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Wind Loads on Structures Claës Dyrbye Department of Structural Engineering and Materials Technical University of Denmark, Lyngby, Denmark Svend Ole Hansen Svend Ole Hansen, Consulting Engineers, Copenhagen, Denmark
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Originally published in Danish as Vindlast pa * bærende konstruktioner © 1989 Statens Byggeforskningsinstitut Copyright © 1997 by John Wiley & Sons Ltd, Baffins Lane, Chichester, West Sussex P019 1UD, England National (01243) 779777 International (+44) 1243 779777 e-mail (for orders and customer service enquiries):
[email protected] Visit our Home Page on http://www.wiley.co.uk or http://www.wiley.com Reprinted with corrections June 1999 All Rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London, UK WIP 9HE, without the permission in writing of the publisher. Other Wiley Editorial Offices John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA WILEY-VCH Verlag GmbH, Pappelallee 3, D-69469 Weinheim, Germany Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W 1L1, Canada Library of Congress Cataloguing-in-Publication Data Dyrbye, Claës. Wind loads on structures / Claës Dyrbye, Svend Ole Hansen. p. cm. Includes bibliographical references and index. ISBN 0 471 95651 1 (alk. paper) 1. Wind-pressure. 2. Structural dynamics. I. Hansen, Svend Ole. II. Title. TA654.5.D97 1996 624.1 '75dc20 96-30346 CIP British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 471 95651 1 file:///D|/Documents/My%20eBooks/Wind%20Engineering/...%20Wind%20Loads%20on%20Structures/files/page_iv.html (1 of 2)8/9/2009 3:43:50 AM
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Typeset in 10/12pt Times from the authors' disk by Laser Words, Madras, India Printed and bound in Great Britain by Bookcraft (Bath) Ltd. This book is printed on acid-free paper responsibly manufactured from sustainable forestation, for which at least two trees are planted for each one used for paper production. Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Preface This book is intended as a guide for consulting engineers designing wind-exposed structures. It may also be useful for students at an advanced level. The book started out as an English version of Vindlast pa * bærende konstruktioner by the same authors, published in Danish in 1989. However, during the preparation of the manuscript the differences between the Danish edition and the present book evolved considerably. We thank the Danish Building Research Institute for their positive attitude towards this English version. The authors have received a great deal of help during the preparation of the manuscript. Valuable advice about presenting different aspects of the subject was provided by Professor Erik Hjorth-Hansen at the Norwegian University of Science and Technology in Trondheim, Mr. Brian W. Smith, senior partner at Flint & Neill Partnership, Consulting Civil and Structural Engineers in the United Kingdom and Lars T. Thorbek B.Sc. at Svend Ole Hansen, Consulting Engineers in Denmark. Time histories of wind velocities measured at selected sites were kindly made available by the Department of Meteorology and Wind Energy at Riso *National Laboratory in Denmark. Mrs. Esther Martens prepared many of the drawings, Mrs. Inge Sorensen *typed a major part of the manuscript, and Ms. Helen Dyrbye eliminated more than a few linguistic errors. We express our thanks for their important assistance. Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Contents
Preface
ix
Symbols
xi
1 Introduction
1
2 Wind Climate
5
2.1 Meterological Classification
2.2 Global Atmospheric Circulation
2.3 Geostrophic Wind and Gradient Wind
2.4 Thermally Generated Secondary Circulation (Typhoons)
2.5 Local Weather Systems 3 The Atmospheric Boundary LayerNatural Wind
3.1 Turbulent Wind
3.2 Mean Wind VelocityWind Profile
3.3 Inhomogeneous Terrain
3.4 Extreme Winds
3.5 Wind Turbulence
3.5.1 Standard deviation of the turbulence components
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3.5.2 Time scales and integral length scales
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3.5.3 Power-spectral density function
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3.5.4 Correlation between turbulence at two points
48
3.5.5 Wind turbulence according to Eurocode 1 4 Static Wind Load
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4.1 Extreme Static Load
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4.2 Wind Load on Buildings
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4.3 Wind Load at a Surface Point-A Mathematical Description Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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4.4 Total Wind Load on a StructureDavenport's Model
4.5 Aerodynamic Admittance Function
4.5.1 Normalized co-spectrum of surface pressures
4.5.2 Line-like areas
4.5.3 Rectangular areas
4.6 Peak Factor for a Gaussian Process
4.7 Internal Wind Load
4.8 Static Wind Load According to Eurocode 1
4.8.1 Wind pressures
4.8.2 Global wind forces
4.8.3 Size-effect factor 5 Along-wind Response, SDOF Structures
5.1 Equivalent Static Load and Dynamic Response
5.2 Wind Load on Point-like Structures
5.3 Wind Load on Large Structures
5.4 Gust Response Factor 6 The Along-wind Response of Bluff Bodies
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6.1 Assumptions
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6.2 Joint Acceptance Functions and Size Reduction Functions
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6.3 Extreme Structural Response
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6.4 Response of Line-like Structures
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6.4.1 Mean response
84
6.4.2 Background turbulent response
87
6.4.3 Resonant turbulent response
91
6.5 Response of Plate-like Structures
91
6.5.1 Mean response
92
6.5.2 Background turbulent response
94
6.5.3 Resonant turbulent response
95
6.5.4 Modes with constant signs
96
6.5.5 Modes with changing signs
97
6.6 Design Procedures
98
