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TALL TIMBER BUILDINGS – A PRELIMINARY STUDY OF WIND-
INDUCED VIBRATIONS OF A 22-STOREY BUILDING
Marie Johansson1, Andreas Linderholt2, Kirsi Jarnerö3, Pierre Landel4,
ABSTRACT: During the last years the interest in multi-storey timber buildings has increased and several medium-to-
high-rise buildings with light-weight timber structures have been designed and built. Examples of such are the 8-storey
building “Limnologen” in Växjö, Sweden, the 9-storey “Stadthouse” in London, UK and the 14-storey building “Treet”
in Bergen, Norway. The structures are all light-weight and flexible timber structures which raise questions regarding
wind induced vibrations.
This paper will present a finite element-model of a 22 storey building with a glulam-CLT structure. The model will be
used to study the effect of different structural properties such as damping, mass and stiffness on the peak acceleration
and will be compared to the ISO 10137 vibration criteria for human comfort. The results show that it is crucial to take
wind-induced vibrations into account in the design of tall timber buildings.
KEYWORDS: Deflection, dynamic properties, stabilisation, sway, wind loads
1 INTRODUCTION 12 3
1.1 Background
During the last decades the interest in multi-storey
timber buildings has increased. This is due to reasons
such as development of performance based codes but
also increased interest in sustainability. The CO2
emissions could be reduced by 40% if building with
timber instead of concrete [1]. The increasing population
and ongoing urbanisation are going to increase the need
for creating cities with higher population densities. This
will lead to an increased need for tall buildings that make
the best use of limited space. The environmental
potential of high-rise buildings lies in a more efficient
use of resources.
By adding these elements together the use of tall
buildings with timber structures would be an opportunity
and provide for ecological, sustainable high and dense
developments in urban regions with housing shortage.
Timber has the benefit of having a high strength-to-
weight ratio compared to other building materials which
in many cases is beneficial. However, for the case with
1 SP Sustainable Built Environment and Linnaeus University,
Sweden, marie.johansson@sp.se
2 Linnaeus University – Mechanical engineering, Sweden,
andreas.linderholt@lnu.se
3 SP Sustainable Built Environment, Sweden,
kirsi.janero@sp.se
4 SP Sustainable Built Environment, Sweden,
pierre.landel@sp.se
medium-to-high-rise buildings this might pose a
challenge since the dynamic properties of the building
will be quite different from a high-rise building with a
load-bearing structure in steel or concrete [2].
High-rise buildings consisting of a timber structure are
therefore the subject of a research project named “Tall
Timber Buildings – Concept Studies” lead by SP
Technical Research institute of Sweden together with
Linnaeus University during the period 2015-2018.
1.2 Research project “Tall Timber Buildings -
Concept Studies”
The aim of the “Tall Timber Buildings – Concept
Studies” is to develop feasible concepts for planning and
designing 22 storey high timber buildings according to
present regulations and during the process identify issues
that need more research. The specific objectives of the
project besides the issues in serviceability limit state
related to wind actions as presented in the present paper
are also to study stability, static vertical deformations,
load transfer through the building to the ground and
connection detailing regarding strength, stiffness and
continuity with respect to both dynamic and static
loading. The objective is also to develop calculation
tools and models for tall timber buildings suitable for
structural engineers and tools for analytical fire design.
The difference between high rise and low rise timber
buildings with regard to life cycle assessment will also
be studied. The aim is to increase the number of
practicing architects and designers with experience of
designing tall timber buildings and to increase the
knowledge of designing tall timber buildings also among
actors not participating in the project. Another important
aim is to develop existing timber building systems and
find new ideas and solutions that are applicable also on
lower buildings. The timber building systems involved
are KLH Sweden with CLT plates, Moelven Töreboda
with glulam columns and beams in combination with
floor elements built up from LVL and Masonite Beams
with a system consisting of planar elements built up
from I-joists. The architectural design of the concept
buildings are made by White architects and by Berg|CF
Möller architects in co-operation with the property
developers/owners VKAB and HSB and the structural
designers Bjerking and BTB that will design one of the
concept buildings each. The two fire design consultants
Briab and Brandskyddslaget as well as acoustic
engineers from WSP on the other hand will follow both
projects in parallel. Researchers from Linnaeus
University and from SP Technical Research Institute will
support the project teams with in-depth studies, detailed
calculations and testing.
