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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/).

Contents lists available at ScienceDirect

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

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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 [29–31].

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 7.47e−6

Optimized 4800 120 990 600 600 50 5.71e−9

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

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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.

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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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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 (𝑓1−𝑓5) 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 𝑓1−𝑓3and

𝑀𝐴𝐶1−𝑀 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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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

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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

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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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