.95 7.11%
2.61 6.15%
[N mm
] 2.14e5 1.52e5 2.16e5
[N mm
] 4.00e4 6.87e4 3.88e4
[N mm
] 0.315 0.191 0.317
[103] 74.9 4.09 4.83 5.36
[102] 58.1 4.72 4.65 4.83
Difference from initial model presented as a percentage of estimated initial mass of the building.
Table 9. Additional parameters for the second model updating.
Parameter Range Description
to 10
Stiffness of the horizontal springs on the locations of piles.
to 10
Stiffness of the vertical springs on the locations of piles.
to 1 N mm
Horizontal area spring stiffness on the foundation walls.
with the sixth mode shape. Matching of the natural frequen-
cies has not improved either. However, the overall results of
the second updating for frequencies and MAC values are
only slightly worse than those obtained in the first updating.
It can be therefore concluded from the above results that
for low frequency range (2 Hz to 10 Hz) and for small
amplitude dynamic response (below 0.005 m/s
), modelling
of foundation is not necessary for the Yoker building.
7. Conclusions
The finite element modelling and the finite element model
updating of seven-storey CLT building have been presented.
The model updating was based on a successful modal test-
ing of a building in operation that resulted in high-quality
FRFs and good quality of modal estimates of the fundamen-
tal and higher modes of vibration, seldom seen in AVT-
based modal testing (Ao & Pavic, 2021). Before performing
the modal testing, the best-engineering-judgement FE model
(called the initial FE model) of the building was prepared.
Comparison of its results with the experimental leads to the
following conclusion. A FE model that does not take into
account the connections can predict the basic bending and
torsion natural frequencies of the considered CLT building
within a reasonable error (below 7%) under the condi-
tions that:
1. A fine mesh of layered shell FEs is used to model the
load-bearing components of the building (discretization
error is 2% in our case).
2. The percentage of the non-load bearing partition walls
that are not included in the model is small (6% in
our case).
3. The dead mass of the building is carefully estimated
from the design documents.
4. The uncertain mass is estimated reasonably (25 kg/
in our case).
5. The mean values for the material parameters are used
(in our case given by CLT manufacturer).
6. The floors are modelled as deformable.
Although not checked, it appears from the sensitivity
analysis that the assumption that the CLT floors behave like
rigid diaphragms might not considerably increase the error
for the lowest natural frequencies. This is in line with
research by Aloisio et al. (2020) where they concluded that
the CLT floors behave like rigid diaphragms for the funda-
mental modes. Let us note, however, that the shear walls of
the studied building are composed storey-wise of large CLT
panels with pre-cut openings, and that any other arrange-
ment with smaller CLT panels would very likely increase
the error.
The basis for the FE model updating were the results of
the input-output FRF-based modal testing, where both the
excitation force and the corresponding dynamic response
are measured. The performed FE model updating gave an
excellent match between the results of the updated model
and the experimental ones for the first six vibration modes.
Based on the FE model updating, the following was found:
1. The greatest influence on the computed vibration
modes has the in-plane shear stiffness of the shear
walls, which is considerably higher than the estimate
based on the mean in-plane shear modulus for CLT
specified by the manufacturer. However, because of
Figure 19. MAC matrix of the 2
updated model.
Figure 20. FMAC plot of the 2
updated model.
Table 11. Comparison of results of two model updatings.
Experiments 1
updating 2
Frequency Deviation MAC
Frequency Deviation MAC
2.85 Hz 2.84 Hz 0.41% 0.83 2.79 Hz 2.11% 0.88
2.93 Hz 2.95 Hz 0.72% 0.99 2.88 Hz 1.71% 0.99
3.13 Hz 3.08 Hz 1.54% 0.97 3.02 Hz 3.51% 0.96
3.63 Hz 3.77 Hz 3.75% 0.96 3.79 Hz 4.41% 0.96
6.73 Hz 6.70 Hz 0.46% 0.95 6.80 Hz 1.04% 0.95
8.74 Hz 8.64 Hz 1.16% 0.90 8.70 Hz 0.46% 0.84
9.68 Hz 9.38 Hz 3.11% 0.78 9.68 Hz 0.07% 0.73
11.9 Hz 12.4 Hz 4.30% 0.56 12.8 Hz 7.67% 0.66
[103] 1.87 4.09
[102] 4.53 4.72
large documented variance in this particular material
moduli, it is difficult to state how much of the increase
can be attributed to the material parameter and how
much to other uncertainties.
