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Currently, there is limited knowledge of the dynamic response of taller glue laminated (glulam) timber buildings due to ambient vibrations. Based on previous studies, glulam frame connections, as well as non-structural elements (external timber walls and internal plasterboard partitions) can have a significant impact on the global stiffness properties, and there is a lack of knowledge in modeling and investigation of their impact on the serviceability level building dynamics. In this paper, a numerical modeling approach with the use of “connection-zones” suitable for analyzing the taller glulam timber frame buildings serviceability level response is presented. The “connection-zones” are generalized beam and shell elements, whose geometry and properties depend on the structural elements that are being connected. By introducing “connection-zones”, the stiffness in the connections can be estimated as modified stiffness with respect to the connected structural elements. This approach allows for the assessment of the impact of both glulam connection stiffness and non-structural element stiffness on the dynamic building response due to service loading. The results of ambient vibration measurements of an 18-storey glulam timber frame building, currently the tallest timber building in the world, are reported and used for validation of the developed numerical model with “connection-zones”. Based on model updating, the stiffness values for glulam connections are presented and the impact of non-structural elements is assessed. The updating procedure showed that the axial stiffness of diagonal connections is the governing parameter, while the rotational stiffness of the beam connections does not have a considerable impact on the dynamic response of the glulam frame type of building. Based on modal updating, connections exhibit a semi-rigid behavior. The impact of non-structural elements on the mode shapes of the building is observed. The obtained values can serve as a practical reference for engineers in their prediction models of taller glulam timber frame buildings serviceability level response.
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Engineering Structures 261 (2022) 114209
Available online 22 April 2022
0141-0296/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
Modeling stiffness of connections and non-structural elements for dynamic
response of taller glulam timber frame buildings
Saule Tulebekova a,, Kjell Arne Maloa, Anders Rønnquist a, Petter Nåvik a,b
aDepartment of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelands vei 1A, Trondheim, 7491, Norway
bSWECO Norge AS, Drammensveien 260, Oslo, 0212, Norway
ARTICLE INFO
Keywords:
Taller timber buildings
Glulam connections
Finite element modeling
Dynamic identification
Model updating
ABSTRACT
Currently, there is limited knowledge of the dynamic response of taller glue laminated (glulam) timber
buildings due to ambient vibrations. Based on previous studies, glulam frame connections, as well as non-
structural elements (external timber walls and internal plasterboard partitions) can have a significant impact
on the global stiffness properties, and there is a lack of knowledge in modeling and investigation of their
impact on the serviceability level building dynamics. In this paper, a numerical modeling approach with the
use of ‘‘connection-zones’’ suitable for analyzing the taller glulam timber frame buildings serviceability level
response is presented. The ‘‘connection-zones’’ are generalized beam and shell elements, whose geometry and
properties depend on the structural elements that are being connected. By introducing ‘‘connection-zones’’,
the stiffness in the connections can be estimated as modified stiffness with respect to the connected structural
elements. This approach allows for the assessment of the impact of both glulam connection stiffness and non-
structural element stiffness on the dynamic building response due to service loading. The results of ambient
vibration measurements of an 18-storey glulam timber frame building, currently the tallest timber building in
the world, are reported and used for validation of the developed numerical model with ‘‘connection-zones’’.
Based on model updating, the stiffness values for glulam connections are presented and the impact of non-
structural elements is assessed. The updating procedure showed that the axial stiffness of diagonal connections
is the governing parameter, while the rotational stiffness of the beam connections does not have a considerable
impact on the dynamic response of the glulam frame type of building. Based on modal updating, connections
exhibit a semi-rigid behavior. The impact of non-structural elements on the mode shapes of the building is
observed. The obtained values can serve as a practical reference for engineers in their prediction models of
taller glulam timber frame buildings serviceability level response.
1. Introduction
Rising awareness of the importance of sustainability in the general
public has led professionals in structural engineering to incorporate the
use of environmentally friendly materials in their design. Therefore, the
focus on timber, which is known for its natural origin and negligible
carbon footprint compared to widely used steel and concrete, is under-
standable. Currently, timber as a structural material is being extensively
utilized in the construction of buildings [1].
In general, the lateral loading on taller glulam timber frame build-
ings is governed by wind-induced vibrations [2]. The intrinsic proper-
ties of wood, including low density and stiffness, make taller timber
buildings susceptible to horizontal excitation under wind loading [3].
Corresponding author.
E-mail address: saule.tulebekova@ntnu.no (S. Tulebekova).
The stiffness, mass, and damping properties and their distributions in
buildings are the factors that affect the vibration response of taller
glulam timber frame buildings. Estimation of stiffness in glulam timber
frame buildings can be challenging and depends on the structural
system used [4]. Experimental results from ambient vibration mea-
surements show that the eigenfrequencies obtained from the numerical
modeling can be systematically underestimated due to the assumption
of pinned connections in glulam timber frames [5,6].
The past studies on taller glulam timber frame buildings emphasize
the fundamental importance of connections in timber structures under
serviceability level dynamic loading [7]. In glulam timber frame build-
ings, the dowel-type connections make a considerable contribution to
https://doi.org/10.1016/j.engstruct.2022.114209
Received 30 October 2021; Received in revised form 19 February 2022; Accepted 27 March 2022
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
the structure stiffness [8]. The estimation of such connection stiffness
can, however, be challenging. In a number of studies, it has been
shown that the static dowel connection stiffness, which is calculated
in accordance with Eurocode 5 [9], is different from the stiffness
calculated from the in-service cyclic tests [8,10]. The common practice
in modeling the dynamic response of glulam timber frame buildings
is to assign pinned conditions to the connections between glulam
elements, [5,6,11,12].
The impact of non-structural elements on the serviceability level
response of tall buildings has been acknowledged in both steel and
reinforced concrete buildings [13]. The previous studies on ambient
vibration measurements of timber buildings suggested that contribu-
tion from the stiffness of non-structural elements, such as internal
plasterboard partition walls and exterior wall cladding (brickwork,
glass, and timber), affects the serviceability level dynamic response
of the building [14,15]. One study where operational modal testing
of a 6-storey timber frame building was performed, showed that the
addition of internal plasterboards had considerably stiffened the whole
building in the translational directions [16]. These studies indicate the
importance of assessment of the effect of non-structural elements on
the dynamic response of buildings.