1.3 Aim and objectives
This paper will present the first results from the project
“Tall Timber Buildings – Concept studies”.
The paper will give a review of the requirements on
vibrations in buildings and address which parameters are
important for the design of tall buildings. The paper will
also present a preliminary finite element (FE)-model of a
22 storey building with a structure consisting of a core of
CLT elements and an outer beam-column structure of
glulam. The model will be used to estimate resonance
frequencies, stiffness and mode shapes. These data will
be used to calculate acceleration levels at the top floor
when the structure is subjected to wind loads according
to Eurocode 1 [3].
The model will be used in the Tall Timber Building
project as a base for studying the effect of changing
stiffness, mass and damping on the acceleration levels of
the structure.
The FE-model will naturally also be used to study the
performance of the building in the ultimate limit state.
2 REQUIREMENTS FOR TALL
TIMBER BUILDINGS
2.1 General requirements
All building systems are designed to withstand both
vertical gravity loads and horizontal loads due to wind.
The main focus when designing a building has always
been the safety aspect calculated based on the maximum
loads expected to occur once every 50 years. The interest
in the serviceability limit state has been attracting more
focus in the last decades. In the horizontal directions
there are limitations both for the static deformation but
also for vibrations/accelerations. For the horizontal
deformation a maximum value of h/500 is set in the
German DIN standard. Even more important for
especially tall buildings is the sway due to wind loads.
The comfort performance of a building during wind
loading is an important building design issue. The
occupants’ perception and tolerance of wind-induced
vibrations is a subjective assessment and presently there
is no single internationally accepted occupant comfort
criteria to set levels for satisfactory vibrations in tall
buildings subjected to wind loading. The requirements
that are set in the international standards are normally
based on acceleration levels where people start to notice
and comment on the motion.
There are three different international standards that deal
with horizontal vibrations in buildings and the human
perception of vibrations. There are two older ISO
standards, ISO 6897 [4] that cover the range from 0.063
Hz to 1Hz and ISO 2631-2 [5] that cover the range 1 Hz
to 80 Hz. These two are in agreement with each other
and use the Root Mean Square (RMS) value for the
acceleration due to a maximum wind velocity with a
return period of five years. ISO 10137 [6] covers the
range from 0.063 Hz to 5 Hz and uses the peak
acceleration calculated for a wind velocity with a return
period of one year. This is the standard referred to in
Eurocode 1 [3]. These two sets of standards will yield
slightly different acceptance levels for the same building.
The Swedish National Annex [7] to the Eurocode 1
states that ISO 6897 is recommended for calculation of
the effect of wind loads. In this paper, calculations
according to ISO10137 and the general requirements in
Eurocode 1 [7] are used.
In this paper the main issue for the studied building is
the sway and vibrations, therefore the horizontal effects
from the wind load are the most important phenomenon
to study.
2.2 Structural dynamics of tall buildings
A tall building is in most cases considered as a line-like
vibrating object, and its structure may be represented as
a vertical cantilever beam, fixed at the foundation and
free at the top. The global dynamics of a multi-story
building can sometimes, in a simplified manner, be
analyzed by approximating the building to be a uniform
cantilever beam, with a neglected axial load, and having
the height h. According to the well-known Euler-
Bernoulli beam theory, the homogeneous part of the
governing equation of motion is
+
= 0
(1)
in which , and constitute the density, cross
sectional area and bending stiffness respectively. The
general solution to this equation is
()=cosh()+
sinh()+
cos()+sin()
(2)
in which =
and ,, and are
constants. When the boundary conditions for a cantilever
beam
(0)=(0)=()=()= 0
(3)
are applied, nontrivial solutions require that
cosh()cos()+ 1 = 0
(4)
which has to be solved numerically. The first solution is
= 1.875. The associated, first bending, mode then
has the mode shape
()=(sin sinh )(sin sinh )
+(cos cosh )(cos
cosh )
(5)
which is valid for 0. Assuming that only the
first bending mode contributes to the displacement and
making the substitute
(,)=()()
(6)
the modal mass (), modal stiffness (
) and modal load
can be calculated as:
= ()
()
(7)
= ()
()
(8)
= ()
()
(9)
In which () is the distributed wind load. The
continuous problem has then been re-placed with a
discrete single-degree-of-freedom system, depicted in
Fig. 1.