2. The CLT floors of the considered building have large
in-plane flexibility, mainly for the in-plane shearing but
also for the in-plane stretching. This can be attributed
to the floor connections and also to the specific floor
plan of the building. Large in-plane flexibility of the
CLT floors is reflected mainly for the higher modes.
Our results thus show that the application of the rigid-
diaphragm assumption for the CLT floors is not justi-
fied for the higher modes, but it is acceptable for the
fundamental modes (as already mentioned above).
3. The wall-floor joints influence the vertical in-plane stiff-
ness of the shear walls, which is reflected mainly for the
lowest modes.
4. Inclusion of the foundation in the FE model is not
necessary for small amplitudes and studied dynamic
response of the observed building.
Finally, let us mention that the presented study is part of
the research campaign for getting reliable data for modelling
wind-induced vibrations of TTBs (see Abrahamsenet al.,
2020). The idea is to estimate the key dynamic parameters
of a set of existing TTBs in operation by combining modal
testing and FE model updating, and make an assessment of
results to generalize the findings.
The support of ERA-NET Cofund Forest Value and the corresponding
funding bodies (Ministry of Education, Science and Sport of the
Republic of Slovenia for BK and BB, and Forestry Commission GB for
WKA) is gratefully acknowledged (DynaTTB project). BK and BB also
acknowledge the financial support of the Slovenian Research Agency
(J2-2490). We thank F. Perez, the designer of the Yoker building, from
Smith and Wallwork Ltd at Cambridge, UK, for helpful discussions,
and prof. B. Pulko from University of Ljubljana for suggestions regard-
ing foundation modelling.
Disclosure statement
No potential conflict of interest was reported by the authors.
ERA-NET Forest Value; Ministrstvo za Izobra
zevanje, Znanost in
Republike Slovenije.
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... The application steps are illustrated in Fig. 3. The building and its FE model were already described in [36]. Therefore, only basic information is given hereinafter. ...
... The FE model for computing eigenfrequencies and eigenvectors of Yoker was prepared by Ansys [37]. The study [36] revealed that modelling of the foundation and the soil is not necessary when dynamic response with small vibration amplitudes is studied. For this reason, only the above ground part of the structure was modelled, with degrees of freedom restrained to zero at the bottom of the mesh. ...
... In this way, the FE model depends on the actual realization of the value of these parameters. The choice was based on professional expertise and an educated guess established by an extensive one-at-thetime sensitivity analysis, as well as on the conclusions drawn from the deterministic FE model updating of Yoker presented in [36]. ...
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A framework for the probabilistic finite element model updating based on measured modal data is presented. The described framework is applied to a seven-storey building made of cross-laminated timber panels. The experimental estimates based on the forced vibration test are used in the process of model updating. First, a generalized Polynomial Chaos surrogate model is derived representing the map from the model parameters to the eigenfrequencies and the eigenvectors. To overcome the difficulties caused by mode switching, we propose a novel approach to mode tracking based on partitioning an extended and low-rank representation of the k mode shapes resulting from different setups of the finite element model into k clusters by the k-means clustering algorithm. Second, the surrogate model derived with the help of mode pairing is used to efficiently perform sensitivity analysis and uncertainty quantification of the first five frequencies and the corresponding mode shapes. Finally, the surrogate-based Bayesian update of the model parameters is efficiently performed, providing engineers not only with a finite element model that gives a good fit to the experimental modal data, but also a stochastic model that represents the uncertainties originating from the initial model and the uncertainties of measuring modal properties.
