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. UNITED STATES fHflonal Bureau of Standards EPARTMENT OF H ^.qI /.u.nin. Bldg.

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National

Bureau

of Standards

Wind Loads

on Buildings

and Structures
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UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Proceedings of Technical Meeting Concerning

Wind Loads on Buildings and Structures

Held at the National Bureau of Standards

Gaithersburg, Maryland, January 27-28, 1969

R. D. Marshall, Editor

Building Research Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

and

H. C. S. Thorn, Editor

Environmental Data Service

Environmental Science Services Administration

Silver Spring, Md. 20910

Building Science Series 30

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 30, 169 pages (November 1970)

CODEN: BSSNB

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NATIONAL BUREAU OF STANDARDS

SEP 1 2 1971

Abstract

A technical meeting concerning wind loads on buildings and structures was

held at the Gaithersburg Facility of the National Bureau of Standards on January

27 and 28, 1969. The meeting, jointly sponsored by the Building Research Division

of the National Bureau of Standards and the Environmental Data Service of the

Environmental Science Services Administration, was intended to promote the ex- change of information between research workers and practicing engineers engaged

in this important area of technology.

Thirteen papers covering four themes were presented. These themes were as

follows: engineering problems in the design of structures to resist wind loads; atmospheric considerations; experimental and theoretical determination of aero- dynamic forces; and recent advances in design procedures and current deficiencies. Presentations were followed by a panel discussion which included a summary of each theme. The last session of the meeting was devoted to open discussion.

Key Words: Aerodynamic forces; atmospheric boundary layer; structural design; turbulence; wind effects; wind loads.

Library of Congress Catalog Card Number: 78-606243
Foreword

The effects of wind on buildings and structures have always presented engineers

with a formidable challenge. That attempts to adequately provide for these effects within reasonable economic bounds have been only partially successful is evidenced

by the number of structural failures directly attributable to wind action. While

much has been learned from past failures, the current rate of innovation in building

materials and construction methods, coupled with the trend toward extremely

slender structures, has created new demands for knowledge of wind loads. Although

the prevention of catastrophic failures must be given priority, the introduction of performance concepts has focused new attention on other effects such as rain penetration, aeolian noise production and the physiological implications of building motions. The effects of buildings on local wind environment are of great importance in the proper design of ancillary items such as courtyards, plaza areas and entryways. In comparison to other areas of engineering technology, progress in assessing

wind effects has been remarkably slow. This can be ascribed to the interdisciplinary nature of the problem which encompasses meteorology, fluid mechanics and struc- tural engineering. That a conference entirely devoted to the subject of wind effects on buildings and structures could provide a channel of communication between re- searchers in these three separate areas was demonstrated by the symposium at Teddington, England in 1963. This was followed 4 years later by an equally successful research seminar at Ottawa, Canada. Here in the United States, the time had

clearly come for a meeting of national scope where representatives from universities, consulting firms, industry and government could exchange information and

ideas.The proceedings that follow represent a significant contribution to the understanding of wind effects on buildings and structures. For their papers and active

participation that made the meeting highly successful, our thanks are extended to

all the speakers.

Washington, D.C. R. D. Marshall

H. C. S. Thom

Conference Co-Chairmen

Contents

Page Foreword Ill Welcome to NBS: A. V. Astin, Director, National Bureau of Standards 1 Session 1. ENGINEERING PROBLEMS IN THE DESIGN OF STRUCTURES TO RESIST WIND

LOADS

Chairman: Dr. A. Allan Bates, Chief, Office of Engineering Standards Liaison National Bureau of Standards Design and Construction for What Wind Loads and Why

L. C. Maugh

University of Michigan 5 Design Wind Loads for Building Wall Elements Wayne F. Koppes, AIA

Architectural Consultant 9

Session 2. ATMOSPHERIC CONSIDERATIONS

Chairman: Mr. H. C. S. Thom, Senior Research Fellow Environmental Data Service Guidelines in Selecting Wind Measuring Instruhients and Their Locations for Wind

Loading Studies Gerald C. Gill University of Michigan 21 The Adequacy of Existing Meteorological Data for Evaluating Structural Problems

Irving A. Singer and Maynard E. Smith

Brookhaven National Laboratory 23 The Characteristics of Atmospheric Turbulence as Related to Wind Loads on Tall Structures George H. Fichtl, John W. Kaufman, and William W. Vaughan

NASA—Marshall Space Flight Center 27

Session 3. EXPERIMENTAL AND THEORETICAL DETERMINATION OF AERODYNAMIC

FORCES

Chairman: Professor A. G. Davenport, University of Western Ontario

Fluctuating Moments on Tall Buildings Produced by Wind Loading

J. E. Cermak, W. Z. Sadeh, and George Hsi Colorado State University 4.') Experience with Wind Pressure Measurements on a Full-Scale Building

W. A. Dalgliesh National Research Council of Canada

Division of Building Research 61

Influence of Architectural Features on the Static Wind Loading of Buildings Hans J. Leutheusser

University of Toronto 73 The Unsteady Surface Pressure Around Circular Cylinders in T\\ o-Dimensional Flow

Wayne E. Simon

Martin-Marietta Corporation 87 On the Reliability of Gust Loading Factors Barry J. Vickery

University of Western Ontario 93

Session 4. RECENT ADVANCES IN DESIGN PROCEDURES AND CURRENT DEFICIENCIES

Chairman: Mr. Edward Cohen, Partner, Ammann & Whitney,

The Treatment of Wind in the Design of Very Tall Buildings

L. E. Robertson and P. W. Chen

Skilling, Helle, Christiansen, Robertson 107 Dynamic Response of Tall Flexible Structures to Wind Loading

Joseph Vellozzi and Edward Cohen

Ammann & Whitney H-' Some Deficiencies in Current Methods of Analysis R. W. Clough

University of California at Berkeley 129

V
Contents—Continued

Page PANEL DISCUSSION—Session Chairmen 135 APPENDIX

Combining a Wind Tunnel Analysis With a Three-Dimensional Analytic Building

Analysis

Gary C. Hart

University of California at Los Angeles 145 The Engineering Interpretation of Weather Bureau Records for Wind Loading on

Structures

S. C. HoUister

Cornell University 151

VI
WELCOME TO NBS

Dr. Allen V. Astin, Director*

National Bureau of Standards

Washington, B.C. 2023^

It is a great pleasure for me to welcome you to

this meeting on the effect of wind loads on buildings.

We are pleased with the opportunity of being able

to join with the Environmental Science Services

Administration in the planning for this symposium,

and actually cooperating with them in some important studies.

I would like to take advantage of my opportunity

to say a few words about the National Bureau of Standards, since this may be the first time a number

of you have been here. We at NBS are concerned

mainly with advancing and exploiting the science

of physical measurement. Vannevar Bush, the dis- tinguished American scientist-engineer, said in the

Foreword he wrote to the recently published Measures f<yr Progress: A History of the National Bureau

of Standards the following:

"If men working together are to accomplish

anything useful whatever, they must, above all, be able to understand one another. That is the reason for a National Bureau of Standards."

We attempt to provide the basis for the language

for meaningful, compatible exchange of quantitative information among scientists and engineers.

This program ranges from providing standards for the basic physical quantities, to the determination

of standard test methods for measuring the properties of materials, mechanisms and structures. Our

program on measurements runs, of course, from the

physical quantities to complex artifacts which our

society uses. One of the most important areas in

this business of how to measure the properties of

artifacts meaningfully is our building research

program. In this area, we have been trying over the

past few years to extend our test methods from those

aimed at determining design characteristics of components to looking at buildings as systems, and

developing criteria for the evaluation of the per- formance of the system in meeting the social and

technological needs for which the system is intended.

We then develop test methods to permit the deter- mination of conformance or nonconformance to such criteria. This emphasis on performance, using more and more the systems approach to building

problems, has led to a real appreciation of the fact that we need to know more about how to design

buildings to resist wind loads. And, in cooperation

with ESSA, we have recently initiated a program

on this. Of course, the whole problem is the one which

you intend to explore during your meeting here. I am pleased to welcome some of our Canadian neighbors to this meeting. The Canadian building reserach

program has long been one which we have respected,

and, in many respects, it has served as a model for some of the things we have tried to do here at the

National Bureau of Standards. It's a pleasure to have you with us. I hope you enjoy your meeting.

Thank you very much.

* Retired.

1
<
SESSION 1.

ENGINEERING PROBLEMS IN THE DESIGN OF STRUCTURES TO

RESIST WIND LOADS

Chairman: Dr. A. Allan Bates

Chief, Office of Engineering Standards Liaison

National Bureau of Standards

Washington, D.C. 20234

DESIGN AND CONSTRUCTION FOR WHAT WIND LOADS AND WHY

L. C. Maugh

Professor of Civil Engineering

University of Michigan

Ann Arbor, Michigan 481 04

This paper is primarily concerned with the design of various structures for wind forces from the viewpoint of the average structural engineer. The subject matter focuses attention upon three important types of structural problems whose solutions are still so uncertain as to require considerably more study and research. These problems are:

1. Wind action upon structural frameworks during construction with emphasis upon the

relatively large number of partial or complete failures.

2. The behavior of completed structures of relatively high frequencies when subjected to wind

loads. An important factor here is the amount and characteristics of motion in high-rise buildings that will be accepted by the occupants.

3. Some dynamic problems associated with wind forces acting upon structures of low frequencies such as tall chimneys and guyed towers. The above problems are discussed from the need for better design criteria and specifications as well as more exact mathematical analysis and more refined wind measurements. The importance

of the latter factor is recognized but the many empirical factors in structural design are also considered in this paper.

Key words: Buildings; design criteria; dynamics; gust factors; smoke stacks; structural failure; wind loads.

1. Introduction

Although many interesting papers and research

reports on the magnitude and distribution of wind

forces on various types of structures have been

pubUshed, I will limit my remarks to the practical use of this information by structural designers. For

purposes of presentation rather than order of importance, I will discuss the action of wmd forces upon structures in terms of the following problems.

1. Wind action upon structural frameworks during

construction with emphasis upon the relatively

large number of partial or complete failures.

2. Wind action upon completed structures of rela- tively high frequencies.

3. Some dynamic problems associated with wind

forces acting upon structures of low frequencies.

2. Wind Action Upon Frameworks

During Construction

I have always been interested in the number of bridges and buildings that have collapsed or have

been severely damaged during construction by

moderate to severe wind storms. Usually the description of such failures in technical literature is not

sufficiently complete as to assign exact reasons for the disasters. I might add that a careful examination

of the debris does not always solve the problem

either. As an example of the problem just mentioned, I will quote from a recent article in the Engineering

News Record, December 12, 1968, as follows,

"Winds Topple Bolted Steel Frame—Winds gusting

to 80 mph during a 20-minute snow and rain squall

last week toppled a steel frame being erected for a

four-story office building in Greenwich, Connecticut.

About 15 workers, warned by swaying that pre- ceded the collapse, escaped the frame and injury."

A further quotation gives, "The frame of a similar,

larger structure had been completed and was not damaged." To me, the significant part of these statements is: "warned by swaying that preceded

the collapse" which is certainly a declaration of dynamic magnification of the internal stresses. Also,

the statement that a larger completed structure was

not damaged is both interesting and typical. In many cases, I believe, an important reason

for construction failures in two to four story buildings goes back to a disregard of a provision in the

codes which, as in the AISC Specifications [1]* states, "Proper provision shall be made for stress

* Figures in brackets indicate the literature references at the end of this paper.
caused by wind during erection and after completion of the building. The wind pressure is dependent

upon the conditions of exposure, geographical location, and shape of the structure." Any practical

designer is aware of the fact that the size of primary

structural members in low buildings is seldom

affected by wind forces because of the permissible

increase in working stresses when wind stresses are included in the total. He therefore tends to minimize

the importance of the wind design and will often

disregard what might happen to the framework

during construction. In my opinion, the statement

given in the Specifications requires that the designer

should study the wind problem during construction

and that provision should be made to provide some

permanent internal bracing if necessary. The primary factors that contribute to construction failures during wind storms are as follows:

(o) No internal bracing that might insure safety

during construction is specified by the designer.

(6) No plans for temporary bracing are furnished

by the contractor and consequently are not checked

by a competent structural engineer before installation. Also the installation is not inspected as the

construction proceeds.

(c) No consideration is given to the dynamic

loads and properties of the structural framework

during erection. Certainly the shape factors of the

various structural elements, the total exposed areas, a possible resonarit condition of first mode vibration

due to a wind forcing function, together with the

low buckling strength of the unbraced beams and

columns should be considered. These problems all add up to trouble. As an illustration of designing for erection, I recall the study that I helped make for the construction of a 325 ft high gunited steel stack. To guard

against lateral vibration and ovalling of the crosssection, it was specified on the plans that the steel erection should proceed in three stages, in the follow- ing manner. When the steel shell with ring stiffeners reached the height of 190 ft above its base, erection

must stop until that portion of the stack is completely gunited and cured; erection may then pro- ceed for another 60 ft and then stopped for guniting

and curing to that elevation; the remainder of the

stack was then erected. On another similar stack

only two stages of erection and guniting were used.

If I appear to be overemphasizing wind problems

during construction, it is not only because of the

loss of life and property, but also because of the

opportunity that such problems offer to clearly

visualize the fundamental principles of wind action

that are associated with practically all types of structures; principles that will be considered in more detail by other speakers at this conference.

3. Wind Action Upon Completed Structures of

Relatively High Frequencies

Wind problems in completed high rise buildings

have increased with the modern trend toward the

use of flexible partitions, large window areas, and

combinations of elements of different materials. The

increased use of lightweight concrete deserves particular mention because of the wide variations in its physical properties. With respect to various types

of structural frameworks currently in use, it is difficult to interpret, in terms of structural behavior,

such designations as: internally braced frames,

externally braced, core braced, unbraced, shear

walls, and partial shear walls. Present trends toward

the stiffness method of analysis using complex computer programs that involve the displacements of the entire structure are appealing in terms of mathematical exactness, but in terms of the actual design,

I still favor more limited computer programs that

will provide information with regard to the relative

stiffness of selected structural combinations of ele- ments. With this information the designer can assign

reasonable paths for the transmission of wind forces through the structure and can make changes as the

design progresses. When the final selection of the

structural elements approaches completion then more sophisticated analytical programs can be

applied. However, if the preliminary design is made

by experienced designers, I am sure that no signifi- cant structural changes will be required. In structural design the function of the structure must occupy a position of importance commensurate

with safety. Therefore, in most high rise buildings

the movement must be controlled so that it is ac- ceptable to the occupants. Unfortunately, I have no

reliable information as to the magnitude and periods

of motion that will be accepted by either short

time or long time occupants. Perhaps some practical

tests upon a considerable number of people can be

conducted so that the motion and conditions will be characteristic of buildings. I recall a pedestrian

bridge that I designed which received some critical comments from people who were accustomed to walking over bridges that were designed for a series of heavy trucks. This experience convinced me that

most people are very sensitive to structural motion

that can initiate fear. To take this fear emotion into

6
consideration, it may be necessary to conduct the

tests at or near the top of a tall building.

To determine the motion of a high rise building

additional information is required concerning the

magnitude, distribution, and the time variation of wind pressures upon exterior walls, both windward

and leeward. This information will require full scale

tests upon buildings of different shapes and the

correlation of the results with small scale wind

tunnel tests. The need for additional tests is exemplified by the recent report of wind pressures on an 18

story office building by Newberry, Eaton, and Mayne

entitled "The Nature of Gust Loading on Tall

Buildings" [2]. This experimental work on a rather

ordinary rectangular type building was performed

in London, England, under the direction of the

British Research Station. Even though familiar to many of you, a few quotations from this report

may be of interest, such as: "Under these winds it

is found that the whole load is carried by the windward face of the building, the load on the leeward

face being negligible. The short duration structural loads are about 60% greater than the one minute

averages that have been the basis of many codes of

practice, but the overall drag coefficient in the

natural wind appears to be less for gust loading

conditions than that assumed in wind load calcula- tions based on model tests. These two effects largely

balance each other." Obviously, the selection of gust loadings must be related to the location, shape,

and period of the building, but from the results of

tests upon actual structures, many engineers will question the need for providing this information by

complicated equations with many uncertain parameters. An important question is, therefore, can we

not aim at improving our building codes and still keep them relatively simple to apply?

4. Structures With Relatively Low Frequencies

Several types of structures with rather large fundamental periods of vibration, say from 1 to 6 seconds,

require more extensive investigation of the vibration due to wind forces. I will mention here only the

wind action upon unbraced tall stacks and guyed

steel towers. In a recent paper [3] on the "Dynamic

Design of Reinforced Concrete Chimneys," my col- league. Dr. W. S. Rumman, and I presented recom- mendations for calculating internal stresses due to resonant wind and seismic vibration. From about

18 years of experience in the design of tall tapered

reinforced concrete chimneys with circular crosssections, we believe that the following statements

from our paper in regard to design criteria for vortex action are both conservative and sufficiently accurate: "However, the assumption that maximum

amplitudes will be obtained when there is sustained

periodicity of the vortex action with the same

period as the chimney is on the safe side and will be

accepted as a reasonable basis for estimating the

maximum lateral wind moments and shears. Further- more, for tapered chimneys, experimental results indicate that the resonant wind velocity is influenced

primarily by the upper portion." In our numerical calculations the following values

are commonly assumed: a Strouhal number of 0.2, a controUing diameter at about one-sixth of the

height from the top, a damping ratio of 0.04 of

critical, a coefficient of lift Cl of 0.66, and a sinusoidal variation of the lateral pressure with respect

to time. Obviously, a design based upon such assumptions must be regarded as primarily empirical. I am

sure that the designs based upon these recommendations are overly conservative but, as the cost of a chimney is affected very little by this conservatism

and since outage time of generators is very costly, I hesitate to suggest any reductions until more reliable information is obtained. One certain thing about the

problem is that chimneys will be built whether the

problem is completely solved or not. More research

work upon the behavior of actual chimneys is needed to check the results of small scale wind

tunnel tests, I hope that such full scale tests will be

made in the near future. The design and construction of tall guyed towers

involves the solution of many special problems

among which the vibration of the guy cables due to wind action is one of the most important and diffi- cult. Solutions to this problem have been discussed

by Klousek [4] in 1947, by Davenport [5] in 1959

and 1965, and just recently, by H. Sarvi [6] in a

dissertation at the University of Michigan. More

observations upon actual towers will be needed to verify the accuracy of these mathematical solutions

when applied to ice covered cables subjected to constantly varying wind gusts.

5. Summary

I have presented only a few examples of the

problems which the structural designer must consider in designing buildings, bridges, towers, and

chimneys for wind forces. The question arises, what

basic information concerning wind forces does the

designer really need to make an adequate design?

Although I have made no survey of professional

7
opinions on this subject, my own experience suggests

the following basic material.

1. A careful study of the final report [7] on "Wind

Forces on Structures" by the Task Committee on Wind Forces, Structural Division, ASCE, Trans.,

Vol. 126, 1961. This paper gives basic information on the nature of wind forces in terms with which

the structural engineer is familiar.

2. An understanding of the calculation of the

basic velocity pressure from the recommended

fastest-mile wind velocity for the geographical loca- tion of the site and the modification of this pressure

for height and terrain as recommended in the November 1965 proposed revision of the USASI Standard A58. 1-1955.

3. Equally important is a careful study of gust

factors, together with shape and pressure coeffi- cients for modifying the basic wind pressures. The

designer should avoid a routine selection of such

data from one code but rather compare the information with similar codes in other countries. The differ- ences znay be quite interesting.

4. For ordinary buildings, incorporating the

dynamic response of the structure into formulas for gust effect should be considered as supplementary

material and not made a basic part of a building

code. In other words, the use of such material should

be optional.

5. The designer should have a good understanding

of the variation of positive and negative pressures

over the surfaces of the walls and members; also the rapid variation of these pressures, particularly

the negative, with respect to time.

6. When the structure is an unusual one, the

designer should seek more information from experts

in the field of wind action. However, his responsibility for the safety and performance of the struc- ture can not be delegated.

6. References

[1] American Institute of Steel Construction "Manual of Steel Construction," 1963, Sec. 1.3.5, p. 5-13.

[2] Newberry, C. W., Eaton, K. J., and Mayne, J. R., "The

Nature of Gust Loading on Tall Buildings," Current Paper

66/68, Building Research Station, Garston, Hertfordshire,

England.

[3] Maugh, L. C, and Rumman, W. S., "Dynamic Design of Reinforced Concrete Chimneys," Journal of the Amer.

Concrete Inst., Sept. 1967, Vol. 64, pp. 558-567.

[4] Klousek, V., "Solution Statique et Dynamique des Pylones d'Antenne Haubanes," Publication, International

Association for Bridge and Structural Engineering, Vol. VIII, 1947.

[5] Davenport, A. G., "Dynamic Behavior of Massive Guy

Cables," Proceedings, ASCE, No. ST2, 1965.

[6] Sarvi, Hassan, "Dynamic Behavior of Guy Cables Subjected to a Small Periodic End Disturbance," Doctoral

Dissertation, The University of Michigan, 1968.

[71 ASCE Task Committee on Wind Forces, "Wind Forces on

Structures," Trans. ASCE, V. 126, Part II, 1961, pp. 1124-1198.

8
DESIGN WIND LOADS FOR BUILDING WALL ELEMENTS

Wayne F. Koppes, AIA

ArcJdtectural Consullanl

Basking Ridge, New Jersey 07920

It is principally the structural engineer who has been concerned with wind forces acting on

buildings, because it is his responsibility to design the structure to resist their overall effect. Recently, however, the importance of localized wind loads acting on the surfaces of buildings has also been receiving much attention. These local loads affect wall design, and are a matter of concern

to both the architect and the manufacturer of wall parts. The important differences between overall and local wind loads include magnitude of intensity, character, period of duration, significance in relation to building size and shape, and importance

in respect to potential property loss. Complete destruction of buildings by wind action is rare, but local failures are not uncommon and, on the whole, are more costly. Because gust and shape factors are highly unpredictable, increasing reliance is being placed on wind tunnel tests and measurements on actual buildings. Both confirm that negative pressures usually exceed positive pressures on parts of wall areas. Few building codes in this country recog- nize this, in specifying design wind loads for walls, though codes in some other countries do. The

importance of terrain conditions is not reflected, either, in code provisions. Failures of windows and other wall elements due to wind loads occur rather frequently, but

relatively few of them are documented. Several interesting examples of such failures can, however, be cited. Another important aspect of local wind effects is the funneling often experienced near the base

of tall buildings. Notable examples of this phenomenon have been observed, and research studies directed at their causes have produced significant findings.

Codes and standards cannot be expected to provide guidance for designers in respect to unique

local wind effects, but they should provide information as to loads which wall surfaces of typical

buildings will likely experience. The only standard currently providing this kind of data is the Tentative Standard for Design Wind Loads on Walls of Rectangular Buildings, published by the National Association of Architectural Metal Manufacturers. The background, purpose and

features of this Standard are noteworthy, and it is serving a useful purpose. A review of current investigations of local wind loads, both by wind tunnel tests and field measurements, indicates that certain common assumptions regarding their intensity and distri- bution on building surfaces should be reexamined. Further information regarding the nature of these loads is urgently needed by, and should be more promptly disseminated to, the designers

and producers of building wall systems.

Key words: Buildings; fluctuating pressure; gust factors; walls; wind damage; wind loads.

Traditionally, it has been chiefly the structural

engineer who has been concerned with the influence

of wind on building design, because it is his responsibility to insure the stability of the structure against

collective wind pressures. It is this overall effect, I believe, which is still of prime interest to most engineers, and perhaps to most of this audience, too. During the past decade or so, however, there has

developed an increasing concern also with what I shall refer to as the local wind effects, as contrasted

to its overall effects, those wind-induced loads acting on all local areas of the building surfaces and affecting

wall design. Although these local effects are of course

related to the overall effects, there are some important differences between the two.

It should be recognized that in most cases the

overall effects and the local effects represent different areas of design responsibility. While it is the structural engineer who is responsible for the "bones" of the structure, it is usually the architect who designs

its "skin." When walls are composed of factorymade units, as is common nowadays, the manufacturers of such units, too, are necessarily concerned

with local wind effects. All of those components

which form the envelope of the building must have

adequate strength and stiffness to resist the loads

to which they will be subjected. Thus there are three parties, not only the engineer but also the

architect and the wall component manufacturer,

who share design responsibilities, and two of these

three parties are more concerned with local wind

loads than with the overall wind effects. The purpose of this paper, therefore, is to stress the importance of local wind loads in wall design.

Being in no position to contribute any new knowledge in this area, I shall attempt simply to summarize

9
current practice and problems, indicate some seeming inconsistencies and perhaps identify some in- formation gaps. Rather than presuming to suggest answers, I shall probably be raising some questions,

in the hope that others may wish to offer opinions on some of the matters discussed.

Perhaps one of the most important contributions

to the concern with local wind loads was the series of pressure coefficient values for variously shaped

buildings and structures published in 1956 by the

Swiss Association of Engineers and Architects.

Parenthetically, the fact that architects apparently were involved in this work tends to substantiate some of my earlier observations. Since 1961, Canadian authorities have referenced these coefficients,

along with some of their own derivation, in that

part of their National Building Code dealing with

design wind loads. I know of no major building code

in this country which has provided such information

as a guide to the designers of building walls. In my view, the important differences between

the overall loads, which must be resisted by the bones

of the structure, and the local loads which act on

the skin, are these:

1. The overall load is the net result of all loads

occurring simultaneously at any time on all building surfaces, whereas the local load is the

peak load which may occur at any time at any

location on any surface.

2. Generally, only gusts of perhaps 2 seconds or more duration are significant in determining

the critical overall loading, but the critical local load is momentary in nature.

3. Overall loads are seldom of much concern on

low buildings of large area, whereas local loads

are significant on buildings of all shapes and

sizes.

4. Local loads are influenced by the configuration

of the buildings surface on which they act, to a much higher degree than are the overall

loads.

5. The most critical local loads are usually negative in character, whereas the overall load repre- sents a combination of positive and negative

pressures.

6. Maximum local loads are usually of greater

intensity than the overall design load. How about the relative significance of the local and overall design wind loads in terms of potential

damage or loss resulting if they are underestimated?

Certainly the results of inadequate provision for the

overall load acting on a building of consequence

might well be catastrophic, as compared with the

loss of its windows or parts of its walls. Fortunately,

as far as I know, this hasn't happened. Tower struc- tures and bridges have failed under wind loading,

and of course buildings have been destroyed in tornados, but I've heard of no important building

having been lost in a lesser windstorm. Some say

this may be because they're all over designed. On

the other hand, we all know of instances where

windows have been blown out, or wall elements

have been blown off of buildings in high winds.

While the complete destruction of a building by

wind action is a very rare occurrence, local failures,

especially to roofs, windows and wall cladding, are not uncommon and, in the aggregate, are much more

costly. It must be remembered, too, that when ex- tensive wind damage does occur, it usually begins

with some small local failure. Any design wind load, whether overall or local,

is generally considered to be equal to the velocity

(or stagnation) pressure at a height of 30 feet or 10

meters, modified by a height factor, a gust factor and a shape factor. In theory, this seems rather

simple, but in practice the determination of the

actual wind pressure existing at a given point on

the surface of a building, even if the velocity is known, is a complex problem, if indeed it's possible at all. This is due largely to the fact that two, at

least, of the modifying factors—the gust factor and

the shape factor, or pressure coefficient—vary with

circumstances and are highly unpredictable. They

change not only with the wind direction, but also the nature of the surroundings and the configuration of the building surface itself. The best we can hope for is a reasonable approximation, not of the

actual wind load, but of the probable maximum

load that may be expected under given conditions, over a given period of time.

It is such uncertainties that have led to increasing

reliance on two methods of obtaining more accurate information about wind action on buildings. One of these is model testing in boundary layer wind tunnels, where surrounding conditions can be simulated

and all wind directions can be studied; the other is the measurement of actual wind forces on real buildings. Both methods have their advantages and their limitations, as I'm sure you'll be hearing from other

speakers who az'e experienced and expert in their

use. My impression, as decidedly a non-expert, is that in the United States we have done some signifi- cant work in model testing but very little work in

field measurements. Other countries, however,

notably Canada, England and Denmark, have done

and are doing important work in this latter area.

10
To those concerned with wall design, one of the

most important facts established by these studies

is that the local negative, or suction loads, are much

higher then previously suspected. They appear generally to be at least equal to, and often greater than,

the positive loads, and on corner areas of tall buildings may be several times as high. I strongly suspect,

though, that most architects don't know this, be- cause they haven't been informed. With the exception of those relatively few who have been involved

in the design of our more important buildings, I believe that the majority of architects, and maybe

even a few engineers, overlook the importance of negative loading on windows and walls. Very rarely

are windows blown into a building in high winds;

nearly all of the wind damage to buildings is due to

glass being sucked out of its frame, or the roofing,

cladding or awnings being blown away from the

structure. Unfortunately, few of the results of research, and

not enough of the current knowledge regarding wind

action has been translated into practical working

guidelines for the architect's use. Generally, his only guidance in respect to design wind loads is the

building code under which he is operating. There

are four nationally recognized codes which govern

most of our building other than in the largest cities, most of which have their own codes. These four are the so-called National Building Code, promulgated

by the American Insurance Association, the BOCA

Code, by the Building Official's Conference of America, the Southern Building Code and, on the

west coast, the Uniform Building Code. Three of these codes call for design wind loads ranging, with

height, from 15 to 40 psf, though the Southern Code

specifies also loads 10 pounds higher for coastal re- gions. The Uniform Code, 1967 edition, specifies

the same design loads as given in the 1955 edition

of ASA Standard A58.1, ranging from 15 to 100

psf. Two of the codes specify that exterior walls

shall be capable of withstanding these loads acting

either inwardly or outwardly, one calls for negative

loads somewhat less than positive loads, and one makes no mention at all of negative loads. The

recently adopted code for New York City has per- haps wisely not attempted to completely define

design wind load requirements. Although it calls for overall loads ranging, with height, from 15 to 40 psf, with a minimum of 30 psf for glass and panels,

the local loads specified are 30 psf positive or 20

psf negative for all heights up to 500 feet, with a requirement that local design loads for greater

heights be specially investigated by engineering

analysis. It's quite apparent that there are confusing

inconsistencies in today's building code requirements, especially with regard to local design loads,

and it's understandable, I think, that the architect

is often uncertain as to how exterior walls should be

designed.

The building codes of some other countries are more explicit. The Canadian Code, by listing pres- sure coefficients for various building shapes, calls for negative pressures ranging from 7/9 to 1.7 times

the maximum positive pressures. The Danish Code

specifies shape factors, or pressure coefficients, for rectangular buildings in terms of a formula which

takes into account the proportions of the building,

and also results in maximum negative loads, particularly near the corners of tall buildings, which

are about 1:^4 times the maximum positive loads. I know of no codes in this country which provide

similar helpful guidance to the designer of walls. Due in large part to Professor Davenport's work, we have come to recognize that the rate of increase

of wind velocity with height above the ground varies

with the type of terrain over which the wind blows.

Obviously there is an infinite variety of terrain conditions, but for practical reasons these must be

reduced to a few categories representing major

differences. I beheve that generally three t3'pes of

terrain, or types of exposure, as I prefer to think of them, are accepted as adequatelj^ representative:

Type A, which, in general terms, is an urban or protected area. Type B, which is a suburban wooded area

or rolling terrain, and

Type C, which is flat open country or the shoreline of a large body of water, fully ex- posed to a long fetch of wind.

I'm sure that most of you are much more knowledgeable than I am about terrain effects and the

theory associated with velocity profiles, so I don't

propose to expound on these matters. As a layman,

however,- 1 would like to offer several observations

bearing on the subject. The first is that although

this important concept has been amply proven and

widely accepted for some time, no major building

code, as far as I know, has yet recognized it. However, the forthcoming USASI Standard—the updated edition of ASA A58.1—will, I understand,

specif}' design wind loads according to type of ter- rain, and the NAAMM Standard for Design Wind

Loads on Walls, which I'll describe later, is also based on this concept.

11
My second observation is that, although wind

loads are undoubtedly affected by the type of terrain or building exposure, there may be some

doubt, at least in my mind, as to whether we should

be thinking in terms of three types of exposure or perhaps only two. The Type C exposure, which is the most severe, is easily identified, and any building

erected along the seacoast is very likely to remain

exposed to a long fetch of wind throughout its life- time. But the distinction between Type A and Type

B exposure is rather vague, often debatable and

perhaps less valid. Suburban locations are fast becoming urban in character, and a good many tall buildings are being built around airports. It's often

impossible to predict, in view of the surge of building

activity which lies ahead, whether, within the next 30 or 40 years, many Type B locations will not be- come Type A, or even whether a building erected

today in a Type A location, surrounded by other

tall buildings, may not, during the course of urban

renewal, demolition, and the creation of open spaces, eventually find itself in a relatively exposed Type

B location. The architect is concerned with knowing

what the maximum intensity of local loads will likely be during the life of the building. For major

buildings, these critical loads may be determined in wind tunnel tests, using models which include all structures and other barriers to wind within a radius

of several miles. I'm questioning whether these sur- roundings should be those currently existing and

planned for the near future or, instead, should repre- sent that combination of structures which will produce the highest local pressures, both positive

and negative, on the building being designed.

