Table Of Contentπ’π’(π‘π‘)
ππ
π‘π‘π‘π‘π‘π‘
π’π’
ππ π’π’(π‘π‘)
π‘π‘π‘π‘π‘π‘
π’π’(π‘π‘) π’π’
ππ
π‘π‘π‘π‘π‘π‘
π’π’
πππ‘π‘π‘π‘π‘π‘ π’π’(π‘π‘) πππ‘π‘π‘π‘π‘π‘ π’π’(π‘π‘) ππ
π’π’ π’π’ π’π’
ππ πππ‘π‘π‘π‘π‘π‘ πππ’π’π‘π‘(π‘π‘π‘π‘π‘π‘) π’π’(π‘π‘)πππππ‘π‘πππ‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘ π’π’π’π’(π’π’(π‘π‘π‘π‘())π‘π‘) π‘π‘ πππ’π’π’π’π’π’π’π’ π’π’ π’π’ π‘π‘ πππππ’π’(π’π’)
ππ
ππ π‘π‘πππ’π’ πππππ’π’πππ’π’π’π’ πππ’π’ ππ(π’π’ΞL) ΞL
ππ πππ‘π‘π‘π‘π‘π‘ ππ π’π’(π‘π‘) ππππ π‘π‘ π‘π‘π‘π‘ π’π’πππ’π’ π‘π‘ πππ’π’πππ’π’ πππππ’π’(π’π’) ΞΌ
π‘π‘ π‘π‘ π‘π‘ ππππ((π’π’π’π’)ππ)(π’π’) ππ(π’π’)
ππ ππ
ππ ππ πππ’π’ πππ’π’πππ’π’π’π’ πππ’π’ ππ(π’π’) ππ(π’π’)ππ(π’π’) ΞΈ(cid:148)(cid:145)(cid:150) ΞΈ(cid:148)(cid:145)(cid:150)
πππ‘π‘π‘π‘π‘π‘ =ππ+π’π’(π‘π‘) πππππ‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘==ππ+πππ’π’+(π‘π‘) π’π’(π‘π‘) π‘π‘ π‘π‘π‘π‘ πππ’π’πππ’π’ πππ’π’πππ’π’π‘π‘ ΞL ΞL ΞΌ
ππ πππ‘π‘π‘π‘ π‘π‘=ππ+π’π’(π‘π‘) π‘π‘ ππ(π’π’)
πππ‘π‘π‘π‘π‘π‘ = πππ‘π‘πππ‘π‘π‘π‘+=π’π’ππ (+π‘π‘ππ)π’π’π‘π‘ π‘π‘(π‘π‘π‘π‘= ) ππ+ π’π’(π‘π‘) πππππ‘π‘π‘π‘πππ‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘===ππππππ+++π’π’π’π’((π’π’π‘π‘π‘π‘())π‘π‘ ) π‘π‘ π‘π‘ π‘π‘ πππ’π’ π‘π‘π‘π‘ π‘π‘ ΞΈ(cid:148)(cid:145)(cid:150) ΞΈ(cid:148)(cid:145)(cid:150)
πππ‘π‘π‘π‘π‘π‘=ππ+π’π’(π‘π‘) π‘π‘
Wind-Induced Acceleration in High-Rise
Buildings
An investigation on the dynamic effects due to a
deep foundation
Masterβs Thesis in the Masterβs Programme Structural Engineering and Building Technology
ALEXANDER NYBERG
GUSTAV SΓDERLUND
Department of Civil and Environmental Engineering
Division of Structural Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Masterβs Thesis BOMX02-17-32
Gothenburg, Sweden 2017
Masterβs Thesis BOMX02-17-32
Wind-Induced Acceleration in High-Rise Buildings
An investigation on the dynamic effects due to a deep foundation
Masterβs Thesis in the Masterβs Programme Structural Engineering and Building Technology
ALEXANDER NYBERG & GUSTAV SΓDERLUND
Department of Civil and Environmental Engineering
Division of Structural Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
GΓΆteborg, Sweden 2017
Wind-Induced Acceleration in High-Rise Buildings
An investigation on the dynamic effects due to a deep foundation
Masterβs Thesis in the Masterβs Programme Structural Engineering and Building
Technology
ALEXANDER NYBERG
GUSTAV SΓDERLUND
Β© ALEXANDER NYBERG & GUSTAV SΓDERLUND, 2017
Examensarbete BOMX02-17-32/ Institutionen fΓΆr bygg- och miljΓΆteknik,
Chalmers tekniska hΓΆgskola 2017
Department of Civil and Environmental Engineering
Division of Structural Engineering
Chalmers University of Technology
SE-412 96 GΓΆteborg
Sweden
Telephone: + 46 (0)31-772 1000
Cover:
Stochastic process for fluctuating wind and illustration of idealization of a high-rise
building on deep foundation. Illustrations created by Isabelle Nyberg.
Department of Civil and Environmental Engineering GΓΆteborg, Sweden, 2017
I
Wind-Induced Acceleration in High-Rise Buildings
An investigation on the dynamic effects due to a deep foundation
Masterβs thesis in the Masterβs Programme Structural Engineering and Building
Technology
ALEXANDER NYBERG & GUSTAV SΓDERLUND
Department of Civil and Environmental Engineering
Division of Structural Engineering
Chalmers University of Technology
ABSTRACT
As Gothenburg expands, several new high-rise buildings are being planned in the area.