... Therefore, structural engineers need guidelines and models to predict the modal properties of a complete building. Investigations combining experimental and numerical methods aim at quantifying the three structural governing parameters Abrahamsen et al. (2020), Kurent et al. (2021), Manthey et al. (2021) and Tulebekova et al. (2022). In the following three parts, simplified estimations and guidelines from several design codes based on traditional building types are presented as well as some main outcomes from the DynaTTB project and highlights from other papers. ...
... Such values are recommended as upper limits. The model updating of a 7-story CLT residential building showed that 20-25 kg/m 2 gave a good correlation with the experimental modal properties, Kurent et al. (2021). Tulebekova et al. (2022) also estimated the mass due to living loads on floors with different occupations to be much lower: 16 kg/m 2 in the office, 21 kg/m 2 in the hotel and 33 kg/m 2 in the apartments. ...
... From vibration tests and model updating, the following highlights have been pointed out to correctly model the modal characteristics of CLT platform buildings with 7-8 story, Auclair et al. (2018), Aloisio et al. (2020) and Kurent et al. (2021): ...
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Climate change and densification of cities are two major global challenges. In the building and construction industry, there are great expectations that tall timber buildings will constitute one of the most sustainable solutions. First, vertical urban growth is energy and resource-efficient. Second, forest-based products store carbon and have one of the highest mechanical strength to den-sity ratios. If the structural substitution of concrete and steel with wood in high-rise buildings awakens fears of fire safety issues, engineers and research-ers are particularly worried about the dynamic response of the trendy tall tim-ber buildings. Indeed, due to the low density of wood, they are lighter, and for the same height, they might be more sensitive to wind-induced vibrations than traditional buildings. To satisfy people’s comfort on the top floors, the ser-viceability design of tall timber buildings must consider wind-induced vibra-tions carefully. Architects and structural engineers need accurate and verified calculation methods, useful numerical models and good knowledge of the dynamical properties of tall timber buildings. Firstly, the research work presented hereby attempts to increase the under-standing of the dynamical phenomena of wind-induced vibration in tall build-ings and evaluate the accuracy of the semi-empirical models available to esti-mate along-wind accelerations in buildings. Secondly, it aims at, experimen-tally and numerically, studying the impact of structural parameters – masses, stiffnesses and damping – on the dynamics of timber structures. Finally, it suggests how tall timber buildings can be modeled to correctly predict modal properties and wind-induced responses. This research thesis confirms the concerns that timber buildings above 15-20 stories are more sensitive to wind excitation than traditional buildings with concrete and steel structures, and solutions are proposed to mitigate this vibra-tion issue. Regarding the comparison of models from different standards to estimate wind-induced accelerations, the spread of the results is found to be very large. From vibration tests on a large glulam truss, the connection stiff-nesses are found to be valuable for predicting modal properties, and numerical reductions with simple spring models yield fair results. Concerning the struc-tural models of conceptual and real tall timber buildings, numerical case stud-ies emphasize the importance of accurately distributed masses and stiffnesses of structural elements, connections and non-structural building parts, and the need for accurate damping values.
... Regarding timber buildings, Riggio and Dilmaghani [21] show in a recent literature review that most of the previous investigations on the dynamic behavior in timber structures have been conducted over a short monitoring period. For example, there are measurements on buildings in the USA [22], Sweden [23], Norway [24], and the United Kingdom [25] that were performed during a single day. In terms of long-term dynamic monitoring of timber buildings, the House of Natural Resources in Switzerland [26] is one example. ...