Reference has already been made to the fact that

failures of windows and other wall elements often

do occur during high winds, indicating, without

question, some weakness in either design or workmanship. In many cases it's problematical which is at fault. Few, if any failures of this kind are very

dramatic. There are no widely publicized classic examples to compare, for instance, with the Tacoma

bridge disaster. In fact local failures are usually

hushed up, by the building owner, the architect, or both, for reasons that are rather obvious, and seldom

do we hear much al)out them. I can, however, cite a few representative case histories, though I'm not

at liberty to identify most of them.

Several years ago, when the wind was gusting to no more than 50 mph, several large sheets of plate

glass, in windows near the corner, and about midheight of a large new office building in downtown

New York City were broken out of their frames by

Figure 1. Wind damage to building on Florida Coast, August 1964.

suction forces and fell into a plaza area some 20 or 30 stories below. Fortunately, no one was hurt. On a gusty day in March 1967, the wind whistled

around the corner of another major skyscraper in uptown Manhattan, ripping off a spandrel panel and

sucking the glass out of corner windows on the 18th

and 21st floors. The third case, illustrated in Figures 1 and 2, involved much more extensive damage to a building on the Florida coast, during Hurricane Cleo, in August 1964. Several hundred windows were blown

out, and many of the window frames themselves were damaged beyond repair. Note that in this in- stance, too, most of the damage occurred near the

corners of the building.

The fourth case, shown in Figure 3, occurred over

10 years ago, when a severe wind storm hit Philadelphia and blew several wall cladding panels off of the Sheraton Hotel. The architect, commenting on

12
Figure 2. Wind damage to building on Florida Coast, August 1964.

this failure later at a technical meeting [1],* reported

in part as follows: "Two bays in from the west

corner, at the 6th and 8th floors, steel clips holding

the mullions of the aluminum grid to the concrete

fireproofing failed dramatically. They had been cold formed at a sharp angle, introducing a flaw in the

metal, and each sheared off at the bend as clean

as if a hacksaw had been used to cut them. This

allowed the mullions to bulge outward, the steel panels pulled away from the grid and one flew across the street and punched a hole in a church roof. Others

fell on our own roof. Fortunately, no one was hurt. The occupants of the rooms were saved from being

blown into the street by the concrete block back-up

wall. On investigation, we found that the cold- formed steel clips which had failed were Z-shaped,

whereas the other clips in the area were U-shaped.

* Figures in brackets indicate literature references at the end of this paper.

Figure 3. Wind damage to wall of Philadelphia Sheraton

Hotel, June 1958.

Only the U clips had been shown on the shop drawings which we had approved."

These are only four examples, but I'm sure that

with diligent searching many more could be found.

It's significant, I think, that in all of these cases, just as in others you may recall, the failures were

completely local in character. In no case was there

any damage, or even any indication of danger, to the structure as a whole.

Another aspect of local wind effects which is also

of concern to knowledgeable architects, rather than

to the engineer, is the funneling effect often experienced near the base of buildings. Many of you, I'm

sure, have learned from experience why Chicago is called the "windy city." It's not only because it's located on a lakefront, but because of the surprising

wind velocities that occur around the bases of many of its tall buildings. You may have experienced

similar aggravations in the canyons of lower

Manhattan.

13
i|liSl

III

1111=1

Slllli

5iili:i

I:-

In

II

II

"I

III

11:1

III

III

IBII

III

III

lllllllll

Figure 4. Earth Sciences Building, M.I.T.

One building, in particular, where this funneling

effect has been a serious problem, is, rather surprisingly, a building on the M.I.T. campus in Cambridge, Massachusetts. This building is the

Earth Sciences Building (Figure 4), a 277 ft high

tower-like structure which is pierced at the ground

level by an arcade 70 ft wide by 21 ft high, where

small cyclones are experienced frequently. Simul- taneous anemometer readings on this building, on

one occasion, showed wind velocities in the 80 to 90

mph range through this arcade, while velocities at the roof level were only 40 to 50 mph. Localized

wind velocities in the area have been a hazard to pedestrians, and a substantial part of the university's

physical plant maintenance fund has been spent on

just keeping hardware on the entrance doors opening on to this arcade. To remedy the situation, a temporary plywood screen wall was erected, but of course this was an architectural eyesore.

Figure 5. Diagram of wind flow, Earth Sciences Building. Source: Michael O'Hare. Michale O'Hare, while still a graduate student at Harvard, made a detailed study of this phenomenon,

using model and wind tunnel techniques [2, 3] and

his findings were both interesting and informative.

He also studied similar problems occurring in the

plaza of Boston's Prudential Center, where it was

found necessary to erect a series of permanent plate

glass wind screens to keep pedestrians from literally

being blown into the reflecting pool. The O'Hare

studies showed that, as might be expected, in both

of these cases, the disposition of the surrounding

buildings, as well as the downward wind flow on the

face of the tall building (Figure 5) both contribute

to these high local wind velocities.

It's unlikely that provisions for unique wind

effects such as funneling and venturi action can be

made in codes or standards. These are phenomena

which result from the nature and arrangement of masses affecting wind flow, and each situation re- quires its own analysis. The architect must be aware

of their possibilities, however, in the planning stage,

should be able to recognize potential problems, and

should know how to cope with them.

Codes or standards should, however, provide

information as to the amount and character of loading to which wall elements of typical buildings

will likely be subjected. At present we have only one standard, as far as I know, which does this. This is the Tentative Standard for Design Wind

Loads for Walls of Rectangular Buildings, published

in 1967 by the National Association of Architectural

Metal Manufacturers and designated as NAAMM

Standard WL-10-67. This standard was developed

over a period of about 23^2 years, by a committee

composed not only of representatives of several member companies of NAAMM, but also repre- sentatives of ASA Committee A58, the National

14
Research Council of Canada, the U.S. Environmental Data Service and other interested bodies,

who served as advisors. The work was prompted

chiefly by two considerations: the recognized need

for information about wind loads on wall surfaces,

and the acknowledged fact that the data on which

ASA Standard A58. 1-1955 was based had become

obsolete. The intent, in providing this standard was

not, in any sense, to question or compete with the

work of Committee A58 of the then ASA, now

USASI. Quite the contrary, in fact. The purpose was to supplement the work of that Committee,

translating it into specific requirements for wall

design. Members of Committee A58 actively assisted in the work, and every effort was made to

reflect in the NAAMM Standard the same philosophies on which the long-awaited and much-needed

USASI Standard was expected to be based.

NAAMM Standard WL-10-67, as stated in its foreword, recognizes that "appropriate wind loads

to be used in the design of building walls and their component parts depend upon several variable

factors: (1) the geographic location of the building,

(2) the degree of exposure or protection provided

by its surroundings, (3) the shape of the building.

(4) the height of the building, and in some cases, (5) the location on the building facade of the wall area

in question." Accordingly, it includes the latest wind velocity map for the country, provided by the

Environmental Data Service, and tabulates recom- mended design loads for various base velocities and

various heights for each of three types of terrain or exposure. Each of these exposures. Type A, Type B

and Type C, is defined as I have previously indicated.

Figure 6 shows the table of design loads recom- mended for Type A exposure. The K,, values in the

second column are pressure coefficients, which in- crease with the height h; Th, in the third column, is an exposure factor, decreasing with height, which is used in deriving the gust factor—or more correctly,

the gust response factor, shown in the fourth column.

The Kh and Tk values were provided by Mr. Vellozzi,

in his work on behalf of Committee ASS, and this work has since been the subject of an ASCE publication [4]. These values, I believe, are based on Professor Davenport's exposure categories and the

power laws governing wind velocity profiles. The

so-called gust factor values listed in the fourth

column are equal, in the case of relatively small

areas, to 0.65 + 41"/,. TABLE A DESIGN WIND PRESSURES (psf) FOR TYPE A EXPOSURE

Height

(feet) Kh Th Gust

Factor

Wind Velocities and (q upvalues)

60

(9.2)

70

(12.5)

80

(16.4)

90

(20.7)

100

(25.6) Over 100

10 0.2 .37 2.13 15* 15 15 15 15 / / / / /

20 0.2 .37 2.13 15 15 15 15 15 30 0.2 .37 2.13 15 15 15 15 15 40 0.24 .337 2.00 15 15 15 15 15 50 0.28 .315 1.91 15 15 15 15 15 100 0.44 .253 1.66 15 15 15 17 21 200 0.69 .201 1.45 15 15 18 23 28

300 0.90 .175 1.35 15 17 22 28 34

400 1.08 .160 1.29 15 19 25 32 39

500 1.27 .149 1.25 16 22 29 36 45

600 1.43 .140 1.21 18 24 31 39 49

800 1.73 .127 1.16 20 28 36 46 57

1000 1.98 .117 1.12 22 30 40 50 62

over 1000

/t)&^gT/\o2(^ Values f6r/Keiglits/and^oi^v^ocide^ryih^t^a detemjjled/b\/^ppa anajysi^ / / / /

*15 psf is minimum design load to be used in any case.

Figure 6. Design Wind Loads for Type A Exposure, NAAMM Standard WL-l(>-67.

15
TABLE C DESIGN WIND PRESSURES (psf) FOR TYPE C EXPOSURE

Height

(feet) Kh Th GustFactor

Wind Velocities and (q3o values)

60

(9.2)

70

(12.5)

80

(16.4)

90

(20.7)

100

(25.6) Over 100

10 1.0 .167 1.32 15* 18 24 30 37

y

20 1.0 .167 1.32 15 18 24 30 37

30 1.0 .167 1.32 15 18 24 30 37

40 1.07 .160 1.29 15 19 25 31 39

50 1.15 .154 1.27 15 20 26 33 41

100 1.40 .140 1.21 17 23 31 39 48

200 1.70 .125 1.15 20 27 35 45 55

///^

300 1.90 .117 1.12 22 29 38 49 60

400 2.05 .112 1.10 23 31 41 51 64

500 2.20 .108 1.08 24 33 43 54 67

600 2.31 .105 1.07 25 34 45 56 70

800 2.53 .102 1.06 27 37 48 61 76

1000 2.60 .098 1.04 27 37 49 62 77

over 1000

'i)p^ie^lp^dy(fk]^s ioT^ vefopiiieg^m/sh£(^ad^a

^tefmilie^V^D^ X / / / /

*15 psf is minimum design load to be used in any case.

Figure 7. Design wind loads for type C e.xposure, NAAMM standard WL-10-67.

Note that the minimum load recommended is 15 psf, and that no loads are tabulated for wind

velocities exceeding 100 mph or heights exceeding

1,000 feet. Special engineering analysis is recom- mended for such conditions. All load values listed are to be used by the designer as both positive and

negative loads, the two being considered equal.

Figure 7 shows the corresponding table for design

loads to be used with Type C exposure. Of course

there is also a similar table for Type B exposure, the values being intermediate between those for Type A and Type C exposure. The standard also includes a graph of the full range of Ku and Tk values, to facilitate determining intermediate values not

listed on the tables. This NAAMM Standard has been rather widely

recognized and commended since its publication

about two years ago and, I think, is serving a useful purpose. It should be emphasized, though, that it's intended as a tentative, being subject to revision as newly developed information may dictate. Before concluding, I'd like to refer very briefly to several examples of recent and current work contributing to our information about critical local wind loads. As you know, our colleagues in Canada

have been engaged for some time now, in recording

wind pressure measurements on several high-rise

buildings, and I'm looking forward to learning more

about recent findings in that work later in this meeting. You are aware, too, that similar important

field work of this nature is being done by the Building

Research Station in England. The drawings of Figure 8, for example, from the report by Newberry,

WIND ANGLE ^;190• 6UST SPEED 49mph (22 M/SEC)

(g) pnessuREs in lb/soft gauge positions thus • (y CONTOURS OF MAXIMUM SUCTION (3 SECC^D MEANS) IN SOUTHERLY WIND SwMi tiWiij , « H«n*, lb* of Om* liflliii M bU art 111^'

Figure 8. Measured wind pressures on walls of Iloycx

Building, London. Source: Newberry, liaton &

Mayne.

16
WIND PRESSURES AS DETERMINED BY TUNNEL TESTS NAAMM Standard WL-10-S7 Cm^fV^ »«Ui.UM-M«l.bi-CM«t>TUUiUN-aoU»aOr«

Figure 9. Wind loads on walls of U.S. Steel Building,

Pittsburgh.

Eaton and Mayne [5], show the pattern of loads

determined by measurements on the Royex Building

in London several years ago. Boundary layer wind

tunnel tests with models are also becoming more

and more important, if not indispensible, as an aid

to both engineers and architects in the design of major high-rise buildings. The two lefthand drawings

in Figure 9, for which I'm indebted to the firm of

Skilling, Helle, Christensen, Robertson, show, for ex- ample, the distribution and intensity of wind loads, as determined by wind tunnel tests, on the walls of the new U.S. Steel building now under construction

in Pittsburgh. For purposes of comparison, I have

taken the liberty of including at the right a diagram

at the same scale, indicating the comparable wind

loads prescribed by the NAAMM Standard. Loads

for both Type A and Type B exposure are shown,

A below the lines and B above, as this is one of those

cases I referred to earlier, where proper classification as to exposure seems questionable. Theie appear to be no glaring discrepancies between the predicted

and the prescribed loads as to their magnitude, but

the distribution pattern of loading consistently

shown by model test, as well as by field measurements, indicates that we are likely in error in assuming, as all codes and standards currently do, that

loads increase consistently with building height, with

the maximum load occuriing at the very top of the

building.

One more item of current interest concerns the

local wind loads being used for the walls of the new

World Trade Center buildings in New York, which,

as you probably know, will be the tallest buildings

in the world. I am informed by a reliable source

that the loads specified for the testing of these walls

are as follows: positive loads which range from 45

psf for the lower 41 stories to 55 psf for the next

67 stories, but are reduced to 40 psf for the top 3

stories; negative loads which are much high(!r,

ranging from 65 psf for the lower 6 stories to 125 psf

for the 101st through 109th stories, with four inter- mediate increments, and are 115 psf for the top

story.

I made reference at the outset to information

gaps, and to me this is a matt(!r of major concern. In many areas of building technology the time lag

between the acquirement of information through

research, and the dissemination of this knowledge

for general use is far too great. This is particularly true in respect to design wind loads. The collective knowledge in this field, represented in this room

today, is tremendous. But it can be of small benefit to the great majority of practitioners until it is translated into practical working data for the designer's use. This process should be hastened. Although, some problems may still remain unsolved,

and certain theories may not yet be fully verified, an organized effort should be made to see that codes

and standards more promptly reflect current knowledge. There should be some central clearing

house which would circulate current technical in- formation, in this field as well as others, at frequent

intervals to all concerned. If the Bureau of Standards could find a means of doing this, it would be

providing a great service to the liuilding industry.

To summarize, then, the more important concerns with respect to the influence of wind on the design

of wall elements are these:

1. Local wind loads acting on the walls of a building are not the same as the overall loads governing the design of its structure; usually their intensity is greater.

2. The maximum negative loads acting on wall areas are usually as large as, if not greater than,

the maximum positive loads, and may be

several times greater.

3. The maximum loads on the faces of tall rec- tangular buildings probably do not occur at the

top of the wall, but at some distance below the

top.

4. In planning the arrangement of building units

within a group, and the relation of voids to mass at the ground level, the possible creation

of wind funneling should be carefully

considered.

5. Accumulated knowledge regarding wind loads

should be more widely and more promptly

disseminated to the design professions.

17
6. Without question there is need for much more

information regarding local wind effects, if designers of building walls are to steer a true course between the creation of hazardous conditions on the one hand and wasteful over- design on the other.

References

[1] Dean, Robert C: "Sheraton Hotel, Philadelphia," Publication 788 National Academy of Spiences—National Research Council (1960).

[21 O'Hare, Michael: "Wind Whistles Through M.I.T. Tower," Progressive Architecture, March 1967.

[3] O'Hare, Michael: "Designing with Wind Tunnels," The

Architectural Forum, April 1968.

[4] Vellozzi, J. and Cohen, E.: "Gust Response Factors," Paper 5980, Proceedings of the American Society of Civil Engineers, Vol. 94, No. ST6, June 1968.

[5] Newberry, C. W., Eaton, K. J. and Mayne, J. R. : "The

Nature of Gust Loading on Tall Buildings," Paper No. 15, Proceedings of the International Research Seminar, National Research Council, Ottawa, Canada, September

1967, Vol. 1.

18
SESSION 2.

ATMOSPHERIC CONSIDERATIONS

Chairman: Mr. H. C. S. Thorn

Senior Research Fellow

Environmental Data Service—ESSA

Silver Spring, Md. 20910

GUIDELINES IN SELECTING WIND MEASURING INSTRUMENTS AND THEIR

LOCATIONS FOR WIND LOADING STUDIES*

Gerald C. Gill

Professor of Meteorology

University of Michigan

Ann Arbor, Michigan 48104

The different types of wind speed sensors (cup, propeller, pressure tube, pressure sphere, hot

wire, and sonic) will be discussed in relation to their suitability for wind loading studies. For very sound reasons the rotational types of anemometers (cup and propeller) have become the standard wind speed sensors used in North America today. Pressure type wind speed sensors will be considered but they have inherent weaknesses as anemometers. In view of the versatility of the

rotational anemometers and in view of all weather records and charts being ba.sod on observations with these instruments it appears advisable for wind loading studies to measure wind speed with

these conventional anemometers. Wind vanes of different types (flat plate, splayed vane, and aerodynamic cross section) will be

discussed and the transducers to be used with them. Very light vanes of the flat plate type are recommended.

The dynamic response and fidelity of recording of both anemometers and wind vanes will be

discussed. The wind-shadow effect of towers on the wind sensors mounted thereon, and the orientation

of the sensors will be discussed. For good exposure the sensors should be moimted one to two

tower widths out from the tower, and, either into the prevailing wind, or, into tiie wind direction

of maximum concern. The height and location of towers relative to the building or structure under study will bo discussed.

Key words: Anemometers; instrumentation; tower interference; transducers; wind vanes; wind

loads.

* Note.—Due to illnes.s, the author was not able to complete

the manu.script in time for publication.

21

THE ADEQUACY OF EXISTING METEOROLOGICAL DATA FOR EVALUATING

STRUCTURAL PROBLEMS

Irving A. Singer and Maynard E. Smith

Brookhaven National Laboratory

Upton, Long Island, New York 11973

Available meteorological data are usually unsuitable for application to structui-al problems

for a variety of reasons. The most obvious deficiency involves instrument location in the three- dimensional sense. Most meteorological observations have been obtained at low elevation in open

country, and they therefore do not reveal the wind structure at the typical heights of modern

urban buildings. Furthermore, few of the data have been processed to reflect the turbulent struc- ture of the flow. More subtle problems are involved with the failure of any current programs to

define the horizontal structure of turbulence, although a small number of appropriate studies have been made in the vertical. Very important also is the lack of data taken under extreme

meteorological conditions, such as thunderstorms and hurricanes. These deficiencies derive in part from the difference in objectives that have led to existing meteorological programs and those that would suit the structural engineer, but they are also associated with the failure of the latter to define his requirements. An experimental program that may fill some of the gaps is outlined

for discussion and criticism.

Key words: Climatology; meteorology; spatial correlation; turbulence; wind observations; wind

profiles.

1. Introduction

Ritter and Ordway, in a presentation before the

New York Academy of Sciences [1]* noted that: "It

is a peculiar fact that until now climate has been a minor factor in the design of our current urban re- newal programs," and they cite a variety of problems

that may be created by, and conversely influence,

the construction of massive buildings of new and

unusual configurations. It is true that there has

been surprisingly little conversation among the

aerodynamicists, architects, structural engineers

and meteorologists, and it is imperative that such

exchanges begin. In our own limited probing into

this field, we have found that a need exists for a review of the available wind data that can be applied

to such problems, and this paper includes such a

review. Since our consideration of the problem re- veals important gaps in the meteorological data,

suggestions for remedying the deficiencies are also included.

2. Standard ESSA Wind Observations

By far the most complete wind data available in the United States reside in the records of the U.S. Weather Bureau (ESSA) stations, which number

* Figures in brackets indicate the literature reference at the end of this paper.

more than 1,000. Many of these stations have been

in operation for one or more decades, and ESSA has

provided an excellent repository and processing

center at Asheville, N.C. so that data can be re- trieved and reprocessed readily.

The typical "surface" wind observation is usually

obtained from a sluggish cup anemometer and vane

assembly, mounted in a well-exposed location about

30 ft above the ground or building structure. The

vast majority of the sites are at airports, and urban

observations are comparatively rare. The standard

observation procedure is to note the indicated wind

speed and direction for a brief period once each

hour, and record them to 10° (formerly 16 compass

points) and the nearest knot or mile per hour.

Normally a contacting device is associated with the

anemometer, from which one can obtain the time

required for one mile of wind flow to pass the in- strument. Observations called PIBALS or RABALS

are taken at many of the stations, using either visual

or electronic tracking of a rising balloon several times per day to determine the variation of wind

with height. These data are processed to reflect the

wind at 1,000-ft intervals above mean sea level. Unfortunately, neither the surface nor upper wind

data offers direct and substantial assistance to the

structural engineer. One can obtain at best a crude

impression of the change of wind with height, and

statistics of the distribution of the "hourly" wind

23
speeds and directions. It is possible to develop

reliable estimates of the maximum winds at ane- mometer elevation, since the length of record is usually sufficient for the purpose and observations

are made during extreme as well as typical meteorological conditions.

Obviously, no indication of short-term wind

fluctuations other than the variable period "fastest mile" can be derived from these records, nor can one

reach any valuable conclusions about the smallscale spatial distribution of the wind field.

3. Specialized Data

Most of our knowledge of the details of wind

fluctuations comes from a limited group of tower

observations, generally extending no more than 500

ft above ground, although there are a few reaching

1,000 ft and more. Unlike the standardized ESSA surface stations,

these towers have been equipped with a variety of wind sensors, ranging from hot-wire anemometers

to Bendix-Friez Aerovanes, and the recording and

processing of the data are almost as varied as the

number of towers themselves. Furthermore, and by

no means trivial, is the fact that few of these in- stallations have been operated during extreme meteorological conditions. Most of the research as- sociated with these towers has been directed toward

typical weather regimes, and equipment is fre- quently removed if the probability of damage by

lightning or strong winds is anticipated.

From these towers, however, we have obtained our only records of the detailed wind structure that

is important in structvu-al design. A fair amount of these data could be reduced to a useful form if this has not been done already. Certainly we are in a

position to define typical vertical wind profiles up

to 500 ft above ground in open country at a minimum of 20 locations within the United States. At

many of these locations spectra or other expressions

of time and space correlation covering wavelengths

of 10 m and longer can be developed for the |u and

V components of the wind, and in rarer instances for the w component. In a few isolated instances, some

of these data are available for extreme wind conditions. Spatial representation is confined almost exclusively to a single vertical line, and horizontal

correlations are available only at very low elevations.

Above 500 ft information becomes very sparse, both in terms of the number of sites and in the suit- ability of the data. Most of the information has been

processed so that fluctuations having periods shorter

than 5 minutes cannot be studied, and in only one

case [2] are we aware of complete three-dimensional

records up to 1,000 ft. To the best of our knowledge we have no current

source of information linking low and high-level

fluctuations in a major urban area, nor do we have

any indication of the horizontal distribution of wind

fluctuations high above the ground, except by blind

dependence on some theoretical transformation

from time to space scales. The current vogue among

meteorologists is Taylor's hypothesis which permits

transfer from one coordinate system to another,

but this approach has been tested only at low elevations and in the direction of the mean wind. Lack of three-dimensional observations extending to higher

elevations is the most serious shortcoming of the

existing data.

4. Suggested Remedies

Despite the foregoing gloomy remarks, there are many constructive steps that could be undertaken,

and in which our organization is interested. The

first is an intensification of exchanges of which the

present meeting is an example. We must determine

what meteorological data would be most valuable

in analyzing structural problems and the form in which they could be most easily utilized. As meteorologists we suspect, for example, that turbulence

measurements on a very fine scale may have no

application to these problems, but we are not

certain of this conclusion. The choice and location

of instrumentation for new studies, however, is strongly dependent upon the time and space scales

of interest. Surely a climatology of mean and maximum

velocity profiles can be established from the tower

data we now have. These profiles should be developed to cover various averaging periods, meteorological conditions and topography (including

cities wherever possible) and they should be ex- pressed in probability statements such as recurrence

intervals. One can also attempt to relate the profile data

to the standard ESSA observations. If this effort is successful, the huge body of standard data will in- crease greatly in value. A climatology of the good data from existing towers should be made. The adjective "good" implies appropriate instrumentation, recording and

processing, so that much of the existing record

would be eliminated, but even the most meagre

climatology, segregated into meteorological, topographic and height classifications should be valuable.

24
I New data obtained with the objectives of structural design as controlhng criteria should obviously

be collected, and appointment of an advisory committee for the program including representation

from the fields of aerodynamics, instrumentation,

meteorology, statistics and structural engineering

should therefore be the first order of business. We

have quite enough experimental data that are not

j suitable for such purposes.

j We believe that the most valuable experimental

I effort should be aimed at determination of the full details of the three-dimensional wind structure at a

relatively simple, I'ural site. The key features of the program should be the utilization of instrumentation of appropriate response, durai:)ility and reli- ability, and the definition of the horizontal spatial

correlations in the flow. An arraj' of towers, one of which should reach 1,000 ft, would be needed.

Several mobile units approximately 150 ft high

should be included to determine the horizontal

variability adequately. Kecording equipment must

be directly suitable for computer analysis, and it is quite possible that an on-line computer should be

assigned to the project to permit immediate analysis

of the data and reorientation of individual

experiments.

An open, uncomplicated site is suggested in preference to an urban installation, since we believe

that the complexities of flow at the lower levels in

cities will always remain unique functions of the

particular locality and may never submit to theoretical analysis. On the contrary, it would seem more

likely that correct judgements concerning the design

of a new urban structure might better be achieved

by wind tunnel reproduction of the profile and

turbulence characteristics of the unimpeded flow

coupled to scale modeling of the salient ui'ban

features. A word of caution about tunnel modeling does seem in order, however. Logically, careful attention

to detail should permit reproduction of many characteristics of the natural wind flow, but one wonders

whether it will become possible to reproduce the

larger scale (though relatively short period) variations in the v and lo components of the natural flow. The wind tunnel provides a fixed mean wind direction, while the atmosphere is under no such

restrictions. Elevated measurements within cities should,

however, be used in developing our understanding

of urban turbulence, and the program should include

study of data from structures within cities and the

establishment of new measuring arrays as well.

The television in<histry has gcuiei'ously provided

a number of spires that may be useful in observing

wind structure within mhan areas, and measui-cments on poles or modest towers above the taller buildings may also be helpful in determining the

differences l)etween urban and countiy wind

structures. One reasonably simple method of establishing the

alterations in natural turbulence; that may be in- duced by the introduction of new structures is by

the use of inflatable buildings. C 'Onsiderable experi- ence with fixed structures has ali'eady been obtained

in wind tunnels and some of this evaluation has been

duplicated in the field, but the emphasis has been

placed on the stresses on the Iniildings rather than

the deformation of atmospheric structure. Inflatable buildings permit extension of wind tunnel "before

and after" techniques to field experiments.

An important criterion also is that the site of the

field experiments be subject to extreme wind conditions with reasonable frequency. Towers such as those in Philadelphia, Cedar Hill and Savannah

River, for example, are too far inland to experience

maximum hurricane winds, but they ceitainly will be more frequently affected by squall lines and

thunderstorms than coastal sites. New field experimentation obviously implies more than a single site if it is to be comprehen.sivc

and effective. The desirability of duplicating certain

measurements at different sites is already clear. The standard deviations of the u, and v and lo components observed at the 500-1,000 ft levels on

the Savannah River tower, for example, are not in agreement with the values that would be derived

from theories that seem to describe lower-l(>vel

measurements, l)ut no one can say whether these

data are incorrect, whether the site is somehow

anomalous or whether the theor}^ is defective. Such a majoi' program to remedy the defects in our knowledge of turbulence would ol)viously be

expensive, but it would seem that the savings that

might accrue in more intelligent structural codes

and designs would greatly outweigh the cost.

5. References

|1| Hitter, A. and Ordway, O. V..: "Tlu; Ronai.ssance of Subsonic Aerodynamics," Annals, X.Y. Acad, of Scienee.s YITA, Art. 2, pp. 777-791, Nov. 196S.

[21 Cooper, R. \\. and Rusche, B. C. : Tlie SRL Motoorological

Systems, Proe., USAKC Mot. Info. Mfg., Sept. 11-14,

1967, Chalk River, Can., AKCL-2787, pp. 51-58.

25

THE CHARACTERISTICS OF ATMOSPHERIC TURBULENCE AS RELATED TO

WIND LOADS ON TALL STRUCTURES

George H. Fichtl,' John W. Kaufman,- and William W. Vaughan''

AerOS-pace Environment Division

Aero-Astrodynamics Laboratory

NASA—Marshall Space Flight Center

Huntsville, Alabama 35812

An engineering boundary layer wind model based upon data collected at the NASA 1.50-meter meteorological tower facility at the Kennedy Space Center, Florida is discussed. A statistical power-law peak wind profile is used to extrapolate peak wind statistics valid at the 10-meter to other levels. The relationship between the instantaneous extreme wind profile and the peak wind

profile for various periods of exposure up to ten minutes is examined. The gust factor profile, which depends on the peak wind speed, height, and averaging time, is applied to the peak wind

profile to obtain a mean wind profile. A spectral model of the longitudinal and lateral components

of turbulence for the neutral boundary layer (high wind .speeds) is presented.

Key words: Atmospheric boundary laj-er; gust factors; peak values; power spectra; turbulence; wind profiles.

Nomenclature

b = parameter that characterizes the statistics oik

Cp = specific heat of dry air at constant pressure C = empirically detcrnuned parameter that occurs

in formulae of the longitudinal and lateral spectra

/ =nzlu

fm = value of / associated with peak of logarithmic

spectrum

g = acceleration of gravity

go = empirical function of Uu and t that occurs in the formula for the gust factor G = gust factor k =peak wind profile parameter

k\ =0.4 = von Karman's constant

L' = stability length n = frequency, Hz

p = empirical function of that occurs in the

formula for the gust factor

r = empirically determined parameter that occurs

in formulae of the longitudinal and lateral spectra

Hi = gradient Richardson number

S{n) = longitudinal or latci-al spectrum of turl)ulenco

52(w) = spectrum of the square of the longitudinal or

lateral components of the wind

' Aerospace Engineer.

- Chief, Atmospheric Dynamics Branch.

' Chief, Aero.spacc ]']nvironment Division.

t = averaging time

f = time average mean temperature

u{z) = peak wind speed at height z u{z) = time averaged mean wind speed at height z u* = surface friction velocity

Zq = surface roughness length

0 = vertical collapsing factor = variance of k or variance of the longitudinal

or lateral components of turbulence = logarithmic wind profile stability defect.

1. Introduction

The purpose of environmental wind criteria is to provide a model of the atmospheric boundary layer

such that when it is used in design studies an ac- ceptable structure results. How one should develop

such a model is determined by the purpose and re- quirements of the structure. Thus, to develop these

models so that they arc meaningful from an engineering viewpoint, it is necessary that the atmospheric scientist and the design engineer work as a team. The National Aeronautics and Space Administration, Marshall Space Flight Center (MSEC),

Huntsville, Alabama, is concerned with developing

and operating launch vehicles like the Saturn V,

which placed three American astronauts into lunar

orbit on December 25, 1968. The Saturn V stands

363 feet tall and weighs over 6 million pounds. Its height makes the vehicle especially vulncral)le to ground wind loads. An artist's concept of this

27
Figure 1. An artist's concept of the Satui-n V space vehicle and the associated ground support equipment.

vehicle and its associated ground support cquipnuMit

is shown in Figure 1. About 2 months before launch,

the vehicle is erected in the Vertical Assembly

Building (see background of Figure 1) on the Mobil(>

Launcher. The vehicle and launcher are then moved

to the launch pad, about 3 miles away, on the

Crawler Transporter. The Mobile Service Structure

is then moved to the vehicle to provide a platform

from which the vehicle can be serviced. Before

launch, the Mobile Service Structure is rolled ofT the pad, and the vehicle is launched from the

Mobile Launcher.

During the design and fabrication stages of space

vehicles, the design engineer must know the final weight of the launch configuration so that unnecessary weight penalties are avoided. Since the ground

support equipment will remain on the ground at launch, the present design philosophy in the industry is to design the auxiliary ground support

(Hjiiipment to alleviate, wherever practical, some of the loads on the vehicle due to the ground winds.

However, it is conceival^le that ground support

equipment niay have to be so sophisticated that

providing this capability will become impractical.

Thus, it is imperative that the ground wind environment be defined in usable engineeiing terms as precisely as possible so that the engineer need not overdesign the ground support equipment and the

vehicle structui'e for a given value of risk. This is especially true if the vehicle is required to withstand

ground wind loads in the event the ground support

equipm(>nt cannot Ix' designed to completely alleviate the entire design ground wind loadings. Although

there are various ways of presenting wind criteria for engineering design, this paper describes only the

principal methods used at the Marshall Space

Flight Center.