The main objective of this paper is to present an alternative numer-
ical modeling approach for connections and non-structural elements
(internal plasterboard partition walls and external timber walls), which
can be used for the investigation of the serviceability level dynamic
response of taller glulam buildings. The information at hand for struc-
tural engineering of serviceability dynamics of buildings is basically
mean values of stiffness and mass of the individual components con-
stituting the building. The structural interactions of the components
are dependent on the layout and are usually much more uncertain
than the properties of the components. The current practice is to
either design the connections as pin elements or to assign a specified
stiffness value. The latter can be a cumbersome process since the
stiffness estimates depend on the connection layout, which may vary
from floor to floor. The ‘‘connection-zones’’ directly relate the stiffness
of connection to the stiffness of the glulam timber element that is
being connected. This approach allows for an automated numerical
investigation of the timber connections under ambient vibrations and a
better interpretation of the estimated connection stiffness. The paper is
written in the following order. First, the experimental results based on
ambient vibration measurements of an 18-storey glulam timber frame
building (Mjøstårnet, Norway) are presented. Then, in the numerical
modeling section, the ‘‘connection-zones’’ approach for modeling con-
nections in glulam and non-structural elements is presented, and overall
numerical modeling of the Mjøstårnet building is described. After that,
a parametric study is conducted to explore the effect of stiffness of
connections and non-structural elements on the dynamic response of
the building. Finally, a model updating study is conducted to obtain
the values for parameters of interest. The goal of this study is to present
values for stiffness of connections and non-structural elements (internal
plasterboard partitions and external timber walls) for practitioners to
use as a reference when developing numerical models of taller glulam
buildings for serviceability level vibration response prediction.
2. Ambient vibrations testing
2.1. Building description
The test building is named Mjøstårnet (the Mjosa Tower, Fig. 1)
and is located in Brumunddal, Norway. The total architectural height
of the building (including the truss work on the top) is 85.4 m and
the total height including the spire is 88.8 m. The plan dimensions are
36.3 m by 15.7 m, see also Fig. 5(b). The summary of the structural
system of the building is shown in Fig. 2. The load-carrying system
of the building consists entirely of timber: glue laminated timber (glu-
lam) beams, columns and diagonals. The strength grade for glulam is
GL30c in accordance with EN 14080:2013 [17]. The average beam
cross-section is 400 mm by 500 mm, the corner column cross-section
is 600 mm by 1500 mm, and the average diagonal cross-section is
600 mm by 750 mm. The glulam truss members are interconnected
with combinations of 10 mm thick slotted-in steel plates and 12 mm
diameter dowels [18]. The steel grade for plates is S355 in accordance
with EN 10025-2, which corresponds to 355 MPa yield strength [19].
The steel grade for dowels is EN 1.4418 in accordance with EN 10088,
and has a measured yield strength of 755 MPa [20]. Cross-laminated
timber (CLT) is used in the elevator and staircase shafts, but is not
designed to be part of the horizontal load carrying system. The average
thickness of CLT panels is 200 mm. The CLT panels consist of 5 layers
of C24 spruce boards in accordance with EN 338 [21]. The first ten
floors are made of ‘‘Trä8’’ system — prefabricated timber decks, which
were developed by Moelven [22]. ‘‘Trä8’’ system is composed of Kerto-
Q®structural laminated veneer lumber (Kerto-Q LVL [23]) beams and
a top flange, which is topped with 36-mm thick acoustic panel and
50-mm thick concrete screed (Fig. 3). Stiffening elements made of
Kerto-S®structural laminated veneer lumber (Kerto-S LVL [23]) were
used for stiffening in the perpendicular to span direction. The bottom
flanges are made of glulam timber. The wooden decks average span
is 7.5 m, average width is 2.6 m and total thickness is 360 mm. The
upper six floors are made of 300 mm thick concrete slabs to increase
the self-weight of the structure in order to meet the serviceability
requirements. The facade of the building is comprised of prefabricated
wooden panels. The truss-type glulam pergola is built on top of the
structure for architectural appearance. All structural timber elements
have been provided by Moelven, a Scandinavian producer of structural
timber. The summary of material properties for structural timber are
shown in Table 1.
The building foundation consists of a set of circular steel piles which
are approximately 30 m long, have a diameter of 400 mm and thickness
of 12.5 mm. The pile head is a 2000-mm thick concrete slab at the
base of the building. The piles are in contact with the bedrock at an
approximate depth of 30 m. Above, the soil consists of sand, clay, and
moraine. Based on foundation conditions, the boundary conditions as
pinned supports under the column ends above the concrete foundation
were chosen for modeling.
Wind loading was determined to be the dominating load in the
design combinations. The calculated wind speed was 22 m/s corre-
sponding to the static wind pressure of 1.12 kN/m2 in accordance with
EN 1991-1-4 [9].
2.2. Experimental setup
Experimental dynamic characterization of the Mjøstårnet building
was performed using ambient vibration measurements. Two different
setups have been used: setup on the roof and setup inside the building.
In both setups, a set of 3 triaxial accelerometers along with a data
acquisition system were used for experimental testing. In setup on the
roof, the accelerometers have been mounted on the pergola truss at
the top of the building as shown in Fig. 4. This setup allowed for
capturing the eigenfrequencies and in-plane movement, but did not
allow for determining the mode shapes along the height of the building.
Therefore, the setup has been moved inside the building and the
accelerometers have been placed at the different levels. In the second
setup, accelerometers were placed on 3 different floors, 10th, 16th,
and 18th, aligned vertically in order to capture higher translational
vibration modes (Fig. 5(a)). The locations of the accelerometers were
based on modal analysis results from the numerical model of the build-
ing. The accelerometers were attached with a magnet to a metal plate,
which was mounted directly on the glulam beam by screws (Fig. 5(c)).
Since the experimental setup is being used for long-term measurements,
the placement of accelerometers was limited to locations that are not
obstructing the service of the building and are not accessible to the
public and residents. The building is in a fully operational mode, which
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Fig. 1. Mjøstårnet building (dimensions in m).
Fig. 2. Building structural system.
Table 1
Orthotropic material properties.
Material 𝜌[kg∕m3]𝐸1[MPa] 𝐸2[MPa] 𝐸3[MPa] 𝐺12 [MPa] 𝐺13 [MPa] 𝐺23 [MPa]
Glulam GL30c 430 13 000 300 300 650 650 91.5
CLT, 5 layers 420 6 960 4 650 300 650 650 650
Kerto-Q®LVL 510 10 500 2 200 130 820 430 22
Kerto-S®LVL 510 13 800 450 130 600 600 11
limited the options for placement of the setup significantly. As seen
from the building plan (Fig. 5(b)), the corners of the building, which
have the highest displacement, were not accessible to the general public
and the setup could not be installed there. After discussion with the
building maintenance company, the staircase for the fire escape, which
is used only for emergency cases, was chosen for mounting the setup.
Since the fire safety system requires that the space be isolated from the
rest of the building, it was not possible to extend the wiring system to
other locations on the same floor. The location of the accelerometers in
the fire staircase is shown on the plan view of the building (Fig. 5(b)).
The triaxial accelerometers have high sensitivity of 2000 mV/g and a
lower frequency range between 0 Hz and 1000 Hz [25]. The sampling
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Fig. 3. Graphical illustration of Trä8 floor system [24].
