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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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