28
2. Peak Wind Statistics

The fundamental surface wind statistics for the

Kennedy Space Center are based on an 8-year

sample of hourly peak wind speeds measured at the

10-meter level for a period of record from September

1958 through June 1967. The sample was constructed

for NASA at the National Weather Records Center,

Asheville, North Carolina, by selecting the peak

wind speed that occurred in each hour of record read

from original wind rolls. Peak wind statistics have

three advantages over mean wind statistics. First,

^eak wind statistics do not depend on an averaging

operation as do mean wind statistics. Second, to construct a sample of mean winds, a chart reader or weather observer must perform an "eye-ball" aver- age of the wind data, thus, causing the averaging

process to vary from day to day according to the

mood of the observer and from observer to observer.

Hourly peak wind speed readings avoid this subjective averaging process because "a peak is a peak is a peak." Third, to monitor winds during the count- down phase of a vehicle launch, it is easier and more

objective to monitor the peak wind speed than the mean wind speed.

Smith et al. [1]* have performed extensive statistical analyses with the Kennedy Space Center peak wind

speed sample. In the course of his work at the Marshall Space Flight Center, he has introduced the

concept of exposure period probabilities into the

design and operation of space vehicles. By deter- mining the distribution functions of peak wind speeds

for various periods of exposure (hour, day, month,

year, etc.), it is possible to determine the probability

that a certain peak wind-speed magnitude will occur

during a prescribed period of exposure of a space

vehicle to the natural environment. Thus, for ex- ample, if an operation requires, say, one hour to complete, and if the critical wind loads on the

vehicle can be defined in terms of the peak wind

speed, then it is the probabihty of occurrence of the

peak wind speed during a 1-hour period that gives a measure of the probable risk of the occurrence of structural failure. Similarly, if an operation requires one day to complete, then it is the probability of oc- currence of the peak wind during a 1-day period

that gives a measure of the probable risk of structural failure. Smith et al. [1] have also shown that the peak wind

speeds at Cape Kennedy for various periods of ex- posure have a Fisher-Tippett Type I distribution

* Figures in bracket.s indicate literature references at the end of this paper.

[2], which is the one used by Gumbel [3]. Although

the Gumbel distribution appears to give a good

theoretical fit to the empirical peak wind speed

distribution, it has the disadvantage that it is unbounded at both ends. Since wind speed ha.s a

physical lower bound at zero, it may be desirable

to investigate other disti'ibution functions. Smith

points out that the Fisher-Tippett Type II distribution, which is indeed bounded from below at zero, would be such a function. Thom [4] has used the

Fisher-Tippett Type II distribution for representing

ground wind statistics. Figure 2 shows an example of Smith's peak wind

speed statistics where the distributions for the month

of October for different reference periods are illus- trated, and the probabilities of the occurrences of peak wind speeds for the indicated reference periods can be determined. Thus, for example, the probability that the peak wind speed during the hour from

0530 to 0630 EST will be less than 32 knots is 0.977. Probabihty statements concerning the capabilities of the space vehicles developed at MSFC and

launched at the Kennedy Space Center (KSC) are given in terms of Smith's peak wind speed exposure

statistics. The statistics are valid at the 10-meter

level. However, to perform loading and response

calculations resulting from steady-state and random

turbulent drag loads and von Karman vortex shedding loads, the engineer requires information

about the vertical variation of the mean wind speed

and the structure of turbulence in the atmospheric

boundary layer. The philosophy at MSFC is to extrapolate the peak wind statistics up into the

K WIND SPEED (knolsl 10 MEIER REFERENCE LEVEL PEAK WIND SPEED Im/

YEARLT PEAK - INCLUDING HURRICANES »/

YEARLY PEAK - EXCLUDING HURRICANES /

TRIMONTHLY PEAK ^^ONIHLY PEAK OCI-NOV- OEC A(' y^

DAILY PEAK,^^^

y^ 32 knoi! y^ H6 5 m/secl

^''"'^^^''''^ ^^^C^ HOURLY PEAK - 1500

.— 1 i

'"'^^^ ^--^^^ ^—HOURLY

J—1—1—1

' 1

'' 1 M—

PEAK - 0600 —1 \ M

' fJ

to

20

0

PROBABILITY OF THE OCCURRENCE OF THE WIND SPEED

Figure 2. Fisher-Tippett distribution collated to peak w ind speed samples at Cape Kennedy, Florida, in October.

29
atmosphere using a peak wind profile, and to obtain

the associated quasi-steady or mean wind speed

profile by applying a gust factor, which is a function

of wind speed and height. At this point, the engineer can calculate the steady-state loads resulting from

the mean wind profile and the response due to dis- crete gusts in the form of a gust factor. The gust

factor accounts for the loads beyond those resulting

from the quasi-steady wind profile—in short, the

turbulence. For some applications, depending on the

response characteristics of the vehicle, the peak

wind speed profile is used directly in the calculations. An alternative, and probably more meaningful,

representation of the turbulence can be given in the

form of a spectral model of the longitudinal and

lateral components of turbulence.

3. The NASA 150-Meter Meteorological Tower

To obtain micrometeorological data representative

of the Cape Kennedy area, especially in the vicinity

of the Apollo/Saturn V launch pads, a 150-meter

meteorological tower was constructed on Merritt

Island at the Kennedy Space Center. The tower

facility,* discussed in detail in a report by Kaufman

and Keene [5], is only briefly described here.

3.1. Terrain Features

Figure 3 shows the location of the facility with

respect to the Saturn V space vehicle launch com-^

Figure 3. NASA Launch Complex 39, Kennedy Space

Center, Florida.

plex 39. Located about 3 miles from the Atlantic

Ocean, the tower is situated in a well-exposed area

free of near-by structures which could interfere with

the air flow. The aerial photograph (Fig. 4) of the terrain sur- rounding the tower (point T) was taken at 3,500 ft above mean sea level. In the quadrant from approximately 300° north azimuth with respect to the tower,

clockwise around to 90°, the terrain is homogeneous

and is covered with vegetation about H to 13^

meters high. Another homogeneous fetch with the same type of vegetation occurs in the 135° to 160°

quadrant. The areas A (230° to 300°), B (90° to 135°),

and C (160° to 180°) are covered with trees from

about 10 to 15 meters tall. The fetch from the

tower to areas A or C is about 200 meters, and the

fetch to area B is about 450 meters. The height of the vegetation over these fetches ranges from 3^ to

13^2 meters, as in the area to the north of the tower. To the south-southwest in the 180° to 230° quadrant

225 meters from the tower, there is a body of water

called Happy Creek.

3.2. Instrumentation

The complete tower facility comprises two towers, one 18 meters and the other 150 meters high (see

Fig. 5). The levels on both towers are instrumented

with Climet (Model Cl-14) wind sensors. Temperature sensors, Climet (Model-016) aspirated thermocouples, are located at the 3- and 18-meter levels on the small tower and at the 30-, 60-, 120-, and

150-meter levels on the large tower. Foxboro (Model

F-2711AG) dewpoint temperature sensors are lo- cated at the 60- and 150-meter levels on the large

tower and at the 3-meter level on the 18-meter tower. Wind speed and direction data can be recorded on

both paper strip charts and analog magnetic tapes

with an Ampex FR-1200 fourteen-channel magnetic

tape recorder which uses a 14-in reel. The temperature and dewpoint data are recorded on paper strip charts. To avoid tower interference of the flow, the

large tower is instrumented with two banks of wind

sensors. The details of how and when one switches

from one bank of instrumentation to the other bank

is discussed by Kaufman and Keene in Reference 5. During a test in which the wind data are stored on magnetic tape, only one bank of instrumentation

is used. This avoids interruption of the wind data

signals within any magnetic tape recording period,

and thus avoids data-processing difficulties when

converting analog tapes to digital tapes.
3.3. Surface Roughness Length (zq)

In an earlier report, Fichtl [6] discussed the sur- face roughness length configuration associated with

the NASA meteorological tower. This analysis was

based upon wind profile laws that are consistent

with the Monin-Obukhov similarity hypothesis.

The calculations of zo were based on wind data obtained at the 18- and 30-meter levels and on temperature data obtained at the 18- and 60-meter

levels. Most of the measurements were obtained

during the hours of 0700 and 1600 EST, and the

gradient Richardson numbers at 23 meters (geometric height between 18 and 30 meters) for the 39

cases ranged between —5.82 and +0.079. The

results of these calculations, shown in Figure 6, show

the effect the terrain features (see Section Ilia)

have upon the surface roughness.

4. Design Wind Profiles

To calculate wind loads on space vehicles, the

engineer requires specific information about the

wind profile. As pointed out in Section II, the fundamental wind statistics for the Kennedy Space

Center are specified in terms of peak wind speeds for various periods of exposure (hour, day, month, etc.) at a reference height of 10 meters. A statistical peak

wind profile model is used to extrapolate this in- formation into the vertical, and the mean wind

profile for various averaging periods is obtained by

applying gust factors.

4.1. Peak Wind Profiles

To develop a peak wind profile model, about 6,000

hourly peak wind speed profiles measured during

1967 at the tower were analyzed. The data seemed

31
BOOM HEIGHTS (meters)

150.0 W120.0 W90.0 W60.0 W30.0

18.0

SWW.T.Th

W, T

TOWER

W, T, T^

W - WIND SPEED AND DIRECTION SENSORS

(CLIMET SERIES C1-14)

T - TEMPERATURE SENSOR

(CLIMET ASPIRATED THERMOCOUPLE SYSTEMS CI-016)

Tj - DEWPOINT TEMPERATURE

SENSOR

(FOXBORO MODEL F-2711AG)

W W, T

777

18.0 (meters

18.0 pW.T

10.0 -W

3.0 -W. T, n I H

NE

Figure 5. Schematic diagram of the location of instrumentation of the NASA 150-meter meteorological tower

at Kennedy Space Center, Florida.

to show that the variation of the peak wind speed

in the vertical, below 150 meters, could be described

with a power law relationship given by

m(z)=Mi8(2/18)*, (1) where u{z) is the peak wind speed at height z above

natural grade and U\% is a known peak wind speed at

2 = 18 meters. The parameter k was determined for each profile by a least-squares analysis of the data. At low wind speeds on the order of 2 m sec~\ the

values varied from about —0.05 to 0.15. Negative

z. (meters)

270 360

WIND DIRECTION (deg)

Figure 6. Distribution of the surface roughness length at the NASA 150-meter meteorological tower site.

values of k occurred for approximately 8% of the

cases in the sample. One should keep in mind that we are analyzing peak wind profiles and that it is possible for the peak wind speed at some or all of the

levels about 18 meters to be less than the 18-meter

level peak wind speed resulting in negative values

of h. This is not to imply that the associated mean

wind speeds decrease in the vertical. A statistical analysis of the data revealed that,

for engineering purposes, k is distributed normally

for any particular value of the peak wind speed at the 18-meter level. Thus, for a given percentile

level of occurrence, it was found that, for peak wind

speeds at the 18-meter level less than approximately

2 m sec~', k is equal to a constant, while for peak

wind speeds greater than 2 m sec~^,

k = h Uis~''

3/4 (2)

where 6 is a parameter that is distributed normally

with mean value k and variance a equal to 0.52 and

0.36 and Mis is in meters per second. The distribution

of /c as a function of Uis is shown in Figure 7. To apply Eqs. (1) and (2) to the peak wind statistics valid at 10 meters, Eq. (1) is evaluated at

2 = 10 m, and it is assumed that the resulting rela- tionship can be inverted to yield uis as a function

of the 10-meter level peak wind speed uw for a

k (dimentionlest

)

Figure 7. The mean, zfco-, ±2cr, and ±3<t values of k as functions of the peak wind speed Uis at the

18-meter level.

32
fixed value of b. This function is then combined with

Eq. (2) to yield k as a function of ttio for a given

value of b. The validity of this inversion process is open to question because Eq. (1) is a stochastic

relationship. However, preliminary analyses of

profiles that include peak wind information obtained

at the 10-meter level seem to show that this inversion is valid. The current design practice at MSEC is to use

the k-\-3a value of k to determine operational limits

for space vehicles. Thus, if a space vehicle designed

to withstand a particular value of the peak wind

speed at the 10-meter level is exposed to that peak

wind speed, the vehicle has at least a 99.87 percent

chance of withstanding the associated peak wind

speed profile.

where p(b) is the p.d.f. of b, a known function. Upon

integrating Eq. (7) over the range of h, we obtain

the marginal p.d.f. of u,:

V2{uz)= j Pi(um{u„b)) (^-^^^p(b) db. (8)

At the present time, we are calculating these inte- grals numerically for the annual hourly peak wind

speed data. To calculate the monthly and seasonal

peak wind speed statistics, we require the associated

monthly and seasonal distributions of k. Programs

are now being written to calculate these statistics. Once we have determined the p.d.f. of the peak

wind speed as a function of height, we can then

calculate design peak wind-speed profile envelopes

for various percentile levels of occurrence.

4.2. Alternative Approach

At the present time, we are developing procedures

to extrapolate peak wind speed distributions valid

at the 10-meter level to other levels. Consider a peak wind speed probability density function (p.d.f.)

Pi(mio) valid at the 10-meter level for a given period

of exposure, say, one hour. The probability that Uw

is less than Uwc is given by

/•"lOc P(mio<Wioc)= / pi{uw) duio.

*' n (3)

To obtain the peak wind speed p.d.f., at level z, we express Eq. (1) in the form

W10(W., b) =M,(10/2)^l""(u.,6)l-3M (4)

where we assume that Eqs. (1) and (2) can be in- verted to yield Uw as a function of b and the peak

wind at level z denoted by Uz. Eq. (4) permits us to express Eq. (3) in the form

p{Uz<u^c\b) = f Pi{uwiuz, b)) (^^) duz, (5)

where p{uz<Uzc \ b) is the conditional probability

that Uz is less than Uzc, given b and p{uz<Uzc \ b) =

p{uio<Uioc) Thus, the integrand in Eq. (5) is the

conditional p.d.f. of Uz, given b, and is given by

P2{uz\b) =pi{uw{uz,b)) ^^^^ . (6)

The quantity {duw/duz)b, a function of Uz and b, can be calculated by differentiating Eq. (4). The

joint p.d.f. of Uz and b is given by

P2{uz,b) =pi{uw{uz,b)) (^) pib), (7)

\duz /ft

4.3. Instantaneous Extreme Wind Profiles

Because the probability that the hourly peak

wind speeds at all levels occur simultaneously is small, the practice of using peak wind profiles intro- duces some conservatism into the design criteria. This section estimates the amount of conservatism

involved.

To gain some insight into this question, about 35

hours of digitized magnetic tape data were analyzed.

The data were digitized at 0.1-second intervals in

real time and partitioned into 0.5-, 2-, 5-, and 10- minute samples. The vertical average peak wind

speed ilp and the 18-meter mean wind Uis were

calculated for each sample. In addition, the in- stantaneous vertical average wind speed time history

at 0.1-second intervals was calculated for each

sample, and the peak instantaneous vertical average

wind speed iii was selected from each sample. The

quantity Uj/up was then interpreted to be a measure

of how well the peak wind profile statistics at the

10-meter level approximate the instantaneous ex- treme wind profile statistics. In Figure 8, a plot of ui/up as a function of u\%, the data points tend to scatter about a mean value

10 M 14 16 18 20

u.o (m/sec)

Figure 8. The ratio Ui/up as a function of the mean wind

speed Mi8 at the 18-meter level for an averaging time equal to 10 minutes.

33
1.0'

A

r B

D

SAMPLE PERIOD: A — 0.5 mil) g — 2.0 ijiifi C — 5.0 min D - 10.0 min

0 2 4

1

6

1 1 1

8 10 12 14 16 1

Figure 9 The ratio uj/ilp as a function of the mean wind

speed Mi8 at the 18-meter level for averaging times equal to 0.5 (A), 2 (B), 5 (C), and 10 minutes (D).

of ui/up^O.93. Since drag loads are proportional to the square of the velocity, this mean value implies

that the peak wind profile may be overestimating

the loads by about 14%. However, the fact that some of the data points have values equal to 0.9S

could mean an overestimate of the loads by only

4%. Figure 9 gives the average values of uilup as a

function of mis for different averaging times (0.5, 2,

5, and 10 minutes).

4.4. Gust Factor

The gust factor G is defined as G = ulu, (9)

where u is the peak wind speed within a data record

of length t in time and u is the mean wind speed

associated with the data record. A simple theory can be constructed to aid in understanding the behavior of the gust factor. If cr denotes the variance

of the fluctuations of velocity about the mean wind

speed, then iZ+3cr is an estimate of the peak wind

speed; therefore,

G = l +

3(7 (10)

The variance is related to the friction velocity, rt*, through the relationship

a = A{Ri, <) w*. (11)

where A is a function of the Richardson number,

Ri, and the averaging time, t. The Richardson

number is given by

f\Cj, dz)

Ri = (12)

where f and u denote the mean Kelvin temperature

and wind speed at height z, g is the acceleration of gravity, and Cp is the specific heat of dry air at constant pressure ((7/Cp~9.S°K/km) . In approximately the first 30 meters of the boundary layer,

the wind profile is given by

^= ^(^ln^~^(i20) (13)

where ki is von Karman's constant with numerical

value approximately equal to 0.4, zo is the surface

roughness length and ip{Ri) is a universal function

of Ri.

Combining Eqs. (9), (10), (11) and (13), we

find that

G=l +

3fciA {Ri, t) (14)

In -i^iRi)

For a neutral atmosphere, Ri = 0, and vanishes,

so that

r;=i+ 3M (0, 0

(15)

In

Zo

We may conclude from this relationship that the

gust factor decreases as the height increases. This

result is also qualitatively true for unstable air {Ri<0). As the averaging time decreases, the vari- ance will decrease so that ^ is a decreasing function

of the averaging time and thus, we may conclude

from (14) that G is an increasing function of the

averaging time.

The functions i/' and A are monotonically decreasing functions of the Richardson number; \J/ vanishes in neutral {Ri. = 0) air, while A is positive

definite. Thus, as the Richardson number decreases, or rather, as the air becomes more unstable, the gust

factor increases. Let us now consider a typical daytime situation

at Cape Kennedy. At low wind speeds the air is unstable and G is large. However, as the wind

speed increases, the wind shear (clu/dz) increases,

causing the Richardson number to tend to zero from the unstable side of Ri = 0. Thus, an increase

in the wind speed will tend to lower the gust factor

in view of the dependence of the gust factor upon

stability. In a typical nighttime situation, the

stratification is stable, and the Richardson number

is usually positive. As the wind speed increases, the

34
Richardson number tends to zero from the stable

side of Ri = 0. This means that the gust factor will increase as the wind speed increases. In both cases the limiting value of the gust factor will be that of a

neutral atmosphere {Ri = 0) as given by Eq. (15). In view of these considerations, a gust factor model

for the Kennedy Space Center was developed with

181 hours of afternoon turbulence data encompassing a broad range of wind speed conditions.

Gust factors were calculated for averaging times

(<) equal to 0.5, 1, 2, 5, 10 and 60 minutes. It was

assumed that the gust factor is a function of the

averaging time t, and the peak wind speed Uis at the 18-meter level. The peak wind speed at the 18- meter level plays the role of a stability parameter.

It was found that the expected value of the gust

factor at any level between 18 and 150 meters can

be represented as

G

t ( m i n )

Figure 10. The gust factor G at the 18-meter level as a

function of the averaging time for various peak

wind speeds at the 18-meter level.

G=l+- (lS/z)r, (16)

On where z is the height in meters. In this equation the

parameters p and go are given by

p = 0.283 -0.435e-''-2"" (17)

and

i/o = 1.98+0.085 (in —j -0.329 In — - 1.8876-" •2"",

(18)

where t and Uu have the units of minutes and meters

per second. The dependence of the 18-meter level gust factor on the averaging time and the peak wind

speed is shown in Figure 10, and the dependence

of the 10-minute gust factor on the peak wind speed

and height is given in Figure 11. Within the range of variation of the data, the 1- hour gust factor and the 10-minute gust factor were

approximately equal, because the spectrum of the

horizontal wind speed near the ground is characterized by a broad energy gap centered at a frequency

approximately equal to 1 cycle hr"^ and typically

extends over the frequency domain 0.5 cycles

G

2.0-

150

12-'—r 1 1 1 1 1 •

4 8 12 16 20 24 28 CD u^g (m/sec)

Figure 11. The gust factor G as a function of the peak wind

Mis at the 18-meter level for various heights above

natural grade associated with a 10-minutc grand

average.

35
1.0-

0.01

III) 1 r

T

1 1—I—I I I 1

1

_

nSJn)

-V- 0.1-tr 18 m

P 30m 60m

90m

120m 150m

-I I I I 1 1 1 1

1

0.01 0.1 1.0 10.0

Figure 12. Dimensionless logarithmic longitudinal spectra

for neutral wind conditions plotted in Monin

coordinates.

10

0.01

I I r I ri

I r

-J I III''' '

I

' ' ' ' "

0.01 0.1 1.0 10.0

Figure 13. Dimensionless logarithmic lateral spectra for neutral wind conditions plotted in Monin

coordinates.

the longitudinal and lateral components of turbulence are decreasing functions of z, so that by scaling

the spectra with the surface value of the friction velocity, the scaled spectra at the upper levels fall below the 18-meter spectra.

By scaling the wave number with z, we have as- sumed that the integral scales of the longitudinal

and lateral components of turbulence are proportional to z. This might be true in the Monin layer;

however, in the Ekman layer one might suspect

from the behavior of eddy coefficients [14] that, if the local integral scales have a vertical variation,

then they should increase at a rate slower than z. In

addition, we have no knowledge that the integral

scales of the longitudinal and lateral spectra should

have the same vertical variation. However, the data

appear to show that Monin coordinates will collapse

spectra with various turbulence intensities at any

particular level in the vertical. To produce a vertical collapse of the data, it was

assumed, for engineering purposes, that the spectra

in Monin coordinates are shape-invariant in the

vertical. This hypothesis appears to be reasonable

and permits a practical approach to developing an

engineering spectral model of turbulence.

5.1. The Longitudinal Spectrum

The vertical variation of the dimensionless wave number associated with the peak of the logarithmic spectrum &u scaled in Monin coordinates is given in Figure 14. A least-squares analysis of the

data in this figure yields the result = 0.03(0/18), (30)

where z is in meters. A plot of nSu{n) /u^c''- versus

f/fmu will shift the spectra at the various levels, so that all the peaks of the logarithmic longitudinal

spectra are located at f/fmu = l- Values of from

other tower sites are indicated in Figure 14. The average ratio of the shifted spectrum at

level z and the 18-meter spectrum,

(S„( z)/Su{f/Uu, IS)),

is shown in Figure 15. A least-squares analysis of these data yielded the result

^„=(2/18)-''-' (31)

where z is in meters. A plot of n*S„(n)/^„M*2 versus

f/fmic will collapse the longitudinal spectra. The col- lapsed longitudinal data are plotted as a function

1.0

0.1

0.01 --

0.001

Figure 14.

10 100

z (meters)

1,000

Vertical distributions of the dimensionless fre- quencies /,„u and/,„i. associated with the peak of the logarithmic longitudinal and lateral spectra

for neutral stabihty conditions.

38
0.1

0 NEUTRAL LONGITUDINAL

o NEUTRAL LATERAL

100

z (meters)

1,000

Figure 15. The vertical distribution of the collapsing factors

i3u and ;8„ for neutral stability conditions.

of O.OSf/Uu in Figure 16. The function

nSuin) ^u f/fmu

(32)

was selected to represent the longitudinal spectrum,

where Cu and r„ are positive constants, determined

by a least-squares analysis. For sufficiently small

values of /, nS„(n)/i8„M*^ asymptotically behaves

like f/fmu which is the correct behavior for a one- dimensional spectrum. At large values of /, nSu{n) /^uUiiP' asymptotically behaves hke

{ f/fmu)

consistent with the concept of the inertial subrange.

The maximum value of (32) occurs at f=fmu.

Various authors have suggested formulae like (32)

to represent the longitudinal spectrum. However,

most of the representations have only one adjustable

parameter available, while Eq. (32) has two: C„

and Tu. In this light (32) appears to be superior.

Upon setting ru = 5/3, we obtain the form of the

longitudinal spectrum suggested by Panofsky [7]

to represent the strong wind spectra of Davenport

[153- Von Karman's longitudinal spectrum [16]

can be obtained by setting ru = 2. A least squares

analysis of the longitudinal data in Figure 16 revealed

that C„ = 8.641 and r„ = 0.845.

5.2. The Lateral Spectrum

The lateral spectra (S„ can be collapsed with a procedure like the one used for the longitudinal

spectra. However, to determine an analj'^tical ex- pression for the lateral spectrum, special attention

must be paid to the inertial subrange to guarantee

that *Su/»S„ = 3/4 [17]. This requirement can be

derived from the mass continuity equation for incompressible flow subject to the condition that the

eddies are isotropic in the inertial subrange. The

experimental values of and /3„ are given in Figures 14 and 15. These data show that /„„ and /3„ can

be represented as power laws as for the longitudinal

spectra. The function

nS,{n) ^

(1 + 1.5 (///„„) ^O''''" (33)

was used to represent the scaled spectra, where

and r„ are positive constants. This function behaves

like the one chosen for the longitudinal spectrum.

For sufficiently large values of /, the asymptotic

behavior of the ratio between Eqs. (32) and (33)

is given by

u yu3 / i

I Jmu

\

V \ fmv/ (3/2) 5/3(l/r„-l/r„) (34)

In the inertial subrange we must have *Su/<S„ = 3/4, so that upon substituting this ratio into (34) we obtain a relationship that can be used as a constraint in the determination of values of C„ and r„ and functions to represent /3„ and fmv The values C„ = 8.686

and n = 0.512, and the functions

and

f„,=o.i{z/i8r-''

I3.= {z/ 18)-°-''

(35)

(36)

along with the longitudinal parameters will satisfy

condition (34) and simultaneously give a good fit to the data {z is in meters). The collapsed lateral spectra and the functions given by (32) and (33) are shown in Figure 16.

SYMBOL C

Figure 16. Dimensionless logarithmic longitudinal and

lateral spectra as functions of 0.03 f/fmu and

0.1 ///mil for neutral stability conditions.

39
5.3. Engineering Application

To apply the spectrum of turbulence to engineering problems, we first select the design peak wind

speed for a prescribed level of risk. The peak wind

speed profile is established by selecting the 99.87

percentile (mean +30-) value of k, and the mean

wind profile is obtained by "backing off" from the

peak wind profile with the appropriate gust factor

profile. The friction velocity tt* is calculated with

Eq. (21) for neutral wind conditions (Ri = 0, 1^(0) =0). Once the mean wind speed profile and the

friction velocity are known, the longitudinal and

lateral spectra are completely specified. This is the

procedure presently used at MSFC.

Thus far, we have been talking about the spectra

of the longitudinal and lateral components of turbulence. Actually, it is the spectra of the square of these components that are important from a loads

viewpoint. If we assume that these components in- dividually constitute Gaussian processes, then it is possible to express the power spectra of {u-\-u')'^ or

v'^ with the Wiener-Khintchine theorem in the form

82(71) = l{u'+2uV)e +a'']8{n) -\-4:€U^Si{n)

+2 f Si{n-^)Sia) d^, (37)

•'-00

where S^in) is defined in the interval — 00 <n< <»

,

6 = 1 (longitudinal loads) or 0 (lateral loads) and

5(n) is the Dirac delta function. In this equation,

the variance of the turbulence is given by

a'= j

S{n) dn, (38)

where S{n) is the longitudinal or lateral spectrum

as define'd by Eqs. (32) and (33) and

Si\n\)

(39)

The details of the derivation of Eq. (37) can be

found in a paper by Wood and Berry [18].

To produce the convolution integral in Eq. (37)

by numerical procedures is straightforward. The

right-hand side of Eq. (37) is directly proportional

to the spectrum of the longitudinal or lateral drag

forces, which are the required inputs for vehicle response studies.

6. Conclusions

Development of space vehicle wind loads design

criteria is not simple, but is a rather complicated

procedure requiring the designer and the atmospheric

scientist to work as a team. The engineer must

specify the risks he is willing to accept, while the

atmospheric scientist must produce a wind model

from which it is possible to determine the appropriate

forcing functions for that accepted risk. The model

presented here for Cape Kennedy, Florida, serves

this purpose in that risk values can be applied to the occurrence of peak wind speeds at a reference level for a given period of exposure; and if these design

peak wind speeds occur, an upper bound risk value

of structural failure can be estimated from statistical information about the wind profile shape (k). By

applying gust factors for an appropriate averaging

period, a peak wind speed environment can be

partitioned into mean wind and turbulence

environments.

7. References

[1] Smith, 0. E., L. W. Falls, and S. C. Brown, "A Statistical Analysis of Winds for Aerospace Vehicle Design, Mission

Planning, and Operations," Research Achievements

Review, Vol. II, Report No. 10, Terrestrial and Space

Environment at MSFC, NASA TM X-53706, George C. Marshall Space Flight Center, Huntsville, Alabama,

1967.

[2] Fisher, R. A., Contributions to Mathematical Statistics, John Wiley and Sons, Inc., New York, 1950.

[3] Gumbel, E. J., Statistics of Extremes, Columbia University

Press, New York, 1958,

[4] Thom, H. C. S., "Distribution of E.xtreme Winds in the United States," Journal of the Structural Division, Proceedings of the American Society of Civil Engineers,

April 1960.

[5] Kaufman, J. W. and L. F. Keene, "NASA's 150-Meter

Meteorological Tower Located at Cape Kennedy

Florida " NASA TM X-53259, George C. Marshall Space

Flight Center, Huntsville, Alabama, May 12, 1965.

[6] Fichtl, G. H., "An Analysis of the Roughness Length

Associated with the NASA 150-Meter Meteorological

Tower," NASA TM X-53690, George C. Marshall Space

Flight Center, Huntsville, Alabama, January 3, 1968.

[7] Lumley, J. L. and H. A. Panofsky, The Structure of Atmospheric Turbulence, John Wiley and Sons, 1964.

[8] Davenport, A. G., "The Relationship of Wind Structure

to Wind Loading," presented at the Meeting on Ground

Wind Load Problems in Relation to Launch Vehicles, NASA Langley Research Center, June 7-8, 1966.

[9] Blackman, R. B. and J. W. Tukey, The Measureynent of Power Spectra, Dover, New York, 1958.

[10] Pasquill, F., Atmospheric Diffusion, D. van Nostrand

Company, Ltd., New York, 1962.

[11] Monin, A. S., "On the Similarity of Turbulence in the Presence of a Mean Vertical Temperature Gradient," J. Geophys. Res., Vol. 64, 1959, pp. 2196-2197.

[12] Berman, S., "Estimating the Longitudinal Wind Spec- trum Near the Ground," Quart. J. Roy. Meteor. Soc, 91, 1965, pp. 302-317.

[13] Busch, N. E. and H. A. Panofsky, "Recent Spectra of Atmospheric Turbulence," Quart. J. Roy. Meteor. Soc,

94, 1968, pp. 132-148.

40
[14] Blackadar, A. K. et al., "Flux of Heat and Momentum

in the Planetary Boundary Layer of the Atmosphere,"

The Pennsylvania State University Mineral Industries Experiment Station, Dept. of Meteorology, Rept. under AFCRL Contract No. AF9604-6641, 1965.

[15] Davenport, A. G., "The Spectrum of Horizontal Gustiness Near the Ground in High Winds," Quart. J. Roy.

Meteor. Soc, Vol. 87, 1961, pp. 194-211.

[16] Pritchard, F. E., C. G. Casterbrook, and G. E. McVehil,

"Spectral and Exceedance Probability Models of Atmospheric Turbulence for Use in Aircraft Design," TR

AFFDL-TR-65-122, Air Force Flight Dynamics Laboratory, Research and Technology Division, Air Force Systems Command, Wright- Patterson AFB, Ohio, 1905.

[17] Batchclor, G. K., The Theory of Ilomogencom Turbulence, Cambridge University Press, New York, 1953.

[18] Wood, J. D. and J. G. Berry, "Random Excitation of Missiles Due to Winds," Proc. of National Symposium on Winds for Aerospace Vehicle Design, Vol. 1, USAF

Geophysics Res. Dir. A.F. Surveys in Geophysics, No.

140, Vol. 1, AFCRL-62-273(I), March 1962, pp. 125-138.

41

SESSION 3.

EXPERIMENTAL AND THEORETICAL DETERMINATION OF

AERODYNAMIC FORCES

Chairman: Professor A. G. Davenport

Faculty of Engineering Science

University of Western Ontario

London, Ontario, Canada

FLUCTUATING MOMENTS ON TALL BUILDINGS PRODUCED BY

WIND LOADING

J. E. Cermak,* W. Z. Sadeh,** and G. Hsi***

Fluid Dynamics and Diffusion Laboratory

College of Engineering

Colorado State University Fort Collins, Colorado 80521

Wind loading on a 1:384 scale model of a building 666 ft high was studied experimentally in a

thick-boundary-layer wind tunnel. Measurements of mean velocity and turbulence intensity

upstream of the model building verified that the wind tunnel flow was an adequate simulation of atmospheric-surface-layer flow over an urban area. Mean pressure distributions and local pressure fluctuations were measured for a variety of upstream roughness conditions and wind directions. Use of a high frequency response pressure- measuring system permitted rms and peak values of the local pressure fluctuations to be de- termined at numerous points on the building surface. Emphasis was placed on direct measurement of mean and fluctuating overturning moments

by means of a strain-gage dynamometer. A stiff model, U/Dn < 1, was used to obtain moments

due to wind action alone. Peak values of the moment fluctuations were found to have a magnitude

of ±34% of the mean moment. Root-mean-square values of the moment fluctuations were also determined in an effort to relate the moment fluctuations to the measured pressure fluctuations.