Ideally, tall buildings are constructed on a foundation close to the bedrock, but for the
city of Gothenburg, where the ground conditions commonly consist of clay, a deep pile
foundation is often necessary. When designing tall buildings, it is important to consider
the wind-induced horizontal acceleration in serviceability limit state. The available
design codes such as, Eurocode 1 Part 1-4 and Swedish national annex EKS 10, are
based on an idealization of a cantilever beam with fixed support. However, this
assumption is reasonable when the foundation lies directly on bedrock, but becomes
more questionable when a deep pile foundation is used.
The aim of this Thesis was to investigate how wind-induced horizontal acceleration in
the along-wind direction was affected when the rotational stiffness of the support
decreases. An objective was also to study the validity of current design norms for
decreasing rotational stiffness of the support.
To be able to determine a representable mode shape and fundamental frequency for a
structure with changeable support conditions, an analytical model was developed where
the foundation was idealized as a rotational spring and the core as a cantilever beam.
To study the effect of support conditions on the horizontal acceleration and the validity
of current design norms, two theoretical approaches with response spectrum analysis
were studied, and all four approaches were evaluated in a parameter study. The
analytical model was implemented in a MATLAB-program with the possibility to
change rotational stiffness of the support, and the effects on mode shape, fundamental
frequency and horizontal acceleration were studied.
The study showed that horizontal acceleration increases for decreasing rotational
stiffness of the support. Further, the results proved that the Swedish national annex,
EKS 10, was conservative for all studied cases and that the estimated wind-induced
acceleration can be reduced by up to 33 % by using the approach suggested in Eurocode
1 Part 1-4 Annex B.
Key words: High-rise buildings, tall buildings, deep foundation, pile foundation, wind-
induced acceleration, response spectrum analysis, dynamics of structures,
Eurocode 1 Part 1-4, EKS 10, Einar StrΓΈmmen, Kamal Handa
I
II
Contents
1 INTRODUCTION 1
1.1 Background 1
1.2 Problem description 1
1.3 Aim and objectives 2
1.4 Methodology 2
1.5 Limitations 2
1.6 Outline of the report 3
2 DYNAMICS OF STRUCTURES 4
2.1 Equation of motion 4
2.2 Single degree of freedom 5
2.2.1 Free vibration 5
2.2.1.1 Undamped systems in free vibration 5
2.2.1.2 Damped systems in free vibration 6
2.2.2 Response to excitation 8
2.2.2.1 Undamped systems with excitation 8
2.2.2.2 Damped systems with excitation 9
2.2.3 Deformation response function 10
2.2.4 Systems with distributed mass and stiffness 12
2.3 Multi degree of freedom 14
2.3.1 Equation of motion for multi degree of freedom systems 14
2.3.2 Free vibration & eigenvalue statement 15
3 WIND LOAD 17
3.1 High-rise buildings 17
3.1.1 Buffeting response and wind induced motion 17
3.1.2 Vortex shedding 17
3.2 Wind field 18
3.3 Statistical parameters 19
3.4 Structural response related to wind 20
3.5 Mean wind velocity 21
3.5.1 Reference wind velocity 21
3.5.2 Terrain categories 22
3.5.3 Wind velocity profile 23
3.5.3.1 Logarithmic profile 23
3.5.3.2 Power law profile 24
3.5.4 Wind velocity pressure 25
CHALMERS Civil and Environmental Engineering, Masterβs Thesis BOMX02-17-32 III
3.6 Wind turbulence 25
3.6.1 Wind-spectral density 25
3.6.2 Turbulence intensity 26
3.7 Wind tunnel test 27
3.8 Human perception of motion 27
3.9 Regulation and norms 28
4 THEORETICAL APPROACHES TO ESTIMATE WIND-INDUCED
ACCELERATION 29
4.1 Displacement response 29
4.1.1 Spectral density of displacement 30
4.1.2 Damping 32
4.1.3 Spectral density of loading 32
4.1.3.1 Joint acceptance function 34
4.1.3.2 Wind-spectral density and Co-spectrums 35
4.1.4 Standard deviation of displacement 37
4.1.5 Resonance and background response 37
4.2 Acceleration 38
4.2.1 Spectral density of acceleration 38
4.2.2 Standard deviation of acceleration 39
4.2.2.1 According to StrΓΈmmen 40
4.2.2.2 According to Handa 40
5 APPROACH SUGGESTED IN DESIGN CODES 42
5.1 Idealization 42
5.2 Acceleration 43
5.2.1 Standard deviation of acceleration according to EKS 10 43
5.2.2 Standard deviation of acceleration according to EN 1991-1-4 44
5.2.3 Peak acceleration 45
5.3 Comfort recommendations 45
5.3.1.1 Peak acceleration 45
5.3.1.2 Standard deviation 46
6 DEVELOPMENT OF ANALYTICAL MODEL WITH VARYING SUPPORT
STIFFNESS 47
6.1 Idealization 47
6.1.1 Foundation 47
6.1.2 Building 48
6.2 Modal analysis 49
6.2.1 Mass and stiffness matrix 49
6.2.2 Fundamental frequency and mode shape 50
6.3 Determination of acceleration 51
IV CHALMERS, Civil and Environmental Engineering, Masterβs Thesis BOMX02-17-32
Description:Gothenburg, Sweden 2017. Wind-Induced Acceleration in High-Rise. Buildings. An investigation on the dynamic effects due to a deep foundation. Master's . Outline of the report. 3. 2 DYNAMICS OF STRUCTURES. 4. 2.1. Equation of motion. 4. 2.2. Single degree of freedom. 5. 2.2.1. Free vibration. 5.