Fig. 4. Accelerometer setup on the roof.
rate for data was 400 Hz. The recorded data was resampled to 20 Hz
using an antialiasing filter in Matlab 2020b [26]. This experimental
setup has been running continuously since December 15, 2020, and
recording the measurements to a server (as of February 2022). Based
on the wind data from the nearest weather station, a 3 hr acceleration
time series from 5th April 2021 with a mean wind speed of 9.8 m/s
were chosen for further analysis.
2.3. Theoretical background
The data was analyzed using the operational modal analysis (OMA)
technique. The family of stochastic subspace identification (SSI) tech-
niques is a common approach to deal with output-only measurements
and is explained in detail in the literature [27]. In the SSI techniques,
a mathematical model with certain parameters adjusted to fit the raw
acceleration time series data is developed and calibrated. In this study,
the data-driven stochastic subspace identification technique (DD-SSI)
approach was used to obtain the modal frequencies, mode shapes,
and damping ratios [27,28]. In DD-SSI, the technique is performed
directly on the measured response data, without pre-processing it. In
SSI techniques, the dynamic system is assumed to be described by the
discrete stochastic state–space model as shown below:
{𝑧𝑘+1} = [𝐴]{𝑧𝑘}+{𝑤𝑘}(1)
{𝑦𝑘}=[𝐶]{𝑧𝑘}+{𝑣𝑘}(2)
where {𝑧𝑘+1}is a state–space vector, which holds the current state of
the system, {𝑦𝑘}is a measured output at a specified sampling rate,
{𝑤𝑘}and {𝑣𝑘}are system noise and measurement noise respectively,
𝑘is a discrete time step, [𝐴]is a state matrix and [𝐶]is an output
matrix. The modal parameters are then extracted from the identified
matrices [𝐴]and [𝐶][29]. The important task is to properly identify the
model with a reasonable number of parameters. This is performed in
the state–space model by choosing the model order, i.e. the dimension
of the A-matrix [28]. The state–space model of order 𝑖is then used to
identify the eigenvalue 𝜇𝑖, from which the corresponding pole 𝜆𝑖can
be obtained at a sampling period 𝑡𝑠. Hence, the modal frequency and
damping ratios, 𝑓𝑖and 𝜁𝑖, can be calculated for each pole as follows:
𝜆𝑖=𝑙𝑛(𝜇𝑖)
𝑡𝑠
𝑓𝑖=𝐼𝑚(𝜆𝑖)
2𝜋𝜁𝑖=𝐼𝑚(𝜆𝑖)
𝜆𝑖(3)
The calculated poles are then plotted on the stabilization diagram
which allows distinguishing between the spurious poles and true poles.
Spurious poles usually appear due to inaccuracies in measurements,
non-stationarity of data, etc. The procedure for determining the true
poles, i.e. the poles containing the eigenfrequency and eigenvalue of
the physical system, is through assigning the tolerance to the frequency
and damping results. The true poles then appear on the stabilization
diagram as the aligned poles which are constant along the specific
frequency. The DD-SSI method has been applied successfully on various
civil engineering structures [2931].
2.4. Results
In this study, the stability criteria for frequency and damping were
1% and 5% respectively and the chosen order number was 100. Fig. 6
shows the stabilization diagram of the combined signals from the
accelerometers in the setup inside the building. The aligned vertical
dots show the identified stable frequencies (6 in total). In addition,
the power spectral densities in two orthogonal in-plane directions were
plotted as gray curves. The left vertical axis represents the model
order and the right vertical axis represents the magnitude of the power
spectral density. The stabilization diagram from the accelerometer data
on the roof showed similar identified frequencies to the ones presented
in Fig. 6. The mode shapes from both setups can be seen in Fig. 7 and
Fig. 8. The first two modes are translational modes in two orthogonal
directions: 1st translational mode at 0.493 Hz in the short direction
(Fig. 1(b)), 2nd translational mode at 0.529 Hz in the long direction
(Fig. 1(a)). The third mode is the torsional mode at 0.813 Hz as seen
from Fig. 8. Mode 4 is the second bending mode at 1.918 Hz in the long
direction, and mode 5 is the second bending mode at 2.146 Hz in the
short direction. The 6th stable frequency at 2.215 Hz is captured in a
long direction, but the mode shape is not possible to determine due to
its higher-order and lack of accelerometers. Damping factor values for
modes 1–6 are 1.5%, 2.3%, 2.2%, 1.2%, 1.7% and 2.0% respectively.
3. Numerical modeling
A numerical model of the building was developed in Abaqus CAE
2017 [32]. Fig. 9 shows the developed FE model of the building with
the mesh geometry. The sensitivity study on the mesh size showed
an insignificant impact on the output natural frequencies. Therefore,
a larger mesh size was chosen to reduce the computational time and
facilitate the optimization process. In Fig. 9(a) the entire assembly
mesh is shown, which includes external walls, glulam frame mem-
bers, CLT shafts, floor elements, and internal partitions. Fig. 9(b)
shows the glulam frame model without the external walls and in-
ternal partitions. ‘‘Connection-zones’’ are added as generalized beam
elements to represent connections between the glulam frame elements.
‘‘Connection-zones’’ are added as shell elements to represent connec-
tions between non-structural elements/CLT shaft and glulam frame, as
well as connections between floor elements. The chart showing the
stages adding ‘‘connection-zones’’ in glulam timber frame elements and
non-structural elements is shown in Fig. 10. In the following sections,
each part of the numerical model of the building is described in detail.
3.1. Structural elements modeling
The glulam frame elements were modeled with one-dimensional
Timoshenko elastic beam elements with an orthotropic material model.
Concrete floors were modeled as 4-node shell elements with the linear
elastic isotropic model. Architectural truss work, (Fig. 1), at the top of
the roof was modeled as added distributed mass on the roof slab. The
balconies at levels 12–17 were modeled as added masses on glulam
beams at the locations of balconies.
The prefabricated timber deck Trä8 is a composite structure and due
to its complexity, a single shell element representing the global defor-
mation model of the floor was chosen for analysis. For this purpose, a
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Fig. 5. Experimental setup.
Fig. 6. Stabilization diagram of the combined signals (vertically aligned dots) and power spectral densities in two orthogonal in-plane directions (gray lines).
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Table 2
Simplified timber deck model properties after optimization.
Model 𝐸1[MPa] 𝐸2[MPa] 𝐸3[MPa] 𝐺12 [MPa] 𝐺13 [MPa] 𝐺23 [MPa] Objective function
Initial 1300 300 300 600 600 50 7.47e6
Optimized 4800 120 990 600 600 50 5.71e9
Fig. 7. Identified mode shapes from merged accelerometer data sets.
Fig. 8. Mode shapes from setup on the roof.
detailed model of the composite timber deck was developed in Abaqus
as shown in Fig. 11. The pressure load was applied in three orthogonal
directions and the resulting deflections were then used as objective
functions to optimize the elastic constants of an orthotropic shell
element, shear properties were kept the same. This shell element was
then used as a simplified model of the composite deck in the building
model to reduce computational time and facilitate model updating. The
resulting material properties after optimization are shown in Table 2
and the thickness of the shell element was 240 mm.