()+
()=()
(10)
Figure 1. A single-degree-of-freedom system representing the
building when one assumed mode is used.
When damping is added the governing equation of
motion becomes
()+() +
()=()
(11)
in which is the modal damping. In the codes used for
calculation of responses due to wind loads, simplified
expressions for the mode shapes are often used.
The expression shows that the important parameters that
have an effect on the relationship between deflection,
velocity, acceleration and the wind load are the mass,
damping and stiffness.
2.3 Wind load
Wind loads vary greatly in speed, force and direction
over time and its effect on buildings are complex and
heterogeneous. To simplify this in codes, the wind is
seen as a quasi-static load for buildings with high
stiffness and damping. For high slender structures also
the gust effect is included as a turbulence factor added to
the quasi-static wind load. The effect of the wind on a
single building will be affected by the terrain around it as
well as the shape and height of the building.
In Europe, wind loads are defined in Eurocode 1, Part 1-
4 [3]. There, the fundamental basic wind velocity is
defined by the 10-minute mean wind speed, at a height
of 10 meter above ground, that is exceeded once every
50 year. The wind velocity for shorter times (in this
case T years) can then be calculated,
=0.75 10.2 11
(12)
The wind velocity in the vicinity of a structure is
dependent on the local terrain around the structure and is
varying with the height z above ground. According to
Eurocode 1-4 [3] the mean wind velocity () at the
height z next to a structure can be expressed as,
() = ()
(13)
The first term () is an orography factor (set to 1.0 in
normal cases) and the second term is a terrain
roughness factor.
= 0.19
,.
(14)
The term is the roughness length that varies between
terrains; the term , is a reference terrain roughness
length. The mean wind pressure () can then be
calculated using,
() = 1
2()
(15)
where ρ is the air density (normally set to 1.25 kg/m3).
For high and flexible buildings it is, however, necessary
to take also the dynamic effects of the wind load into
account. This is done by including a turbulence intensity
factor Iv(z), defined as the standard deviation of the
turbulence divided by the mean velocity as,
() =
()
(16)
where is the standard deviation of the turbulence and
() is the mean wind velocity. The standard
deviation of the turbulence is calculated as the basic
wind velocity times the terrain roughness factor .
The response of the structure due to the turbulence
intensity can be divided into two parts; the background
response () and the resonance response (). The
background response is due to the quasi-static part of the
wind load while the resonance response is due to the
dynamic properties of the building and the dynamic part
of the wind load. Eurocode 1-4, annex B gives the
following expression for calculating the Root Mean
Square (RMS) value for the acceleration, ():
() = ()()
()
(17)
Where is the shape factor for force, b the width of the
building, is the equivalent (modal) mass, a
dimensionless variable and () the mode shape
associated with the first resonance frequency. From this,
the horizontal peak acceleration of the structure () can
be written as,
() = ()
(18)
where is a peak factor that relates the mean and the
standard deviation of the response.
3 BASIC MODEL OF THE 22-STOREY
BUILDING
3.1 Structural principles for tall timber buildings
There are of course many ways to design tall buildings.
For steel structures rigid frame systems, with or without
trusses, have been used for buildings up to 70 storeys
and for higher buildings tubular systems are often used.
When using concrete a central core system with concrete
walls are often used together with columns in the
perimeter.