Key words: Boundary layer; buildings; pressure fluctuations; instrumentation; overturning moments; wind loads; wind tunnel modeling.

1. Introduction

The study of aerodynamic forces on tall buildings

produced by strong turbulent winds can now be ac- complished through the use of scale models placed

in a wind tunnel capable of simulating the atmospheric surface layer. Existing wind tunnels capable

of simulating the mean velocity variation and turbulence structures with height up to about 1,600 ft because of their special long test sections are located

at Colorado State University [1]^ and the University of Western Ontario [2]. Past studies have been

devoted primarily to determination of pressure coefficients for the mean wind, local pressure fluctuations, and in the case of an aeroelastic model, deflections of the buildings, e.g., Marshall and Cermak

[33, Davenport and Isyumov [2] and Ostrowski,

Marshall and Cermak [4].

Knowledge of the distribution of mean pressure

coefficients permits calculation of mean overturning

moments and mean shear while rms and peak values

* Professor-in-Charge, Fluid Mechanics Program.

** Assistant Professor of Engineering.

*** Research Associate.

1 Figures in brackets indicate literature references at end of

this paper.

of local pressure fluctuations enable a proper choice

of window glass and outer skin panelling to be

made. However, these data do not give adequate

information on a quantity of prime importance to the structural engineer, the fluctuating overturning

moment. Mean pressure coefficients yield the mean

overturning moment but the local pressure fluctua- tion data do not yield the fluctuations in overturning

moment because the space correlation of pressure

fluctuations on the building surface is not known.

The research reported in this paper emphasizes an exploratory effort to measure directly the fluc- tuating overturning moment produced by a turbulent wind. By using a high-frequency-response sys- tem the total moment, i.e., mean and fluctuating

moment, was measured. The natural frequency of the strain-gage dynamometer-building shell system was about 200 Hz. Furthermore, the structure was

stiff enough, i.e., the reduced velocity U/Dn<l,

such that the measured moments are determined

completely by the wind characteristics and not by

structural dynamic action.

2. Experimental Apparatus

The main objective of this study was the direct

measurement of the total overturning moment, i.e..

45
mean and fluctuating moment. This was accomplished by using a suitable dynamic balance. The

latter was designed to respond only to this moment.

Prior to moment measurement an investigation to obtain the local and overall wind loading on a rigid

tall rectangular building was conducted. The latter

is defined by both the mean and fluctuating values

of pressure acting on the structure. Furthermore,

for certain structural considerations the instantane- ous peak value of pressure is also of interest. Therefore, an exploration of pressure distribution, i.e., mean, fluctuating (rms) and peak pressure, over a

scaled building model was carried out in a wind

tunnel. The experimental objective could not be attained

by simply placing an appropriate model in a regular

aerodynamic wind tunnel [5, 6]. A rather detailed

discussion of this problem is reported in References

1, 2 and 7. It was desired to obtain a mean velocity

profile similar to the natural wind. Moreover, a

suitable thick turbulent boundarj'^ layer was neces- sary for simulating the real flow conditions. Consequently, the experiments were performed in an appropriate wind tunnel which is described later. The flow around structures can be considered

similar to flow around bluff bodies at relatively large

Reynolds numbers. When the flow is simulated in a wind tunnel, dynamic similarity needs to be satisfied. For relatively large Reynolds numbers and sharp

edged structures, i.e., Reynolds number on the

order of 10'', the drag coefficient and, thus, the pres- sure distribution and the resulting forces are independent of the Reynolds number [1, 8]. Since the

Reynolds number of the experimental flow was of

this order it follows that the flow pattern and, hence,

the pressure distribution and the overturning moment are Reynolds-number independent. The former was based on the largest dimension of the building

model cross section and/or on the equivalent (hydraulic) diameter of the model.

For these reasons, it was decided to use a simple

model placed in a relatively thick turbulent boundary

layer formed over a surface with roughness (upstream of buildings) scaled to the same scale as the

structure of interest. A schematic diagram of the

experimental arrangement and of the low-speed

wind tunnel used is displayed in Figure 1 which also shows all important dimensions.

2.1. The Model Building

A scaled model of the two towers planned for the

Atlantic-Richfield Plaza in Los Angeles was made

of "Lucite" 0.375 in thick. The buildings are of

1 [>H<-

- Workinq Seclion — 1

ij In 36 5

Top View of ihe Low Speed Wind Tunnil

Vortei Generolor

I Smooth H 13 , Surfoce ki—

. Upsiream Roughness

Pilot- Stoti "Tube

2-43 Buildin Surrounding Model

Bwldrngs

Smooth

0.55 Suftoce 1^

Side View of Working Section

All Dimensions in Feet

Figure 1. Sketch of the experimental arrangement and the low-speed wind tunnel.

rectangular shape and 666 ft high. A geometrical

scale of 1:384 was employed. This scale was chosen

for obtaining a meaningful simulation of the natural

wind over a built-up urban area. The atmospheric

boundary layer is about 1600 ft thick, thus, about

2.4 times the building height. Therefore, a boundary

layer about 50 in. in thickness was desired.

1

Pressure Tap Levels (I- 10)

^Building Wall

3/8" Lucife

Stiffening Aluminum Rib

1/4" Thick

Adjustable Transmitting Pins

Attactiment Rods

Base / //

All Dimensions in Inches Figure 2. Sketch of the building model.

46
Figure 3. Overall view of the building model. A sketch of the model is portrayed in Figure 2 which also shows the system of coordinates used

and all important dimensions. On its faces 54 static pressure taps of 1/16-in. diameter were drilled. The

taps were located as follows: 32 pressure taps on its wide face and 22 on its narrow- face. The taps were

bored only on two faces of the model. For measuring

the pressure over the other two faces it was neces- sary to rotate the model by 180°. Furthermore, 13 pressure taps were also drilled on the building roof. Hence, it was possible to monitor the pressure at

121 locations for each building. The static pressure tap stations are also shown in Figure 2. The surrounding buildings in the immediate

vicinity were also simulated using a scale of 1:384.

The former were constructed of styrafoam. Both the towers and these buildings were mounted on a ro- tatable plywood sheet base. For investigating the

pressure-distribution dependence on the wind direction it was possible to rotate the table 360°. The

rotating table permitted visualization studies of the

flow pattern for various wind directions. A photograph of this arrangement is provided by Figure 3.

2.2. Wind Tunnel

The experimental investigation reported herein was conducted in the Colorado State University,

Fluid Dynamics and Diffusion Laboratory, lowspeed wind tunnel. This tunnel is of closed circuit type and has a working section about 36.5 ft long.

Its axial-flow blower is driven by a 75 hp constant speed motor. The fan is capable of generating air speeds up to 65 ft/sec in a 6X6 ft test section. The

air speed can be changed continuously by varying

the fan pitch. The model was placed at about 29 ft downstream of the entrance section. Therefore, it was located in the thick boundary-layer region.

The removable side panels of the working section are made of glass in order to allow visualization

47
Figure 4. Overall view of the test section.

studies of the flow. Along the center line of the top

panel a Pitot-static tube was inserted above the upstream building for continuous monitoring of the

free-stream velocity, i.e., outside the boundary layer.

Its location is shown in Figure 1. An electrically operated traversing and positioning

mechanism was used for continuous movement of the Pitot-static tube and/or hot-wire probe. This

mechanism permitted fine control of position within

0.005 in. along lines parallel to the r, y and 2-axes.

2.3. Upstream Conditions

A complete simulation of the natural wind characteristics includes the generation of a suitably thick

and turbulent boundary layer [1, 2]. Furthermore,

the modeling of the upstream urban configuration

is necessary for simulating the real flow conditions.

As a result, the upstream urban topography was appropriately modeled using the same scale as for the

building. This model extended over a distance of more than 1 mile (see Fig. 1) upstream of the

studied buildings. It was simulated by covering the

tunnel floor with an adequate configuration of modular bricks (2jX3fX7| in.). A photograph of the latter for the NE wind direction is shown in Figure 4. For every particular wind azimuth, i.e., free-stream velocity direction, an appropriate upstream roughness was employed.

Next, for generating a higher turbulence level, a

vortex generator [9] was installed at the entrance

of the working section (see Fig. 1). This generator

also caused an initial thickening of the boundary

layer. For this purpose an asymmetric arrangement

of two rows of modular bricks 1.3 ft total height was

used. Both the upstream roughness, i.e., the upstream modeled city, and the vortex generator

caused the necessary thickening of the boundary

layer and the desired turbulence intensity level.

48
3. Experimental Technique and

and Instrumentation

3.1. Flow Visualization

Two visualization methods were employed, paper

tufts and thread tufts. The former, attached to wire grids and placed upstream and/or downstream

of the buildings, were used to obtain a qualitative

picture of the flow pattern for various wind

directions. The thread tufts were glued directly on the model

faces. They permitted an acceptable qualitative in- dication of the flow pattern along the building faces to be obtained. As will be seen later both visualization methods established clearly the overall flow

pattern and the existence of vortices downstream

of the buildings. Moreover, the influence of the

surrounding buildings on the flow was also visualized.

3.2. Pressure and Velocity Measurement

Average static pressures on the model faces were measured by means of an electronic pressure meter

(Trans-Sonic, Type 120) with a resolution of 0.0001 mm Hg. The overall range of this manometer

is 30 mm Hg.

A Pitot-static tube located 2.43 ft above the model

as shown in Figure 1 was employed to measure the

static pressure and the mean velocity in the uniform

flow. A Prandtl standard Pitot-static tube with a

hemispherical impact head was utilized [10]. Its impact orifice is 1/32-in. in diameter. This probe was also used to measure the velocity profile upstream of the building. The velocity change along

the 2-axis was measured at 1 ft upstream of the

model. In performing these measurements the

Trans-Sonic pressure meter was utilized. Furthermore, the velocity change along the vertical direc- tion was also recorded on an x-y plotter (F. L. Moseley Co., Model 135). When the latter was

carried out, the Pitot-static probe was moved continuously by means of the traversing mechanism.

The fluctuating pressm-es, rms and instantaneous

peak pressure, on the model faces were measured at

all the pressure taps by means of low-pressure differ- ential pressure transducers (Statham, Model PM

283). Six similar transducers were utilized. These

transducers were installed inside the model and were

connected closely to the pressure taps. The trans- ducers with the associated tubing (|-in. I.D. vinyl

tubing) had a frequency response larger than about

200 Hz. The transducers exhibited a reasonable linear

calibration curve. The latter was carried out utilizing a precise micromanometer (The Meriam Instru- mentation Co., Model 34FB2). The pressure difference was measured with respect to the static pres- sure of the uniform free-stream. The latter was

obtained from the Pitot-static tube located above the

model (see Fig. 1 ) . The reproducibility of the calibration curves was within 1% to 3%. In connection

with these measurements the following auxiliary

equipment was used

(1) A variable range amplifier (Dana, Model

3500) . Usually, an amplification of 200 was

utilized;

(2) A seven channel tape-recorded (Mincom,

Type 100) for recording and storing the

amplified signal for further analysis;

(3) An electronic voltmeter (Bruel & Kjaer,

Type 2416) for measurement of rms and

peak values;

(4) A recording wave analyzer (General Radio,

Recording Sound and Vibration Analyzer,

Type 191 1-A) for frequency spectra meas- urement ; (5) A dual-beam oscilloscope (Tektronix Storage

Oscilloscope, Type 564) for quick assessment

of the output signal pattern;

(6) A Polaroid camera (Type C-12) for taking

oscillograms of the output signal;

(7) A digital DC voltmeter (Hewlett-Packard,

Model 3440A) for monitoring various output

signals.

A simplified block diagram of this system is shown

in Figure 5 and, a general view of the auxiliary equipment is provided by Figure 6.

Oscilloscope

Digital

Voltmeter

r Pressure

Amplifier[-

1 Transducer

Bridge

TRMS

Meter

Wave

Analyzer

X - y Plotter

Tape

Recorder

Figure 5. Simplified block diagram of the pressure-trans- ducer system.

49
Figure 6. General view of the equipment.

3.3. Turbulence Intensity Measurement

The longitudinal turbulence intensity was measured upstream of the model by means of a hot-wire

anemometer. The measurements were carried out

at the same distance from the model as for the mean

velocity, i.e., at 1 ft upstream of the model, along

the 0-axis. When performing these measurements

the hot-wire probe was positioned by means of the

traversing mechanism. The hot-wire anemometer

unit used in the present experiment is a constant- temperature fully transistorized system conceived,

designed and built at the Fluid Dynamics and

Diffusion Laboratory. Its output noise level is less than about 200 /xF and its frequency response is beyond 100 KHz. A detailed report about this unit,

its characteristics and performances, is under preparation. A copper-plated tungsten wire of 0.00025- in nominal diameter and 0.06-in effective length

(l/(i = 240) was employed.

The hot-wire calibration was effected by locating

it in the free-stream above the model. It was carried out employing a Pitot-static tube. The calibration curves obtained revealed that the so-called King's

law [11], i.e., the § power linear relation (E- \/ U) was satisfied reasonably well for the velocity range

of interest. The latter ranged from about 10 to 60

ft/sec. It was reproducible within about 3%. The

turbulence intensity, which is commonly defined as Urms/U, is given by [12]

where the subscript rms denotes square-root of mean (time-averaged) square values, i.e., -s/ and

-y/g^, and, the over bar denotes time-averaged (or

mean values). In the above relationship the mean

velocity is designated by U and E stands for the

time-averaged voltage drop across the wire, i.e., the DC voltage necessary to balance the bridge

under steady conditions. The fluctuating velocity is denoted by u and the corresponding instantaneous

voltage drop by e, i.e., the instantaneous AC voltage.

The voltage drop across the wire in still air (zero

velocity or shielded hot-wire) is denoted by Eq. It is constant for a chosen resistance ratio (overheating

ratio). In connection with the hot-wire unit, a true RMS meter, a digital DC voltmeter and a dual-beam

oscilloscope were used. This equipment is described

in Section 3.2.

3.4. Moment Measurements

As mentioned earlier, the direct measurement of the total overtui'ning moment, i.e., mean and

fluctuating, was particularly stressed. In order to eliminate all the other force components a suitable

strain-gage dynamometer system was conceived

and built. Hence, the model was mounted in the

wind tunnel by attaching it rigidly to an aluminum

beam (2X1X5 in.) by means of four rods 90°

apart. In turn, the beam was rigidly anchored to a massive base located underneath the wind tunnel

floor. Thus, the dynamometer-building model system

constituted a cantelever beam with end-load. The

aerodynamic force acting on the model building was

transmitted to the beam by two adjustable pins

180° apart. The pins were positioned close to the

beam's free-end and they were tightened manually

to the former. At the lower end of the beam four

foil strain gages (Micro-Measurement, Type EDDY-250B6-350) were cemented. They constituted

the four arms of a Wheatstone bridge. Thus, the

overall sensitivity of the straift-gage system was in- creased four times. This balance was sensitive only

to the overturning moment about the weak axis of the building. The response of the strain-gage for any

lateral load was about 20 times smaller than for the

frontal force producing the overturning moment.

In order to stiffen the model and to increase its natural frequency an aluminum rib and stiffening

rods were mounted rigidly between its two wider

faces. The balance system is portrayed in Figure 2. For obtaining reliable and dependable measure- ments of the moment due only to aerodynamic

forces in a stationary structure the natural frequency

of the entire aeroelastic system, i.e., the beam and

the building model, should be larger than any forcing

frequency expected. The pressure survey revealed

that the maximum frequency of interest was smaller

50
than about 200 Hz. Consequently, the balance

system was conceived such that its natural frequency was 200 Hz. The strain for a moment of about 25

Ib-in. was of the order of 6 juin/in.

As a result, a relatively stiff model was obtained.

For a free-stream velocity of 50 fps the reduced

velocity [2] I]JDn was about 0.43. In the latter, d is the largest dimension of the model cross-section

and n is the natural frequency of the dynamometer

system. Thus, the tip deflections of the model were

negligible.

Building Model

Strain-gage

Fficlionless Pulley

A simplified block diagram of the moment measuring system is provided by Figure 7. Essentially

the same auxiliary equipment as employed for the

pressure measuring system was utilized. The excitation and balance network of the strain-gage is also shown in Figure 7.

The balance was calibrated by applying various

forces at different heights along the building. A

sample of the kind of calibration curves obtained is shown in Figure 8. A satisfactory linear change was

obtained. The reproducibility of the calibration curves was within 2% to 5%.

Strain Gage

Signal

Excitation

Circuit Bolance Amplifier — x-y Plotter

Tape Recorder

Oscilloscope

TRMS

IVleter

Wove

Analyzer

= 12V I* . 100 K

i

out

-Strain Gages 350X2 ±03%

Figure 7. Simplified block diagram of the moment measuring system.

Figure 8. Typical calibration curve of the balance.

4. Results

The measurements were carried out for three

different wind directions (free-stream velocity direc- tions) —NE, N and NW. This was achieved by

suitable rotation of the turnable base. However,

only the results for the NE direction are presented

with emphasis on overturning moment of the upwind building. No significant basic changes, except

for the absolute value of the pressure distribution, were obtained for the other two directions. Moreover, it was found that this particular direction was

the most suited for performing the direct measure- ment of the overturning moment. This choice was

determined by structural consideration of the aero- dynamic balance design.

The system of coordinates used in the presentation

of the results is portrayed in Figures 1 and 2. For

generality, the results are presented in dimensionless

form. Dimensional variables, wherever employed,

are denoted bj^ an asterisk. As the experimental

results are presented below, some pertinent discussions are interspersed wherever it is deemed helpful

for the proper interpretation of the results.

4.1. Establishment of the Flow

An extensive •series of flow visualization trials were carried out for the purpose of studying the

overall flow pattern upstream and, principally,

downstream of the building. Visualization of the

flow by means of paper tufts gave a clear picture of the flow pattern. Particularly, the tufts indicated

the flow within the wake. Its strongly turbulent

character and its vortex structure were clearly observed. The wake extended vertically above the

model up to about 10% of its height. The longitudinal extent of the wake was not evaluated due

to the interference of the two model buildings. The

51
Figure 9. Visualization of the flow by means of paper tufts.

second tower was situated in the wake of the front

building. The vertical extent was similar for both

buildings. Figure 9 is a photograph of paper tufts showing the wake.

The thread tufts glued to the model walls showed

distinctly the flow pattern along them. Generally, a down draft was discerned along the front wall. Near

its bottom a clear rotational trend was observed.

On the other hand, along the leewind wall an updraft and a rather turbulent rotational pattern were indicated by the tufts. Photographs of these

patterns are shown in Figure 10. A similar flow

pattern is reported in Reference 8.

4.2. Mean Velocity Survey

The wind velocity gradient upstream of the building is of utmost importance in determining the flow

characteristics. Its variation with height depends on

the particular configuration of the roughness struc- ture [13]. Furthermore, for finding the Reynoldsnumber dependence, the velocity gradient and the

resulting average pressure distribution should be

practically independent of the upstream velocity

variation.

Figure 10. Visualization of the flow pattern along the model

walls by means of thread tufts.

Generally, the mean velocity profile over terrains

of differing roughness configuration is given either

by a logarithmic law or a power law [13]. The lat- ter may be described by

C7*oc2*«' (2)

where z* denotes the height and the value of the

exponent a depends on the particular roughness

structure. This representation was employed in the

present work.

The mean velocity variation along the z direction was measured upstream of the model, i.e., at 1 ft upstream of the building model, at more than

15 stations over a distance of about 55 in. Concurrently, it was also recorded for continuous traverses along the z axis. All the measurements were per- formed at a uniform free-stream velocity of 50 ft/sec. At this velocity, denoted by UJ", a sufficiently thick

boundary layer at the building model location could

be obtained. The Reynolds number based on the

52
largest dimension of the cross-section was about

182,000.

Next, the mean velocity was measured for various

upstream conditions. This investigation was per- formed for verifying the adequacy of the atmospheric surface-layer flow simulation in the wind

tunnel. The measurements were carried out for the

following cases: (1) clear wind tunnel; (2) vortex

generator installed; (3) vortex generator and upstream roughness, i.e., the scaled model of the upstream urban configuration, installed (real flow

conditions) . In all these three cases the scaled model

of the building and of the adjacent buildings were

located in the wind tunnel (see Fig. 1). It was found

that the velocity change is strongly affected by the

upstream conditions. The power-law variation was

satisfied for all the cases, but the value of the expo- nent differed for each case. Hereafter, all the results are presented in dimensionless form. The dimensionless coordinates are defined by

x,y,z = x*/h, y*/h, z*/h, (3)

where h is the building height, and the dimensionless

velocity by

H = H/C7i*, (4)

where U* is the mean velocity at z* = h. Hence, the

dimensionless mean velocity is given by

U = z<^. (5)

The measured mean velocity distributions along

the z direction for the above three cases are displayed

in Figure 11. The results were reproducible within

3% to 5%. The field wind profile is also shown in Figure 11 (case 4). The latter is based on 100-year

wind data at 250 ft height above the surface. For

obtaining the wind variation a y-power law was

utilized for selected heights between 250 and 1,000

ft. On the other hand, a ^-power law was employed

for heights below 250 ft [14].

For the sake of comparison the res\ilts for all the

three cases and the field wind (case 4) are summarized below:

Case Ui* {feet /sec) (X

1 47 0.107

2 45 0.206

3 45 0.446

4 96.8 0.157

Note that /i = 20.75 in. for cases (1), (2) and (3)

whereas /i = 666 feet for case (4). The values of the exponent are in general agreement with repreU = 2° a o ( 1 ) Clear Wind Tunnel 0,107 • (2) Vortex Generator 0206

D (3) Vortex Generator and r\/\/ic: Upstreann Roughness A (4) Field Wind [|4] 0157

——fr

1

1

rf

-if 4)-/ /-

J-

(3)

2) /

{ 1 )

0 0.2 0.4 06 08 1,0 U

Figure 11. Mean velocity profile upstream of the model.

sentative values reported by Davenport [13]. The

influence of the upstream conditions, i.e., vortex

generator and/or upstream roughness is easily observed. Thus, the atmospheric surface-layer flow

simulation was acceptable. In the following, the results for case (3) are pre- sented. This is the case of interest since the upstream

urban configuration was appropriately modeled, i.e., the case of the real flow conditions.

As mentioned earlier, a suitably thick boundary

layer is desired for a meaningful simulation of atmospheric-surface-layer conditions. Consequently, it was important to find out the vertical extent of the

boundary layer immediately upstream of the model.

The boundary-layer thickness was defined, as is commonly done, as the distance from the wind

tunnel floor where U*/U„* = 0.99. The recorded

velocity profile, i.e., dynamic head, at 1 ft upstream

of the model is displayed in Figure 12. This record was obtained by continuously moving the Pitotstatic tube using the traversing mechanism. The

probe was moved at a suflficiently small speed to allow a suitable response. A boundary-layer thickness

of about 49.7 in. was measured. Thus, the dimensionless boundary-layer thickness 5*//i = 2.4. This corre- sponds to a real boundary layer about 1,600 ft thick.

53
10

0.8

0-6 Ap

(mmHg) 0.4 02

0

- 4- H - -

1 —i

— - — fIT t- -r

ilJ.,i!ilLi 4- 1=

,

- - —

-J -!- 1.

' - r

^-

H1 ... -f

-(-

J-. - 1- - '7- ^- - -j-

-- !j

1 i_

i

h

1 20.75

1 t

-^ "f Model B uildim 1 H el; hi in -L 1 —\—

1 ^ X' "

-l: -

10 15 20 25 30 35

z (in)

Figure 12. Record of velocity profile upstream of the model.

40 45 50

As a result, a sufficiently thick boundary layer was

obtained. Hence, the simulation conditions were

fulfilled.

4.3. Turbulence Intensity Measurement

Simultaneously with mean velocity measurements

the turbulence intensity based on local mean

velocity,

^rms (^) Tu,=

U{z) ' (6)

was monitored. In this relation u is the fluctuating

velocity parallel to the mean flow velocity U. The

subscript rms denotes square-root of mean (timeaveraged) square value, i.e., a/m'.

. ,

, , T _ ^rms< z ' ° U(z)

• Ref. 15

)Sio 1 ) Based or IJ (7 1

(2) —

Bosed on •

•

0.10 0,20

Figure 13. Turbulence intensity variation upstream of the model.

The results for case (3) are displayed in Figure

13. They were reproducible within 2 to 3%. Both

the turbulence intensity based on local and on free- stream mean velocity, i.e., based on U{z) and U

are shown. Based on the local mean velocity a maximum turbulence intensity of about 29% was measui'ed at 2 = 0.05. When it was based on the free- stream velocity a maximum of about 12.5% was

monitored at 2 = 0.4. The different location of the

maximum is caused by the- local mean velocity

variation. As the free-stream region is approached

the difference between them decreases. It can be

obsei'ved that, at a distance of about 0.2 h above the

building model, they are practically equal. The

turbulence intensity at the outer edge of the boundary layer, i.e., at 2 = 2.4, was about 0.2%. The latter

is practically the free-stream turbulence intensity.;

The relatively high turbulence level throughout the

boundary layer was caused by the upstream conditions, i.e., vortex generator and upstream roughness.

The high level of turbulence within the boundary

layer can also be observed from the recorded velocity

profile along the 2-axis. The latter is portrayed in Figure 12. Unfortunately, no field data are available for comparing the turbulence intensity distribution. On

the other hand, the results exhibit a reasonable

agreement with the measurements in the lowest

atmosphere reported by Singer [153-

4.4. Pressure Survey | The aerodynamics forces and moments acting on a

structure are determined by the wind characteristics. Due to the velocity gradient and the turbulence

structure within the atmospheric surface layer (the

boundary layer) both mean and fluctuating forces are of importance in finding the structural response

to wind loading. Furthermore, the local instantane- ous peak force together with the fluctuating force is also important in designing outer skin panelling and

54
window glass. Knowledge of the pressure distribution, i.e., mean, fluctuating and peak pressure, per- mits computation of these forces. A detailed survey of the pressure distribution along

the building model was carried out. The local pres- sure was measured with respect to the static pressure

of the uniform free-stream above the model, i.e., the static pressure outside the boundary layer. The

latter was monitored by means of a Pitot-static tube

located as shown in Figure 1. The total local pressure at any point along the

model wall is p-Poo={P+p')-Poo, (7)

where p is the total local pressure, p the local mean

pressure, p' the local fluctuating pressure and p^ is the free-stream static pressure. The overbar denotes

time-averaged (or mean) values. Next, Eq. (7) can

be written

Ap = Ap+p', (8)

where

Ap = p-p„. (9)

The fluctuations of the free-stream static pre.ssure are completely negligible with respect to the local fluctuating pressure. Then, by taking the meansquare of the total local pressure we obtain

Ap2 = ^p2-(-p'2 (10)

Next, for incompressible flow at small velocities the

local mean pressure coefficient is defined by

Ap

XnTI *2 ' (11)

whereas the local fluctuating pressure coefficient

„ _ Prms 29^ «

(12)

where prms denotes square-root of mean (timeaveraged) square values, i.e., \^p'^. In the above

two relationships UJ^ represents the free-stream

velocity above the model and p is the air density. In

a similar fashion the local instantaneous peak pressure coefficient is

P' (13)

where p'max is \ of instantaneous peak-to-peak pres- sure fluctuation. In terms of the mean pressure coefficient, the local fluctuating and peak pressure

coefficients are

Op, — Op —_ ,

Ap

(14)

(15)

In order to test the variation in time of the pres- sure fluctuations at every position on the model,

the pressure transducer signal was monitored on an

oscilloscope over a period of several minutes. The

observed changes were completely negligible. A

typical oscillogram of the transducer output signal

is displayed in Figure 14. As mentioned earlier, the results reported herein were obtained for C/„* = 50 ft/sec and for a NE

wind. Consequently, the flow had an incident angle

of 6° with respect to the x-axis (see Fig. 15). For

purposes of calculating the mean force the flow can

be considered normal to the wider face of the model.

The mean pressure coefficient distribution and the

isobars of the ratio of the fluctuating and the peak

pressure coefficient to the former on the front face

of the model are shown in Figure 15. On the leewind

face negative mean pressure coefficients were measured. Generally, the fluctuating pressure coefficient (rms) is smaller than the mean coefficient. Only

near the model base is the former larger or of the same order as the latter. Within this domain the mean pressure is relatively small. On the other hand,

over most of the face, the peak pressure is larger

than the mean pressure. Peak pressures as large as 4 times the mean pressure were measured. It is, further, important to notice that the maximum peak

40 60

f (msec)

Figure 14. Oscillogram of the fluctuating pressure at

x = 0.07, !/=0.17, 2 = 0.75, (2;* = 1.45in.,

J/* = 3.5 in., 2* = 15.6 in.); sweep 10 msec/cm,

sensitivity 100 mv/cm.

55
Figure 15. Mean, fluctuating and peak pressure coefficient distribution on the front face.

pressure occurred within regions where the fluc- tuating pressure was the largest. The large increase

in both fluctuating and peak pressure near the building base may be attributed to the upstream roughness and the concomittant large turbulence intensity.

z

2 ,4 .6 .8

Figure 16. Variation of average mean, fluctuating and peak

pressure coefficient as a function of height.

For each cross-wise area element (area element

normal to the mean velocity) it was possible to compute an average pressure coefficient, i.e., pres- sure coefficient per unit area. The change of the

average mean, fluctuating and peak pressure coefl5- cient with height is depicted in Figure 16. The mean

and fluctuating pressure exhibit a linear variation

while the peak pressure reveals a periodical change.

Simultaneously with pressure measurements a survey of pressure fluctuating-energy was carried

out. The frequency spectrum at each station was

recorded by a wave analyzer. The signal to noise

ratio (S/N) was larger than 10 for all the transducers

employed. A characteristic frequency spectrum is shown in Figure 17. It was taken at the same station

as the oscillogram displayed in Figure 14. Most of the pressure fluctuating-energy was concentrated

at low frequencies. No significant contributions

Figure 17. Typical frequency spectrum of pressure fluctua- ting-energy; x = 0.07, )/ = 0.17, 2 = 0.75, (x* =

1.45 in., y*=3.5 in., 2* = 15.6 in.).

56
were obtained at frequencies larger than about 200

to 250 Hz. A predominant frequency of about 17 Hz was observed. On the other hand, the oscillogram

indicated a predominant frequency of about 20 Hz. A report on the pressure fluctuating-energy survey

is under preparation.

It was important to check the pressure distribution invariance with Reynolds number. For this purpose the mean pressure coefficient was measured

for two different upstream velocities, i.e., for

i[/oo* = 30 and 50 feet/sec, while the other conditions were unchanged. Then, a normalized pressure coefficient difference

7 =

Cp(50)-Cp(30)

(16)

was computed at about 97 sample points. In Figure

18 the number of points for a constant value of y are

displayed. At 77 sample stations 7<0.2. Furthermore, at 41 locations 7 = 0.025. On the other hand,

only at 1 sample station 7>0.8. Hence, at most of the stations the change in pressure coefficient is negligible.

4.5. Moment Measurement

The direct measurement of the total overturning

moment was particularly emphasized. The main

objective of this investigation was to obtain an ac- curate measurement of the fluctuating moment. As

mentioned earlier, the local fluctuating and peak

50

40

30

20

10

Sampled from 97 Data Points N- Number of Sample Points

Cp(50) -Cp(30)

Co (50)

_i_L

pressure do not yield sufficient information for appropriate estimation of the fluctuating overturning

moment. The reason for this is that the correlation

of pressure fluctuations on the structure is not known.

The total overturning moment is defined by

M= M+m', (17)

where M is the mean (time-averaged) moment and

in' is the fluctuating moment. It was measured with

a relatively high-frequency response dynamometer

system sensitive only this moment (see Sec. 3.4)

.

Its natural frequency / vas about 200 Hz. Based on

the pressure fluctuating-energy spectrum most of the energy was concentrated at low frequencies, i.e., up to about 30 Hz.

The measurements were carried out under similar

conditions as for the pressure survey, i.e., NE wind

of 50 ft/sec. Initially, the moment for smooth upstream conditions, i.e., without the upstream roughness, was measured. Its variation is shown in Figure

20. The mean moment was about 37 Ib-in and the

peak value of the fluctuating moment reached a maximum of 8% of the former. All the measure- ments were reproducible within less than 4%.

Next, a thorough survey of the overturning moment for the real flow conditions, i.e., the upstream

roughness installed, was performed. An oscillogram

of the fluctuating moment is shown in Figure 19. It reveals a predominant frequency of about 25 Hz.

On the other hand, the predominant frequency

monitored during the pressure measurement ranged

roughly from 15 to 30 Hz depending on the position

along the model. Thus, both measurements indicated

the existence of definite predominant frequencies,

i.e., a predominant eddy size.

.4 ,8 1.0 r 40 80 120

t (msec)

160

Figure 18. Histogram of normalized pressure coefficient

difference. Figure 19. Oscillogram of the fluctuating moment; sweep

20 msec/cm, sensitivity 100 mv/cm.

57
Figure 20. Total overturning moment variation : (a) without

upstream roughness; (b) with upstream

roughness.

In Figure 20 the total overturning moment time

variation for both cases, i.e., with and without the

upstream roughness, is portrayed. The mean moment for the former was found to be about 23.6

Ib-in., 37% smaller than without the upstream

roughness. It is smaller since the wind load does

depend on the upstream mean velocity dis- tribution.