The material properties used for wooden elements in the numer-
ical modeling are given in Table 1. The concrete with a density of
2400 kg/m3, an elastic modulus of 34 GPa, and a Poisson ratio of 0.2
was used for modeling.
3.2. Modeling mass
Building structural system consists mainly of prefabricated timber
elements with known material and geometric properties. Thus, it is
assumed that it is possible to estimate the dead load distribution
accurately. Estimates of added mass, which include the mass of non-
structural elements and live load contribution were made. The added
mass was applied as a uniformly distributed load on the floor elements.
The mass estimates of external walls and internal partitions were taken
from the technical report of the Norwegian research organization [33].
The weight of the external wall is 1 kN/m2and the weight of internal
partitions is 0.5 kN/m2. According to the Eurocode 1 [9], the specified
live load values shall be based on the occupation type of the floor
and a fraction of this live load shall be assigned as structural load
for serviceability limit state (SLS) (Table 3). However, these values
significantly overestimate the actual live load in the current building.
Based on the architectural layout of different occupational floors, the
actual live loads were investigated and calculated and results are shown
Table 3
Live load estimates.
Occupational type Actual load [kN∕m2]Code (SLS) [kN∕m2]
Office 0.16 0.9
Hotel 0.21 0.6
Apartment 0.33 0.6
Rooftop deck 0.16 1.2
in Table 3. The actual live load estimates were applied to the building
model.
3.3. Glulam frame connections
In engineering practice, it is common to assume a pinned connection
between timber elements due to a lack of accurate information about
the connection [34]. In reality, the connection between the timber
elements is neither pinned, nor rigid, but rather semi-rigid, i.e. it
partially transfers the action. Therefore, it is convenient to directly
relate the stiffness properties of the connection to the main timber
elements. Manually calculating and assigning stiffness properties to
the connections and conducting sensitivity study on them can be a
cumbersome task due to the large scale of the model and large variety
of cross-sections. Keeping that in mind, modeling of connections in this
study was performed by introducing the so-called ‘‘connection-zones’’.
The stiffness properties of these ‘‘connection-zones’’ are directly related
to the connected glulam elements, which facilitates the parametric
modeling process. These zones are separate elements with generalized
properties which allow to arbitrarily assign cross-sectional area and mo-
ment of inertia. The approach of representing the axial stiffness of the
connection with ‘‘connection-zones’’ was previously described in the
study by [4]. In this study, the axial and rotational stiffness are assumed
to be linearly dependent on cross-sectional area and the second moment
of inertia respectively. Thus, reduction factors can be introduced, which
account for the reduced cross-sectional area and reduced moment of
inertia in the connections. A dimensionless reduction factor equals the
ratio between the reduced property of the ‘‘connection-zone’’ and the
connected element, e.g. 𝑘𝑟𝑒𝑑,𝐴 =𝐴𝑟𝑒𝑑 𝐴𝑚𝑎𝑖𝑛 or 𝑘𝑟𝑒𝑑,𝐼 =𝐼𝑟𝑒𝑑 𝐼𝑚𝑎𝑖𝑛 .
The glulam frame in the current study consists of a set of beams,
columns, and diagonals, which are connected to each other with dowels
and slotted-in steel plates (Fig. 12(a)). The ‘‘connection-zones’’ were
assigned at the endpoints of beams and diagonals, (Fig. 12(b)). The
ends of ‘‘connection-zones’’ are tied to the connected elements at their
centerlines. The ‘‘main’’ element in this context is either the glulam
beam element which is connected to the column with the dowel con-
nection or the glulam diagonal element, which is connected to the
glulam column, and beam elements with the dowel connection. The
length of ‘‘connection-zones’’ is assumed to be equal to the height of
the main element (beam or diagonal). The cross-sectional area and
moment of inertia are related to the connected structural element
through the reduction factor 𝑘𝑟𝑒𝑑 . Material properties of the connected
glulam section are assigned to the ‘‘connection-zone’’ element and the
density is modified according to the change in geometry to keep the
mass unaltered.
3.4. Non-structural elements
External walls and internal partitions were modeled for the purpose
of investigating their contribution to the global dynamic behavior of the
building. External walls in the building of interest are composite and
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Fig. 9. Numerical model of the building with mesh geometry.
Fig. 10. Sequence of adding ‘‘connection-zones’’ to the building model.
Fig. 11. Model of the composite timber deck.
consist of several layers. The inner layer starts with the 13-mm gypsum
plasterboard, followed by the 198-mm isolation made of mineral wool
and 13-mm wind barrier made of gypsum plasterboard. The outer layer
consists of the external timber cladding followed by timber framing
work with 73-mm air gap. The external wall is attached to the Kerto-
Q timber panel with screws and angles. The Kerto-Q panel is in turn
supported by the composite timber floor which transfers the load to
the load-carrying glulam beams.
External walls were modeled as simplified 4-node elastic shell el-
ements in order to investigate their stiffness contribution to the dy-
namics of the whole structure. Similar to the ‘‘connection-zones’’ in
glulam frames described earlier in this chapter, separate shell elements
were assigned also between the external wall and the glulam element to
represent the ‘‘connection-zone’’ (Fig. 13). The in-plane stiffness of the
connection represented by the shell element is assumed to be directly
related to its thickness. The variation of stiffness in the shell connection
is performed by introducing the reduction factor, 𝑘𝑟𝑒𝑑 , which represents
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Fig. 12. Modeling of glulam frame with ‘‘connection-zone’’ beam elements.
reduction in thickness of the ‘‘connection-zone’’ element with respect to
the main shell element, 𝑡𝑟𝑒𝑑 𝑡𝑚𝑎𝑖𝑛. In this context, the ‘‘main shell’’ ele-
ment is an external wall element (or a partition wall element described
later in the section), which is connected to the adjacent structural
timber elements such as glulam frame and floors. The length of the shell
‘‘connection-zone’’ element is assigned to be equal to the thickness of
the external wall element. The ‘‘connection-zone’’ elements are tied to
the adjacent elements at the centerlines (Fig. 13).
Based on the composition of the external wall, only gypsum plas-
terboard can be considered as a material with stiffness contribution.