In timber many of the tallest buildings at the moment are
built with platform framing using CLT-elements, that is
a structure that has been used up to 8-10-storey buildings
such as the 8-storey building Limnologen in Växjö,
Sweden, the 9-storey Stadthouse in London, UK
For the tallest timber building so far, the 14-storey high
“Treet” in Bergen, Norway, a glulam beam/column/truss
system was used. For taller timber buildings MGB [8]
suggested a continuous core of CLT or LVL elements
together with glulam columns in the perimeter of the
building. In their concept study, they plan for 20-30
storeys. There are also plans for a building with up to 25
storeys in Vienna, but in that case utilizing a hybrid
structure with a concrete core and CLT-element in the
outer walls.
3.2 Structure
For the concept study in this project the plan is for a 22-
storey building only using timber as structural material
located in Växjö or Stockholm. The maximum outer plan
was set to 20 x 20 meters with a storey height of 3.4
meters. The structure is planned as a residential building.
The first design attempt for this building is a floor plan
that is 17 x 21 meter as outer measurements and with a
total building height of 75 meters. The building is made
with a central core of CLT elements that are continuous
over three storeys and connected with a butt joint. The
core has a measure of 12.5 x 8.6 meters with areas for
elevators, stairs, hallways and bathroom areas inside the
core. The CLT walls used in the design are planned with
the outer layers in the vertical direction. In the outer
perimeter of the building there are continuous glulam
columns at a distance of 4.1 meter. The core and the
columns are connected at each floor plan with glulam
beams. The floors structure which will consist of CLT
plates is planned to be hanging on the inside of the
CLT/glulam beams to have the vertical structure
continuous, see Figure 2.
Figure 2. Sketch of the main structural system.
From earlier calculation of tall timber buildings it is
known that sway is the criterion that is the most difficult
to meet for the structure [2]. The calculation in the
ultimate limit state is therefore in this first step only done
as a hand calculation where the structure is seen as a
cantilever beam with full interaction between all the
elements.
The chosen dimensions of the structural elements are
enough to withstand the snow, gravity and wind loads in
the ultimate limit state. The connections, especially to
the ground, will need more evaluation and development.
The proposed floor plan for the building can be seen in
Figure 3. The inner core (light gray) will be made up of
7-layer CLT elements with a thickness of 230 mm with a
width of either 2500 mm or 2720 mm. The CLT wall
elements are made with the two outer layers and the
middle layer in the vertical direction and with layer 3
and 5 in the horizontal direction. The CLT elements is
planned to be continuous over three storeys and jointed
with butt joints. To avoid joints at the same height the
joints between the CLT elements will be staggered. The
joints between the CLT elements in the vertical
directions will be made with a spline LVL joint which is
a standard connection type for CLT structures.
20930
16940
12500
8616
4100 4100 4100 4100
4100 4100 4100 4100 4100
Figure 3. Sketch of the main structural system, an inner core
with CLT elements and some non-load bearing walls in the
core, glulam columns in the outer facades and glulam beams
connecting the columns and the core structure.
The columns are in the first design made of glulam
GL30c with a dimension of 340 x 540 mm. The columns
are planned to be made as continuous to act as one high
column. The beams in the perimeter and between the
columns and the core are also made of glulam GL30c
and with a dimension of 215 x 405 mm. The glulam
beam-column system is inspired by Moelven Törebodas
“Trä 8” system [9]. The floors are in the first version
made up of a 5 layer CLT elements with a thickness of
200 mm.
The same floor plan /structural elements dimensions are
used for all storeys in this first model.
4 FE-MODEL
The model representing the assembled 22 storey building
was made using MSC SimXpert and the calculations
were made by MSC Nastran version 14.1. which is a
general FE-program originally developed for the
aerospace and automotive industry and therefore has
well developed code for dynamic analysis. The model
consists of 186,836 nodes and 186,340 shell, beam,
bushing and rigid elements; CBAR, CSHELL, CBUSH
and RBE2 respectively.
