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Structure and Infrastructure Engineering

Maintenance, Management, Life-Cycle Design and Performance

ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/nsie20

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: https://doi.org/10.1080/15732479.2021.1931893

© 2021 The Author(s). Published by Informa

UK Limited, trading as Taylor & Francis

Group

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

Bla

z Kurent

a

,Bo

stjan Brank

a

and Wai Kei Ao

b

a

Faculty of Civil and Geodetic Engineering, University of Ljubljana, Ljubljana, Slovenia;

b

College of Engineering, Mathematics and Physical

Sciences, University of Exeter, Exeter, UK

ABSTRACT

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.

ARTICLE HISTORY

Received 16 February 2021

Revised 16 April 2021

Accepted 17 April 2021

KEYWORDS

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.

Edsk€

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

CONTACT Bo

stjan Brank bbrank@fgg.uni-lj.si 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 (http://creativecommons.org/licenses/by-nc-nd/4.

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.

STRUCTURE AND INFRASTRUCTURE ENGINEERING

https://doi.org/10.1080/15732479.2021.1931893

connections/joints on the stiffness of TTB’s 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), D’Arenzo, 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)andD’Arenzo 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.

2 B. KURENT ET AL.

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

2

gross floor area, and 550 m

2

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

AnsysV

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. Poisson’s ratio

12

is assumed as 0.3 (we

note that various values for

12

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

thetotalmassoftheload-bearingstructure).Wealsoneglect

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

2

. 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.

STRUCTURE AND INFRASTRUCTURE ENGINEERING 3

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

i

and mesh Mas:

DiðMÞ ¼ fiðMÞ fiðMfÞ

fiðMfÞ(1)

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

DiðMaÞ¼fiðMaÞfiðMfÞ

fiðMfÞ(2)

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

st

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 the”web”and

the”flange”of 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

th

Figure 2. Some details of the Yoker building.

Table 1. Types of CLT panels used.

CLT panel type Thickness [mm] Area [m

2

]

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

1

[MPa] 12 000 11 000

Elastic modulus E

2

¼E

3

[MPa] by EN 338 370

Shear modulus G12 ¼G13 [MPa] 460 690

Shear modulus G

23

[MPa] 50 /

Density q[kg/m

3

] 470 420

4 B. KURENT ET AL.

Table 3. First six FE mode shapes and respective deformations of the 6

th

floor (the experimental mode order is adopted).

Mode Frequency Mode shape 6

th

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

STRUCTURE AND INFRASTRUCTURE ENGINEERING 5

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

th

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

i

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

6 B. KURENT ET AL.

responses of 0.005 m/s

2

and 0.004 m/s

2

in the xand ydirec-

tions, respectively. The excitation signal was wide frequency

bandwidth white noise (0 Hz–10 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:

MACðwi,e,wj,nÞ¼

wT

i,ew

j,n

2

wT

i,ew

i,e

wT

j,nw

j,n

, (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

th

floor.

Figure 7. Layout of shakers and sensors.

STRUCTURE AND INFRASTRUCTURE ENGINEERING 7

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

st

row of the experimental Auto-MAC matrix

strongly resembles the 2

nd

row of the MAC matrix, but it is

also very similar to the 4

th

row of the MAC matrix.

Comparing also the frequencies of those modes, it can be

concluded that the 1

st

experimental mode matches the 2

nd

FE mode. In a similar fashion, we connected the 2

nd

experi-

mental to the 1

st

FE mode, the 4

th

experimental to the 4

th

FE mode, the 5

th

experimental to the 6

th

FE mode, and the

6

th

experimental to the 5

th

FE mode. This leaves us with the

only reasonable connection left between the 3

rd

experimen-

tal and the 3

rd

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

i

val-

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

i

is

defined as the MAC value of i

th

matching pair, i¼1, ...,8

(the order coincides with the order of experimental modes),

and the relative error of the numerical frequency is defined

as

fi,exp fi,FEM

fi,exp

:(4)

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

1

, in-plane shear modulus G

12

, 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.

8 B. KURENT ET AL.

conclude that elastic modulus E

2

, out-of-plane shear moduli

(G

13

and G

23

), and Poisson’s ratio

12

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 be”polluted”

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

1

will

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

0

¼E

1

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, a2½0:6, 0:7:It can be seen that

this simple analysis gives l2ð0:5, 0:7Þfor c2½1, 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,

the”web”and the”flange”of 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

1

and g

2

were introduced. Moreover, another

parameter, e

3

, was introduced to capture the effect of the

floor connections in a smeared sense (besides g

2

).

