Wind Loads on Structures

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Start of Citation[PU]John Wiley & Sons, Ltd. (UK)[/PU][DP]1997[/DP]End of Citation title : author : publisher : isbn10 | asin : print isbn13 : ebook isbn13 : language : subject publication date : lcc : ddc : subject :

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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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Page iv

Ltd,

Baffins Lane, Chichester,

West Sussex P019 1UD, England National (01243) 779777 International (+44) 1243 779777

e-mail (for orders and customer service enquiries): cs-books@wiley.co.uk 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

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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

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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.

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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.

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Page v Contents Preface ix Symbols xi 1 Introduction 1 2 Wind Climate 5 2.1 Meterological Classification 5

2.2 Global Atmospheric Circulation 6

2.3 Geostrophic Wind and Gradient Wind 11

2.4 Thermally Generated Secondary Circulation (Typhoons) 15

2.5 Local Weather Systems 16

3

The Atmospheric Boundary LayerNatural Wind

19

3.1 Turbulent Wind 19

3.2 Mean Wind VelocityWind Profile 24

3.3 Inhomogeneous Terrain 31

3.4 Extreme Winds 33

3.5 Wind Turbulence 38

3.5.1 Standard deviation of the turbulence components 38

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3.5.2 Time scales and integral length scales 39

3.5.3 Power-spectral density function 41

3.5.4 Correlation between turbulence at two points 44

3.5.5 Wind turbulence according to Eurocode 1 48

4

Static Wind Load

49

4.1 Extreme Static Load 49

4.2 Wind Load on Buildings 50

4.3 Wind Load at a Surface Point-A Mathematical Description 55

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4.4 Total Wind Load on a StructureDavenport's Model 56

4.5 Aerodynamic Admittance Function 61

4.5.1 Normalized co-spectrum of surface pressures 61

4.5.2 Line-like areas 62

4.5.3 Rectangular areas 64

4.6 Peak Factor for a Gaussian Process 66

4.7 Internal Wind Load 68

4.8 Static Wind Load According to Eurocode 1 68

4.8.1 Wind pressures 68

4.8.2 Global wind forces 70

4.8.3 Size-effect factor 73

5

Along-wind Response, SDOF Structures

75

5.1 Equivalent Static Load and Dynamic Response 75

5.2 Wind Load on Point-like Structures 76

5.3 Wind Load on Large Structures 77

5.4 Gust Response Factor 78

6

The Along-wind Response of Bluff Bodies

79

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6.1 Assumptions 79

6.2 Joint Acceptance Functions and Size Reduction Functions 81

6.3 Extreme Structural Response 81

6.4 Response of Line-like Structures 82

6.4.1 Mean response 83

6.4.2 Background turbulent response 84

6.4.3 Resonant turbulent response 87

6.5 Response of Plate-like Structures 91

6.5.1 Mean response 91

6.5.2 Background turbulent response 92

6.5.3 Resonant turbulent response 94

6.5.4 Modes with constant signs 95

6.5.5 Modes with changing signs 96

6.6 Design Procedures 97

6.6.1 Design procedure for mode shapes with constant sign 98

6.6.2 Design procedure for mode shapes with changing sign 102

6.6.3 Structures with complicated mode shapes 104

6.7 Discussion of Eurocode 1 106

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7

Cross-wind Vibrations Induced by Vortex Shedding

109

7.1 Physical Background 110

7.2 Vortex Shedding on a Nominally Stationary Structure 113

7.3 Crosswind Loading Caused by Structural Motion 116

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7.4 Vortex Shedding Response Based on the Spectral Model 121

7.4.1 Spectral vortex shedding response 121

7.4.2 The Canadian code NBC 1990 124

7.4.3 The CICIND model code 126

7.4.4 Comparison of predicted and observed 127

7.5 Vortex Shedding Response Based on the Vortex Resonance Model 128

7.5.1 Vortex resonance response 128

7.5.2 Eurocode 1 130

7.5.3 Comparison between predicted and observed responsesteel structures 132

7.6 Design 135

7.7 Reduction of Vortex-induced Vibrations 136

7.8 Example: A Steel Chimney 60 Metres Tall 137

8

Wind Load on Bridges

143

8.1 Mean Wind Load on Bridge Decks 145

8.2 Motion-induced Wind Load 147

8.2.1 Bridge-deck sections 148

8.2.2 Modal loads 149

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8.2.3 Aerodynamic derivatives 150

8.2.4 Natural frequencies and damping ratios in wind 153

8.3 Buffeting Vibrations 155

8.4 Coupled Flutter Vibrations 161

8.5 Flutter Vibrations of Suspension Bridges During Construction 166

8.6 Eurocode 1 Clauses on Bridges 172

9 Galloping 173 10 Wind-tunnel Testing 177 10.1 Model Laws 178

10.1.1 Froude's model law 180

10.1.2 Reynolds' model law 180

10.1.3 Jensen's model law 183

10.2 Wind-tunnel Technique 186

Appendix A

Random Variables and Stochastic Processes

191

A.1 One Random Variable 191

A.2 Two Random Variables 194

A.3 Stochastic Processes 196

A.4 Threshold Crossings and Extreme Values 202

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Appendix B

Calculation of Multiple Integrals

207

Appendix C

Vibrations of Linear Structures

211

C.1 Orthogonality of Mode Shapes 211

C.2 Equation of Motion 213

C.3 Response to External Loading 213

Appendix D

Solving Flutter Equations

217

References 221

Index 227

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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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page_xi 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

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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 :43:52 AM file:///D|/Documents/My%20eBooks/Wind%20Engineering/0...20Wind%20Loads%20on%20Structures/files/page_xiii.html (2 of 3)8/9/2009 3

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page_xiii 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

α rotation

ξ deflection

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