The instantaneous peak values of the fluctuating

moment were found to be of the order of ±34% of the mean moment. Thus, it was about 8 Ib-in. This

large increase with respect to the smooth upstream

conditions is produced by the turbulence caused by

the upstream roughness. The rms-value of the fluc- tuating moment was found to be about 4.8 Ib-in., about 20% of the mean moment. It is important

to notice that the turbulence intensity averaged

over the length of the building was roughly of the same order of magnitude.

Lastly, we note that the important result remains

that the aerodynamic balance yields immediately a

direct and rapid measurement of the total over- turning moment. Furthermore, the overall fluc- tuating moment can be measured accurately and

directly. Since the results are obtained for a sta- tionary model structure they may be used as a standard reference loading in numerical analysis for dynamic response of a building with specified elastic and mass distribution characteristics.

5. Conclusions

The experimental results presented indicate quite

clearly that the direct measurement of the total overturning moment is feasible and desirable. In

order to obtain the moment due to the wind action a relatively stiff model has to be used. Both the

mean and the fluctuating moment depend strongly on the upstream conditions. Particularly, a strong

dependence of the fluctuating moment on the upstream turbulence intensity was observed. A sys- tematic study of this correlation is intended.

Use of the balance technique will permit accurate and rapid measurement of the mean and fluctuating

moments. Moments, mean and fluctuating, obtained

for a stationary model provide integrated wind

loading data which can be utilized in conducting

numerical studies of a building with a variety of

elastic and mass distribution characteristics. Thus,

a standard reference loading is obtained. Further- more, the use of an aerodynamic balance for measuring other wind loading components is also practicable.

The flow was found to be Reynolds-number in- dependent. No significant changes in the pressure

distribution were observed for ambient wind speeds

of 30 and 50 ft/sec. The surveys of the mean velocity,

turbulence intensity and boundary-layer structure showed that the wind-tunnel flow provided an ac- ceptable simulation of the atmospheric surface- layer flow conditions.

The peak pressure fluctuation ranged up to about

4 times the mean pressure. Knowledge of the in- stantaneous local pressure fluctuation is essential

for adequate "skin" design of buildings.

The partial support of this work by Metronics

Associates, Inc. is gratefully acknowledged.

6. References

[1] Cermak, J. E. et al., "Simulation of atmospheric motion

by wind tunnel flow," TR CER66JEC-SI17, FDDL,

Colorado State Univ., Fort Collins, Colorado (1966).

[2] Davenport, A. G. and Isyumov, N., "The application of the boundary layer wind tunnel to the prediction of wind

loading," Proceedings of the Intern. Res. Seminar on Wind Effects on Buildings and Structures, Vol. 1, N.R.C.,

Ottawa, Canada (1967).

[3] Marshall, R. D. and Cermak, J. E., "Wind studies of Bank of America World Headquarters Building,"

TR CER66-67RDM-JEC19, FDDL, Colorado State

Univ., Fort Collins, Colorado (1966).

[4] Ostrowski, J. S., Marshall, R. D. and Cermak, J. E., "Vortex formation and pressure fluctuations on buildings," Proceedings of the Intern. Res. Seminar on Wind

Effects on Buildings and Structures, Vol. 1, N.R.C.,

Ottawa, Canada (1967).

[5] Jensen, M., "The model-law for phenomena in natural wind," Ingenioren, Int. Ed. 2 (1958).

[6] Jensen, M. and Franck, N., "Model-scale tests in turbulent wind," Part I and II, The Danish Tech. Press, Copenhagen (1965).

58
[7] McVehil, G. E., Ludwig, G. R. and Sundaram, T. R., "On the feasibility of modeling small scale atmospheric

motions," TR ZB-2328-P-1, Cornell Aero. Lab,

Buffalo, N.Y. (1967).

[8] Leutheusser, H. J. and Baines, W. D., "Similitude problems in building aerodynamics," Proceedings

ASCE, J. Hyd. Div., HY3, 35-49 (1967).

[9J Armitt, J., "The simulation of the atmospheric boundary

layer in a wind tunnel," C.E.G.B., Lab. Note No. RD/L/N 83/66 (1966).

[10] Pankhurst, R. C. and Holder, D. W., Wind Tunnel

Technique (Sir Isaac Pitman & Sons, Ltd., London, 1952).

[11] Landenburg, R. W. et al., (editors) Physical Measurements in Gas Dynamics and Combustion, Article F, 2, Kovasznay, L.S.G., "Hot-wire method," 219-285 (High

Speed Aerodynamics and Jet Propulsion, Vol. 12, Princeton Univ. Pre.ss, Princeton, N.J., 1954).

[12] Sadeh, W. Z., Sutera, S. P. and Maedcr, P. F., "An

investigation of vorticity amplification in stagnation

flow," TR AF 1754/4, WT50, Brown Univ., Div. of Eng., Providence, R.L (1968).

[13] Davenport, A. G., "Gust loading factors," Proceedings

ASCE, J. Struc. Div., ST3, 11-34, (1967).

[14] Pavelka, B. R., "Wind study, Atlantic-Richfield Plaza, Los Angeles, California," Met. Report, TR 151, Aerosol Lab., Metronics Associated Inc., Palo Alto,

Calif., (1968).

[15] Singer, I. A., "A study of the wind profile in the lowest 400 ft of the atmosphere," PR 5, Brookhaven Nat. Lab.

(1960).

59

EXPERIENCE WITH WIND PRESSURE MEASUREMENTS ON

A FULL-SCALE BUILDING

W. A. Dalgliesh

National Research Council of Canada

Division of Building Research

Ottawa 7, Ontario, Canada

Wind pressure measurements made over a 4-year period on a 34-story building in downtown

Montreal were used to obtain data for checking and improving wind tunnel techniques of modeling

flow characteristics of wind and aerodynamic behavior of buildings. It had been hoped that the measurements could be applied directly to certain problems of design such as evaluation of peak

suction load over small wall areas. The small number of pressures recorded, however, combined

with limitations of field measurements made direct application of the data extremely difficult. The major problems involved in making field measurements and in comparing them with wind

tunnel measurements were found to be:

(a) difficulty of establishing a static reference pressure and its relation to the static pressui-e

in the wind tunnel;

(b) inadequacy of wind velocity information, which in this case consisted of one anemometer

and wind vane located 1,500 ft southwest of the building;

(c) lack of stationarity and homogeneity of the velocity field as compared with the wind tunnel

situation. Comparisons with model measurements are made on the basis of mean pressures, rms pressures, power spectra, and the correlation between selected pairs of pressures measured at various points on the building. Examples have been found of excellent agreement in almost all respects, but for some wind directions the comparisons gave unsatisfactory correlation. The lack of agreement

is attributed mainly to differences between indicated and actual on-site wind direction, but this cannot be shown conclusively because of incomplete wind information. The total cost of the project over the 4-year period was of the order of $100,000. A greater expenditure would have been advisable, primarily for instrumentation to permit a better defi- nition of the wind velocity around the building. Measurements are now under way on a 600-ft

office building using a much more sophisticated data acquisition system by means of which it should be possible to acquire the desired information more efficiently and in a shorter period of time.

Key words: Buildings; full-scale tests; power spectra; pressure fluctuations; wind loads; wind

tunnel modeling.

1. Development of Methods for Wind Research

Investigation of wind effects on buildings and

structures by the Division of Building Research,

National Research Council of Canada, began in 1958

when an extensive survey of the available literature

[1]* was made in connection with the revision of design wind load information for the 1960 edition of the National Building Code. In this code, as in most

other building codes, the conversion from design

wind speeds to design wind pressures and suctions on various building surfaces was given in the form

of pressure coefficients determined experimentally by

testing small-scale models in wind tunnels.

* Figures in brackets indicate the literature references at

the end of this paper.

1.1. Need for Full-Scale Data on Pressure

Coefficients

Study of the literature revealed serious discrepancies among pressure coefficients for geometrically

similar models tested by different researchers. Modeling laws were obviously a matter for debate,

which brought into serious question the applicabiUty

of the results to full-scale structures [2]. A need clearly existed for field measurement of wind pressures on full-scale buildings to answer the

questions of applicability to full-scale situations,

and the correctness of similitude rules. There was

surprisingly little full-scale information available,

however, up to 1960, and the few comparisons with

model results that had been made were at best

inconclusive.

61
1.2. Objectives for Field Measurements in

Canada

A project was therefore set up within the Structures Section of DBR/NRC to measure pressures and suctions on full-scale buildings. The main objectives were to check wind tunnel data and possibly to indicate how to improve modeling techniques. It had been thought at first that such field information might also prove directly useful to designers in assessing, for example, peak suctions over small areas or for similar problems of detailed

conditions in which wind tunnel results seemed in- adequate. The limited instrumentation, however,

coupled with other problems to be discussed in Section 3, made direct design application of these

particular measurements very difficult.

1.3. Full-Scale Measurements in Other

Countries

In contrast with the limited activity before 1960,

interest in field investigations of wind effects on

structures since that time has been very great. In England an extensive program of full-scale measure- ments of wind pressures has been under way for nearly 10 years, and interim results from measure- ments on a 200-ft tall slab-like office building have

been reported [3, 4, 5]. The program for the future

involves measurements on the new 600-ft G.P.O.

tower in London.

Full-scale measurements of wind pressure were

also carried out on a 150-ft slab-like university

building in Melbourne, Australia. Results were compared with wind tunnel tests of a conventional type

and with those using a turbulent boundary-layer

flow [6]. Dissatisfaction with the correlation achieved

led to more fundamental laboratory work on the

flow around wall-mounted bluff objects (buildings on the ground).

Wind loading of a 145-ft slab-like apartment

building in Delft, Holland, was investigated without

the use of pressure taps, using instead a single deformation gage mounted on one of the steel columns

[7]. These results were correlated to some extent with calculations based on the statistical approach

to wind loading proposed by Davenport [8]. The widespread interest in full-scale measurements

shows no sign of slackening. Construction is now well advanced on a 10-story welded steel-frame building

in Hong Kong to be used exclusively for full-scale research on wind forces during typhoons [9].

1.4. New Developments in Wind Tunnel

Techniques

The special problem of building aerodynamics as opposed to conventional aeronautical wind tunnel

work has also been receiving attention [10], with

gieat emphasis on simulating the turbulent shear

flow usually found during strong winds. One method

of creating a turbulent shear flow that has been

used with considerable success involves the so- called boundary-layer wind tunnel, in which a thick

boundary layer is allowed to grow over the long,

specially roughened floor of the tunnel. Over the

past 3 or 4 years the boundary-layer wind tunnel

has been applied as a design tool for predicting wind

loading on several major structures [11]. The parallel development of laboratory and field techniques, and the availability of full-scale results for comparison with model results have already ex- plained some of the discrepancies of earlier wind

tunnel work, but much checking and improvement

remains to be done. The measurement of wind pres- sures and suctions on a full-scale building in down- j town Montreal, Canada, constitutes the most

recently completed portion of the investigations : under way in the Structures Section of DBR/NRC. | These results have been compared with wind tunnel

| tests done in a boundary-layer wind tunnel. A brief description of the field measurements, of the problems of analysis and interpretation of the results,

and of the correlation with wind tunnel results follows.

2. Instrumentation of 34-Story Office Building

Arrangements were made with the owner of a 34-

story office building in Montreal to permit the in- ' strumentation of the two mechanical floors for wind pressure measurements. Most of the office floors of the building had already been rented at the

time of instrumentation (spring, 1964), and this made it impossible to instrument other levels with- i out seriously inconveniencing the tenants. The i mounting of an anemometer and tower on the build- '

ing itself was not practicable, and wind speed and , direction signals were transmitted through telephone

wires from instruments mounted in the fall of 1964 on an existing 200-ft mast atop a 600-ft building to the southwest.

2.1. Influence of Surrounding Terrain

The location of the two buildings involved and ^ the nature of the surrounding terrain are shown in ; Figure 1. As may be seen from the ground contours,

62

I

[
Figure 1. Contour map of the terrain surrounding test buildings.

63
X120 " 1 BUILDING i

0 200 400 600

Figure 2. Plan showing heights of adjacent buildings.

the area is fairly level except for Mount Royal to the northwest. Figure 2 is an enlarged view of the

immediate surroundings. Wind pressures on the 34-

story building (building B) were found to be significantly influenced by the presence of the nearby tall buildings, particularly the 600-ft cruciform building

to the northwest.

2.2. Installation of Pressure Taps

The instrumented floors are the 10th and the 33d,

at heights, respectively, of 134 and 413 ft above the

street. The total height of the building is 440 ft and

the plan dimensions are 119 by 173 ft. The exterior

wall surface is plane except for 8-in. deep mullions,

4 ft 8 in. apart, which run the full height of the

building. At the mechanical floors, however, there

are horizontal louvers, and the curtain wall is set back about 5 in. from the plane of the exterior wall. The louvers show up as dark bands on the wall sur- faces in figure 3. Holes H-in in diameter were drilled through

the curtain wall into the space behind the louvers

about 2 ft above floor level at intervals of approximately 24 ft all around the building at the two levels,

except where locations were inaccessible because of equipment placed in the way. Any 12 of a total of 49 holes could be used as outside pressure taps for the 12 transducers, which were used to convert

pressure differences into electrical signals for con- venient transmission to a central recording location.

Figure 3. Thirty-four-story office building looking southeast (relative to building). Dark bands are at 10th and 33d floors, where mechanical services are located and wind pressure measurements were

taken.

2.3. Sensors and Recording Equipment

The turbulent nature of wind requires that speed,

direction, and pressure at several locations on the

building be recorded simultaneously and continuously for periods preferably longer than 10 or 15

minutes at a time. The response of the sensors and

the capacity of the recording equipment should

be sufficiently high to record fluctuations with fre- quencies up to several cycles per second. The equipment used for the instrumentation of the 34-story

office building met most of the requirements, but in the final analysis of the records an upper frequency

limit of 0.5 cycle/sec was imposed to keep the task

of manually preparing digitized records within

reasonable bounds.

The pressure sensor, or transducer, of which there were 12, comprises an elastic steel diaphragm dividing a chamber connected, on one side, by about 2 ft

64
of plastic tubing to the outside air pressure tap,

and on the other side by up to 200 ft of plastic tubing

to the air pressure at a central location inside the

building. The pressure difference between the two

sides of the chamber is measured in terms of the

diaphragm deflection by an unbonded 4-arm resist- ance strain gage bridge. The power and signal are transmitted by strain gage cables over distances

of up to 600 ft to the central recording location on

the 10th floor. The wind vane and 3-cup anemometer are of the

type U-2A used by the Meteorological Branch of the Canadian Department of Transport and were

located about 1,500 ft away at a height of 800 ft above street level on building A (see Figs. 1, 2). Electrical wind speed and direction signals, trans- mitted via telephone lines, were recorded with the

12 pressure signals on an 18-channel ultraviolet

Ught beam type oscillograph. Chart speed was

limited to 4 in./min for most of the recording, and

the full-scale deflection of each signal was made

±2 in. (±10 psf).

2.4. Field Trips and Processing of Records

Trips were made from Ottawa to Montreal (120

miles) whenever strong winds seemed imminent. It was necessary upon arrival to select the 12 most

desirable tapping locations (depending on the wind

direction), set up transducers, and begin recording.

Set-up time was usually about 1 hour and recording

usually continued for 1 to 3 hours longer. Of the

results obtained on eight such trips between 5 March 1964 and 23 September 1966 five sets were

selected for detailed study.

After visual examination of each strip chart

record, portions representing recording intervals

from 15 min to over an hour were selected and

digitized, using a semiautomated procedure, at time intervals of 1 sec. The digitized values, either on punched cards or digital magnetic tape, were

then processed by a digital computer.

3. Differences Between Field Measurements

and Wind Tunnel Measurements

The model scale investigations were made in a boundary-layer wind tunnel rather than in a conventional low-turbulence aeronautical wind tunnel

because of the undoubted importance of modeling

the gustiness of real wind. Care was taken to simulate field conditions as closely as possible, but in

spite of this certain differences remain. As an ex- ample of the precautions taken, the model of building B was carefully machined from plastic to a

scale of 1:400, including the muUions. Pressure taps were made at locations corresponding to those

where full-scale taps on the two instrumented levels were situated, and three additional levels were tapped to give a more complete picture of pressure

distribution than was possible in the field measurements. All major structures within a 1,600-ft radius were modeled to the 1:400 scale from wood, and

upwind land contours and surface roughness were

also simulated, as is shown in Figure 4. A fundamental difference between the field meas- urements and the wind tunnel measurements is re- lated to control of flow conditions and the reproducibility of an experiment. The main advantage of wind tunnel testing over full-scale testing is the

fact that investigations can proceed systematically

and efficiently. Full-scale measurements, on the

other hand, are dependent on the random behavior

of weather, making systematic investigations impractical. This is particularly true for such features

as the phenomenon of extreme suctions near the

corners of the buildings, for which wind angle is fairly critical.

3.1. Stationarity and Homogeneity of Flow

The basic difficulty associated with field measure- ments arises because of the random nature of wind.

Not only is the acquisition of useful records made

difficult and time-consuming, but the interpretation

and comparison with laboratory results may be- come confusing. Much of the confusion can be

avoided if a distinction is made between "weather"

and "gustiness" on the basis of the time scales in- volved. The shortest period associated with weather

changes and, in particular, strong winds is usually an hour or more, except for thunderstorms, whereas

the longest period associated with gustiness is about

5 minutes. Thunderstorms may have to be treated

somewhat differently from other types of strong

wind storms. The randomness of the gusts superimposed on the mean wind speed can be analyzed using statistical procedures developed over the past 20 years by

communications engineers and others [12, 13]. These

statistical procedures have been applied recently to wind effects on structures [8]. The application of established methods for measurement and analysis

of random data is greatly simplified if it can be

assumed that the wind is at least weakly stationary

and homogeneous. This implies that the means and

variances of wind velocity and pressures are con65
Figure 4. Model of downtown Montreal with major topographical features in the boundary-layer wind tunnel at the University

of Western Ontario for comparison with full-scale measurements.

stant with respect to time and with respect to position in space. Stationarity and homogeneity hold

only approximately for field measurements, if at all, and then only if care is used in selecting suitable

portions of the total record for detailed analysis. In

principle, it would be best to use as long a record as possible to improve the reliability of estimates of means, variances, and distributions of variances ac- cording to frequency (power spectral density). It was found, however, that portions of record much

over 5 to 10 minutes often contained "trends" or variations in the mean value, and these complicated

the analysis.

There was no particular difficulty in satisfying

the requirements of stationarity in the wind tunnel,

but in consideration of the objective of simulating

field conditions it was thought more important to

reflect the nonhomogeneities of the prototype situa- tion rather than to have the theoretical advantages

of the homogeneous flow. The land contours of the

eastern end of Mount Royal were, therefore, modeled

in order to introduce the same sort of spatial variation of velocity as might be found in the field (Fig. 4)

.

3.2. Time Scaling

The time interval over which mean velocities and

pressures were averaged was chosen to distinguish

between (a) the random fluctuations about the mean,

and (b) the much slower variation of the mean wind

velocity and the corresponding pressures in response

to changing weather conditions. A scaling parameter

with respect to time must therefore be considered

when comparing field and model measurements.

For purposes of comparing averaging times the

nondimensional parameter to be kept the same for model and full scale is:

VtL

where 'F = mean velocity in ft/sec,

< = time in sec, L = characteristic length in ft. The ratio of mean velocity in the tunnel to mean

velocity in the field ranged from about 0.50 to 0.75,

and the length scale for the model was 1:400. An

averaging time of 30 min in field measurements

66
would therefore be represented by a tunnel time of 6 to 9 sec. The averaging time actually used in the

tunnel was 30 sec, and the length scale of the gusts

proved to be approximately 1:700; the corresponding full-scale averaging time would be about 175 to 260 min, based on the scale of turbulence. A much

longer averaging period can be used in the wind

tunnel because the slow-moving trends associated

with the weather system in the field situation are not present.

3.3. Reference Static Pressure

Wind tunnel measurements of pressures on a tapped model are expressed in terms of differences

from a reference static pressure, divided by a refer- ence dynamic pressure. The resulting nondimensional ratio, the pressure coefficient, is defined as

follows:

where Cj,. = pressure coefficient,

Pi = pressure at ith tap,

Po = reference static pressure, Ib/ft^

p = mass density of air, slugs/ft^,

F= reference mean velocity, ft/sec.

The usual reference static pressure Po is the ambient barometric pressure inside the tunnel, measured either at a flush wall tap or at the static side

of a pitot tube mounted upwind of the model.

The reference side of each transducer in the field measurements was connected by a long plastic tube

to the ambient barometric pressure at a point near

the center of the 9th floor of the 34-story building.

The reference tubing was present to ensure that all transducers were at least measuring with respect to a common reference pressure, even though it was

not necessarily completely static. The difference between the reference static pressure in the field and that used in the tunnel proved

to be one of the most troublesome aspects of the

comparison of results. The difference, of the same

order of magnitude as the measurements themselves, was caused by a combination of factors:

(a) chimney action—the temperature differential during cold months, combined with the very

considerable effective stack height, caused

pressure differences of the order of 2 to 5

(b) operation of the air-handling equipment

building pressurization of as much as 1 or 2

Ib/ft^ was common;

(c) wind effect—assuming an internal pressure

coefficient of —0.3, the action of the wind

could produce a lowering of the internal pres- sure by 1 or 2 Ib/ftl

Simulation of these effects would be extremely

complicated in the wind tunnel because of the very

complex system of flow resistances and leakages

throughout the building. As a result, no adjustment was made to the wind tunnel technique ; a correction was made, instead, in the comparison of the pressure

coefficients.

3.4. Reference Dynamic Pressure

The dynamic pressure of the reference mean

velocity of equation (1) was measured in the wind

tunnel at a height of 24 in. midway between building

A and building B (see Figs. 1 and 2). This height cor- responds to 800 ft in actual field measurement, but

the pitot tube had to be moved away from building

A to avoid the interference effect of the tunnel wall. The use of this dynamic pressure as a reference

in the wind tunnel should not seriously affect comparison, provided the spatial variation of velocity

is small from building A to the pitot tube location,

and similar in model and full scale.

4. Comparison of Field and Wind

Tunnel Results

When the mean pressure coefficients, Cp., derived

from the field measurements, were first compared

with the from the wind tunnel, allowance had

not yet been made for the difference in reference

static pressure. The comparison was consequently

quite unsatisfactory. The effects of chimney action

and building pressurization by the air-handling

system were frequently sufficient to overcome the

wind pressure on the windward wall. The transducers

at all locations around the building therefore registered suctions in relation to the reference internal

pressure. A correction was then applied to the reference

static pressure at each level for each of the records

of full-scale measurements. Corrections were calculated using the least squares principle to produce the

best fit of the full-scale pressure distribution to the

model pressure distribution. This procedure seems

reasonable as long as there is a definite correlation

between the two sets of pressure coefficients and

the deviations that remain after fitting appear to be

small and random. It is interesting to note that cor67
rections made in this way to the reference static pressure are independent of the dynamic reference

pressure. The same correction of the reference static pressure (in Ib/ft^) is obtained even if completely

different dynamic reference pressures are used in the wind tunnel and in full scale. The corrections

arrived at by least squares fitting were checked in each instance and found to be consistent with ap- proximate calculations of chimney action and building pressurization.

4.1. Comparison of Mean Pressure Distribution on 34-Story Building

The relation between full-scale and model mean

pressure distributions in terms of the nondimensional pressure coefficients, Cp^, is plotted for two

different wind directions in Figures 5 and 6. The

agreement in the first case (wind at right angle to building), particularly at the 33d floor level, is very good with regard to both distribution and scale. Many similar portions of record for approximately

the same indicated wind angle gave equally good

0. 8 -

0. 4

Dl RECTION

FULL

SCALE

MOD EL I i LJ^-^[

33RD FLOOR

lOTH FLOOR

Figure 5. Comparison of full scale with model results; mean pressure coefficients on 34-story office building, northwest wind.

agreement in terms of pressure distribution, but no

other sample was as close to the model results in terms of dynamic pressure, which governs the scale of the pressure distribution.

Figure 6 does not show the same agreement for distribution. The probable explanation for suction on the southwest wall of the 33d floor in the full- scale result is that the indicated wind direction at building A (where the anemometer and vane are located) may have differed by perhaps as much as 10° from the actual wind direction at the building.

If such a difference existed it was evidently not simulated by the model.

4.2. Comparison of Mean Pressure Distribution

in the Empire State Building

Agreement between wind tunnel tests and full- scale tests, unless it is either uniformly good or com0. 8

0. 4

0 L

lOTH FLOOR

Figure 6. Comparison of full scale with model results; mean pressure coefficients on 34-story office building, south wind.

68
i

MODEL

WIND

Dl RECTION

•-^

?

36TH FLOOR

Figure 7. Comparison of full scale with model results; mean pressure coefficients on Empire State

Building, SSW wind (from Rathbun, Dryden, and

Hill).

WIND

Dl RECTION

36TH FLOOR

Figure 8. Comparison of full scale with model results; mean

pressure coefficients on Empire State Building,

ENE wind (from Rathbun, Dryden, and Hill).

pletely unsatisfactory, is hard to assess in objective

terms. To help estabhsh some perspective for making

at least a subjective assessment of the results the

author studied comparisons made by others who

had done full-scale tests [5, 6]. Of particular interest were measurements on the

Empire State Building, reported nearly 30 years ago

by Rathbun [14]. The wind tunnel tests for this building were carried out at the National Bureau

of Standards and the results were presented in 1933

by Dryden and Hill [15]. No comparison of the pressures on the model and those on the building was

presented in the paper by Rathbun, presumably

because there appeared to be very little agreement.

The author therefore made several comparisons

similar to the two illustrated in Figures 5 and 6 for the 34-story building. Agreement was poor for

some of the "items" tabulated by Rathbun. There

were, however, other items for which the agreement

in pressure distribution was good, except that the

scale (i.e. the reference dynamic pressure) seemed

considerably smaller for the full-scale results. The

two examples given in Figures 7 and 8 were chosen

to parallel as closely as possible the examples of Figures 5 and 6. One reading on the 75th floor in Figure 7 seems to be a clear case of mistaken sign,

and has been plotted at its probable value as a cross. The deviations from the model pressure distributions in Figures 7 and 8 are rather larger than those

in Figures 5 and 6, and the scale is consistently

smaller. The improved agreement of the recent comparison can be attributed to improvements in both the instrumentation of the full-scale building

and the modeling techniques used in the wind tunnel.

69
The disparity in scale of the work on the Empire

State Building probably results from use of a constant velocity profile and the absence of terrain

roughness or the shelter of other buildings in the

wind tunnel. A similar difference in scale would no doubt have been found for the Montreal building if the effects of terrain roughness and the other tall buildings nearby had not been simulated. Thirty

years ago pressures were measured by U-tube

manometers, either by observers or by photographing the manometer banks; in either case it was diffi- cult to get an accurate record of mean pressures. Much of the scatter and disagreement of the results must have been caused by gustiness in the wind

that could not be accounted for in the analysis of the records. Modern data acquisition systems now make it possible to distinguish between mean and

gust readings to a large extent and to treat mean

and fluctuating components separately.

4.3. Analysis of Fluctuating Components

For purposes of analysis the fluctuating component of a record of wind speed or pressure versus time is treated as a stationary random process. The

parameters estimated by analysis of the records are

useful for determining equivalent static loads or for estimating the probable number of load cycles at

different stress levels. It is consequently a matter

of considerable importance to demonstrate agree- ment between full-scale and model results for parameters relating to the fluctuating component such as standard deviation, or rms pressure coefficients, and

power spectral density as a function of frequency.

Agreement of shape and location on the frequency

axis of the power spectral density curve implies a proper scaling of the turbulence in the wind tunnel.

Figure 9 is a combined plot of both full-scale and

10-4 2 4 6 8 10-3 2 4 6 8 lO'^ FULL-SCALE WAVE NUMBER, FT"1 Figure 9. Sample power spectral density curves obtained from both model and full-scale experiments on an

office building in Montreal.

model information for the pressure records obtained

at a corresponding tap location on the 33d floor on the windward wall. An empirical curve based on wind speed data, suggested by Davenport, is also shown. The scale of turbulence was probably about

1:700 in this particular model test, and did not

therefore agree with the length scale of the building

(1:400). The ratio of velocities happened to compensate for the difference to a large extent, and as a

result the spectral peaks appear to occur at approximately the same reduced frequency.

5. Evaluation of Field Measurements

The sample comparisons in Section 4 are fairly

representative of the sort of agreement that has been

found between wind tunnel tests in a boundarylayer type wind tunnel and measurements of wind

pressure on the full-scale building in Montreal. The

need for considerably more full-scale information is indicated although the results can be considered

encouraging in many respects.

5.1. Suggested Improvements

Several improvements in instrumentation and

data processing can be suggested on the basis of experience with that part of the project now completed. There is merit in recording data in a visual

form, such as an oscillograph chart, for pilot studies or short-term projects. For the main part of an in- vestigation, however, data processing should be

handled by computer. The data acquisition should

therefore employ punched cards, paper tape or magnetic tape storage, compatible with computer

input requirements.

A second improvement would be an automated

system for initiating recording whenever suitably

strong winds occur. Approximately five of eight

trips to Montreal produced successful runs in the

project just completed but many good storms were undoubtedly missed because of insufficient fore- warning.

The third suggestion for improved procedure concerns the scheduling of wind tunnel tests. One of the

weaker areas of field installations is often the ac- quisition of wind velocity records. On the one hand, one can strive for more and better anemometer sites; on the other, maximum use should be made of the

wind tunnel in searching for those conditions, particularly angle of attack, that best simulate a particular field experiment.

Measurements of building accelerations, strains j in columns, or deflections can provide valuable in-

'

formation about the integrated effect of wind over

70
the whole structure, and comparisons can be made

on models articulated at the base and suitably adjusted for damping and period of vibration.

The separation of wind effects into a mean component and a superimposed fluctuating component

made the analysis and the comparison between

model and full scale much easier to understand. It was necessary to apply a correction to the reference

static pressure for the mean component of the pressure, and the difference in time scales had to be taken

into account in dealing with fluctuating components.

5.2. Approximate Costs

The part of the project involving measurements

on the 34-story building covered the period from

spring 1964 to approximately December 1967. The

overall cost for the 4 years was approximately

$100,000. Of this, instrumentation, including installation, maintenance, and field trips accounted for $30,000, engineers' and technicians' time about

$60,000, and computer processing at standard commercial rates $10,000.

6. Conclusion

Wind pressure measurements are now under way

in the building marked A in Figures 1 and 2. This

is a 600-ft high office building with a much more

open exposure, particularly to the southwest. A

new data acquisition system incorporating most of the suggested improvements has been installed at a

cost of nearly $40,000, and arrangements are being

made to record the particle velocity of the top of the building. The main objective, as in the previous

measurements, is the gathering of essential field data for the development and checking of wind

tunnel techniques so that eventually they can be

used with confidence for the determination of wind

effects on buildings and structures.

Field measurements on the 34-story office building

could not have been made without the permission

of the owners. The Division of Building Research is grateful to Dorchester University Holdings Limited

for their cooperation. Many people have contributed

in various ways to the project; all are appreciated;

in particular, the efforts of Mr. W. von Tobel deserve special recognition.

The wind tunnel tests were made at the University of Western Ontario Boundary-Layer Wind

Tunnel under the direction of Dr. A. G. Davenport

and N. Isyumov. Their interest and assistance is gratefully acknowledged.

This paper is a contribution from the Division of Building Research, National Research (youiicil,

Canada, and is published with the approval of the

Director of the Division.

7. References

[l] Davenport, A. G. "Wind Loads on Structures." Division

of Building Research, National Research Council,

Canada, NRC 5576, March 1960.

[2] Jensen, M. "The Model-law for Phenomena in Natural Wind." Ingeni^ren, International Edition, Vol. 2, No. 4, 1968.

[3| Newberry, C. W. "The Measurement of Wind Pressures on Tall Buildings." p. 113-150, NPL Symposium on Wind Effects on Buildings and Structures, Vol. 1, London,

HMSO, 1965.

[4] Newberry, C. W., K. J. Eaton, and .J. R. Mayne. "The

Nature of Gust Loading on Tall Buildings." p. 339-428,

Proc. International Research Seminar on Wind Effects on

Buildings and Structures, Ottawa, Canada, September

1967, Vol. 1, University of Toronto Press, 1968.

[5] Newberry, C. W. and J. R. Mayne. "Wind Loading of a

Tall Building in an Urban Environment; A comparison

of Full Scale and Wind Tunnel Tests." Paper 3, Symposium on Wind Effects on Buildings and Structures, April 1968, Loughborough University of Technology,

Vol. 1, England, 1968.

(6] .Joubert, P. N. et al. "The Drag of Bluff Bodies Immersed

in a Turbulent Boundary Layer." p. 297-336, Proc,

International Research Seminar on Wind Effects on

Buildings and Structures, Ottawa, Canada, September

1967, University of Toronto Press, 1968.

[7| Van Koten, H. "Wind Measurements of High Buildings

in the Netherlands." p. 685-704, Proc, International Research Seminar on Wind Effects on Buildings and

Structures, Ottawa, Canada, September 1967, University

of Toronto Press, 1968.