However, the numerical implementation of such small ‘‘connection-
zone’’ elements in comparison to their length is not feasible, since it
requires much finer mesh, which in turn leads to significantly increased
computational time. Thus, the lowest value for plasterboard thickness
in the numerical implementation was limited to 100 mm, which is
around 10 times higher than the actual single gypsum plasterboard
thickness. Since the thickness of the gypsum plasterboard in the nu-
merical model increased in comparison to actual thickness, the values
for the stiffness should be reduced accordingly to represent the actual
panel behavior. Therefore, FEM models of the external wall consisting
of double-layer 13-mm gypsum plasterboard and 100-mm plasterboard
were developed and an optimization study with a deflection as objec-
tive function was conducted. The elastic modulus of a single 13-mm
gypsum plasterboard was taken from the literature and is equal to 140
MPa [35], the shear modulus was taken as 70 MPa. Then, the optimiza-
tion study was conducted on the 100-mm plasterboard to determine
the stiffness properties of the panel with the objective function being
shear deflection values. Gypsum plasterboards were modeled with 4-
node elastic isotropic shell elements. The resulting elastic and shear
moduli of the 100-mm plasterboard corresponding to the double layer
gypsum plasterboard from the external wall after optimization were
36.4 MPa and 18.2 MPa respectively.
Internal partition walls in the building are made of two layers of
13-mm gypsum plasterboards on each side of the wall, separated by a
100-mm gap for steel framing studs. Internal partitions are structurally
connected to the floors elements. Similar to the external walls, the
in-plane stiffness contribution is assumed to come from the gypsum
plasterboards. Therefore, the modeling approach described in the pre-
vious paragraph was applied. The ‘‘connection-zone’’ elements were
introduced at the top and bottom of the partition wall elements at the
location where they are attached to the floor elements. The lower limit
Fig. 13. Modeling of the external wall with ‘‘connection-zone’’ shell elements.
for modeling the thickness of internal partition elements was 100 mm,
which is around 2 times higher than the actual gypsum plasterboard
thickness. Thus, a similar optimization technique to the one used for
external walls was implemented. The resulting values of elastic and
shear moduli after optimization were 72.8 MPa and 36.4 MPa for an
isotropic model of the 100-mm gypsum plasterboard.
The elevator and staircase shafts in the building are made of CLT
panels stacked on top of each other. The shafts are not intended to carry
any lateral load and were not considered as part of the load-carrying
system during the design process. The CLT panels are connected to the
floors at each level by means of steel brackets and screws. ‘‘Connection-
zone’’ shell elements have been added between the CLT shaft elements
and a sensitivity study has been conducted, where the thickness of
the ‘‘connection-zone’’ element was varied in the range 0.1–1.0 while
keeping all other parameters fixed. The change in the outputs of
interest, i.e. eigenfrequencies and MAC values (explained in the further
sections) was negligible, with maximum change reaching 0.4%. Thus,
the study on the impact of the stiffness contribution from CLT shafts
was not included in the present parametric study. The fixed value for
the thickness of the ‘‘connection-zone’’ between the CLT shafts and floor
elements (𝑡𝐶𝐿𝑇 = 0.5) was used.
Engineering Structures 261 (2022) 114209
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4. Model updating
Sensitivity-based model updating based on ambient vibration data
has been proven to be effective in their application on real structures
in structural engineering [36]. The numerical model of the building
presented in this study was scripted in Python [37], and the properties
of interest were parametrized in order to investigate their sensitivity
and conduct model updating using the results from the experimental
setup.
4.1. Parameter selection
The dynamic modal response of the numerical model of the building
depends on both mass and stiffness properties. Optimization of both
mass and stiffness can lead to an underdetermined problem with an
infinite number of solutions as mentioned in [38]. The mass properties
are not investigated in the current study since it is assumed that density
and geometric properties of the prefabricated elements can be well
estimated in comparison to the connection stiffness properties. The
glulam bending modulus of elasticity (MOE) and density (𝜌) have a
coefficient of variance values (𝐶𝑂𝑉 ) of 0.13 and 0.1 respectively [39].
In addition, the actual live load estimates were calculated based on the
architectural drawings and site visits, and these values are applied to
the numerical model. The stiffness properties in the numerical model
include the stiffness of main load-carrying elements (glulam frame
and slabs), connections between those elements, and potentially non-
structural elements. The stiffness parameters of the timber structural
elements, such as Young’s modulus, are taken from the specification
of the manufacturer and the highly layered composition of the glulam
elements ensures the mean value properties of the wooden elements.
On the other hand, the stiffness of connections in timber lacks accurate
representation. The current practices on the prediction of connection
stiffness do not give accurate values for the stiffness of the connection.
Additionally, the effect of non-structural elements is generally excluded
but might contribute significantly in low-level dynamics. Therefore,
stiffness of connections in the glulam frame as well as connections in
the non-structural elements were chosen for parametric analysis.
Based on the results from the ambient vibration measurements, it
can be seen that the first two bending mode frequencies, as well as the
two second bending mode frequencies, are very close to each other.
This might be due to the fact that the span of diagonals, which are
part of the lateral load resisting system, is similar in both directions
(Fig. 5(a)). Therefore, the connection stiffness was studied separately
in two directions of the building plane in order to investigate their
effect on the dynamic response of the building. Table 4 shows the list
of parameters of interest. Each of those parameters is a ‘‘connection-
zone’’ element in the numerical model. ‘‘Long’’ and ‘‘short’’ subscripts
stand for ‘‘connection-zone’’ elements in the long and short direction
of the building respectively (Fig. 9(b)). 𝐼𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑙𝑜𝑛𝑔 are moments
of inertia of the ‘‘connection-zone’’ elements at the end of a beam
element, where it is connected to the column. The range in values for
𝐼𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑙𝑜𝑛𝑔 is given as a percentage of the main element and is
representative of reduction in the rotational stiffness of ‘‘connection-
zone’’ elements, 𝑘𝑟𝑒𝑑 . The range of values for 𝐴𝑙𝑜𝑛𝑔 and 𝐴𝑠ℎ𝑜𝑟𝑡 is given
as a percentage of the connected element and give the reduction in
axial stiffness of ‘‘connection-zone’’ elements, 𝑘𝑟𝑒𝑑 . Similarly, 𝐴𝑙𝑜𝑛𝑔 and
𝐴𝑠ℎ𝑜𝑟𝑡 represent the ‘‘connection-zone’’ in the truss diagonals at the
points where they are connected to the beams and columns (Fig. 9(b)).
A preliminary parameter study showed that the moment of inertia in
diagonals and axial stiffness of the beams have no significant effect on
the eigenfrequencies of the building. This is consistent with the truss-
type structural system of the building, where diagonals were designed
to carry the horizontal loads, which leads to insignificant axial stiffness
contribution from beams. Therefore, only moments of inertia of beam
connections and areas of the diagonal connections are studied in the
glulam frame.
The connections between the non-structural elements and the main
structure are given in terms of the thickness of the connection (Table 4).
𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 is the thickness of ‘‘connection-zone’’ elements which are lo-
cated at the top and bottom ends of the external wall panels where they
are connected to glulam beams. The range of values for 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 is given
as a percentage of the thickness of the external wall and represents a
reduction in the in-plane stiffness of the ‘‘connection-zone’’ elements.
𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 is the thickness of the ‘‘connection-zone’’ elements which are
located at the top and bottom ends of the partition wall elements, where
they are connected to the floor elements. The range of values for 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛
is given as a percentage of the thickness of the internal partition walls
and represents a reduction in the in-plane stiffness of the ‘‘connection-
zone’’ elements. Both 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 represent the reduction in
stiffness contribution to the main structure.
4.2. Sensitivity analysis
Sensitivity analysis was performed to assess the effect of the pa-
rameters of interest on eigenfrequencies and modal assurance criterion
(MAC, explained below) values. The range for each parameter was set
as a percentage value of the property of the main element, Table 4. The
lowest value represents the negligible stiffness transfer, whereas the
highest value represents the full stiffness transfer, i.e. rigid connection.
MAC is the measure of the correlation between the two sets of modes
and is calculated as shown below [40]:
𝑀𝐴𝐶 (𝑟, 𝑞) = {𝜑𝐴}𝑇
𝑟{𝜑𝑋}𝑞
2
{𝜑𝐴}𝑇
𝑟{𝜑𝐴}𝑟{𝜑𝑋}𝑇
𝑟{𝜑𝑋}𝑞(4)
where {𝜑𝑋}𝑞is the experiment modal vector for mode 𝑞,{𝜑𝐴}𝑟is
the analytical modal vector for mode 𝑟. MAC takes values between 0
(no similarity between modes) and 1 (high similarity between modes).
When several modes are compared, the result is a MAC matrix where
diagonal elements have values of 1 in ideal situation.
The Latin Hypercube Sampling (LHS) method was adopted for the
current sensitivity study. LHS is a Monte-Carlo type technique, which
allows for exploring the entire parameter range with minimized compu-
tational demand [41]. In LHS, the parameter design space is uniformly
divided with the same number of divisions 𝑁for all factors. The pa-
rameter levels are then randomly combined to create a Latin Hypercube
design matrix with 𝑁points. In this study, the sensitivity analysis with
LHS was performed using the Design of Experiments (DOE) component
of ISight, a tool for automated simulations which can be integrated into
Abaqus CAE [42]. The number of samples, 𝑁=100 was selected for
analysis and a uniform distribution was chosen for each parameter, 𝐾.
The 𝑁𝑥𝐾 matrix is generated from the randomly sampled values and
based on this matrix simulations explore the sensitivities of the input
parameters and evaluate their significance by calculating the partial
rank correlation coefficients (𝑃 𝑅𝐶𝐶 ). 𝑃 𝑅𝐶𝐶 is the measure of the
linear relationship between the parameter of interest and the output.
Sensitivity analysis was performed on a total of 6 input parameters
with respect to 9 outputs (5 natural frequencies and 4 MAC values).
The summary of the sensitivity study is shown in Fig. 14. For better
representations, the absolute values of partial rank correlation coeffi-
cients of each parameter were plotted both against eigenfrequencies
and MAC values. Based on the sensitivity ranks for eigenfrequencies,
parameters 𝐴𝑙𝑜𝑛𝑔 and 𝐴𝑠ℎ𝑜𝑟𝑡 have the largest contributions to most
frequencies (Fig. 14(a)). Parameter 𝐼𝑠ℎ𝑜𝑟𝑡 has a significant effect on
natural frequencies as well. Natural frequencies from mode 2, 4 and
5 have some contribution from 𝐼𝑙𝑜𝑛𝑔 ,𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 and 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 . Most of the
MAC values, Fig. 14(b), have the dominant contribution from 𝐴𝑠ℎ𝑜𝑟𝑡.
The first two MAC values are affected by 𝐴𝑙𝑜𝑛𝑔 , whereas the last two
MAC values are affected by 𝐴𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑠ℎ𝑜𝑟𝑡. Most of the MAC values
have minor contributions from 𝐼𝑙𝑜𝑛𝑔 ,𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛. Mode 4 is
affected considerably by 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙. Based on the results of the sensitivity
analysis, all 6 parameters from Table 4 were chosen for model updating.
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S. Tulebekova et al.
Table 4
Parameters for sensitivity analysis and model updating.
‘‘Connection-zone’’
parameter
Description Range of 𝑘𝑟𝑒𝑑
[% of main element]
𝐼𝑠ℎ𝑜𝑟𝑡 Moment of inertia of beams in long direction 1–100
𝐼𝑙𝑜𝑛𝑔 Moment of inertia of beams in short direction 1–100
𝐴𝑠ℎ𝑜𝑟𝑡 Cross-sectional area of diagonals in short direction 1–100
𝐴𝑙𝑜𝑛𝑔 Cross-sectional area of diagonals in long direction 1–100
𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 Thickness of connection between external wall and beam 1–100
𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 Thickness of connection between internal partition and floors 1–100
Fig. 14. Absolute partial rank correlation coefficients.
4.3. Model updating
The purpose of the model updating is to minimize the difference
between the numerical model and the experimental modal response.
The objective function for model updating included the modal pa-
rameters: 5 lowermost eigenfrequencies (𝑓1𝑓5) and MAC values
for the 1st and 2nd bending modes in two translational directions
(𝑀𝐴𝐶1, 𝑀 𝐴𝐶2, 𝑀 𝐴𝐶4, 𝑀𝐴𝐶5). MAC value for torsional mode (𝑀 𝐴𝐶3)
was not included in model updating due to the lack of sensors to
accurately estimate the mode shape. The objective functions used in
the model updating are given as follows:
𝐹𝑓𝑟𝑒𝑞 =
𝑛
𝑖=1
𝛾𝑖𝑓𝑖,𝑒𝑥𝑝 𝑓𝑖,𝑛𝑢𝑚
𝑓𝑖,𝑒𝑥𝑝 2
(5)
𝐹𝑀𝐴𝐶 =
𝑛
𝑖=1
𝛾𝑖1 − 𝑑𝑖𝑎𝑔(𝑀𝐴𝐶 (𝜙𝑖,𝑒𝑥𝑝, 𝜙𝑖,𝑛𝑢𝑚 ))(6)
where 𝐹is an objective function, (∗)𝑖,𝑒𝑥𝑝 is the experimental output
of mode 𝑖,(∗)𝑖,𝑛𝑢𝑚 is the numerical output of mode 𝑖,𝜙is the mode
shape vector, 𝛾𝑖is the weight factor, which was set to 1 for 𝑓1𝑓3and
𝑀𝐴𝐶1𝑀 𝐴𝐶2values, the higher modes weight factors were set to
0.5. The higher weight factor was used for lower modes due to the fact,
that they are better identified in the OMA analysis and the mode shapes
have the simple cantilever form, while higher modes have a higher level
of uncertainty.