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With the increased availability of timber materials, such as cross-laminated timber, the number of buildings using timber as a structural material has been rapidly increasing. As these buildings are new to the market, limited data and research on their long-term structural modal performance are available. This is particularly important in timber buildings since the material properties of wood are highly affected by environmental factors, especially the moisture content. Over time, the evolution of the dynamic properties is essential for damage indication in structural health monitoring systems since natural changes can mask the influence of damage. This work presents three years of observations from a structural monitoring system collecting data ever since completing a four-story timber-concrete hybrid building in Sweden. Ambient vibrations of the building were measured using geophones, resulting in 3,100 datasets. The temperature and relative humidity were measured both externally using a weather station and internally using sensors embedded in several walls and a slab in the building. The observed natural frequencies of the building vary with ± 0.2 Hz around the mean value over time. Linear regression analysis shows a significant correlation between the moisture content of a cross-laminated timber slab and the natural frequencies (coefficient of determination R2 up to 0.84). A predictive model for the natural frequencies is presented, taking seasonal variations and a dry-out of the structure into account. Variations from the expected values are ± 0.1 Hz at most. The model clearly narrows the error margins for damage indication in a structural health monitoring system.
... Therefore, assessing the effects of timber plasticization is crucial. In addition, the effect of CLT floor on the rocking response of the CLT panel is significant as it affects both the structural capacity [32] and the low-vibration dynamic response [33]. ...
This paper investigates the effect of timber plasticization on the ultimate lateral capacity of rocking Cross-Laminated Timber shear walls with different characteristics. Simplified capacity models predict a CLT wall ultimate capacity by multiplying the hold-down ultimate resistance by its distance to an assumed pivot point, often coincident with the panel edge. However, timber plasticization at the interface with the foundation can significantly reduce the lever arm of the hold down reaction. This paper aims at assessing the effect of timber plasticization and panel characteristics (geometry, width, presence of openings, etc.) on the position of the pivot point, expressed by the dimensionless lever arm , namely the ratio between the distance of the hold-down geometrical axis from the compressed timber resultant and the distance between the hold-down geometrical axis and the panel edge. An extended covariance-based sensitivity analysis of several Finite Element (FE) models, representing all the CLT shear wall design variability was carried out. The FE model, developed in Abaqus, has been calibrated on the experimental cyclic response of a CLT wall panel. Among the chosen parameters, the sensitivity analysis proved that the most significant ones affecting are two: the ratio between the hold-down reaction and the maximum resistance of the compressed timber, and the width of the opening. Accordingly, the authors estimated an elementary empirical regression equation based on the FE model results for predicting the dimensionless lever arm () in the capacity equation of CLT panels. The use of this elementary formulation allows the designer to estimate with considerable accuracy the lateral capacity of a CLT panel given the panel geometry, the ultimate resistance of the hold-down, the compression strength of timber perpendicular to the grain and the vertical load. Almost all points used for the linear regression fall within the confidence bounds, thus proving the accuracy of the proposed empirical formula for the dimensionless lever arm.
... Indeed, vibration and cyclic tests have been performed to explore stiffness and energy dissipation in engineered timber products [14][15][16][17][18], in mechanical connections with steel plates and dowels [19,20], and for different lateral-resisting truss or frame prototypes [21][22][23][24]. During the last decade, many ambient vibration campaigns, on real buildings, that focus on the lowest eigenfrequencies and damping ratio have been performed [25][26][27][28], and recently, taller timber buildings have been excited with mass inertia shakers to improve estimates of modal properties [29][30][31][32]. ...
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The rise of wood buildings in the skylines of cities forces structural dynamic and timber experts to team up to solve one of the new civil-engineering challenges, namely comfort at the higher levels, in light weight buildings, with respect to wind-induced vibrations. Large laminated timber structures with mechanical joints are exposed to turbulent horizontal excitation with most of the wind energy blowing around the lowest resonance frequencies of 50 to 150 m tall buildings. Good knowledge of the spatial distribution of mass, stiffness and damping is needed to predict and mitigate the sway in lighter, flexible buildings. This paper presents vibration tests and reductions of a detailed FE-model of a truss with dowel-type connections leading to models that will be useful for structural engineers. The models also enable further investigations about the parameters of the slotted-in steel plates and dowels connections governing the dynamical response of timber trusses.