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 Sobol’method or Sobol’variance 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

i

.Itis

computed through the expected value EXiðYjXi¼x

iÞof

response Yover all parameters except X

i

at fixed value Xi¼

x

i:Large variance of this expected value VXiðEXiðYjXiÞÞ

over the parameter space of X

i

implies a high influence of

parameter X

i

on response Y. The first-order sensitivity index

is computed as a ratio between conditional and total vari-

ance:

Si¼VXiðEXiðYjXiÞÞ

VðYÞ:(5)

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

Ti

is defined as:

STi ¼1VXiðEXiðYjXXiÞÞ

VðYÞ:(6)

The expected value of response Yover parameter X

i

was

computed by fixing all but parameter X

i

and finding its

variance over all parameters except X

i

. If the values of S

i

and S

Ti

are close to zero, parameter X

i

does not have much

influence on response Y. The higher the values of S

i

and S

Ti

the greater the influence of parameter X

i

on response Y.If

the values of S

i

and S

Ti

are similar, there is little interaction

of parameter X

i

with other parameters. Also, if the sum of

all terms S

i

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

Ti

are very close to S

i

. Parameter g

1

has a strong

influence on all but the 5

th

natural frequency. On the other

hand, g

2

strongly influences the 5

th

, but has a negligible

STRUCTURE AND INFRASTRUCTURE ENGINEERING 9

effect on the first three frequencies. Parameter e

1

effects the

first natural frequency. It has also a minor impact on the

other frequencies, except on the 5

th

. Parameter e

2

has a neg-

ligible effect on all natural frequencies. The same can be

said for parameter e

3

for the first three frequencies, while e

3

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

MAC

i

values. Figure 14(b) and (d) show that the total-effect

indices S

Ti

are much higher than the first-order indices S

i

.

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:

dMAC ¼X

6

i¼1

ð1MACiÞ2, (7)

and the other relates to the difference in natural frequen-

cies:

dfreq ¼X

6

i¼1

fi,exp fi,FEM

fi,exp

!

2

, (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

d

freq

and d

MAC

.

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

3

rd

mode and the natural frequencies of the 4

th

and the 5

th

modes. The remaining two modes that are not included in

the objective function (i.e. 7

th

and 8

th

mode) are shown

Figure 10. Auto-MAC matrices.

Figure 11. FMAC plot for the initial FE model.

10 B. KURENT ET AL.

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

th

to 9

th

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

1

is updated to 50:9%of the initial value. As

expected, e

1

captures the effect of the wall-floor joint

explained in Section 5.2. With this in mind, the updated

value for e

1

seems a reasonable solution. Parameter e

2

is

4:6%higher than what the CLT manufacturer claims for E

1

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

i

values are almost unaffected by the change of the

Table 5. Parameters used in sensitivity analysis and model updating.

Parameter Range Property Application

e

1

6 to 12 GPa E

1

Used for CLT panels in walls. Only for layers with fibres in vertical direction.

e

2

10 to 13 GPa E

1

Used for CLT panels in walls. Only for layers with fibres in horizontal direction.

e

3

6 to 12 GPa E

1

Used for CLT panels in floor slabs. All layers.

g

1

400 to 750 MPa G

12

Used for CLT panels in walls. All layers.

g

2

200 to 500 MPa G

12

Used for CLT panels in floor slabs. All layers.

q5 to 100 kg m

–2

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

0

¼E

1

and E90 ¼E2).

Figure 13. Domain of values for factor lfrom Figure 12.

STRUCTURE AND INFRASTRUCTURE ENGINEERING 11

value for e

2

(thus the updated result for e

2

may not be very

trustworthy). Parameter e

3

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

2

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

2

significantly affects the 5

th

mode, as

well as the 4

th

and the 6

th

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

2

. 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

1

. In this con-

text, let us note that the uncertainty in the material param-

eter G

12

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

1

is

only 7:8%higher than the value given for G

12

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

1

may be attributed to

a large extent to the stochastic nature of G

12

, 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

2

,

include the effects of the modelling error. Thus, the updated

values for e1,e3,g1and g

2

are not material properties. The

modelling error is most pronounced for e

1

(due to the wall-

floor joints) and for g

2

(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.