Model updating was performed using the ISight tool which can be
integrated into the Abaqus CAE, where the numerical model of the
building was created. The Multi-Island Genetic Algorithm was chosen
for optimization [43]. Genetic Algorithms (GAs) are optimization al-
gorithms based on natural selection and genetics concepts. GAs work
on the population of possible solutions, where each individual solution
is assessed based on the quality of the result (how far it is from the
target values). The mating pool is then generated from the high-quality
individual solutions, and parent combinations are selected from this
pool to produce an even higher quality offspring. In Multi-Island GA,
there are several mating pools in which high-quality individual solu-
tions are generated, and periodically these pools exchange a portion of
their population in a process called migration. In this study the number
of islands (mating pools) was set to 10, the sub-population size and the
number of generations were set to 10, the rate of migration was set to
0.01.
4.4. Model updating results
Model updating has been performed using four different sets of
parameters. In Set 1, all of the parameters from Table 4 were used
for model updating. In Set 2, parameters 𝐼𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑙𝑜𝑛𝑔 were com-
bined into one parameter 𝐼𝑏𝑒𝑎𝑚, and parameters 𝐴𝑠ℎ𝑜𝑟𝑡 and 𝐴𝑙𝑜𝑛𝑔 were
combined into one parameter 𝐴𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙 . Parameters 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛
were included into the second set as well. The purpose of generalizing
stiffness parameters into 𝐼𝑏𝑒𝑎𝑚 and 𝐴𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙 is to compare with the
results of the first set updating and observe whether the generalized
axial and rotational stiffness parameters will be able to predict the
building dynamic response. Set 3 includes parameters 𝐼𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑙𝑜𝑛𝑔 for
beam rotational stiffness and parameters 𝐴𝑠ℎ𝑜𝑟𝑡 and 𝐴𝑙𝑜𝑛𝑔 for diagonal
axial stiffness. Parameters 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 are excluded from model
updating in Set 3. Set 4 includes only two parameters: 𝐼𝑏𝑒𝑎𝑚 and
𝐴𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙 . Parameters 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 were kept constant and were
excluded from model updating in Set 4.
The results of the FE model updating with Set 1 parameters are
shown in Tables 5 and 6. The range for parameters in model updating
was chosen the same as in the sensitivity analysis, confer Table 4.
Approximately 1000 iterations were performed in model updating to
explore the entire design space. The initial values in Table 6 were
chosen to represent the starting assumption of pinned connections
in the glulam frame and negligible stiffness contribution from non-
structural elements. Table 5 shows the natural frequencies and MAC
Engineering Structures 261 (2022) 114209
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S. Tulebekova et al.
Table 5
Comparison between experimental and numerical modal properties (Set 1).
Mode Initial model Updated model (Set 1) Experimental
𝑓[Hz] Difference 𝑀𝐴𝐶 𝑓 [Hz] Difference 𝑀𝐴𝐶 𝑓 [Hz]
1 0.506 2.64% 0.82 0.511 3.65% 0.93 0.493
2 0.509 3.78% 0.88 0.518 2.08% 0.97 0.529
3 0.820 0.86% 0.817 0.49% 0.813
4 1.915 0.16% 0.25 1.954 1.88% 0.85 1.918
5 1.957 8.81% 0.38 1.972 8.11% 0.97 2.146
Table 6
𝑘𝑟𝑒𝑑 values for Set 1 after model updating.
Parameter Initial Updated
𝐼𝑠ℎ𝑜𝑟𝑡 1% 65.3%
𝐼𝑙𝑜𝑛𝑔 1% 92.7%
𝐴𝑠ℎ𝑜𝑟𝑡 100% 33.5%
𝐴𝑙𝑜𝑛𝑔 100% 68.3%
𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 1% 94.1%
𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 1% 45.8%
values after model updating along with the initial model results and
experimental natural frequencies. It can be seen that while there is a
slight improvement in natural frequencies, MAC values have improved
significantly after model updating. In particular, considerable improve-
ment in mode shape prediction is observed for modes 1 and 2. The total
objective function improved from 0.647 to 0.071 after model updating,
resulting in an 89% decrease. The numerical mode shapes after model
updating are shown in Fig. 15.
The updated values of 𝐼𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑙𝑜𝑛𝑔 increased considerably com-
pared to the initial values (Table 5). This means that the glulam
connections have considerable rotational stiffness contribution which is
different from the pin-condition assumption that was selected initially.
The value of 𝐼𝑙𝑜𝑛𝑔 updated to 92.7% of the main element, while the
updated value for 𝐼𝑠ℎ𝑜𝑟𝑡 is 65.3%. The values of 𝐴𝑠ℎ𝑜𝑟𝑡 and 𝐴𝑙𝑜𝑛𝑔 were
reduced in comparison with the initial values, which means that the
initial assumption of full axial load transfer in the connection was not
sufficient. Similarly to the moments of inertia, updated 𝐴𝑙𝑜𝑛𝑔 value is
larger than the updated 𝐴𝑠ℎ𝑜𝑟𝑡, 68.3% and 33.5% respectively ( Table 6).
The parameters 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛, which represent the non-structural
elements contribution, increased significantly from their initial value.
Tables 7 and 8show the summary of the model updating for Sets 1–4. In
comparison with the Initial Set, the objective function for Sets 1–4 was
lower after model updating. However, the objective function for Sets
2–4 was higher than for Set 1, which had an objective function value of
0.071. As seen from Table 7, the eigenfrequencies achieved after model
updating with Sets 1–4 were in good accordance with the experimental
results. Model updating with Sets 1–3 achieved acceptable MAC values.
5. Discussion
The discussion of the model updating results in this section is based
on the assumption that the structural masses, live loads, and structural
material stiffness properties were estimated with an acceptable level
of uncertainty. While the authors have used their best engineering
judgment in the calculation of structural masses and live loads, the
uncertainty related to these estimations can still be considerable. The
presented numerical modeling approach of the glulam building using
‘‘connection-zones’’ helps to generalize the connection properties mak-
ing it easier for practicing engineers to use the obtained results as a
reference for their prediction models.
5.1. Glulam connections
Dowelled glulam connections exhibit a nonlinear behavior even at
low excitation levels due to several factors including an initial slip of
dowels inside the drilled holes and inherent cracks and imperfections
of the applied timber material [4]. Therefore, the structural behavior of
the dowelled connections is subject to uncertainty. Several sensitivity
studies have been done to explore the effect of both axial and rotational
stiffness of glulam frame connections on the vibration response of the
building [4,6]. The studies on the sensitivity of the rotational stiffness
showed a negligible difference between the pinned connections and
connections with stiffness values based on Eurocode 5 calculations [6].
The Eurocode 5 calculations, however, lack the accurate representation
of the connection stiffness and underestimate the actual value based
on the sub-assembly experimental results [10]. On the other hand, the
rigid connection scenario in the study by [6], showed a considerable
increase in fundamental frequencies of the building.