4.1 Model of one storey
The model is first made as a detailed model for one
storey, see Figure 4. This model is made for studying the
properties of one storey before expanding the model to
the full 22-storey building.
The CLT elements are made as shell elements and with
laminates made up by orthotropic material. The
properties of the laminates are = 12000 MPa in the
fiber direction and = 0 MPa in the direction
perpendicular to the grain, the shear stiffness is set as
= 690 MPa and = 50 MPa. The density is 500
kg/m3. The CLT elements are in this first model fixed to
the ground. The spline connections between the CLT
elements are made with springs with a stiffness of
1.3·106 kN/m in all three directions. In total 10 springs
are used between two CLT elements in the height
direction, the same spring stiffness are used in the
corners of the CLT core. This stiffness is what can be
expected for a spline connection based on tests [10 and
11].
The glulam beams and columns are modelled with beam
elements with an isotropic material model with the
stiffness of 13000 MPa with a density of 500 kg/m3. The
columns are fixed to the ground. The beams also have
pinned connections to the columns and the CLT core.
The floor in the structure is modelled as 200 mm thick
CLT plate with a layered structure with 5 layers. The
material properties for the layers are set to the same
values as for the CLT elements in the core. Inside the
core the model is made with one whole slab attached to
the inside of the CLT elements with pinned connections
on all four sides. In a real structure it will be necessary to
support this floor with beams/walls to avoid too large
deformations. The floor structure is also connected to the
glulam beams with pinned connections at all four sides.
Figure 4. FE-model for the first storey, showing CLT elements
in the core and as floor structures and glulam beams out to the
glulam columns in the facades.
4.2 Model for the 22-storey building
The model was then expanded to a 22-storey building.
The connections between the storeys were made by
assuming rigid connections between the CLT elements
in the vertical direction, the same assumption was made
for the columns.
Figure 5. FE-Model for the complete 22-storey building.
The model was used in a modal analysis calculating the
resonance frequencies and the mode shapes for the total
building. The model was in this first step run without the
gravity field, which results in a slightly higher resonance
frequency than if the gravity field had been used to pre-
compress the structure. In this case the first ten elastic
eigenmodes were extracted The results showed that the
first mode shape is a bending mode in the weak direction
of the building with a resonance frequency of 0.6 Hz, see
Figure 6.
Figure 6. Mode shape for the lowest bending mode in the weak
direction from the FE-model, resonance frequency f1 =
0.60 Hz.
Eurocode 1-4 gives as a rule of thumb a first resonance
frequency for buildings higher than 50 m that is
expressed as:
=46
(19)
Where h is the total height of the building. Utilizing the
building height of 75 m this will mean a first resonance
frequency of 0.61 Hz mainly based on experience from
steel and concrete buildings. The building in this model
showed a result that was surprisingly close to this value.
The bending mode shapes for the first resonance
frequency for a tall slender building is in Eurocode
expressed as:
() =
(20)
Where z is the height above ground and h is the total
height of the building. The shape factor is in Eurocode
1991-1-4 recommended as 1.0 for a building with a stiff
central core surrounded by columns in the façade. The
mode shape will in that case be almost linear with
change in height. Figure 6 show that this is a quite good
approximation for this building. The mode shape shows
a lot of shear deformation, especially for the higher
storeys.
The second mode is a bending mode in the strong
direction with a resonance frequency of 0.8 Hz and the
third is a rotational mode with a resonance frequency of
1.1 Hz, see Figure 7 and Table 1.
Figure 7. Mode shape for the first torsional mode from the FE-
model, resonance frequency f3 = 1.10 Hz.
The first resonance frequency is lower than what is
measured in already built timber buildings, but they are
on the other only a third of the height of this structure.
The 14-storey building “Treet” in Bergen, Norway had
based on a FE-model a frequency of 0.75 Hz but that
building had more mass [2].
Table 1. The three lowest modes for the building, mode shapes
and resonance frequencies for the building according to the
FE-analysis.
Mode
no.