12 B. KURENT ET AL.

captured also by e

3

. It might be that parameter g

1

also

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

3

, modulus of elasticity E¼32

MPa and Poisson’s 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

h

and k

v

,

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

d

. 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

3

Nmm

1

to 2.3 10

4

Nmm

1

for k

h

and

from 7.9 10

3

Nmm

1

to 1.4 10

5

Nmm

1

for k

v

.

Another estimate for the vertical stiffness of the pile is

obtained by simply treating the pile as a bar and obtaining

kv¼EpAp

Lp¼1:67 105Nmm

1

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

v

,k

h

and k

d

, 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

e

1

[GPa] 12 6.11 50.9% 6.23 51.9% 6.24 52.0%

e

2

[GPa] 12 12.55 104.6% 12.45 103.8% 12.57 104.8%

e

3

[GPa] 12 8.85 73.8% 8.98 74.8% 8.98 74.8%

g

1

[MPa] 460 744.1 161.7% 748.0 162.6% 747.8 162.6%

g

2

[MPa] 460 219.0 47.6% 216.1 47.0% 212.0 46.1%

q[kg m

–2

] 25 36.63 þ2.59%

1

36.88 þ2.64%

1

36.37 þ2.53%

1

d

freq

[103] 74.9 1.87 1.90 1.92

d

MAC

[102] 58.1 4.53 4.83 4.87

1

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

i

Frequency Deviation MAC

i

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

STRUCTURE AND INFRASTRUCTURE ENGINEERING 13

Table 8. Graphical comparison of initial and updated model with experimental data.

Experiments Initial model Updated model

14 B. KURENT ET AL.

stiffness of parameters k

h

and k

d

worsens the results

obtained by the first updating from Section 5.5, while the

value of parameter k

v

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

2

. 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

freq

, 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

1

, 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

3

,g

1

and g

2

) or they are around the mean value of the material par-

ameter (5.2% less than the initial value for e

2

). It can be con-

cluded that for the parameter values for e1,e2,e3,g1and g

2

from

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

2

,which,

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

h

and k

d

) settled on

Figure 15. FMAC plot of the updated model.

Figure 16. MAC matrix of updated model.

Figure 17. Modelling of the foundation.

STRUCTURE AND INFRASTRUCTURE ENGINEERING 15

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

v

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

e

1

[GPa] 12 7.17 59.8% 8.52 71.0% 7.16 59.7%

e

2

[GPa] 12 11.38 94.8% 10.87 90.6% 10.34 86.2%

e

3

[GPa] 12 8.42 70.2% 6.76 56.3% 7.77 64.8%

g

1

[MPa] 460 726.1 157.8% 741.5 161.2% 704.8 153.2%

g

2

[MPa] 460 213.0 46.3% 210.7 45.8% 213.0 46.3%

q[kg m

–2

]252.95 –6.22%

1

6.95 –7.11%

1

2.61 –6.15%

1

k

v

[N mm

–1

] 2.14e5 1.52e5 2.16e5

k

h

[N mm

–1

] 4.00e4 6.87e4 3.88e4

k

d

[N mm

–3

] 0.315 0.191 0.317

d

freq

[103] 74.9 4.09 4.83 5.36

d

MAC

[102] 58.1 4.72 4.65 4.83

1

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

k

h

10

4

to 10

5

Nmm

–1

Stiffness of the horizontal springs on the locations of piles.

k

v

10

5

to 10

7

Nmm

–1

Stiffness of the vertical springs on the locations of piles.

k

d

10

-2

to 1 N mm

–3

Horizontal area spring stiffness on the foundation walls.

16 B. KURENT ET AL.

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

2

), 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/

m

2

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

nd

updated model.

Figure 20. FMAC plot of the 2

nd

updated model.

Table 11. Comparison of results of two model updatings.

Experiments 1

st

updating 2

nd

updating

Frequency Deviation MAC

i

Frequency Deviation MAC

i

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

d

freq

[103] 1.87 4.09

d

MAC

[102] 4.53 4.72

STRUCTURE AND INFRASTRUCTURE ENGINEERING 17

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.

Acknowledgements

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.

Funding

ERA-NET Forest Value; Ministrstvo za Izobra

zevanje, Znanost in

Sport

Republike Slovenije.