... They performed a detailed experimental modal analysis of the slab with dimensions 16 × 11 m. Kurent et al. [29] performed the finite element (FE) model updating based on the experimental estimation of the key dynamic properties of a seven-story building made entirely of cross-laminated timber (CLT) panels. The dynamic properties were obtained from an input-output full-scale modal testing of the building in operation. ...
This study presents the experimental and numerical assessment of natural frequencies and corresponding mode shapes of cross-laminated timber (CLT) beams subjected to a series of damage cases. To this aim, two different cantilever CLT beams consisting of three layers are considered. Damages on the beam are represented by transversal notches (cracks) through the thickness. Six damage scenarios on the beam models are considered. Experimental measurements via the operational modal analysis are performed to extract the natural frequencies and corresponding modes shapes of the beams under the considered damage cases. To verify the experimental results, the finite element modal analysis is also performed by ANSYS® finite element software. The material moduli necessary for the numerical analyses are determined from a single-layer cantilevered timber beam by applying the finite element model updating procedure. The effect of damages (cracks) on the modal characteristics of CLT beams is investigated. Experimental and numerical results show that especially the cracks near the fixed-end are highly effective on the natural frequencies, corresponding mode shapes, and damping ratios of the beams considered. In cases of multiple damages, the serious damage severity causes a change in the order of mode shapes. There is not found a direct relationship between the gluing applied to the piecewise material in the core layer and the modal characteristics. The results from this study can highly benefit the emerging research field of structural health monitoring on timber structures.
Based on the Modal Stability Procedure (MSP), this paper investigates numerical variability of vibration frequencies of novel adhesive free engineered wood products (AFEWPs), namely adhesive free laminated timber beams (AFLB) and adhesive free cross-laminated timber panels (AFCLT), assembled through thermo-mechanically compressed wood dowels. Structures are modelled by finite element method with twenty-node hexahedral solid elements. Several new variants of MSP formulation for the twenty-node solid element have been developed, and the most suitable one using an efficient diagonal mass matrix was selected for the study. Statistical characteristics of the frequencies obtained from the MSP formulation are compared with those obtained from a direct Monte Carlo Simulation. Comparison of computational cost between the MSP formulation and the direct Monte Carlo Simulation is also presented, showing the efficiency of the MSP formulation.
Conference Paper
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Wind-induced dynamic excitation is becoming a governing design action determining size and shape of modern Tall Timber Buildings (TTBs). The wind actions generate dynamic loading, causing discomfort or annoyance for occupants due to the perceived horizontal sway – i.e. vibration serviceability failure. Although some TTBs have been instrumented and measured to estimate their key dynamic properties (natural frequencies and damping), no systematic evaluation of dynamic performance pertinent to wind loading has been performed for the new and evolving construction technology used in TTBs. The DynaTTB project, funded by the Forest Value research program, mixes on site measurements on existing buildings excited by heavy shakers, for identification of the structural system, with laboratory identification of building elements mechanical features coupled with numerical modelling of timber structures. The goal is to identify and quantify the causes of vibration energy dissipation in modern TTBs and provide key elements to FE modelers.
