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Wind Loads on Structures
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Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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Wind Loads on Structures
Clas 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 * brende 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
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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, Clas. Wind loads on structures / Clas 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
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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 * brende 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 Classification5
2.2 Global Atmospheric Circulation6
2.3 Geostrophic Wind and Gradient Wind11
2.4 Thermally Generated Secondary Circulation (Typhoons)15
2.5 Local Weather Systems16
3 The Atmospheric Boundary LayerNatural Wind
19
3.1 Turbulent Wind19
3.2 Mean Wind VelocityWind Profile24
3.3 Inhomogeneous Terrain31
3.4 Extreme Winds33
3.5 Wind Turbulence38
3.5.1 Standard deviation of the turbulence components38
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3.5.2 Time scales and integral length scales39
3.5.3 Power-spectral density function41
3.5.4 Correlation between turbulence at two points44
3.5.5 Wind turbulence according to Eurocode 148
4 Static Wind Load
49
4.1 Extreme Static Load49
4.2 Wind Load on Buildings50
4.3 Wind Load at a Surface Point-A Mathematical Description55
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 Model56
4.5 Aerodynamic Admittance Function61
4.5.1 Normalized co-spectrum of surface pressures61
4.5.2 Line-like areas62
4.5.3 Rectangular areas64
4.6 Peak Factor for a Gaussian Process66
4.7 Internal Wind Load68
4.8 Static Wind Load According to Eurocode 168
4.8.1 Wind pressures68
4.8.2 Global wind forces70
4.8.3 Size-effect factor73
5 Along-wind Response, SDOF Structures
75
5.1 Equivalent Static Load and Dynamic Response75
5.2 Wind Load on Point-like Structures76
5.3 Wind Load on Large Structures77
5.4 Gust Response Factor78
6 The Along-wind Response of Bluff Bodies
79
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6.1 Assumptions79
6.2 Joint Acceptance Functions and Size Reduction Functions81
6.3 Extreme Structural Response81
6.4 Response of Line-like Structures82
6.4.1 Mean response83
6.4.2 Background turbulent response84
6.4.3 Resonant turbulent response87
6.5 Response of Plate-like Structures91
6.5.1 Mean response91
6.5.2 Background turbulent response92
6.5.3 Resonant turbulent response94
6.5.4 Modes with constant signs95
6.5.5 Modes with changing signs96
6.6 Design Procedures97
6.6.1 Design procedure for mode shapes with constant sign98
6.6.2 Design procedure for mode shapes with changing sign102
6.6.3 Structures with complicated mode shapes104
6.7 Discussion of Eurocode 1106
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7 Cross-wind Vibrations Induced by Vortex Shedding
109
7.1 Physical Background110
7.2 Vortex Shedding on a Nominally Stationary Structure113
7.3 Crosswind Loading Caused by Structural Motion116
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7.4 Vortex Shedding Response Based on the Spectral Model121
7.4.1 Spectral vortex shedding response121
7.4.2 The Canadian code NBC 1990124
7.4.3 The CICIND model code126
7.4.4 Comparison of predicted and observed127
7.5 Vortex Shedding Response Based on the Vortex Resonance Model128
7.5.1 Vortex resonance response128
7.5.2 Eurocode 1130
7.5.3 Comparison between predicted and observed responsesteel structures132
7.6 Design135
7.7 Reduction of Vortex-induced Vibrations136
7.8 Example: A Steel Chimney 60 Metres Tall137
8 Wind Load on Bridges
143
8.1 Mean Wind Load on Bridge Decks145
8.2 Motion-induced Wind Load147
8.2.1 Bridge-deck sections148
8.2.2 Modal loads149
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8.2.3 Aerodynamic derivatives150
8.2.4 Natural frequencies and damping ratios in wind153
8.3 Buffeting Vibrations155
8.4 Coupled Flutter Vibrations161
8.5 Flutter Vibrations of Suspension Bridges During Construction166
8.6 Eurocode 1 Clauses on Bridges172
9 Galloping
173
10 Wind-tunnel Testing
177
10.1 Model Laws178
10.1.1 Froude's model law180
10.1.2 Reynolds' model law180
10.1.3 Jensen's model law183
10.2 Wind-tunnel Technique186
Appendix A Random Variables and Stochastic Processes
191
A.1 One Random Variable191
A.2 Two Random Variables194
A.3 Stochastic Processes196
A.4 Threshold Crossings and Extreme Values202
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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
C.1 Orthogonality of Mode Shapes211
C.2 Equation of Motion213
C.3 Response to External Loading213
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
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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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exponent in power law profile
angle
( ) torsional mode shape
def angular rotation of structure
Euler's constant
gl non-dimensional, normalized mass moment of inertia
m non-dimensional, normalized mass
gw frequency ratio
logarithmic decrement
damping ratio
factor concerning response
k von Krmns constant
non-dimensional length parameter
mean value
frequency and kinematic viscosity of air
( ) flexural mode shape
def deflection of structure
density of air
( ) correlation function
standard deviation
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time lag
j gust factor
f non-dimensional parameter
x2( ) aerodynamic admittance function
normalized co-spectrum
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
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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
rotation
deflection
Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation
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