[8| Davenport, A. G. "The Application of Statistical Concepts to the Wind Loading of Structures." Proc,

Institution of Civil Engineers, August 1961.

[9] "Tenantless Building Will Rise in Path of Typhoons."

Engineering News Record, March 14, 1968, p. 29.

[10] Leutheusser, H. J. and W. D. Baines. "Similitude Problems in Building Aerodynamics." Journal of Hydraulics Division, Proc, American Society of Civil Engineers, p. 35-49, May 1967.

[11] Davenport, A. G. and N. Isyumov. "The Application of the Boimilary Layer Wind Tunnel to the Prediction of Wind Loading." p. 201-230, Proc, International Research Seminar on Wind Effects on Buildings and

Structures, Ottawa, Canada, September 1967, L^niversity of Toronto Press, 1968.

[12] Bendat, J. S. and A. G. Piersol. Measurement and Analysis

of Random Data. New York, John Wiley and Sons, 1966.

[13] Lee, Y. W. Statistical Theory of Communication. New

York, John Wiley and Sons, 1960.

[14] Rathbun, J. C. "Wind Forces on a Tall Building." Trans. American Society of Civil Engineers, Pai)er No.

2056, Vol. 105, p. 1-41, 1940.

[15| Dryden, H. L. and G. C. Hill. "Wind Pressure on a Model of the I'jnpire State Building." Joinnal of Research, National Bureau of Standards, Vol. 10, [). 493-

523, 1933.

71
I..
INFLUENCE OF ARCHITECTURAL FEATURES ON THE STATIC WIND

LOADING OF BUILDINGS

Hans J. Leutheusser

Department of Mechanical Engineering

University of Toronto

Toronto 6, Ontario, Canada

The paper deals with the exploration, by model tests, of the effects of roof parapets and roof projections onto the roof wind-loading, and of wall mullions (or ribs) onto the wall wind-loading,

of bluff building forms. Results are presented which suggest that parapets are effective in equalizing the pressure distribution over the roof surface while slightly reducing the uplift force. Roof projections, on the other hand, have the opposite effects. The presence of wall mullions causes sawtooth like deviations from the peripheral wall pressure-distribution for the no-rib case. The devi- ations are particularly significant in regions of attached flow and tend to become more pronounced

with an increase in rib spacing.

Key words: Architectural features; buildings; mullions; parapets; roof projections; static pressures; wind effects; wind tunnel modeling.

1. Introduction

For the majority of conventional buildings knowledge of the time-averaged, or static, wind loading

(as opposed to the dynamic loading due to vortex shedding and turbulence) is usually sufficient to allow adequate design of exterior walls, roofs and

cladding, and to test the stability of a structure as a

whole against overturning. Because of its great

utility, hence, information on the static wind loading

is usually summarized for a wide range of building

configurations in the building codes of most

countries. The bulk of these code data originates from model

tests which are performed, with various degrees of sophistication, in wind or water tunnels of laboratories specializing in experimental building aero- dynamics. Since the physical size of models in rela- tion to their full-scale counterparts is very small

(linear scale ratios of 1 : 200 to 1 : 400 are common)

it proves rarely possible to reproduce in a model

with sufficient detail all of the architectural features

of a prototype structure which would assure exact geometric similarity between the two. As a conse- quence, it has long been recognized that models

may be inadvertently oversimplified and, hence,

that tests may yield incomplete or even misleading

results. In order to ascertain the influence which architectural features might have on the static wind loading

of buildings a number of systematic investigations

have been performed in the Fluid Mechanics

Laboratory of the Department of Mechanical Engineering, University of Toronto. In particular, tests

were undertaken to study the effects of roof parapets

and roof projections onto the roof wind-loading of flat-topped, block-type structures and circular cyl- inders. Furthermore, an investigation has now been

initiated to explore the effects of wall mullions (or

ribs) on the peripheral wall pressure-distribution of very tall structures of rectangular plan. This latter study is still in progress, but some results for the

square-plan building configuration are already available. All of the various investigations, which are described in some detail in the following, were stimulated by the keen interest taken in the subject

matter by the Division of Building Research of the

National Research Council of Canada.

2. Investigative Procedure

Wind action on buildings and structures is a con- sequence of what in Fluid Mechanics is referred to

as flow about bluff bodies at large Reynolds number.

This statement implies that the flow field can be

divided into a potential flow zone, a boundary-layer

region and a turbulent wake. Although the field can

be described by equations of motion, the complexity

of them precludes mathematical solution. Hence,

the experimental approach must be adopted for the solution of most practical problems such as the

determination of the static wind loading on buildings.

The investigations under consideration here were

variously carried out in one of two essentially

identical micrometeorological wind-tunnel facilities. These tunnels are of the open-return type, have

test sections 8 ft wide, 4 ft high and 36 ft long and

are equipped with continuously variable speed

73
drives at their downstream ends. At its upstream

end, each tunnel contains a honeycomb followed

by a stilling chamber with screens and a gradual

constriction. The maximum air speed realizable in the two tunnels is, respectively, about 25 and about

60 ft per second.

All tests were performed with the models installed

in the uniform velocity field of the potential flow

core of the wind-tunnel test-section. This was done

although it is well recognized that this classical ex- perimental technique can yield results of only limited

practical utility [1].* However, the method was

judged to be applicable in the present instance since

the main concern of the various studies was to ex- plore relative changes. In other words, the investigations were based on the premise that relative effects on pressure distributions brought about by minor

modifications in building geometry are sensibly in- dependent of the mean flow and turbulence characteristics of the velocity field. Throughout the testing program special pre- cautions were taken to effectively seal the leeward,

low-pressure, building wake against falsifying en- trainment of ambient-pressure fluid [1]. This was

accomplished by using ground and separating

plates of sufficient size, and by carefully blocking all possible leakage paths between high and low pres- sure zones on the models.

For the purpose of determining the pressure dis- tribution, selected regions of the model exteriors were provided with closely spaced and carefully

finished static pressure taps. Local pressures (p) were determined with respect to the ambient static pressure (po) prevailing in the field of undisturbed

flow velocity immediately upstream of the

model, as indicated by the static holes of a strategically arranged Pitot-static tube. Pressure diff'er- ences evaluated from the readings of a sensitive

micromanometer were rendered nondimensional by

division with the dynamic pressure of the undisturbed airstream to yield nondimensional local pressure coefficients, viz.

(2)

Cn (1)

where p is the fluid density. Average pressure coeffi- cients were deduced by numerically integrating the

local pressure coefficients over appropriate building

surfaces, i.e..

* Figures in brackets indicate references at the end of paper.

where A is the total area, and is the area element

contributoiy to an individual pressure tap.

3, Study of Roof Parapets

3.1. Scope and Experimental Details

A very common feature of flat-roofed buildings is the parapet, a low wall around the edges of the roof. Parapets are usually integral parts of the outside

walls of buildings and are designed to provide positive anchorage of roof to structure. However, as

first suggested by Nacy [2], parapets may also be

beneficial in reducing local extremes of wind suction

by equalizing the wind pressure distribution over the

roof surface. Since the occurrence of local pressure extremes, or more specifically, of the associated steep pressure gradients, often entails wind damage to cladding, parapets would thus appear to represent an appealing combination of accepted architectural

feature and wind safeguard. In an effort to explore the promising characteristics of parapets in some greater detail, a study

program was devised encompassing representative ranges of both building configuration and para- pet height [3]. The general configurations of the

building models investigated are illustrated in the

definition diagrams of Figure 1. In particular, for the block-type structure, the aspect ratio of the

building plan h/l was either 3^ (oblong) or 1 (square), and for both the block-type and the

cylindrical structures the relative building height

h/h (or h/d) varied between }/2, 1, and 2. Similarly,

the relative parapet height p/h ranged from 0 to

}4, for both building configurations.

The models were manufactured from clear acrylic

plastic at an actual size of 6 = d = 6 in. and with a uniform parapet thickness of 3^ in. Each of the

three basic building shapes (i.e. oblong, square and

round) comprised three main components, viz. three

interchangeable wall shells, five interchangeable

parapet rings, and the roof proper which was pro- vided with pressure taps. The top photograph of Figure 2 represents an "exploded" view of the oblong

block-type structure, and the bottom photograph

shows this structure mounted on a ground plate and

installed in the wind tunnel.

All tests were performed at a free-stream velocity

Vo of about 20 ft per second (corresponding to a Reynolds number, based on the minimum model

dimension h or d, of about 6X 10^), and each building

74
Definition Diagram of ROOF PARAPETS

MODEL STUDY OF ROOF PARAPETS

Figure 1. Definition diagram of roof parapets.

configuration was tested at all of the principal wind

directions.

3.2. Results and Discussion

By way of example, figures 3a and 3b depict ex- perimentally determined distributions of nondimensionalized relative pressure over the roof surface of the square-plan block-type structure {h/b=l) for

six values of relative parapet height and for the two

i principal wind directions applicable in this case,

j The information conveyed by the various plots is

I representative of the sum total of general findings

i of the investigation which can be summarized as

follows

:

j In general, the nonuniformity of pressure dis- tribution is greatest for a p/h-ratio equal to zero. Increasing the height of parapets tends to equalize

the pressure over the roof surface. This effect be- comes more pronounced with an increase in building

height.

Complete Set of Model Componets of

Structure with b/X = 1/2

Model Installed in Wind Tunnel

(b/U =1/2, h/b=l/2, p/h=l/6,<e.=45°)

Figure 2. Parapet study, model components and model

installation.

For block-type structures, 45° winds result in large negative pressures close to the leading corner. In the case of low buildings, parapets of small height

make these pressures even more severe. Similarly,

these extreme negative pressures increase with decreasing aspect ratio b/l of the building plan.

Addition of parapets may result in some instances

in locally positive pressures. These will occur mainly

in leeward roof areas of low block-type structures equipped with high parapets and subjected to cornering winds.

A more concise summary of the test results than

can be provided by plots of isobars is offered in Figure 4. Here the effectiveness of parapets in rela- tion to pressure equalization is expressed in terms

75
Archit'l Feature: ROOF PARAPETS

ISOBARS (cp- Contours) on ROOF

of

BLQCK-TVPE STRUCTURE

p/h

IA8

\/zw

1/12

1/6

b/l = 1I h/h n/ D i •0°

1 1

SECTION

\

Figure 3a. Effects of parapets on roof pressure-distribution

for frontal wind.

Rectangubr Plan

(b/l - U2>

*s.o

n.o

*i.O —

V2-M>

*2.0

flO

Arcfiitectunl Feafure: ROOF PARAF€TS EFFECTS ON PRESSURE DISTRIBUTION AND LIFT COEFFIOENT

Square Plan h/b (h/d) = 1/2 ' 1 ' 2

C/rcutor Plan

0 mt 1/12 3/2t l/S fl/7l 0 l/2i l/!2 3/21. p/h 0 l/2( Vt2 3/24 l/S

^

Figure 4. Neteffects of roof parapets on pressure distribu- tion and on lift coefficient.

of an index (tending toward unity for complete

uniformity)

Archit'l Feature: ROOF PARAPETS

ISOBARS (cp- Contours) on ROOF

of

BLOCK-TYPE STRUCTURE

p/h

1/^8

1/24

1/12

Figure 3b. Effects of parapets on roof pressure-distribution

for cornering wind.

(Cp) ex t r c.

(3)

in which (Cp)extr is the largest measured local pres- sure coefficient of a particular pressure distribution,

and Cl is the lift coefficient or, what is the same in

this case, the average pressure coefficient for the

whole roof as defined by Eq. 2, where A is the total roof area inside of the parapet. Since for design

purposes, at least, distinction between wind direc- tions is irrelevant, both e and Cl are plotted in Figure 4 as function of relative parapet height p/h

with relative building height h/b (or h/d) as a parameter, but irrespective of wind angle. As a conse- quence, the curves in Figure 4 actually represent

the envelopes of the most critical values of e and Cl

for all of the wind directions tested. The systematic variation of e in Figure 4

is remarkable, particularly in view of the some- what more erratic behavior of the corresponding lift coefficients. It is immediately apparent that

76
for all structures not only relative parapet height

but also relative building height has a pronounced

effect on the nonuniformity of pressure distribution

as measured by e. The latter decreases in general

with increasing values of p/h and h/h (or h/d). As

suggested also by the isobar plots, addition of parapets of insufficient height to low block-type

structures may cause the nonuniformity of pressure

distribution to become more severe. It is noteworthy

that this effect is particularly pronounced in the

case of the oblong block-type structure. It is also apparent that, for the purpose of pressure equalization, parapets are not likely to be very useful on

tall block-type structures and on cyhndrical structures of any height.

The variation of lift coefficient with relative parapet height depicted in Figure 4 shows a generally

decreasing trend for all three types of structure and

for all building heights. Over the range of relative parapet heights tested, this load relieving effect of parapets increases to about 10% of the uplift force on an unprotected roof (i.e., one for which p//i = 0). It is also apparent that lift coefficients become numerically larger with an increase in building height

whether or not parapets are present. Indeed, from

the data available it is clear that it is relative building height rather than relative parapet height which

is the significant parameter in determining the applicable roof lift coefficient for a particular building.

However, somewhat inconclusive experimental evi- dence [3] suggests that the lift coefficient will be- come independent of relative building height at values of h/h (or h/d) of about 10, in which case then relative parapet height would assume the role

of governing parameter.

4. Study of Roof Projections

4.1. Scope and Experimental Details

The term "projections" refers to those portions of the roof which overhang the side walls of a building.

Roof projections are a normal and, indeed, necessary

feature of practically all residential buildings insofar as they serve to protect outside walls against the

direct roof runoff of precipitation, and provide

shade. Even elementary aerodynamic considerations

suggest that roof projections will have an adverse

effect on the static wind loading of both roof and

walls, particularly in the case of flat-topped buildings. However, no concerted attempt at clarifying

their role seems to have ever been made.

In an attempt to provide some quantitative in- formation on the influence of projections onto the

roof wind-loading of flat-topped buildings, a study

program similar in scope to that of the previously reported parapet study was executed [4]. The

general configurations of the various building models

investigated are depicted in Figure 5. As before,

the aspect ratio h/l of the plan of the block-type

structures was either }/2 (oblong) or 1 (square), and

the relative building height h/h (or h/d) varied

between 3^, 1, and 2. Similarly, the relative roof

projection e/h ranged in uneven increments between

0 and

The models were manufactured out of plastic and

built at an actual size of 6 = d = 6 inches. The over- hanging portions of the roofs had a uniform thick- ness of ^6 inch. Each of the three basic building

shapes, i.e., oblong, square, and round, comprised

two main components, viz. three interchangable

Definition Diagram of ROOF PROJECTIONS

Figure 5. Definition diagram of roof projections.

77
wall shells and four interchangable roofs. Each roof

consisted of three laminated layers of sheet plastic.

The bottom layer was 3^-inch thick, fitted into the

appropriate wall shell and accommodated the

manometer-lead receptacles for pressure taps strategically arranged in bot-h the top surface of the whole

roof and the underside of the roof projections. The

3/8-inch thick center layer and the J^g-iiich top layer

together constituted the roof proper. Its two-layer

construction was necessitated by the requirement

for having internal connections between the pres- sure taps in the projecting portions of the roof and

their corresponding manometer-lead receptacles in the interior of the model. The internal connections were realized by milling shallow channels into the

upper surface of the center layer of the roof, and by

MODEL STUDY OF ROOF PROJECTIONS

Complete Set of Model Components of

Structure with b/"C = 1/2

Model Installed in Wind Tunnel

(b/X =1, h/b=2, e/h=l/l2,'e =0*^)

Figure 6. Projection study, model components, and model

installation.

subsequently cementing the top layer to this surface. Static pressure holes were drilled after the three

layers had been laminated together, and all internal

channels, as well as all straight-through taps, were

carefully pressure-tested for cross-leakage. By way

of example, the top photograph of Figure 6 portrays

the complete complement of components for the

oblong block-type structure, and the bottom photograph shows the square-plan block-type structure

installed in the wind tunnel. As in the case of the parapet study all tests were

run with a free-stream velocity of about 20 feet per

second, and each building configuration was tested

at all of the principal wind directions.

4.2. Results and Discussion

Figures 7a and 7b show the pressure distributions over the upper and lower roof surfaces of the square- plan block-type structure {h/b = l) for six values of

relative roof projection and for the two principal

wind directions applicable to this building shape.

These diagrams are representative examples of all of the isobar plots prepared in the course of the data

evaluation.

Inspection reveals that an increase in relative roof projection causes the pressure distributions to become more nonuniform, particularly for frontal winds. However, the changes do not appear to be

very drastic, at least not for the range of e/Zi-values

studied. As would be expected, 45° winds acting on

the block-type structures give rise to local suction extremes on the top surface of the roof in the immediate vicinity of the leading corner. To be sure, the measured values of these pressure extremes for the various e/h-values pertaining to a particular

combination of b/l and h/b do not permit direct

comparison because the members of such a series of models are not geometrically similar. However, in overall view of the experimental evidence available

it would appear that also local suction extremes ought to be relatively insensitive to changes in e/h. Of particular interest are the pressure distributions over the underside of roof projections. Positive pressures prevail generally over all eaves over- shadowing windward building walls. In the case of cylindrical structures the positive pressure region is restricted to the upwind 60° sector. The balance of the eaves is subject to relatively weak suction as in- dicated by measured negative pressure coefficients which nowhere exceed an absolute value of 0.9. Integration of the various pressure distributions over the roof surfaces of all structures tested showed

78
ArchitectufX]l Feature: ROOF PROJECTIONS

ISOBARS (cp-Contours") on ROOF of BLOCK-TYPE STRUCTURE

Architectural Feature: ROOF PROJECTIONS

TOP SURFACE

t-048

,

1

;—=i

1 o

V'.ND DIRECTION,

b/l= 1 h/b- I

UNDE.RSIDE

(as f^een from above)

J-0-73

iA8

-OLM -037 -asij

1/24

:—r- 1

Figure 7a. Effects of projections on roof pressure-distribution for frontal wind.

that both the average pressure coefficient (cpr) for the top surface of the roof {At), and the average

pressure coefficient (cpu) for the underside of the roof

projection {Au) are invariably negative, i.e. that

there is always an upward directed upUft force acting on the top surface, and a downward directed

downpull force acting on the eaves. As a consequence,

the net Hft coefficient for the whole roof, i.e.,

^ L/At —

tL= — =CpT- Cpu{Au/At) (4)

where L is the net lift force, is found to vary little and, indeed, may even tend to decrease with an in- crease in relative roof projection.

However, by its very definition Cl is not a direct measure of the net uphft force acting on the roof of a given structure since it depends on At and, hence, on e/h. More meaningful for judging the effects of variable relative roof projection on the net lift force

is the "specific" lift coefficient defined as

O

VINO oiRe.cTiO''

b/'l= 1. h/b- 1

-1

UNDERSIDE

(as 'j^e'.^ti 'iram above)

I As

1/24

\ •

\

-OM -slz -OM -tSK

»«• *— — IJ-

- 1 I \^

-0.58 -oU -aii

1/12

1/6

Figure 7b. Effects of projections on roof pressure-distribution for cornering wind.

Cl+ = Cl{At/A+) =

L/A+

(5)

which is referred to the plan area (i.e., 6X/ or

d'^Tr/4:) of the structure proper. The variation of the

maximum (i.e., irrespective of wind direction) specific lift coefficient as a function of e/h with h/b (or

h/d) as a parameter is plotted in Figure 8. Inspection

of the curves leads to the interesting conclusion that

the net uplift force on roofs of cylindrical structures

is, over a certain range of the argument, practically

independent of e/h and, hence, of the roof diameter.

The range is longest for the lowest structure and decreases quite systematically with increasing building

height. On the other hand, only the two lowest of the block-type structures exhibit a similar characteristic, but the behavior is less pronounced particularly in the case of the oblong configuration. It

is further apparent from Figure 8 that for all of the

79
Rectangular Pkn

Architectural Feature: ROOF PROJECTIONS EFFECTS ON PRESSURE aSTRIBUTION AND UFT COEFFICIENT

•rrr

7'h/t 1 f

Square Pkin

h/b (h/d) = 1/2 - 7 - 2

Circular Pkm

1

0 lOi ya 3Qi iM e/h 1 3/2i i/s e/h o im tm im ik

Figure 8. Net effects of roof projections on top-surface

building shapes investigated, Cl"^ (and hence, the net uphft force) increases strongly with building

height.

Also plotted on Figure 8 is an index illustrating

the degree of nonuniformity existing on the top

surface of the roof. This index is defined similar to Eq. 3, i.e.,

(Cpr) extr (6)

where (Cpr)extr is the largest measured local pressure

coefficient on the top surface. The variation of with e/h and /i/6 (or /i/d), though rather erratic,

certainly suggests that no benefit can be derived

from roof projection with regard to pressure

equalization.

5. Study of Wall Mullions

5.1. Scope and Experimental Details

Mullions, or vertical ribs, protruding from the

exterior surface of outside building walls seem to become increasingly popular with architects designing high-rise office towers and apartment buildings.

More often than not these ribs have no functional

purpose and are used strictly for appearance's sake. Some limited information on the pressure distribution over the outside walls of cylindrical tanks with

vertical fins [5] suggests that there may occur

significant pressure differences across wall projections and, hence, that mullions may be subjected to possibly very large aerodynamic forces due to wind

action. However, no pertinent design data which

would be directly applicable to angular buildings

with plane walls appears to be presently available

in the literature.

In an effort to at least partially close this information gap a study program was devised around the

concept of a very tall, i.e., essentially two-dimensional, building of rectangular plan configuration

equipped with mullions of identical cross-section

geometry but of variable spacing between fixed corner arrangements.

The general characteristics of this building are indicated in Figure 9. Although the model of this structure permits changing the aspect ratio h/l of the building plan from Yi (oblong) to 1 (square),

only tests on the square-plan configuration have so

far been undertaken. Similarly, the model is actually

designed in such a way that a wide variety of types

of ribbed building walls can be studied. However,

during the investigation here under consideration

only mullions of square plan arranged with variable

spacings s/h of 1/27, 3/27 and 5/27 have been used.

The square-plan model tested has an actual

physical size of 6=13.5 inches. It consists of four

main components, viz. model stand, one set of

(scjuare) end plates, one set of separating plates

(attached to the end plates and serving as wake

seals), and four sets of wall panels. Each set of wall

panels (three provided with ribs at different spacings

and one without ribs for the purpose of comparison)

Definition Diagram of WALL MULLIONS

BLOCK- TYPE STRUCTURE

Figure 9. Definition diagram of wall mullions.

80
MODEL STUDY OF WALL MULLIONS

Complete Set of Model Walls with s/b=l/27

Model installed in Wind Tunnel

(b/l = l, e/b=l/27, s/b=l/27, =45° )

Figure 10. Mullion study, model components and model

installation.

comprise four panels of which one only is provided

with pressure taps.

The arrangement of the pressure taps is staggered over the center third of the 12-in. high model, and

there are a minimum of three taps in each half-inch

of peripheral length including each mullion face. Hook-up of the pressure taps to a bundle of manometer leads which is permanently installed in the hollow shaft of the model stand is effected by bolting a lead-terminal contact plate leak-proof against the

interior surface of the tapped wall panel.

The top photograph of Figure 10 portrays a complete set of wall panels for the oblong structure sur- rounding one of the corresponding model end-plates,

and the bottom photograph shows the square-plan

MODEL STUDY OF WALL MULLION.S

Model Interior Showing Contact Plate

Close-Up of Exterior Model Surface

(s/b = 1/27)

Figure 1L Mullion study, model details.

model installed in the wind tunnel. Details of the

pressure-tap hook-up, and the outside appearance

of the tapped wall panel with the closest mullion

spacing are shown in the two photographs of Figure

11.All tests of the investigation were run at a fi-ec- stream velocity of al)out 50 ft per second (corresponding to a Reynolds number, based on the dimension b, of about 2.3X10^), and each mullion

configuration was tested for both fi'ontal and cornering (i.e., 45°) winds.

5.2. Results and Discussion

In the order to assure two-dimensional flow about

the model, the building wake had to be perfectly

81
Square -Ran Cylinder EFFECTS OF WAKE SEAUNG BY PLATES

ON PERIPHERAL PRESSURE DISTRIBUTION

Figure 12. Pressure distribution on a square-plan cylinder.

sealed against inflow from above and below. Results

of an incidental series of tests with various designs

of separating plates attached to the plain structure

are depicted in Figure 12. In this, cases A, B and C

pertain to : absence of any plates ; circular separating

plates; and circular separating plates with tails; respectively. From a study of the flow behavior in the wake region with the aid of a tuft probe, case C

was confirmed as providing complete wake sealing,

and the corresponding distribution of peripheral

wall pressure forms the basis of comparison to which

are referred the results of the mullion study proper. Throughout this study the model was always equipped with separating plates corresponding to case C. Figures 13a through 14c are plots of the nondimensional peripheral wall pressure-distribution on

the square-plan structure for three cases of mullion

spacing and two wind directions. In these, the solid

lines correspond to pressures measured normal to

the basic shell (i.e., 6X0 of the model, and the dots measure the average pressure difference across individual mullions. The latter type of data repre- sentation is made conveniently possible by the

experimentally established fact that the pressure dis- tribution over the mullion side-walls is essentially

uniform.

Inspection of the various diagrams reveals that

mullions may, indeed, cause serious modifications of the peripheral pressure distribution for the no-rib

case shown as a dashed line. The modifications consist essentially of saw-tooth like deviations from the

plain-wall case which increase in magnitude with an

increase in mullion spacing. The effects of mullions on the pressure distribution are particularly signifi- cant in those regions of the building plan where, in the case of no ribs, the flow is attached to the structure. The static loading on mullions can be severe as indicated by the pressure conditions recorded for the windward corner shown in Figure 13c. Here the

measurements indicate the existence of pressure differ- ences in the neighborhood of twice the dynamic

pressure in both directions across the mullion section.

It appears, that still more critical conditions could

result from larger mullion spacings than were tested

so far.

6. Conclusions

True appreciation of the effects which architectural

features might have on the static wind loading of buildings can only come through carefully performed

model tests. While the paper summarizes a considerable body of hopefully useful information in this regard, the data presented actually pertain only to a very small number of features, viz. roof parapets,

roof projections, and wall mullions. There are many

other common architectural details which deserve

to be studied in a similar systematic manner and

much remains to be done before a really significant

advance in the understanding of wind effects in this

field of building aerodynamics will become apparent.

82
mil Mullions

b/l' 1 c/b *1/27

s/b-1/27

1 1 1 6 ^ §

> O -rT CD O

h1 -p- -7

l"ja_

<

Figure 13a. Effects of wall mullions on peripheral pressure distribution for frontal wind (s/6 = l/27).

Cp

-;.o

-o.e

-0.5

-a2 • lO >» IN UM. o CS a cj + 4. 4. 4. ^— —-~

: 1 a cs

1 1 / —

s/b -(

mil Mullions

b/l - ; c/b -1/27

s/b '3/27

I I I

I

J; ») <» o

c/f F/^ure fer s/b = 1/27

FiGUBE 13b. Effects of wall mullions on peripheral pressure distribution for frontal wind (s/6 = 3/'27).

83
Cp

-10

-0.8

-0.6

-0.4

-02

/b m 0O

-\-

Wall Mullions

M - ; c/b'1/27

s/b'5/27

p p p .o «L7

K< K ffi OB w

—

-1

Figure 13c. Effects of wall mullions on peripheral pressure distribution for frontal wind (s/b = 5/27).

• « avg. kiteral press, difference across mullions / positive if tending to turn dockwise

J'

mil Mullions

b/l - ; c/b - 1/27

s/b'1/27

If -45'

Figure 14a. Effects of wall mullions on peripheral pressure distribution for cornering wind (s/6 = l/27).

84
• * c/f Figure for s/b - 1/27

si'

Figure 14b. Effects of wall mullions on peripheral pressure distribution for cornering wind (s/6 = 3/27). • * cf. Figure for s/b - 1/27

09

mil Mullions

b/l - 1

c/b ' 1/27

s/b '5/27

Figure 14c. Effects of wall mullions on peripheral pressure distribution for cornering wind (s/6 = 5/27).

85
The work described herein covers several years

and was made possible through grants by the National Research Council of Canada. The writer is indebted to his many co-workers who, at various

times, rendered able assistance to his research

program.

7. References

[1] Leutheusser, H. J. and Baines, W. D., "Similitude Problems in Building Aerodynamics," Journal of the Hydraulics Division, Proceedings of the American Society

of Civil Engineers, Volume 93, No. HY3, May 1967.

[2] Nacy, P. S., "Modification of Pressure Distribution around Buildings due to Parapets," M.S.-Thesis, unpublished. Department of Mechanics and Hydraulics,

Graduate College, State University of Iowa, June 1951.

[3] Leutheusser, H. J., "The Effects of Wall Parapets on the Roof Pressure-Coefficients of Block-Type and Cylindrical Structures," University of Toronto, Department of Mechanical Engineering, Technical Publication Series, TP 6404, April 1964.

[4] Leutheusser, H. J., "The Effects of Eaves on the Roof

Pressure-Coefficients of Block-Type and Cylindrical Structures," University of Toronto, Department of Mechanical Engineering, Technical Publication Series, TP 6503, April 1965.

[5] Hoerner, S. F., "Fluid-Dynamic Drag, Practical Information on Aerodynamic Drag and Hydrodynamic Resist- ance," published by the author, Midland Park, N.J., 1965.

86
THE UNSTEADY SURFACE PRESSURE AROUND CIRCULAR CYLINDERS IN

TWO-DIMENSIONAL FLOW*

Wayne E. Simon

Martin Marietta Corporation Denver Division

Denver, Colorado 80201

The unsteady surface pressure around circular cylinders in two-dimensional flow has been measured in the subcritical, supercritical, and transcritical flow regions. A representation of the crosspower spectral density has been developed which is a reasonable representation of the data and which applies to all three regions. The most important result is the essential similarity of the subcritical and transcritical regions.

Key words: Circular cylinders; power spectra; pressure fluctuations; subcritical flow; .supercritical flow; transcritical flow; turbulence.

1. Introduction

The original flow field parameter analysis was, in essence, a semiempirical representation of the unsteady aerodynamic force exerted on a boost vehicle

in the vertical launch position. It was so constructed

that the calculated response of the Saturn V wind

tunnel model was a reasonably good representation

of the wind tunnel data. In this work, it was found

necessary to postulate a relationship between

Strouhal frequency and the second derivative of the

steady pressure at the separation point [1].** An experimental program was then planned to investigate this postulate. The work reported in Chapter II, Section C of Reference 2 showed that

this postulate was valid. Another portion of the flow field parameter

analysis postulated an exponential decay in the cross- correlation of the unsteady force as a function of axial displacement. In addition, an effect of vehicle

motion on the correlation length was also assumed.

Although these assumptions were necessary to give a mathematical model that agreed with response measurements in the wind tunnel, data were not

available to establish their validity. One fact indi- cated that some factor was still missing in the

analysis. This fact was the observation that when

* This work was performed under Contract NAS8-5322,

from the National Aeronautics and Space Administration,

George C. Marshall Space Flight Center, Huntsville, Alabama.

** Figures in brackets indicate references at the end of this paper.

the Strouhal frequency and the model frequency were the same, thus giving very high response, the

observed motion of the model was approximately

periodic and nearly sinusoidal. The flow field parameter analysis computations gave a response of the

right magnitude, but with a narrow-band random

response that was not periodic.

Since the purpose of the flow field parameter

analysis is to predict vehicle response based on data

from a wind tunnel, it is very important that the

analysis correctly reflects the physical situation. An experimental program was then planned to

investigate the unsteady surface pressure around a

circular cylinder in two-dimensional flow. This

program was designed to obtain data on the unsteady pressure for a relatively simple flow condition.

To incorporate the unsteady pressure into the flow

field parameter analysis, it will be necessary to obtain additional data for the effect of three-dimensional flow (change of section and presence of the

tip of the vehicle) and for the effect of vehicle motion

on the unsteady pressure.

2. Nomenclature

Cp^ base pressure coefficient

Cd^, viscous drag coefficient q free stream dynamic pressure

Fp^p^{o}) power spectral density of pi

FpiPiM cross power spectral density of pi and p2

p unsteady pressure

(Tp standard deviation of unsteady pressure = RMS

87
o) frequency in radians/sec

D cjdinder diameter

U free stream velocity z axial distance coordinate on cylinder

6 angular position coordinate on cylinder

^ V(j:i-X2)2+3^(| 01-^0 I D)2= geodesic

distance between (a, ^i) and (j-2, ^2) on

surface of cylinder

5 Dirac delta function

3. Data Analysis

The experimental program used two tunnelspanning cylinders (10 in. and 2-i in. diameters) with

smooth and rough surfaces and with low and high

tunnel turbulence. It is then possible to produce

subcritical flow by using the smooth 10-in. cylinder

in a clean tunnel. Supercritical flow is produced

either by using a smooth 10-in. cylinder with a turbulence grid in the tunnel, or by using the smooth 24-

in. cylinder in a clean tunnel. Finally, transcritical flow is produced by using a rough 24-in. cylinder

with a turbulence grid.