Model updating of parameters 𝐼𝑙𝑜𝑛𝑔 and 𝐼𝑠ℎ𝑜𝑟𝑡 in this study showed
that the rotational stiffness in glulam connections is neither negligible,
nor rigid, but rather exhibits a semi-rigid behavior. Similarly, the axial
stiffness parameters 𝐴𝑙𝑜𝑛𝑔 and 𝐴𝑠ℎ𝑜𝑟𝑡 have updated values which are
less than the initial value of 100% of the main elements, meaning that
connection is semi-rigid in the axial direction as well. The sensitivity
study by [4] showed that variation of axial stiffness in glulam truss has
an effect on the eigenfrequencies of the structure, which is consistent
with the findings in this paper. As seen from Table 6, both 𝐴𝑙𝑜𝑛𝑔 and
𝐼𝑙𝑜𝑛𝑔 have updated values, which are consistently higher than the values
of 𝐴𝑠ℎ𝑜𝑟𝑡 and 𝐼𝑠ℎ𝑜𝑟𝑡 respectively. The model updating of glulam timber
frame connections implies that there exists significant variation in the
stiffness, which should be investigated further. The geometry of the
building might have a considerable impact on the updated stiffness
of the connections since it can be seen that the model updating with
separate elements for long and short directions achieves better results
in comparison with other sets.
5.2. Non-structural elements
The study explored the effect of the external wall and internal parti-
tion stiffness on the dynamic response of the building. By modifying the
connection thickness parameters, 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and 𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛, the contribution
of non-structural member stiffness was varied from negligible, 𝑡= 1%,
to a full stiffness transfer, 𝑡= 100%. Based on the sensitivity study, the
external partition stiffness contribution to the natural frequencies was
insignificant since the load-bearing contribution consisted only of two
13-mm thick gypsum plasterboards and low stiffness. However, there
was a noticeable effect on the MAC values (Fig. 14(b)) for modes 1 and
4 (Fig. 15). After Set 1 model updating the value of 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 was 94.1%
of the main shell element, whereas after Set 2 model updating the value
of 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 was 88.6%. The actual connection between the external wall
and main structure is, however, not very rigid based on the detailing
drawings. On the other hand, the stiffness contribution from non-
structural elements might be considerable at low-level vibrations and
further investigation is required on the topic. The internal partitions
have a slightly higher stiffness contribution compared to external walls
since they consist of the 2-ply double-sided gypsum plasterboard with
a steel frame. Therefore, non-structural element parameters 𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 and
𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 have contributions to mode shapes of the structure and should
be accounted for when performing modal analysis of the building.
The results of the model updating showed that under ambient vibra-
tions, the non-structural members have a considerable impact on the
MAC values in the dynamic response of the timber building, which is
consistent with the previous studies [14,15].
Engineering Structures 261 (2022) 114209
12
S. Tulebekova et al.
Fig. 15. Numerical mode shapes after model updating with the first set.
Table 7
Comparison between experimental and numerical modal properties for all sets.
Mode Set 1 Set 2 Set 3 Set 4 Experim.
𝑓[Hz] Change [%] MAC 𝑓[Hz] Change [%] MAC 𝑓[Hz] Change [%] MAC 𝑓[Hz] Change [%] MAC 𝑓[Hz]
1 0.511 3.6 0.93 0.510 3.4 0.88 0.513 4.0 0.93 0.507 2.8 0.73 0.493
2 0.518 2.0 0.97 0.513 3.0 0.93 0.519 1.89 0.97 0.509 3.7 0.79 0.529
3 0.817 0.4 0.826 1.6 0.817 0.4 0.821 0.98 0.813
4 1.954 1.8 0.85 1.961 2.24 0.81 1.966 2.5 0.84 1.954 1.88 0.70 1.918
5 1.972 8.1 0.97 1.970 8.2 0.93 1.979 7.7 0.96 1.959 8.71 0.85 2.146
6. Conclusions
This paper presents an approach to model connections in glulam
frame buildings. ‘‘Connection-zones’’ are introduced in the model and
represent the rotational and axial stiffness, in this case, of doweled con-
nections. This approach allows for the implementation of modeling of
the connection stiffness influence on the dynamic response of building
in a parametrized manner. The dynamic properties of the glulam timber
frame building have been achieved successfully using the proposed
approach for connections modeling. An ambient vibration procedure
and subsequent system identification of an instrumented 18-storey
glulam building identified 5 vibrational modes, which were used for
model validation and model updating. In summary, the axial stiffness
parameter has the largest impact on both fundamental frequencies and
Engineering Structures 261 (2022) 114209
13
S. Tulebekova et al.
Table 8
𝑘𝑟𝑒𝑑 values for all sets after model updating.
Parameter Initial Set 1 Set2 Set 3 Set 4
𝐼𝑠ℎ𝑜𝑟𝑡 1% 65.3% 3.4% 83.1% 1.0%
𝐼𝑙𝑜𝑛𝑔 1% 92.7% 3.4% 51.0% 1.0%
𝐴𝑠ℎ𝑜𝑟𝑡 100% 33.5% 88.1% 34.0% 97.0%
𝐴𝑙𝑜𝑛𝑔 100% 68.3% 88.1% 94.9% 97.0%
𝑡𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 1% 94.1% 88.6% –
𝑡𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛 1% 45.8% 82.6% –
𝑂𝑏𝑗.𝑓 𝑢𝑛𝑐 𝑡𝑖𝑜𝑛 0.647 0.071 0.119 0.075 0.360
MAC values, whereas the rotational stiffness parameter has the least
impact. The non-structural parameters accounting for external walls
and internal partitions have a considerable effect on the MAC values
of the structure. The assumption of an accurately predicted mass was
adopted, which is the main limitation in the current study since there is
some uncertainty in relation to the mass estimates. A future study will
include the long-term monitoring of the building in order to evaluate
the dependence of the amplitude of the wind-induced vibrations. The
authors believe that the stiffness ratios for ‘‘connection-zones’’ in this
study can serve as a useful reference for practitioners designing glulam
timber frame buildings.
CRediT authorship contribution statement
Saule Tulebekova: Conceptualization, Methodology, Validation,
Investigation, Formal analysis, Writing – original draft, Writing – re-
view & editing, Visualization. Kjell Arne Malo: Conceptualization,
Methodology, Writing – review & editing, Supervision, Project admin-
istration, Funding acquisition. Anders Rønnquist: Conceptualization,
Methodology, Writing – review & editing, Supervision. Petter Nåvik:
Investigation, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgments
This research has been conducted as part of the Dynamic Response
of Timber Buildings under Service Load (DynaTTB) project. The au-
thors are grateful to the ERA-NET Cofund Forest Value and all the
corresponding funding bodies for their assistance and financial support.
In Norway funding was provided by the Research Council of Norway,
grant no. 297513. The authors would also like to thank students Daniel
Hjolman Reed and Lars Håkon Wiig for parametrizing the numerical
model of timber building in Python. The authors are grateful to Moel-
ven Limtre, and in particular Rune Abrahamsen; and SWECO Norge and
in particular Magne Aanstad Bjertnæs for their help and cooperation in
connection to the Mjøstårnet project.
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