ORCID

Bla

z Kurent http://orcid.org/0000-0002-9066-6433

References

Abrahamsen, R., Bjertnæs, M. A., Bouillot, J., Brank, B., Cabaton, L.,

Crocetti, R., …Tulebekova, S. (2020). Dynamic response of tall

timber buildings under service load –The DynaTTB research pro-

gram. Eurodyn 2020 Conference (online).

Allemang, R. (2003). The modal assurance criterion –Twenty years of

use and abuse. Sound and Vibration,37(8), 14–21.

Aloisio, A., Pasca, D., Tomasi, R., & Fragiacomo, M. (2020). Dynamic

identification and model updating of an eight-storey CLT building.

Engineering Structures,413, 110593.

Ansys

V

R

. (2020). Ansys Academic Research Mechanical (Release 2020 R1).

Ao, W. K., & Pavic, A. (2020). FRF-based modal testing of sway modes

using OCXO synchronised accelerometers for simultaneous force and

response measurements. Eurodyn 2020 Conference (online).

Ao, W. K., & Pavic, A. (2021). Novel wirelessly synchronised modal test-

ing of operational buildings using distributed OCXO high-precision

data loggers. IMAC XXXIX Conference (online).

Ashtari, S., Haukaas, T., & Lam, F. (2014). In-plane stiffness of cross-

laminated timber floors. WCTE 2014 Conference.

Borgonovo, E., & Plischke, E. (2016). Sensitivity analysis: A review of

recent advances. European Journal of Operational Research,248(3),

869–887. doi:10.1016/j.ejor.2015.06.032

Brandner, R., Dietsch, P., Dr€

oscher, J., Schulte-Wrede, M., Kreuzinger, H.,

& Sieder, M. (2017). Cross laminated timber (CLT) diaphragms under

shear: Test configuration, properties and design. Construction and

Building Materials,147,312–327. doi:10.1016/j.conbuildmat.2017.04.153

Brandner, R., Flatscher, G., Ringhofer, A., Schickhofer, G., & Thiel, A.

(2016). Cross laminated timber (CLT): Overview and development.

European Journal of Wood and Wood Products,74, 331–351.

Brank, B., & Carrera, E. (2000). Multilayered shell finite element with

interlaminar continuous shear stresses: A refinement of the

Reissner–Mindlin formulation. International Journal for Numerical

Methods in Engineering,48(6), 843–874. doi:10.1002/(SICI)1097-

0207(20000630)48:6<843::AID-NME903>3.0.CO;2-E

D’Arenzo, G., Casagrande, D., Reynolds, T., & Fossetti, M. (2019). In-

plane elastic flexibility of cross laminated timber floor diaphragms.

Construction and Building Materials,209, 709–724. doi:10.1016/j.

conbuildmat.2019.03.060

Edsk€

ar, I., & Lidel€

ow, H. (2017). Wind–induced vibrations in timber

buildings–parameter study of cross–laminated timber residential

structures. Structural Engineering International,27(2), 205–216. doi:

10.2749/101686617X14881932435619

Ewins, D. J. (2000). Model validation: correlation for updating.

Sadhana - Sadhana,25(3), 221–234. doi:10.1007/BF02703541

Fotsch, D., & Ewins, D. (2000). Application of MAC in the frequency

domain. Proceedings of the International Modal Analysis

Conference - IMAC, Vol. 1, pp. 1225–1231.

Fotsch, D., & Ewins, D. (2001). Further applications of the FMAC.

Proceedings of the International Modal Analysis Conference -

IMAC, Vol. 1, pp. 635–639.

Gavric, I., Fragiacomo, M., & Ceccotti, A. (2015). Cyclic behavior of

CLT wall systems: Experimental tests and analytical prediction mod-

els. Journal of Structural Engineering,141(11), 04015034. doi:10.

1061/(ASCE)ST.1943-541X.0001246

Herman, J., & Usher, W. (2017). SALib: An open-source python library

for sensitivity analysis. The Journal of Open Source Software,2(9),

97. doi:10.21105/joss.00097

Johansson, M., et al. (2016). Tall timber buildings –A preliminary

study of wind-induced vibrations of a 22-storey building. WCTE

2016 - Word Conference on Timber Engineering.