The first regime to be analyzed was the supercritical Reynolds Number range. Examination of the RIMS unsteady pressure indicated a sharp peak

at the separation point, with a rapid and reasonably

symmetric drop in both directions. Figure 1 presents

the representation which was developed. Note that

the factor [9(1 •

is just the local free stream dynamic pressure at the

separation point. Next a representation of the power

0-10 inch Cylinder

- 24 inch Cylinder

(I-Cp,)q20 Co,

Normalized Standard Deviation

(|e|-e, |)'''^, e, = Seporatlon Angle

Figure 1. Normalized standard deviation of surface pressure on 10-in. and 24-in. cylinders in supercritical flow.

spectral density is obtained, as presented in Figure

2. Finally, a representation of cross-power spectral

density is obtained as shown in Figure 3. Note that

the representation is real. The data analysis showed

small imaginary components (phase angle <10 deg)

with no observable trends. Combining these results,

Eq (1) is obtained for the cross-power spectral

density of the unsteady pressure in supercritical

flow.

Fpip2(w; Xi, X2, 61, d'l) 2D

U

C(i- Cp,) q -200nJ

exp -2 (1^1-^. I)

1/2

,1/2

+

[Fp|p,(a,)] / [<r|| (2D/U)] , NORMALIZED POWER SPECTRAL DENSITY

(Reduced Frequency)

Figure 2. Normalized power spectral density of surface pressure on 10-in. and 24-in. cylinders in supercritical flow.

88
0), Radians /sec -

10 inch Cylinder -

24 inch Cylinder -

[|f>,P2M|]/[Fp|P|(w) Fp2P2

5.45 - 21.8 O - o -

43.6

O

O

174.5A

A

O- 10 inch Cylinder in Subcriticol Flow

- 24 inch Cylinder in Tronscritical Flow

(w)]'''^ Normalized

Cross. Power Spectrol Density

4 = Geodesic Distance between P| and pg. Figure 3. Normalized cross power spectral density of surface pressure on 10-in. and 24-in. cylinders in supercritical flow.

where

(j-l-^2)- +

do I -D

Next the data for subcritical and transcritical flow were analyzed. It had originall.y been intended to consider the regimes separately, but it soon became

evident that no qualitative difference could be found

between the two regimes. Examining the RMS unsteady pressure (and excluding the region around

the separation point where the random unsteady

pressure would be significant, it was seen that the

important variable was the local dynamic pressure. Figure 4 presents the representation of RMS unsteady pressure which was developed. Figure 5 presents power spectral density computations for the two regimes. It is obvious that the results are

essentially identical except for a difference in fre-

<rp|/(q 10 Cq^) ~ Normalized

Standard Deviation

0.5 1.0 5.0

(l-Cp) ~ Local/Free Stream Dynamic Pressure

Figure 4. Normalized standard deviation of surface pressure on 10-in. cylinder in subcritical flow and 24-in. cylinder in transcritical flow.

quenc}^, and that the principal component of the

signal has a bandwidth less than the analysis bandwidth of either the wideband or the narrow band

analysis. The technique developed in Chapter II of Reference 3 is then used to indicate the nature of the signal. Figure 6 presents the results. It is indi- cated that the signals are a combination of wide

band random with a strong periodic component,

with no discernible difference between the subcritical and transcritical regimes. It is interesting to note

that the oscillator response amplitude distributions

show the same characteristics as response of the

wind tunnel model. That is, when the oscillator fre- quency coincides with the Strouhal frequency the

amplitude distribution approaches a sinusoidal dis- tribution. Away from the Strouhal frequency, the

amplitude distribution approaches a Gaussian dis- tribution. Figure 7 presents plots of surface pressure time history for the two regimes. If allowance is made for the fact that the sampling rate per cycle

for transcritical flow is double that for subcritical

flow, the two signals have the same appearance. Note

that although the signals are periodic, they are not

sinusoidal.

Finally, when the cross-power spectral density at the Strouhal frequency is computed, the result is

89
extremely simple. All signals on each side of the

cylinder are in phase, and one side is just 180 deg

out of phase with the other (again within about

±10 deg). The correlation is essentially unity

(>0.95) for all signals. Combining these results with Eq (1), Eq (2) is obtained for the unsteady

surface pressure on a circular cylinder in two-dimensional flow. 2D

X,, X2, du 6,) = — L{l-CJq-20CnJ

• exp 1 1/2

+ (1 e,-ds 1)1/2+

.Ci-Cp(eO][i-Cp(02)]

.[,.ioc.jm(s-^)

where

(2)

7r<0<7r

Note that the range of d has set so the cross-power

spectral density of the periodic pressure has the

proper phase angle. Since S = 0 in the supercritical

flow regime, the periodic component vanishes in that regime but is otherwise present. It is interesting

to note, in this connection, that satellite pictures of

islands in ocean currents show a vortex system in the wake behind the island.

4. Comparison with Work Under Contract

NAS8-11277

Direct comparisons with the work under Contract

NAS8-11277 [4] are difficult since Reference 4 re- ports measurements of the unsteady aerodynamic

force on a segment of a tunnel-spanning cylinder.

However, qualitative comparisons can be made.

First, Reference 3 presents data indicating that the

Strouhal Number increases from 0.15 at J? = 2X10*^

to 0.3 at R = 7X10^ and then is constant at 0.3 at higher Reynolds Number. Reference 1, presenting

the original flow field parameter analysis, computes

a Strouhal Number for the Saturn V model which

Note: Amplifier Gain Adjusted to Give Approx. 0.2 Volt Signal RMS to IVlinimize Error

in Digitizing

24 inch Cylinder — - Wide Band ( 600 Samples of Signal)

- —O -Narrow Band (4000 Samples of Signal)

POWER SPECTRAL DENSITY

(Volt)2- sec/Radian

10 inch

Cylinder

O —

A

0.00010

0.00001

FREQUENCY, cps Figure 5. Effect of bandwidth on computed power spectral

density of surface pressure signal for 10-in. cylinder in subcritical flow and 24-in. cylinder in transcritical flow.

is 0.14 at ie = 3X10^ increases to .30 at = 7X106,

and is approximately constant at higher Reynolds

Numbers.

Second, Reference 4 interprets the observed data

to indicate a wide-band random aerodynamic force

in the supercritical range, a narrow-band random

force in the low transcritical range, and finally a

periodic plus random force in the high transcritical range. The flow field parameter analysis, [1], as- sumed a wide-band random force in the supercritical

and a narrow-band random force in the transcritical Reynolds Number range. The present results indi- cate that the aerodynamic force is wide-band random

in the supercritical range, and random plus periodic

in both the subcritical and transcritical Reynolds

Number regimes. Comparisons with the conclusions

90
10 inch Cylinder SURFACE PRESSURE SIGNAL, Volts Acceleration of Wide Band Oscillotor (600 Samples of Signal, Ca^ 1.0 1) A Acceleration of Narrow Band Oscillotor (4000 Samples of Signal, Ca= 1.00)

24 inch Cylinder Acceleration of Wide Bond Oscillator (600 Samples of Signal, C8= 0.943)

O Acceleration of Narrow Bond Oscillator (4000 Samples of Signal, C8=0.97)

NOFSVIALIZED EIGHTH MOMENT COEFFICIENT

FREQUENCY, cps

2 3 TIME, seconds

Figure 7. Time history of surface pressure signal for 10-in. cylinder in subcritieal flow and 24-in. cylinder in transcritical flow.

Figure 6. Effect of bandwidth on amplitude distribution of

acceleration of oscillator driven by surface pressure signal for 10-in. cylinder in subcritieal flow and 24-in. cylinder in transcritical flow.

of Reference 4 concerning the motion dependence

of the force and the presence of negative aerodynamic

damping cannot be made until measurements of un- steady surface pressure on a moving model can be

performed.

5. Conclusions

An extremely simple representation of the cross power spectral density of the unsteady surface pres- sure on a circular cylinder in two dimensional flow

has been developed that is a reasonable approximation to measured data. The most important result is

the essential similarity between the subcritieal and

transcritical Reynolds Number regimes.

6. References

[1] Peterson, H. C. and W. E. Simon: Investigations Relative

to Wind Induced Oscillations of the Saturn Boosters in the Vertical Launch Position (1 June 1963 thru 30 June 1961i.), September 1964.

[2] Simon, W. E., C. R. Howard, and H. C. Peterson:

Investigations Relative to Wind-Induced Oscillations of Saturn Boosters in the Vertical Launch Position. Annual

Report, Contract NAS8-5322, March, 1967.

[3] Simon W. E. : Investigations Relative to Wind-Induced

Oscillations of the Saturn Boosters in the Vertical Launch

Position. Final Report, Contract NAS8-5322, March,

1968.

[4] Cincotta, J. J.: Experimental Investigation of WindInduced Oscillation Effects on a Circular Cylinder in Two

Dimensional Flow. Contract NAS8-11277 (no date).

91

ON THE RELIABILITY OF GUST LOADING FACTORS

Barry J. Vickery

Faculty of Engineering Science

University of Western Ontario

London, Ontario, Canada

The accuracy of the simpHfied gust factor approach to the determination of wind loads is examined. An expression for the gust factor is derived which treats the scale of turbulence, mode

shape of vibration, and parameters defining the vertical and crosswind cospectra as variables. The method formulated in this paper differs from previous methods primarily in the size reduction

factor and in the form of the spectrum of velocity fluctuations. Predicted values of gust factors are compared with those observed on eight different aeroelastic models tested in a boundary layer

wind tunnel. The gust factor relates only to overall loads in the mean wind direction. Where basic data are well defined, the ratio of expected peak values of wind-induced stress or deflection to their average values can be predicted to an accuracy of typically 5 percent to 10 percent.

Key words: Buildings; dynamics; gust factor; mode shape; probability theory; wind loads.

1. Introduction

While the dynamic action of wind on tall buildings, towers and other structures has been of some concern to structural engineers for many years, there

have been few references to this action in the various

building codes. This omission can be explained, in part, by the absence of comparatively simple

analyses or rules which would provide a reliable in- dication of the severity of dynamic action. Attempts

to formulate such a set of rules have recently been

made by Davenport [1],* Vickery [2], and Vellozzi

and Cohen [3]. The aim of all three of these attempts

has been the definition of a "gust factor" to be applied to the steady wind forces in order to account

for dynamic action.

It is the object of this paper to examine the ac- curacy of the simplified "gust factor" approach to the assessment of wind loads. In Section 2, an ex- pression for a gust factor is derived. The formulation

of the gust factor is similar to that presented by

Davenport [1] but an endeavor has been made to reduce the necessary simplifications to a minimum.

The parameters involved in the computation of the

gust factor are more flexible than those adopted by

Davenport and allow the user to take advantage of meteorological data which might be available for a

particular site. The scale of turbulence, the parameters defining the vertical and cross-wind cospectra

and also the shape of the mode of vibration are

* Figures in brackets indicate literature references at the end of this paper.

treated as variables. In previous formulations of a gust factor, these quantities have been assigned

specific values. In Section 3, the validity of the basic assumptions

used in the derivation are examined in the light of recent experimental data obtained from both models

and full scale structures. The experimental data are employed to obtain a measure of the accuracy of the gust factor approach when used in conjunction

with well defined meteorological, aerodynamic, and

structural parameters. The loss of accuracy associ- ated with the use of available meteorological data,

which may often be poorly defined, is examined in Section 4. A comparison of gust factors computed by the

methods proposed by Davenport, Vickery, and

Vellozzi and Cohen with those computed in accord- ance with this paper is presented in Section 5.

2. Derivation of a Gust Factor for a Linear

Elastic Structure in Turbulent Shear Flow

The analysis which follows is based on numerous

assumptions and simplifications, these are identified

in the analysis and in subsequent sections; the

major points will be examined more closely. The

basic assumptions on which the analysis is based are

as follows:

(a) The load per unit area, projected on a plane

normal to the mean wind can be expressed in the form,

q{y, z) =Cp(y, z)p - {y, z)

93
in which

Cp{y, z) is a pressure coefficient,

u{y,z) is the instantaneous velocity at {y, z) in the absence of the structure.

(6) The response of the structure in the fundamental mode is dominant for both mean and

fluctuating deformations.

(c) The intensity of turbulence, V'^/ti, is much

less than unity and terms of order u'V^^ may

be neglected.

{d) The wind velocity fluctuations constitute a

stationary random process and are distributed

according to the normal error law (Gaussian)

.

The generalized force Q for the fundamental mode

of vibration may now be expressed in terms of its mean and time dependent components. If n{y, z) is the fundamental mode shape and u{y,z), u'{y,z)

the mean and time dependent components of the

"along-wind" velocity, then the mean force may be

written as: Q=

J

Cj,(y,z)p— {y,z)fiiy,z) dA (1)

and the time dependent component as

:

Q'= j

Cp{y, z)puiy, z)u'{y, z)n{y, z) dA (2)

The spectral density function (*Sq(/)) of Q' may

be expressed as

:

Sq = pW jjSuiyiZiy2Z2f)iiyiZi)\l/{y2Z2) dAi dAi (3)

in which

\piy, z) =Cp{y, z)p.{y, z) u{y, z) Uo

where Uo is a reference velocity and SuiyiZiy-iZif) is the cross-spectral density function of the fluctuating

along-wind components of velocity at {yi, zi) and

(2/2, 22) • In order to reduce the expression for Sgif) to a form suitable for the derivation of a gust factor,

certain simplifications and restrictions are necessary. The simplifications to be made at this stage are as follows

:

(e) The structure is free-standing with a fundamental mode shape that is adequately ap- proximated by power law variation in dis- placement from zero at the base to a

maximum at the tip, i.e. niy, z) =

Khj

if) The projected area of the structure is rec- tangular in shape with a height h and breadth

b.

(g) The mean velocity is a function of z only and

can be expressed in the form,

ujz) _ u{h) \h (4)

(h) The cross - spectral density function,

SuiyiZiyiZif), can be expressed in the form:

{yiziy^zif) =Su{f) -Riyiy^ziZif)

in which,

Suif) is the spectral density function of u' and is invariant with y and z, (^) The function RiyxyiZiZif) can be expressed

in the form:

^= exp , (5)

}i{u{zi) -j-u{z2)

)

in which Cy and Cz are constants, invariant with y and z. (j) Cp{y,z) is constant over the structure and

equal to Cd where:

(6)

2) dA

The spectral density function »Sq(/) may then

be expressed as follows:

2(l-|-;8+a)J u'^ih)

in which.

- F V(2i-22)2+A2(2/i-2/2)2'

exp

K(2l« +22«)

dyi dy2 dzi dz2

)

(8)

and

Cyb CJH

CM ' u{H)

94
The function x^(^, ^) is also a function of the

power-law exponents a, ^ but the variation with a

and |8 about average values of these quantities is small and may be ignored. The function has been

computed by numerical integration and is presented

in Figure 1. For the limiting cases of and

the function can be evaluated analytically:

(9)

,.(^»l,X).2..1|il±^l (10) ^ ^ ' ' X [l+2(8+4a J

^ '

The mean deflection of the structure dfi{z) and

the root-mean-square deflection \/a''^'n{Z) may be

expressed as follows

:

1

(l+/3+«)

CDP bh 2-iif (ii;

u{H)

{f^ SJif) \H{f) l^xHF, \)df

1/2

(2x/„)2.M

(12)

in which,

M= \ m\z)y}{z) clz

m{z) = mass per unit height

fo= natural frequency of vibration

1 H{f) \' =

rj= damping ratio (fraction of critical).

The ratio of the RMS value to the mean value

(the coefficient of variation) of the response is then,

VP l+i8+2a 2\/¥^

a ~ u{h)

• II

SJif)- \Hif) \^ 'x'{F,\) df^ (13)

The integral with respect to frequency can conveniently be approximated by the following

expression

: r SJif)- \H{f) l^x'iF, X) df

'o

= r sj{f)x'{F,x) df

•'o

+SJ{fo) ~x'{Fo,X) (14)

4:71

in which,

fo = natural frequency,

Fo = CJoh/uih).

The form of SJif) after Davenport [4] is:

2 fLjh) Ljh)

3

" ilih)' u{h)

Su'if)

1 + (

f-L{h) V]

\ u{h) J I

(15)

4/3

in which L{h) is a length scale and is equal to \/3

times the wavelength which the function /•!§„'( /)

is a maximum. Davenport originally suggested that

L(h) =4000

ujh)

u{33) '

however, there are advantages in retaining the more

flexible form of Equation 15. If a reduced frequency

n =

fLjh)

u{h)

is introduced, then Equation 15 may be re-written

as follows:

a I l+^+a u{h)

|2 /•* n

1 1 1/2 - -xKFo, X) V

= r {B +

S-F 1/2 (16)

where

l+/3+2a 2u'' }= • —-- (roughness factor) l+0+a u{h)

95
= Function {terrain roughness, building height

mode shape}

S = x^{Fo, X) {size reduction factor}

Function

Czfoh Cyh

u{h) ' Czh

F =

6 (l +no2)*/3 [gust energy factor}

Function

B= Function

'foL{h)

u{h)

^Czh CyB

(Background

[L{h) CzH] excitation factor)

The parameters S, B, F and r have been computed

and are presented in Figures 1 to 4. A gust factor G is defined as the ratio of the ex- pected peak value of displacement in a period T to

Figure 1. Size reduction factor "S."

foL(h)/iIlh)

Figure 3. Gust energy factor "f."

HEIGHT ABOVE GROUND - FEET (h)

Figure 4. Suggested values of

the mean value. The gust factor may now be written

as:

G = l+gT \B+ SFy

n J (17)

in which ^ is a "peak factor" and is equal to the ratio of the expected maximum value of the dynamic dis- placement to the root-meaii-square value of dynamic displacement. Davenport [5] has derived

the relationship:

(j==V2 logevT+

0.577

V2 log. vT

(18)

ff is the average or expected value (over a large

number of periods each of duration T) of g, the

ratio of the maximum to root-mean-square values

in each period of duration T. The standard deviation

of g has also been derived by Davenport and is

:

r/V6

V2 loge vT

(19)

Figure 2. Backround factor "B."

In Equations IS and 19, v is the equivalent fre- quency and is given by the relationship:

96
fs{f)-fdf

p'= (20)

r sif)df

•'o S{f)= spectral density function of the dynamic

response. Equations (18) and (19) are valid only for large

values of vT, for lightly damped low frequency

structures the value oi pT is not sufficiently great

(for T'~20 min. say) and the use of Equations (18)

and (19) will result in an overestimate of g and

underestimate ag. In the work which follows, it will be assumed that

g is equal to 3.5. The value of 3.5 is, on average,

slightly conservative; for values of T between 10

and 30 minutes and for a wide range of structures g

will usually lie between 3.0 and 3.7.

3. Experimental Confirmation of Gust

Factor Computations

Basic to the derivation of a gust factor is the as- sumed relationship between pressure and velocity. In Section 2, it is taken that the force per unit

projected area is proportional to momentum flux

(in the absence of the structure). In detail this as- sumption is far from adequate, however when the concern is with total effects (e.g. total force on a

building) many of the inadequacies in detail vanish

during the integration. Pressure measurements on

both model [6, 7] and full scale [8] buildings in turbulent shear flow indicate that both mean and

fluctuating pressures on the windward face do reflect the variations in momentum flux. This is particularly true away from the edges of the face; near both

the side and the top edges there is a reduction in both the mean and the fluctuating components of pressure. Measurements of the spectrum of the

pressure fluctuations on the windward face have

shown [8], on both model and full scale structures,

the same form as that observed for the velocity

spectrum. In general, the pressures on the leeward

face, and on side faces, do not reflect the variations

in momentum flux but are more or less uniform.

Although this latter feature is a major departure

from the basic assumption, these wake pressures do

not contribute markedly to the total force on a

building. Field observations [8, 9] on buildings in a

city environment indicate that the load on the lee- ward face is less than 10% to 20% of the total load. This proportion would undoubtedly be higher for

tower-like structures with b/h ratios substantially

less than the values of 0.4 and 1.6 applicable to the

structures examined in references [8] and [9]. The

wake pressures for very slender structures will, however, reflect the bulk of the turbulent velocity

fluctuations; this has been observed in model studies

of a very slender taperod stack but the results are as yet unpublished.

3.1. Experimental Determinations of the Size

Reduction Factor, S

The adequacy of the pressure/velocity assumption, in so far as it influences the computation of a

gust factor, is best examined by a comparison of ex- perimental and predicted values of the size reduction factor S. Measurements of this quantity, to- gether with the predicted values, are presented in Figure 5. Three sets of measurements are presented;

the most complete of these is that obtained by

wind tunnel studies and described elsewhere [10]

in some detail. This set of measurements was obtained from plates and prisms of various aspect

ratios, the hatched area in Figure 5 indicates the

spread in the observations. The remaining two sets of data are from measurements in the atmosphere

and are described in references [11] and [12]. The

set described in reference [12] was obtained from

observations of the fluctuating loads on three mesh

targets with areas from 20 ft^ to 60 ft^ and mounted

about 40 ft above ground. The remaining results were obtained from measurements on a building in an urban environment; unfortunately, the atmospheric conditions existing for this set were poorly

defined and the results must be regarded with some

degree of suspicion.

Figure 5. Comparison of experimental and theoretical values of the size factor "S."

97
The predicted values of S are in reasonable agree- ment with the wind tunnel observations, the atmospheric results show similar trends but are limited

and, unfortunately, of doubtful value. The most

significant values of S are those corresponding to excitation at the natural frequency of vibration.

For most structures such excitation will correspond

to values of

u \CzhJ

in the vicinity of lOitS. Within this range it would

appear that the predicted values of S will be within

±30% of the true value. While this may appear to be an excessive discrepancy the error induced in a

predicted gust factor would generally be from 5%

to 10%.

3.2. Experimental

Parameter B

Determinations of the

The background excitation factor B is largely

dependent of S and, hence, on the assumed load/

velocity relationship. Predicted and measured values

of \/B are presented in Figure 6; the experimental

measurements are described in detail elsewhere

[10, 13]. The results were obtained in wind tunnels

PREDICTED VALUES OF 1^

Figure 6. Comparison of observed and predicted values of Vb.

and on a wide range of models of different cross- sectional shapes and aspect ratios. In all, 45 models

were tested and the average value of the ratio Vbpredicted Vbobs- was 0.98 and the standard deviation of this ratio, 0.18. This deviation would result in errors of typically 5% to 10% in predicted gust factors.

3.3. Experimental

Factor

Measurements of Gust

A direct measure of the reliability of gust factors can be obtained from a comparison of predicted

values with those observed on model structures tested in a boundary layer wind tunnel. The shapes

of eight aeroelastic models that have been studied

in the Boundary Layer Wind Tunnel Laboratory of The University of Western Ontario are shown in Figure 7. The experimental observations for models I to VI are reported in reference [6] and the observations for models VII and VIII in reference [7] and

reference [14] respectively. The structure of the

flow in the boundary layer wind tunnel is also described in these three reports and is summarized

in Table 1. The predicted and observed gust factors for Models I to VI are presented in Table II. Also in- cluded in this table are observed values of a lateral gust factor, this factor is the ratio of the peak lateral response in direction XX, (i.e. with wind along YY)

to the mean drag response in direction XX. There

are no predicted values of lateral response since, at

f LEVATION MODELS T 10 V!

MODEL VII

Figure 7. Elevations and cross-sections of models studied in B.L.W.T.

98
Table I. Properties of turbulent shear flow in boundary layer wind tunnel

Urban Open

exposure exposure

Approximate height of roughness elements U.25 It. U.Ul It. Thickness of boundary layer 4 it. 2.5 ft. Mean velocity profile (exponent a) - 0.36 0. 15 Turbulent intensity a,tz = 2.0ft.,. 0.14 0.10

L{z) at 2 = 2.0 feet 14 ft. 10 ft. C. ==^10 2^10

Cy c^l2 c^l2

present, no adequate theory exists. It will be noted

that in six of the eighteen tests, the lateral response

exceeds the predicted drag response and in each in- stance the reduced velocity was the higher of the

two velocities examined. The two velocities corre- spond to approximately 65 mph and 120 mph at prototype scale. Neglecting the lateral response, the observed and predicted gust factors are in satis- factory agreement. The ratio of the predicted to the

observed values has an average of 1 .04 and a standard deviation of 0.05. The predicted and observed gust factors for Model VII are presented in figures 8 and 9. All results

refer to the response along the YY axis or normal

to the broader face of the model, gust factors were

obtained for both urban and open exposures. In Figure

8 the variation of gust factor with total damping is presented while in Figure 9, the gust factor is shown

as a function of wind speed. The agreement between

the predicted and the observed gust factors is satis- factory and the dependence of the gust factor on

both wind speed and damping is clearly demonstrated. The lateral gust factor is the more sensitive

to both damping and wind speed.

The gust factors for Model VIII, a tapered stack

of circular cross-section, are shown in Figure 10. In

this case two predicted values of gust factor are shown, one of these is that derived from the gust

factor equation and the second is the result of a more complete analysis which accounts for the true mode shapes and for contributions from modes other

than the fundamental. The two predicted values

differ only slightly and both are in satisfactory

agreement with the observed values. The results presented in Figures 8, 9, 10 and in Table II cover, in all, 34 evaluations of the gust

factor. The range of variables is wide and includes a

variety of cross-sections, aspect ratios from 3 to

20, two conditions of exposure and values of structural damping from 0.001 to 0.02. The average

ratio of the predicted to the observed gust factor is 1.02 and the standard deviation 0.07. The standard

Table II. Measured and predicted gust factors for models I to VI (urban exposure)

Model Line of response u{h)/n\/A CpRED GDBS (?PRED GoBB

<?LATERAL

I YY 7 0 2 48 2 55 0 97 1.53

3 8 2 17 2 39 0 91 1.14 XX 7 0 3 02 2 62 1 15 *4.94

3 8 2 45 2 35 1 04 2.36

II YY 7 0 2 44 2 40 1 02 1.99

3 8 2 13 2 03 1 05 1.65

. XX 7 0 2 61 2 33 1 12 1.58

3 8 2 21 2 12 1 04 0.82

III XX & YY 7 0 2 83 2 63 1 08 *3.64

3 8 2 33 2 12 1 10 1.52 IV XX & YY 7 0 2 75 2 64 1 04 *4.47

3 8 2 29 2 29 1 00 1.71 V YY 7 0 2 65 2 64 1 00 *3.08

3 8 2 24 2 08 1 08 2.00 XX 7 0 2 73 2 73 1 00 *3.32

3 8 2 30 2 24 1 03 1.38 VI XX & YY 7 0 2 77 2 77 1 00 *3.93

3 8 2 28 2 18 1 05 1.57

A'rerage: 1 .04±.05

99
PREDICTED GUST FACTOR"] OBSERVED GUST FACTOR^DRAG

OBSERVED (LATERAL)

URBAN EXPOSURE

MODEL Vil

.010 _J.015 _J.020 _1

025 _J TOTAL DAMPING C/C,

(C/Cr), = .0044 ^ Aero

OBSERVED GUST FACTOR

PREDICTED GUST FACTOR

OBSERVED (LATERAL)—'

OPEN EXPOSURE

MODEL Vn

.005 ,010 .015

I I .020

I TOTAL DAMPING C/C^

Figure 8. Variation of gust factor with damping.

deviation is in agreement with that (ieduced from

the earlier comparisons of experimental and pre- dicted values of the parameters S and B.

4. The Reliability of Gust Factor Estimates in

Relation to The Adequacy of Meteorological

and Other Data

The reliability or accuracy of an estimate of a

gust factor is dependent firstly upon the adequacy

of the theory and the basic assumptions on which

this is founded and, secondly, the accuracy or reli- ability of the data (meteorological, aerodynamic and

structural). The adequacy of the theory has been

examined in the previous section; under controlled

test conditions with reliable data the theory leads

to estimates of the gust factor which are generally

within 10% of observed values. The use of the gust

factor to predict the response of a proposed struc- ture to atmospheric winds involves data which, in many instances, is poorly defined. It is intended to determine the relationship between the accuracy of an estimate of a gust factor and the accuracy of the

MODEL VII

-OBSERVED (LATERAL) URBAN EXPOSURE

(C/Cc);,, = 0.01

120

I I GRADIENT WIND SPEED mph

MODEL VII

GRADIENT WIND SPEED mph

Figure 9. Variation of gust factor with wind speed.

PREDICTED (GUST FACTOR EO'N) PREDICTED ( "EXACT" ANALYSIS ) BSERVED

OBSERVED (LATERAL)

WIND SPEED AT TIP — FT/ SEC

Figure 10. Observed and predicted gust factors for a model

tapered stack of circular cross-section.

data, or the independent variables of which it is a

function. In the derivation of a gust factor presented

in Section 2, it is shown that the gust factor can be

expressed as follows:

i, Lih), V, Cz, Cy/Cz, 0,fo, r,)

in whicha = power law exponent of mean velocity

profile,

i= intensity of turbulence,

L{h) = a length proportional to the scale of turbulence.

100
a coefficient representing the variation in the dimensionless spectral density function at a given frequency about some as- sumed value of the spectral density, i.e., S{fo) =vSaifo) where S(fo) is the true

spectral density function at a given site, and Saifo) is the assumed value determined in accordance with, say, the suggestions of Davenport.

a coefficient (defined in Section 2) related

to the vertical scale of a turbulence component of a given wavelength.

Cy/Cz = the ratio of the horizontal to the vertical

scale coefficient. i8= the power law exponent of a curve ap- proximating to the mode shape of the

fundamental mode of vibration,

the natural frequency of vibration of the

fundamental mode.

the total damping, expressed as a fraction

of critical.

fo =

1 =

None of the nine independent variables can be

defined with complete confidence. It is difficult to assign an accuracy with which any one variable can

be estimated for a given site and structure, but from

a survey of existing data the writer suggests that

reasonable values of the coefficient of variation for each variable would be as shown in Table III.

Table III. Estimated coefficients of variation

Variable

I

VC._.. Cy/C

/o—

.

ri

Estimated coefficient of variation

0.10

0.20

0.20

0.15 0.15

0.25

0.10 0.10

0.25

The values suggested in Table III are estimates

only. In quoting values for the coefficients of variation of /3 and /„, it is assumed that the estimates of

13 and /„ have resulted from an analysis of the particular structure rather than some empirical rela- tionship (such as /o~10/A'', N= 'No. of stories).

The coefficients of variation of a, i, v, Lz, C,, and Cy/

Cz. are estimates based on the scatter observed in measurements of these quantities obtained over

similar terrains and at similar heights. The coeffi- cient of variation in the damping parameter (77) is based on the scatter of field measurements obtained

for similar types of structure, e.g. the scatter in measurements on concrete chimneys or the scatter

for steel structures. In the case of most of the vari- ables involved the number of field measurements

available is very limited and the assigned coeffi- cients of variation are largely subjective rather than

the results of rigorous statistical analysis.

The coefficient of variation of a gust factor Go determined by values of the independent variables

{a = ao, i = io etc.) can be expressed as.

in which

OCo (dG\

io (dG\

etc.

and Ca, Ci, etc., are the coefficients of variation of

a, i, etc The weights w^^, w,^ etc. and the resulting value of Cgo have been computed for three structures and the

results are presented in Table V. The three structures

. examined range from a comparatively stiff structure

for which resonant effects are negligible to a tall lightly damped structure of low natural frequency

and a dynamic response dominated by resonance. The properties of the three structures and the rele- vant meteorological data are presented in Table IV. For all three structures it is apparent that ac- curacy depends largely on the specification of tlie intensity of turbulence. In the structure "A," for which resonant effects are small, the errors intro- duced by poorly defined data are due almost entirely

to the definition of the intensity of turbulence. As

the contribution of resonant effects increases, the

influence of other parameters is of increasing importance. The specification of Cz, Cy/Cz, v, L{h)

and fo are of approximately equal importance while

the specification of damping is somewhat more

significant. In no case is the gust factor particularly

sensitive to the choice of the mode shape or the mean velocity profile. The coefficient of variation

associated with the variability of data is approximately 0.10 and, as could be anticipated, increases

with an increase in the relative significance of reso- nant effects.

101
Table IV. Structural and meteorological data

Description

u.(H)...

Exposure

B

H

fo

ria

Vifo) —-

CzCb/Cz - - g

rB

SF/r,.,..

G

Structure

"A"

R.C. framed

apartment

block

100 ft/sec--_

Suburban

150 200

1.0 0.6 cps 0.020

0.25

0.15 6,400 ft

110

1.6 3.5 0.33 0.70 0.085

2.04

"B"

R.C. frame

office block

120 ft/sec City

150 600

1.0 0.2 cps-..