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Mass timber construction has been gaining momentum in multi-story residential and commercial construction sectors in North America. As taller mass timber buildings are being planned and constructed, in-situ dynamic tests of this type of construction can be performed to further validate their design and use. As part of this larger effort, an in-situ dynamic characterization testing campaign based on ambient vibration measurements was conducted on a recently constructed four-story mass timber building located in Portland, Oregon. The building features cross-laminated timber (CLT) floors, a glued laminated timber (GLT) framing gravity system, and light-frame shear walls and steel HSS hold-downs that compose the lateral resisting system of the building. Ambient vibration acceleration testing data were collected using 18 accelerometers that were wired to a portable data acquisition system in two experimental setups. Approximately 2 h of bi-directional horizontal acceleration data were recorded. In this paper, two operational modal analysis methods are used for estimating the modal parameters (frequency, damping, and mode shapes) based on the data collected. In addition, a multi-stage linear Finite Element (FE) model updating procedure is presented for this building type and the FE estimates of frequencies and mode shapes are compared to estimates from the collected data. The calibrated FE model provides confidence to the operational modal results and presents a comprehensive modal characterization of the building. At ambient levels of excitation, the developed FE model suggests that stiffness of the non-structural elements, such as the exterior wall cladding, and glazing affects the modal response of the building considerably. Lessons learnt on this unique and first of a kind four-story structure constructed in the United States and implications for taller mass timber buildings are summarized and provide valuable insight for the design and assessment for this building type under future dynamic excitation events.
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Cross laminated timber (CLT) is usually comprised of multiple timber layers having alternating grain directions. Because individual boards are glued on their faces between layers, but usually not glued on their edges within layers, those edges define “precracks” in the composite. When exposed to differential thermal and moisture expansion after installation, CLT, like all cross-laminated composites, is prone to formation of “additional cracks”. Confidant CLT design must be able to account for changes in CLT properties during life of a structure caused by such additional cracks. By extending variational mechanics methods for aerospace composites, this paper provides analytical solutions for all in-plane mechanical, thermal expansion, and moisture expansion properties of a three-layer CLT panel. By using the three-layer solution to evaluate effective layer properties as a function of the number of cracks, the analysis can be extended to in-plane mechanical, out-of-plane bending, and expansion properties for CLT panels with any number or arrangement of layers. Some sample calculations are provided along with comments on limitations of the approximations and needs for future work.
Conference Paper
This paper describes a novel and oven-controlled crystal oscillator (OCXO) high-precision synchronised wireless data acquisi-tion system for modal testing of large structures. The system was used for the first time for a rare FRF-based modal testing ofa full-scale multi-storey building in operation. National Instruments CompactRIO and LabVIEW were utilised to develop wire-less multi-channel data loggers to resolve typical, and sometimes insurmountable, problems related to the logistics of longcables connecting sensors with data acquisition in ambient vibration testing (AVT) exercises on operational structures. SeveralOCXO-based data loggers were used to distribute sensors wirelessly across the structure, using a sub-microsecond sensorsynchronisation procedure to measure simultaneously not only the structural vibration response but also the forcing functionneeded in FRF-measurements. As part of the setup, a spectrum analyser (SA) was used to provide the shakers’ excitationsignal and perform a point accelerance FRF measurement at a location close to the data acquisition centre and with minimumwired infrastructure. Two different data acquisition systems (OCXO- and SA-based) used independent time clocks. To validate the OCXO-based FRF measurement in buildings, modal testing was carried out on a 15-tonne laboratory-based testfloor and a full-scale 7-storey condominium building made of cross-laminated timber. The combination of distributed OXCO-based wireless and synchronised data loggers coupled with an SA-based force generation and FRF point-mobility quality assur-ance measurement was successfully used to identify the sway modes’ dynamic properties of the structure.
No appropriate method exists to calculate the in-plane flexibility of Cross Laminated Timber as a floor diaphragm. This flexibility affects the load distribution between shear walls, bracing or cores, as well as adding to local deflections and inter-storey drift. This paper presents a sensitivity analysis based on experimentally measured connection behaviour from the literature and the present study. An important new contributing factor is described: the connection of the floor panels to the supporting wall panels below allows the walls to act as top and bottom chords in the bending and shear of the panel. A new equivalent frame model is described to capture the significant mechanisms of deformation of the diaphragm, validated against a planar finite element model of the elastic behaviour of the panels and the connections between them. The low computational cost of the simplified model allows a wide sensitivity analysis to be carried out, and also makes it suitable for practical design calculations. The flexibility of the floors studied here was seen to be dominated by the slip between panels, rather than panel rotation or bending of the panels themselves. The supporting walls have a strong influence on the moment distribution, but do not strongly influence the slip between panels.