Liu, K., Yan, R. J., & Guedes Soares, C. (2018). Optimal sensor place-

ment and assessment for modal identification. Ocean Engineering,

165, 209–220. doi:10.1016/j.oceaneng.2018.07.034

Malo, K. A., Abrahamsen, R. B., & Bjertnaes, M. A. (2016). Some

structural design issues of the 14-storey timber framed building

Treet in Norway. European Journal of Wood and Wood Products,

74(3), 407–424. doi:10.1007/s00107-016-1022-5

Mottershead, J. E., Link, M., & Friswell, M. I. (2011). The sensitivity

method in finite element model updating: A tutorial. Mechanical

Systems and Signal Processing,25(7), 2275–2296. doi:10.1016/j.

ymssp.2010.10.012

18 B. KURENT ET AL.

Mugabo, I., Barbosa, A. R., & Riggio, M. (2019). Dynamic characteriza-

tion and vibration analysis of a four-story mass timber building.

Frontiers in Built Environment,5, 86. doi:10.3389/fbuil.2019.00086

Nairn, J. A. (2017). Cross laminated timber properties including effects

of non-glued edges and additional cracks. European Journal of

Wood and Wood Products,75(6), 973–983. doi:10.1007/s00107-017-

1202-y

Oh, J. K., Hong, J. P., Kim, C. K., Pang, S. J., Lee, S. J., & Lee, J. J.

(2017). Shear behavior of cross-laminated timber wall consisting of

small panels. Journal of Wood Science,63(1), 45–55. doi:10.1007/

s10086-016-1591-2

Petersen, Ø. W., & Øiseth, O. (2017). Sensitivity-based finite element

model updating of a pontoon bridge. Engineering Structures,150,

573–584. doi:10.1016/j.engstruct.2017.07.025

Reynolds, T., Casagrande, D., & Tomasi, R. (2016). Comparison of

multi–storey cross–laminated timber and timber frame buildings by

in situ modal analysis. Construction and Building Materials,102,

1009–1017. doi:10.1016/j.conbuildmat.2015.09.056

Reynolds, T., Harris, R., Chang, W.-S., Bregulla, J., & Bawcombe, J.

(2015). Ambient vibration tests of a cross-laminated timber build-

ing. Proceedings of the Institution of Civil Engineers - Construction

Materials,168(3), 121–131. doi:10.1680/coma.14.00047

Rocco Lahr, F. A., Christoforo, A. L., Chahud, E., Branco, L. A. M. N.,

Battistelle, R. A., & Valarelli, I. D. (2015). Poisson’s ratios for wood

species for structural purposes. Advanced Materials Research,1088,

690–693. doi:10.4028/www.scientific.net/AMR.1088.690

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., &

Gatelli, D. (2008). Global sensitivity analysis. The primer. West

Sussex, UK: John Wiley & Sons, Ltd.

Shahnewaz, M., Tannert, T., Alam, M. S., & Popovski, M. (2017). In-

plane stiffness of cross-laminated timber panels with openings.

Structural Engineering International,27(2), 217–223. doi:10.2749/

101686617X14881932436131

Stewart, J., Crouse, J. C., Hutchinson, T. C., Lizundia, B., Naeim, F., &

Ostadan, F. (2012, 9). Soil-structure interaction for building struc-

tures [Tech. Rep. No. 12-917-21]. Gaithersburg, US: National

Institute of Standards and Technology.

Stora Enso. (2019). European Technical Assesment ETA-14/0349 of

03.06.2019 [Tech. Rep.]. Austrian Institute of Construction

Engineering.

St€

urzenbecher, R., Hofstetter, K., & Eberhardsteiner, J. (2010). Cross

laminated timber: A multi-layer, shear compliant plate and its mech-

anical behavior. 11th World Conference on Timber Engineering

2010, WCTE 2010, Vol. 1, pp. 423–432.

Yaghoubi, V., Abrahamsson, T. (2014). The modal observability correl-

ation as a modal correlation metric. In Allemang R., De Clerck J.,

Niezrecki C., Wicks A. (Eds.), Topics in modal analysis (Vol. 7, pp.

487–494). New York, NY: Springer.

Yasumura, M., Kobayashi, K., Okabe, M., Miyake, T., &

Matsumoto, K. (2016). Full-scale tests and numerical analysis of

low-rise CLT structures under lateral loading. Journal of

Structural Engineering,142(4), 1–12. doi:10.1061/(ASCE)ST.1943-

541X.0001348

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