Shape
Resonance
frequency
1
Bending weak direction
0.6 Hz
2
Bending strong direction
0.8 Hz
3
Torsion
1.1 Hz
The results for this structure is, however, not realistic as
there are many issues that are not dealt with such as real
stiffness of the connections to the ground, holes for
openings in the core mass of non-structural material and
so on.
4.3 Accelerations level for the building according to
EC1
The value of the first resonance frequency is one of the
key parameters to calculate the acceleration level on the
top of the building to compare it to the comfort criteria.
In this case the comfort criteria used is the peak
acceleration calculated for a 2-year return period of the
wind [7]. The building is in this case placed in Växjö in
Sweden with a basic wind velocity of 24 m/s and in
terrain type II (area with low vegetation). The
acceleration level is calculated according to the method
in Annex B in EN 1991-1-4:2005 [3]. The parameters
calculated with this method can be found in Table 2.
Table 2. Parameters for calculating acceleration levels
according to Eurocode 1-4 [3] and ISO10137[6]. The rows
with light grey background are input parameters and the dark
grey rows shows the resulting acceleration levels.
Parameter
Value
Unit
Heigth of the building
H
74.8
m
Width of the building
B
20.9
m
Depth of the building
D
16.9
m
Reference height
44.9
m
Equivalent mass, height
20850
kg/m
Equivalent mass, area
996
kg/m2
Basic wind velocity
24
m/s
Roughness length
0.05
m
Minimum height, wind
2
m
Maximum height, wind
200
m
Terrain factor
0.19
Roughness factor
1.4
Wind turbulence intensity
0.15
Mean wind velocity 2 years
19.1
m/s
Force coefficient
1.47
First resonance frequency
0.6
Hz
Damping, mechanical
0.09
Damping, aeroelastic
0.05
Reference length scale
300
m
Alfa
0.52
Turbulence length scale
()
138
m
Non-dimensional
frequency
4.3
Spectral density
()
0.05
Background response
factor
()
0.76
Aerodynamic admittance
0.11
Aerodynamic admittance
0.34
Resonance response factor
()
0.27
Up-crossing frequency
0.20
Hz
Peak factor
()
3.28
Dimensionless coefficient
1.5
RMS of the acceleration
()
0.04
m/s2
Peak acceleration
()
0.13
m/s2
The result for the peak acceleration can then be plotted
into the diagram for acceptable acceleration levels from
the ISO10137 [6]. The result show that the building
having the structure studied now has a too high
acceleration level, see Figure 8.
Figure 8. The peak acceleration level for the structure plotted
into the ISO10137 diagram.
5 CONCLUSIONS
This paper presents a first FE-model able to capture the
dynamic behavior of a 22-storey building. The structure
of the building is made with a core of continuous CLT
wall elements with a seven layer structure and an outer
structure of continuous glulam columns and glulam
beams. The floor structure is made up of CLT elements
that in this first study are pinned to the glulam structure.
The results show that the first resonance frequency is
about 0.6 Hz which might be reasonable for a building of
this height in concrete or steel but combined with the
low mass of the timber structure it leads to acceleration
levels that are too high at the top floors of the building.
The main aim of creating the FE-model is, however, to
use it in further studies were different methods to reach
acceptable acceleration levels will be tested. These
further studies will include investigating such parameters
as:
- Changes in the design and dimensions of the
structural elements such as beams, columns and
wall thickness.
- Changes of the material properties of the timber
elements; create CLT elements better designed
for large shear forces.
- Determine necessary stiffness requirements for
connections in the system.
- Improve the modeling of the mass and its effect
- Test different methods for damping such as
tuned mass dampers or visco-elastic dampers.
- Include bracing systems in the facades as well
as out-rigger structures.
- Study the effect of openings in the CLT-core
and include more stabilizing walls in the core.
- Develop the model for checking also the
ultimate limit state.
ACKNOWLEDGEMENT
The authors gratefully acknowledge the funding for the
project “Tall Timber Buildings – concept studies” from
Formas the Swedish Research Council for Environment,
Agricultural Science and Spatial Planning [Dnr: 942-
2015-115].
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