6.6.1 Design procedure for mode shapes with constant sign
6.6.2 Design procedure for mode shapes with changing sign
6.6.3 Structures with complicated mode shapes
6.7 Discussion of Eurocode 1
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7 Cross-wind Vibrations Induced by Vortex Shedding
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7.1 Physical Background
7.2 Vortex Shedding on a Nominally Stationary Structure
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7.3 Crosswind Loading Caused by Structural Motion Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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7.4 Vortex Shedding Response Based on the Spectral Model
7.4.1 Spectral vortex shedding response
7.4.2 The Canadian code NBC 1990
7.4.3 The CICIND model code
7.4.4 Comparison of predicted and observed
7.5 Vortex Shedding Response Based on the Vortex Resonance Model
7.5.1 Vortex resonance response
7.5.2 Eurocode 1
7.5.3 Comparison between predicted and observed responsesteel structures
7.6 Design
7.7 Reduction of Vortex-induced Vibrations
7.8 Example: A Steel Chimney 60 Metres Tall 8 Wind Load on Bridges
8.1 Mean Wind Load on Bridge Decks
8.2 Motion-induced Wind Load
8.2.1 Bridge-deck sections
8.2.2 Modal loads
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8.2.3 Aerodynamic derivatives
8.2.4 Natural frequencies and damping ratios in wind
8.3 Buffeting Vibrations
8.4 Coupled Flutter Vibrations
8.5 Flutter Vibrations of Suspension Bridges During Construction
8.6 Eurocode 1 Clauses on Bridges
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155
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166
172
9 Galloping
173
10 Wind-tunnel Testing
177
10.1 Model Laws
10.1.1 Froude's model law
10.1.2 Reynolds' model law
10.1.3 Jensen's model law
10.2 Wind-tunnel Technique Appendix A Random Variables and Stochastic Processes
A.1 One Random Variable
A.2 Two Random Variables
A.3 Stochastic Processes
A.4 Threshold Crossings and Extreme Values
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Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Appendix B Calculation of Multiple Integrals
207
Appendix C Vibrations of Linear Structures
211
211
C.1 Orthogonality of Mode Shapes
213
C.2 Equation of Motion
213
C.3 Response to External Loading Appendix D Solving Flutter Equations
217
References
221
Index
227
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Symbols
a(t)
stochastic amplitude function
A
area
A
scale parameter
A*
aerodynamic derivatives
b
length of horizontal structure or bridge-deck width
B
spectral bandwidth
cd
dynamic coefficient
ce
exposure coefficient
cf
force coefficient
cpe
external pressure coefficient
cpi
internal pressure coefficient
ctt
topography coefficient
C
shape factor
C
decay constant
Coh
coherence standard deviation of the normalized lift force CL
d
width of structure
E{ }
expected value
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f
non-dimensional frequency
fc
Coriolis parameter
F
wind load
Fr
Froude number
g
acceleration of gravity
g( )
effect influence function
h
height of structure
H( )
frequency response function
H*
aerodynamic derivatives
I
mass moment of inertia
IR( )
response-influence function
Iu
turbulence intensity
J2b
non-dimensional response variance
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Je
Jensen number
|J( )|2
joint acceptance function
k
structural stiffness
k
turbulence factor
k( )
co-influence function
kp
peak factor
kT
terrain factor
K
reduced frequency
Ks( )
size reduction function
l
length
L
integral length scale
m
mass
n
frequency in Hz
ne
natural frequency
ns
frequency of vortex shedding
p
pressure
p
probability of excedance
q
velocity pressure
Q( )
generalized fluctuating load
r
separation
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R
response
Re
Reynolds number
RN
non-dimensional power spectral density function
s
non-dimensional distance
S( )
spectrum
Sc
Scruton number
St
Strouhal number
t
time
T
time interval
T
time scale
u
fluctuating wind velocity in the wind direction
u*
friction velocity
U
10-minute mean wind velocity
Ubas
reference wind velocity with return period of 50 years
Ur
reduced wind velocity
v
fluctuating wind velocity in the lateral direction
w
fluctuating wind velocity in the vertical direction
x
axis in wind direction
y
horizontal axis normal to the wind direction
z
vertical axis
z0
roughness length
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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α
exponent in power law profile
α
angle
α( )
torsional mode shape
αdef
angular rotation of structure
γ
Euler's constant
γl
non-dimensional, normalized mass moment of inertia
γm
non-dimensional, normalized mass
γω
frequency ratio
ξ
logarithmic decrement
ζ
damping ratio
θ
factor concerning response
κ
von Kármáns constant
λ
non-dimensional length parameter
µ
mean value
ν
frequency and kinematic viscosity of air
ξ( )
flexural mode shape
ξdef
deflection of structure
ρ
density of air
ρ( )
correlation function
σ
standard deviation
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τ
time lag
ϕ
gust factor
φ
non-dimensional parameter
x2( )
aerodynamic admittance function
ψ
normalized co-spectrum
ω
angular frequency
Subscripts a
aerodynamic
ALT
altitude
b
background
c
critical flutter
crit
critical vortex shedding
d
damping
d
design value
div
divergence
D
aerodynamic drag
DIR
direction
e
equivalent
geo
geostrophic
gr
gradient
L
aerodynamic lift
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m
motion-induced
max
characteristic
min
minimum
M
aerodynamic moment
p
pressure
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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q
mean wind load pressure
r
resonance
red
reduced
ref
reference
R
response
s
structure
t
turbulence
tot
total
TEM
temporary (seasonal)
u
longitudinal turbulence component
v
vortex shedding or lateral turbulence component
w
vertical turbulence component
x
longitudinal
y
lateral
z
vertical
α
rotation
ξ
deflection
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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