A review is presented on a wide range of optimal sensor placement (OSP) strategies and ways of evaluation. An assessment-guided optimal sensor placement algorithm based on minimal root mean square is proposed to give quantitative comparison on these options. The algorithm is applied to an example of a cantilever beam, as well as to a jacket-platform where model uncertainty and measurement error are included simultaneously. The results reveal the influence of the number of desired sensors and the number of modes of interest. It is shown that the optimal sensor placement selected by the proposed strategy yields the best modal orthogonality of the corresponding mode shapes, and competitive results are derived on the other two assessment standards, i.e. the condition number of the reduced mode shape matrix and the determinant of the Fisher information matrix. The conclusions also show that the effective independence method keeps the largest determinant, and there seems no regular trend on the condition number but unexpected biased solutions can be derived when unreasonable combination for number of wanted sensors and modes of interest are chosen. The proposed minimal root mean square algorithm is capable of avoiding this drawback.
Numerical models of large civil engineering structures are prone to errors and uncertain system parameters, which inevitably affect the ability of such models to accurately predict dynamic behavior. Finite element (FE) model updating can be used to calibrate the numerical models towards the observed behavior. In this paper, a case study of the sensitivity method in FE model updating is presented. The methodology is applied to the Bergsøysund Bridge, which is a long-span floating pontoon bridge in Norway. A system identification is performed based on acceleration data and thirty vibration modes are identified. The FE model is calibrated by reducing the difference between the identified and numerical natural frequencies and mode shapes of the bridge. The model uncertainties are parametrized with a total of 27 parameters. We demonstrate how an analytical sensitivity matrix can be constructed for floating structures, where the system mass and damping matrices are functions of frequency due to fluid-structure interaction. After updating, the mean error in natural frequencies is decreased from 3.23% to 2.34%, and the average MAC number is increased from 0.87 to 0.94. Although the largest errors are significantly reduced, the updated parameters are believed to be affected by noise from the system identification. Challenges related to the presence of very closely spaced vibration modes are also shown, in which matching the identified modes to the modeled modes becomes difficult. This study indicates that models of large bridges can be significantly improved, but many practical issues still exist.
A current trend (2016) to construct high-rise timber buildings is seen. In order to understand the limitations posed by the timber material, wind-induced dynamic behaviour causing vibrations in the serviceability limit state has to be studied. The aim of this research is to calculate the natural frequency and acceleration levels of timber buildings having a cross-laminated timber structure to further the understanding of its behaviour and how a change in parameters affects building performance as reflected against comfort criteria. The results were calculated through finite element modelling using commercial software and by performing a modal analysis. The parameters under scrutiny were material stiffness, wall density, damping ratio, building height, and building footprint. The results show that even at moderate building heights (12-14 storeys), the comfort criteria are not fulfilled. Furthermore, the interaction between stiffness and mass for timber buildings needs to be explored further. And since the change of building footprint has a strong influence on the dynamic behaviour, the interplay between architectural and structural design becomes more important. Finally, more data on measurements of damping in timber buildings need to be collected to further validate simulation models.
Cross-laminated timber (CLT) is increasingly being used in residential and nonresidential applications. While the quantification of the in-plane stiffness of CLT shear walls is required to design a CLT structure subjected to lateral loads, the design guidance, specifically for walls with openings, is limited. The study quantified the stiffness of CLT panels under in-plane loading. A finite element analysis model of CLT panels was developed and verified with test results of CLT panels under in-plane loading. The influence of openings on the stiffness was evaluated using a parametric study varying the size and shape of the openings and the aspect ratios of the openings as well as the wall aspect ratios. Based on the results, equations were proposed to calculate the in-plane stiffness of CLT walls with openings. Subsequently, a sensitivity analysis was performed to evaluate the contribution of each parameter to the model response.