0.02

0.36

0.14 10,000 ft. 110

1.6 3.5 0.32

0.68

0.48

2.21

"C"

Steel frame

office block

150 ft/sec City 200

1,200

1.0 0.08 cps 0.015

0.36

0.11 18,000 ft

110

1.6 3.50 0.25

0.68

1.84 2.42

Table V. Coefficients of variation of gust factor estimates for structures A, B, & C

Structure "A" Structure "B" Structure "C"

Variable 100 100 100 X X X

C 03 coC CO coC u wC

a 0.10 0.05 0.5 0.06 0.6 0.06 0.6

i. .15 .51 7.7 .54 8.1 .56 8.4 Lz .20 + .03 0.6 -0.4 0.8 -.13 2.6

V .15 .03 0.5 .11 1.7 .20 3.0 Cz .15 -.09 1.4 -.20 3.0 -.18 2.7 Cy/Cz---- .25 -.05 1.3 -.08 2.0 -.08 2.0

13 0.10 -.02 0.2 -.03 0.3 -.03 0.3

fo 0.10 -.04 0.4 -.21 2.1 -.29 2.9

V 0.25 -.03 0.8 -.11 2.7 -.21 5.3

2a)2C2 64X10--4 95X10-" 135X10-"

Coefficient

of Variation of G 0.08 0.10 0.12

5. A Comparison of Gust Factors Computed

by the Various Proposed Methods

Gust factors have been computed for three structures, in open and urban terrain and for two values

of structural damping. The properties of the buildings and the flow conditions are presented in Table

VI. The computed values of the gust factor are presented in Table VII. In order to maintain uniformity the "peak factor" g has been taken as 3.5

in all computations. The wind speed chosen in each

case corresponds to a gradient wind speed of ap- proximately 150 ft./sec. The gust factors computed in accordance with

Section 1 of this paper will be taken as reference

values and nominally correct. The gust factors as computed by the method of Davenport are, on

average, low by 5% while those computed by the

method of Vickery are, on average, 5% high. In view

of the accuracy estimates of the previous sections

these discrepancies are barely significant. It should

be noted that in neither case are the methods employed and attributed to Davenport and Vickery

identical with those proposed in reference [1] and

[2J. A modified form of Davenport's original pro- posal was prepared for studies conducted in connection with the Building Code of Canada and it is this modified form that has been adopted. A modified

form of Vickery's proposal has also been adopted,

this modified form will be published as part of a

discussion [15] on the paper by Vellozzi and Cohen

[3].

The gust factors computed by the method pro- posed by Vellozzi and Cohen are, on average, 17%

low while for the larger structures the discrepancy

is approximately 25%. This discrepancy is highly

significant and can be attributed to the size reduction

factor used by Vellozzi and Cohen. Vellozzi and

Cohen evaluate the size reduction factor in a manner

similar to that used in Section 2 of this paper but

compute the correlation integral over a rectangular

prism rather than a plane rectangle. The depth of the prism is taken as four times the least dimension

of the frontal rectangle. The argument put forward

in support of this approach is that a gust must

envelop a large portion of the wake before it becomes

fully effective. This may well be true in regard to wake pressures but not in regard to the more signifi- cant pressure fluctuations on the front face of a

building. In comparison with experimental observations the size reduction factor proposed by Vellozzi

and Cohen is a severe underestimate.

The differences between the methods proposed in references [1] and [2] and that proposed in this paper lie primarily in the size reduction factor and

the form of the spectrum of velocity fluctuations.

These differences are discussed in a contribution to the discussion on the paper by Vellozzi and Cohen.

Although the differences are quite substantial it

102
Table VI. Gust factors for 3 buildings

Building 1 Building 2 Building 3

TTpio-ht 150 500

150 200

f 1 . 0 cps 0.2 cps 0.01, 0.02 0.01, 0.02 n ni n 09 P 1 \

'

1 'offQ in TTPRATVr Ur JdiiN U xtUAiN UrlLIN TIPBAN

U . oO n 1

U . 11 U.oO U . 14 0.35 0. 14

\ /ii(h'\ U . 10 nil U . 1

0 12 0.93

in in lU lU 10 10

ID 1

10 1 A10 16 16

Li(n) T <h\ (ft ^ (11.) 6,500 5,000 10 , 000 6,000 14 000 6 500

nttnl ft /ciai^ 65 110 95 130 130 150 r^h /T.(h\ 0.23 0.30 0.50 0.83 0.85 1 .85

y^z Jon/ u\n) lO . 0

1 o ^ 7 7 9.2 8.0

1.6 1.6 0.64 0,64 0.27 0.27

]oLi\h)IU 100 45 21 9.2 10.7 4.3

U . 00 U . o/ 0.28 .201 R 0.71 0.67 0.68 0.60 0.64 0.51 s .010 .025 .026 .101 . 140 .330 F .024 .039 .068 .117 .107 .185

OOd. 00^; .005 .006

g 3.5 3.5 3.5 3.5 3.5 3.5 SF— ,(r,, = .01) V .022 .081 .126 .79 1.00 3.81 — (vs = .02) V .011 .044 .074 .47 0.60 2.35

1 SF

G = l+ gryjB + — 2.67 1.83 2.16 1.97 2.26 2.45

vs = 0.01

Vs = 0.02 2.66 1.83 2.12 1.88 2.09 2.18

Table VII. Comparison of computed gust factors

Basis of calculation TERRAIN DAMPING

Section Davenport Vickery Vellozzi & Cohen

2 ref. (1) ref. (2) ref. (3)

1 Urban . 0.01 2.67 2.57 2.87 2.59

0.02 2.66 2.57 2.82 2.59 Open -

0.01 1.83 1.74 1.85 1.72 0.02 1.83 1.72 1.82 1.72

2 Urban 0.01 2.16 2.28 2.39 1.80 0.02 2.12 2.10 2.28 1.80 Open . 0.01 1.97 1.93 2.13 1.56 0.02 1.88 1.78 1.97 1.54

3 Urban . . 0.01 2.26 2.48 2.44 1.63 0.02 2.09 2.08 2.23 1.61 Open 0.01 2.45 2.03 2.44 1.58 0.02 2.18 1.95 2.17 1.52

103
would appear, from the results presented in Table

VII, that their influence of the gust factor is, on

average, quite small. There could well be, however,

circumstances in which this would not be the case. In particular, the method proposed by Davenport

results in relatively large estimates of the contribution by resonance and underestimates of the background effects. This change in the distribution is of significance with respect to estimates of acceleration

which depend more on resonance than on the background excitation.

6. Conclusions

(i) The ratio of expected peak values of wind

induced stress of deflection to their average values can be predicted by the use of a gust factor to an

accuracy of typically 5% to 10%.

(ii) The gust factor relates only the overall loads

in the direction of the mean wind. Lateral loads or

local pressures are not predictable by the gust

factor.

(iii) The method is suitable only for free standing

structures and should not be applied to such struc- tures as guyed masts or suspension bridges.

(iv) The accuracy or reliability quoted above

applies only in instances where the basic data are well

defined. When used in conjunction with data nor- mally available at any given site the accuracy of the

gust factor will be typically 10% to 15%.

7. References

[1] Davenport, A. G., "Gust Loading Factors." J. Struct. Div., Proc. A.S.C.E., Vol. 93, No. ST3, June 1967.

[2] Vickery, B. J., "On the Assessment of Wind Effects on

Elastic Structures." C.E. Trans., Inst. Aust., pp. 183-192.

[3] Vellozzi, J., and Cohen, E., "Gust Response Factors."

J. Struct. Div., Proc. A.S.C.E., Vol. 94, No. ST6, June

1968.

[4] Davenport, A. G., "The Spectrum of Horizontal

Gustiness Near the Ground in High Winds." Quart. J., Roy. Met. Soc, Vol. 87, 1961.

[5] Davenport, A. G., "A Note on the Distribution of the Largest Value of a Random Function with Application to Gust Loading." Proc. I.C.E., Vol. 28, pp. 187-195, June 1964.

[6] Davenport, A. G., and Isyumov, N., "A Wind Tunnel

Study for the United States Steel Building." Eng. Sc. Res. Rep. BLWT-5-67, The University of Western

Ontario, November 1967.

[7] Davenport, A. G., and Isyumov, N., "A Wind Tunnel

Study for a Proposed 53 Story Building for the SeattleFirst National Bank Building." Eng. Sc. Res. Rep.

BLWT-1-67, The University of Western Ontario, 1967.

[8] Dalgliesh, W. A., Wright, W., and Schriever, W. R., "Wind Pressure Measurements on a Full Scale High-Rise

Office Building." Paper No. 6, Wind Effects on Buildings

and Structures, University of Toronto Press, 1968.

[9] Newberry, C. W., Eaton, K. J., and Mayne, J. R., "The

Nature of Gust Loading on Tall Buildings." Paper No.

15, Wind Effects on Buildings and Structures, University

of Toronto Press, 1968.

[10] Vickery, B. J., "A Model of Atmospheric Turbulence for Studies of Wind Loads on Buildings." Proc. 2nd. Aust. Conf. on Hyd. & Fluid Mech., Aukland, N.Z., 1965.

[11] Smart, H. R., Stevens, L. K., and Joubert, P. N., "Dynamic Structural Response to Natural Wind."

Paper No. 22, Wind Effects on Buildings and Structures, University of Toronto Press, 1968.

[12] Van Koten, H., "Wind Measurements on High Buildings

in the Netherlands." Paper No. 25, Wind Effects on

Buildings and Structures, University of Toronto Press, 1968.

[13] Vickery, B. J., "Load Fluctuations in Turbulent Flow."

J. Eng. Mech. Div., Proc. A.S.C.E., pp. 31-46, Vol. 94, No. EMI, Feb. 1968.

[14] Vickery, B. J., and Davenport, A. G., "The Response to Wind Load of a 1200' R.C. Stack for the American

Electric Power Service Corporation." Eng. Sc. Res. Rep.

BLWT-4-68, The University of Western Ontario,

August 1968.

[15] Vickery, B. J., "Discussion on 'Gust Response Factors' by

Vellozzi, J., and Cohen, E." To be published, Proc. A.S.C.E., J. Struct. Div.

104
SESSION 4.

RECENT ADVANCES IN DESIGN PROCEDURES

AND CURRENT DEFICIENCIES

Chairman: Mr. Edward Cohen

Ammann & Whitney

New York, New York 10011

THE TREATMENT OF WIND IN THE DESIGN OF VERY TALL BUILDINGS

Leslie E. Robertson and Peter W. Chen

Skilling, Helle, Christiansen, Robertson

New York, New York 10017

This paper describes briefly some highlights of a study of the wind effects for the design of the United States Steel Office Building in Pittsburgh, Pennsylvania. Throe types of models were

used in a boundary layer wind tunnel to obtain data of the wind effects on the building. The

wind tunnel results are combined with Weather Bureau data to obtain statistical estimates of the

design parameters. These parameters include the envelopes of maximum deflections, the contours

of maximum and minimum wind pressures on the exterior walls, and the expected number of cycles of oscillation per year which exceeds specific values of acceleration and of deflection.

Key words: Aeroelasticity; buildings; dynamics; statistical analysis; structural engineering; wind

loads; wind tunnel modeling.

1. Introduction

Research on the structure of wind has clearly

shown the random and turbulent character of wind

which varies with the height above ground and with

the topographic features of the ground surface. Furthermore, a realistic estimation of the responses

of the structures to natural wind has been shown by

researchers to require dynamic and statistical concepts.

The firm of Skilling, Helle, Christiansen, Robertson

has been engaged during the last few years in the

design of several tall buildings. Among them is the

United States Steel Office Building which is now

under construction in Pittsburgh. These tall buildings

have provided the opportunity to incorporate many

of these new concepts in the treatment of wind

effects during the design of those buildings.

A rendering of the United States Steel Office Building is shown in Figure 1. This building is triangular in plan with 64 occupied stories exclusive

of basements and heliport, has a total of 78 framed

levels, and its height is 839 ft above the plaza. The

area of each floor is 41,400 sq ft to the building line.

2. Scope of the Wind Study

The program for the study of the wind effects on

the United States Steel Office Building consists of three coordinated phases, as follows:

(a) Environmental study—the gathering and

analyses of all pertinent data for wind velocity

and temperature.

{h) Simulation by wind tunnel models—the topographic model to establish the wind structures appropriate for the testing of building models;

the aeroelastic model for static and dynamic

deflections; and the pressure model for local pressures and for cross-checking of results,

(c) Synthesis of environmental criteria with the

results of the wind tunnel measurements.

Figure 1. Rendering of United States Steel Office Building,

Pittsburgh, Pennsj'lvania.

107
3. Environmental Study

The most useful parameter that defines the wind

cUmate of a locahty is the mean gradient wind

velocity taken over a time period between 5 minutes

and 1 hour, as suggested by Professor Davenport [1]*. The interval that has been adopted is 20 minutes. Our

task is then to determine the probability distribution

of the annual maximum gradient wind velocity

averaged over 20 minutes for the city in which the

building will be built. Three types of wind data were utilized, namely, the

weather balloon data, the hourly observations, and

records of annual maximum wind speeds. On the

basis of the gradient wind speeds estimated from the

three types of data, one probability distribution of the annual maximum gradient wind speeds is chosen

as the design distribution [2]. This distribution is shown in Figure 2. Wind and temperature data are combined in Figure 3 and Figure 4, to indicate the joint probability of the simultaneous occurrence of specific

wind speeds and specific temperatures.

lOO

lO

fSefurn Pertod (year^

QjOestgn di9ir'bufion baaecJ on cloto of onnao/

_^ FoafSSf' rni/e Spsec/S of" 0/r/Dort.S ,^-£stimafed -from c/afa of annua/ max S noinute ^ ove Speeds af City Off/ce.

{ZjEsfin^afed frorn dora of Wmd A/of^ Sunnmary ^ at 300 mehsrs.

^E^fimcitecf from data of hourly obser\^at'cns

ai Oirporf, /95& - / 9<i,0.

Figure 2. Probability distribution of annual maximum 20 minute average gradient wind speeds.

* Figures in brackets indicate the literature references at the end of this paper.

Ternperofure C^) lav^^r than

sia fed values. Example : The protxibi/ify is '/so '0 O2

+ha4 oir temperature i lO°f

arid gradient wind speed

i SO mph vs/ould occur in a year

Figure 3. Joint probability of gradient wind speed and air temperature at site.

Exomp/e : The probahi/if'^ is '/so- O OZ +haf air temperofwe

> 90" P and gradient

\r/inid speed 2 S3 mph

y/ould occur m a year.

Figure 4. Joint probability of gradient wind speed and air temperature at site.

4. Wind Tunnel Studies

The wind tunnel studies consisted of four stages

which were carried out at the Boundary Layer Wind

Tunnel of the University of Western Ontario.

4.1. Stage I During the preliminary concept stage of the

design, various shapes of the building were con108
Figure 5. Models used in aeroelastic comparison study of building shapes.

sidered. In order to assess the relative aerodynamic

merits of different building shapes, an aeroelastic

study of six building shapes was made in a simulated

city atmosphere. The six models that were tested are shown in Figure 5. The results are compared in Figure 6 by means of the envelopes of peak deflections

for all wind directions. The aerodynamic characteristics of the modified triangular building shape, which was preferred for structural and architectural reasons, was found to be favorable and to be aerodynamically

superior to the conventional rectangular shape—thus

confirming its adoption for the final design of the

United States Steel Office Building.

4.2. Stage II A model of the Pittsburgh area was built to a scale

of 1:2000 and tested in the boundary layer wind

tunnel. Figure 7 shows a photograph of the topographical model in the wind tunnel. The vertical

profiles of mean velocity and the profiles of intensity

of turbulence at the building site were obtained for

y/ooo/v J

J i.i y . J

Genera/iy/-ta/7 aj(/30S£/r<T: ^ • (^^s) 4'f£>c/f'//e<:3^ 7?-/}rrj^/a S^iy<y/'£ C/^ss

C/rc/£

Figure 6. Envelopes of peak deflections of six building

shapes.

109
Figure 7. View of 1 : 2000 scale topographical model in wind tunnel.

Figure 8. View of "rough" exposure showing 1:400 scale aeroelastic model of United States Steel Office Building.

the eight principal compass directions. These tests 4.3. Stage III were completed in order to assess the extremes of exposure for later use in studying models of the The wind tunnel study of the final building design

building itself. included both the measurements of the responses of

110
the aeroelastic model and the measurements of the

pressures on the exterior faces of the static model.

The tests were carried out in two extremes of exposure

which had been established in Stage II. Figure 8 gives a view of the aeroelastic model of the United States

Steel Office Building in the boundary layer wind

tunnel. The aeroelastic responses of tall buildings are usually dominated by the fundamental modes of vibration which may be adequately approximated by

a linear shape. Thus, the aeroelastic model of the

building consists of a rigid model dynamically

mounted so that the lowest mode of vibration is modelled in each of two transverse directions. The

profiles of wind speeds are adjusted to match those

found in the topographic model by varying the

roughness of the floor surface of the wind tunnel. The

buildings in the vicinity of the project site are reproduced to scale in the wind tunnel. Measurements of the mean and of the RMS values

of the deflection in two orthogonal axes are made for various angles of attack at different wind speeds and

for various combinations of damping, building

density, exposure and frequency ratio. Both static and dynamic deflections at the top of the building are plotted in Figures 9 and 10 for various wind direction. These two graphs clearly demonstrate the dynamic

nature of the wind effects on the building.

The static model has pressure taps located at all points of interest such as the large glass curtain walls

of the lobby. Figure 11 shows the static model with

one of the faces opened. The mean and the RMS

-X

Figure 9. Static and dynamic responses along X axis.

Figure 10. Static and dynamic responses along Y axis.

value of the pressures are measured for various

angles of attack and for two extremes of exposure. The pressures are converted into dimensionless form

by dividing the local pressures by the dynamic

pressure of the gradient level.

Figure 11. View of pressure model showing pressure sensing

unit and piezometric pressure tap connections.

Ill
4.4. Stage IV

The efficient operation of a rooftop landing field may be significantly influenced by the characteristics of the airflow in the region immediately above the

building. Thus, the nature of the airflow over the

proposed heliport atop the United States Steel Office Building was studied in detail by means of wind

tunnel models [3]. The models were built to a scale of 1:96. Both flow visuaUzation technique and

hot-film anemometer sensor were used. It is found

that the magnitude of the maximum turbulence

intensity and the positions of the vortex layer over

the United States Steel Oflfice Building are similar to those over the Pan Am Building in New York City on which a heliport has been successfully operated.

5. Statistical Prediction of Building

Performance in Service

Procedures have been developed in the last few

years to make statistical estimation of various

parameters of building performance in wind [4, 5, 6]. Such prediction is based on the probability distribution of the annual maximum gradient wind velocity

and on the static and dynamic response characteristics of the building models obtained by tests in a boundary layer wind tunnel.

The parameters that are predicted include the

maximum deflections, the maximum amplitudes of

oscillation, the maximum and the minimum wind

pressures on the exterior wall, and the expected

number of cycles of oscillation per year which exceeds

given values of deflection and of acceleration. These

parameters are relevant to an evaluation of the

building performance with respect to

(1) the stresses of the structural frames,

(2) the adequacy of the partitions and of the

curtain wall; and

(3) the comfort of the building occupants.

Because of the directional characteristics of the wind

effects on the building, the probability distributions

of the parameters such as deflections and pressures

are only indirectly related to the probability distribution of wind velocity. A specific value of deflection or some other parameter can arise from either a low

wind speed coming from a critical direction or a

higher wind speed coming from a non-critical

direction. The procedures for estimating the combined

" probabilities of these events have been described in

detail in the reference already cited. Some of the

estimated results for the United States Steel Office

Building are shown in Figures 12 through 17. These

figures show:

(a) Probability distributions of annual maximum

deflection at top of the building (Fig. 12).

(6) Envelope of maximum deflections with 50

year return period (Fig. 13).

(c) Probability distribution of annual maximum

peak amplitudes of oscillation at top of the

building (Fig. 14).

(d) Expected number of cycles of oscillation per year having amplitudes exceeding specific

values (Fig. 15).

(e) Maximum exterior pressure for wind speed of 50 year return period (Fig. 16).

(/) Minimum exterior pressure for wind speed of 50 year return period (Fig. 17).

6. Conclusion

A comprehensive treatment of the wind effects has

been accomplished for the design of very tall buildings

which incorporates the statistical and dynamical

concept developed by the researchers in the recent

years.

1 1 1 ; 1 ,

o I 1 1 1 1 1 1 ^ s /o ao so /oo

N\

Figure 12. Probability distributions of annual maximum

deflections at top of United States Steel Office Building in Pittsburgh.

112
Figure 14. Probability distribution of annual maximum

peak amplitudes of oscillation at top of United

States Steel Office Building.

'I

1

1

1 11

4!

.

1 _L- > —1

<J <f- e a /o <fo ao (SO so /oo

Figure 15. Expected number of cycles of oscillation per year having amplitudes exceeding specfic values.

113
1 1

0

vy

/S

/li

/z

24

Z3

-Z3 )

-z/

-2-3

'Z4

'Z4-

-ZS

-2Z

-ZO

^

1^/0 or

-/•r

/Or /H///^.

S. Pr<^^^r^ of^SO yS% a/^c:>^r?/o£rr^

Figure 16. Maximum exterior pressure for wind speed of 50

year return period.

Figure 17. Minimum exterior pressure for wind speed of 50

year return period.

7. References

[1] Davenport, A. G., "The Relationship of Wind Structure to Wind Loading," Proceedings of the Symposium: Wind

Effects on Buildings and Structures, National Physical

Laboratory, June 1963, Her Majesty's Stationary Office, London 1965.

[2] Wind and Temperature—The United States Steel Office Building, A Report of Skilling, Helle, Christiansen,

Robertson, to The United States Steel Corporation,

March 1968.

[3] A Wind Tunnel Investigation For A Rooftop Landing

Field—The United States Steel Office Building, A Report

of Skilling, Helle, Christiansen, Robertson, to The United

States Steel Corporation, April 1968.

[4] Davenport, A. G., "The Estimation of Load Repetitions on Structures with Application to Wind Induced Fatigue

and Overload." Rilem International Symposium on the

Effects of Repeated Loading of Materials and Structures, Mexico City, September 15-17, 1966.

[5] Robertson, L. E., "A Study of the Wind Effects on the

Seattle First National Bank Building," Notes from a Design Seminar on Buildings in Earthquake and Wind,

pp. 9.1-9.49, A.S.C.E., 1967.

[6] Robertson, L. E. and Chen, P. W., "Glass Design and

Code Implications for Extremely Tall Buildings,"

Building Research, pp. 6-11, May-June 1967, Building Research Institute, Washington, D.C.

114
DYNAMIC RESPONSE OF TALL FLEXIBLE STRUCTURES TO WIND LOADING

Joseph Vellozzi and Edward Cohen

Ammann & Whitney

New York, New York 10011

The purpose of this paper is to present and discuss methods of calculating the dynamic response

of tall, flexible structures, such as towers, stacks and masts, to wind loading. The paper is presented

in two parts; the first part deals with the dynamic response of cylindrical structures to vortex shedding and the second part deals with dynamic response to gust loading.

Key words: Aeroelasticity ; buildings; circular cylinders; gust factors; masts; structural engineering; towers; vortex shedding; wind loads.

1. Vortex Shedding

1.1. General

A cylindrical structure subjected to wind stream

normal to its axis vibrates in a lateral direction

(transverse to the direction of the wind) due to the

formation of vortices on alternating sides. The

resulting pattern of flow on the downwind side is known as the von Karman Vortex Street [1]*. In a

certain range of wind velocity and cylinder diameter

these vortices are formed and shed from opposite

sides of the cylinder at a regular frequency; conse- quently, alternating differential pressures are exerted

upon the cylinder by the moving fluid. When the vortex frequency approaches the frequency of one of the normal modes of vibration of the structure, resonant oscillation results due to the alternating

pressures. The frequency of the oscillation remains

close to the natural frequency of the structure. The

alternating pressures also cause oscillations in the

direction of the wind stream but the major oscilla- tions are transverse to the wind. The oscillations will continue to build until the energy dissipated by the

damping in the structure equals the energy supplied

by the wind stream. Hence, lightly damped structures

are especially susceptible to this phenomenon.

The manner in which vortices are shed from a

cyHndrical structure depends upon the Reynolds

number, Nr, where:

NR=Ud/v, (1)

where U is the velocity of the wind, v is its kinematic

viscosity, and d is a characteristic dimension such as the diameter of the cylinder. At extremely small

* Figures in brackets indicate literature references at the end of this paper.

Reynolds numbers the flow in the immediate vicinity

of the cylinder is very much like ideal flow and no

vortices are formed. At somewhat higher values, up

to Nr = '^0, the flow separates from the surface and

forms two symmetrical stationary vortices [2]. Above

^^• = 40, however, the stationary vortices become

distorted and unstable, and an asymmetrical flow

condition develops wherein vortices are formed at opposite sides of the cylinder. These vortices grow in strength in the vicinity of the cylinder and move

downstream with the flow in an alternating pattern

as they detach from the cylinder. The flow in the vortex street is viscous from A'/j = 40 to approximately 150, and the vortices decay by viscous

diffusion [2]. The range from iV/e = 150 to 300 is a

transition region in which the flow changes from

laminar to turbulent in the free vortex layer which

separates from each side of the cylinder [3]. Above

NR = 'iQQ, the flow becomes turbulent at the separation point. In this range, called the irregular range, the vortex shedding is periodic, but the velocity in the immediate vicinity of the cylinder fluctuates in an irregular manner because of the flow turbulence.

The irregular manner in which the velocity fluctuates

is augmented by the turbulence in the natural wind.

The result of these fluctuations is that the amplitudes

of the lift or side forces on the cylinder are more or

less random, and the randomness becomes more

pronounced with increasing Reynolds numbers.

The frequency of the vortex shedding is fairly

periodic for Reynolds numbers in the range of about

40 to 3X101 At or near the latter Reynolds number,

the flow in the boundary layer on the forward portion

of the cylinder changes from laminar to turbulent,

and the separation points move rearward on the

cylinder. There follows an abrupt drop in the drag

coefficient and the wake becomes narrower and

apparently aperiodic [4]. The result is that the

115
frequency of the vortex shedding and the ampHtudes

of the Uft forces are both random. Again, the natural

wind turbulence augments this randomness. The

frequency of the vortex shedding remains random

with increasing Reynolds numbers up to about

3.5 X 10*'; however, with increasing Reynolds numbers

above 3.5X10®, the frequency of vortex shedding

imdergoes another change whereby there is a gradual

return to definite periodicity [5, 6]. The frequency at which vortices are shed from a

cylinder is usually expressed non-dimensionally as the

Strouhal number *S:

S-- 'u

(2)

where/ is the frequency of the shedding, d is a typical

dimension and U is the wind speed. When the vortex shedding is periodic, / is the frequency of this shedding; however, when the shedding is random, it is necessary to speak of a power spectrum, or a correla- tion function, rather than a single dominant fre- quency. For random vortex shedding, an aerodynamic

Strouhal number is sometimes defined by, "the

predominant frequency measured from an autocorrelation function (or the peak power of the power

spectrum) of the unsteady aerodynamic lift forces"

[5].The variation of the Strouhal number, S, with

Reynolds number, Nr, is shown in Figure 1. It is noted that in the Reynolds number range less than

3X10^ where the vortex shedding is periodic, the

value of the Strouhal number is fairly constant and in the order of 0.2, the value generally accepted for the

circular cylinder. For greater Reynolds numbers in

the range of 3X10^^ to 3.5X10", where the vortex shedding is random, there is a gradual rise in the

"aerodynamic" Strouhal number, and with increasing

Reynolds numbers above 3.5X10", where there is a

gradual return of definite periodic vortex shedding,

the Strouhal number increases to a constant value

of about 0.3. In the range where the vortex shedding

is random, the Strouhal number determined from an

autocorrelation function, which is essentially the

center frequency point of the power spectral density,

is shown as a dashed line; the effective bandwidth of the unsteady force is presented in terms of the

Strouhal number by the solid lines. The characteristic

narrowing of the Strouhal number bandwidth with

increasiiag Reynolds numbers above 3.5X10" is an

indication of the return of periodicity in the vortex shedding at these Reynolds numbers.

For tapered structures where both the diameter

and wind speed U vary with height, the Strouhal

number will likewise vary with height. Some recent experiments on this variation for tapered stacks [7] have indicated that the tendency is for the frequency

of the vortex shedding to be constant over a substantial part of the axial length at a value determined

by the wind speed and diameter at the top. In other

words, the frequency of vortex shedding on a tapered

cylinder would be "locked in," at least for a considerable length of the height, to the Strouhal

frequency appropriate to the least diameter. These

experiments also suggest that the top diameter of cylindrical towers and stacks should be as small as possible since critical wind speed and excitation

(which varies with V^) is thereby kept to a minimum,

and less structural damping is needed to prevent

oscillations. When a cylindrical structure is vibrating in resonance with periodic vortex shedding forces, the

vibration itself causes an increase in the magnitude

of the forces. The additional aerodynamic force is probably associated with a periodic shifting of the

separation points of the flow from the surface of the

structure, thereby causing increased circulation. At

the same time, the vortices in the wake are larger and

stronger than would be the case if the cylinder were

stationary. Steinman [16] hypothesized that if vortices are shed at or near each end of the amplitude

range, the normal width of the vortex street is increased by the ratio h±2y

h = 1 +

2y_

1. 3d

(3)

Figure 1. Variation of Strouhal number with Reynolds

number for circular cylinder.

in which h (^ 1.3d) is the width between the centers

of the two rows of vortices behind a non-oscillating

116
cylinder, y is the half amplitude of vibration, and d is the diameter of the cylinder. For the vortices to be

stable, the distance between the vortices in each row must also increase in the same ratio. Figure 2 (after

Weaver [17] shows schematically the increased

dimensions of the vortex street due to vibration of the

cylinder. The increase in distance between shedding

vortices decreases the shedding frequency and the

Strouhal number by the reciprocal of Equation 3. Hence, resonant vibrations of large amplitude cannot

be attained when the Strouhal frequency for a stationary cylinder exactly equals the natural

frequency of an elastic body. In this instance, as soon

as oscillation begins, the Strouhal frequency decreases

and goes out of phase from the natural frequency.

However, when oscillation begins at a wind speed

slightly higher than the critical velocity, the Strouhal

frequency decreases to the point where it matches the

natural frequency, and the vibrations are sustained

or increased. The ratio of the velocity Up at which

peak amplitude occurs to the critical velocity based on S=fd/U for a stationary cylinder is in the same

ratio as the dimensional increase in the vortex

street; i.e.

[/p/[/= 1 + 1.54 y/d (4)

Similarly, the ratio between the Strouhal number Sp

at which peak vibration occurs and the Strouhal

number *S for a stationary cylinder is

Sp/S =

1 + 1.54 y/d

(5)

It has been suggested by Steinman [16] and others

[18] that the limiting ratio of y/d is unity, and this is generally supported by experiments in which

structural damping is very small.

3.31 (1.3d* 2y)

d + 2y

Figure 2. Dimensional increase in vortex street due to vibration (after Weaver).

1.2. Stochastic Excitation

The Reynolds numbers of primary interest for cylindrical towers and stacks are in the supercritical range. In the range of supercritical Reynolds numbers

from about SXlO'^ to 3.5X10^ where the unsteady

lift forces are random, the theory of random excitation

[8] may be used to obtain estimates of the probable

peak deflections. According to this theory, the

mean-squared bending response y(zy in a direction

normal to the wind can be written as: (considering

only the first bending mode of the structure)

1 d W<^i(2)2 yizy=^-CL'F{S) -^i^ (6) 8 U

where

W1= / q{z) d{x)<t>iiz) dz

Mi= f m{z){Mz)ydz

m = mass per unit height

q{z) = dynamic wind pressure per unit height = VipUizY

d= diameter at height z L = total height of structure 01= mode shape of first bending mode of vibration

Uiz) = velocity at height z p= Air density

d= diameter at top of structure U = Wind speed at top of structure

/3 = percentage of critical damping

coi= natural (circular) frequency of first bending mode = 2irf f= frequency in cycles per second

fd S= — = Strouhal number

F{S) = power spectrum of lift forces Cl^= mean-squared lift coefficient

The power spectral term Cl'^F{S) in Equation 6 is a measure of the mean-square lift forces on the

structure. For cylindrical structures. Figure 3 shows a

typical variation of Cl^F{S) with Strouhal number *S. This plot is based on experimental results obtained

by Fung [4]. Fung measured the fluctuating lift forces

117
0.1 6

0. 1 2

0 0.1 02 0.3 04 0.5 0.6 S = f d /U

Figure 3. Fung's power spectrum for lift on a circular cylinder.

acting on a stationary circular cylinder for Reynolds

numbers in the range of 0.3X10'' to 1.4X10'' and

obtained its power spectrum as a function of Strouhal

number by use of a wave analyzer.

It is seen from Figure 3 that Cl^ F{S) is a maximum

at a Strouhal number of about 0.05. With increasing

Strouhal numbers the value of Ci} F(S) gradually

falls to zero. The results in Figure 3 are normalized

such that:

f

F{S)dS = 1.0 (7)

Based on this equality, the mean-squared lift coefficient can be shown by integration to be

C? = 0.274. Nakagawa et al. [9] also determined the power

spectrum of the fluctuating lift forces by measuring

amplitudes of both oscillating circular cylinders in a wind tunnel and steel stacks in the field. The wind

tunnel tests covered a Reynolds number range from

1.5 to 10^ to 1.5X10^ and the field measurements

covered a range from 2X10" to 8X10". Both Fung's

and Nakagawa's wind tunnel data are in general

agreement with the field measurements.

Figure 4 presents calculated deflections of the top

of an actual 250 foot high, unlined steel stack

(Stack A) which exhibited severe lateral oscillations at moderate wind speeds. (This stack has since been

fitted with a spiral arrangement of vertical strakes to suppress the oscillations [19]. The efflux of the stack

is 9 feet and the fundamental frequency, confirmed

by field observation, is 1.16 cps. The Reynolds

number, based on the efflux diameter, ranges from

0.8X10" for a wind speed of 15 fps to 8.75X10" for a design speed of 160 fps. Estimates of the maximum

deflections were obtained from Equation 6 using

A

m

MEASURED VALUES STACK A

MEASURED VALUES STACK B

001

.0025 .

6

9 0 20 40 60 80 IOC 120 140 )60

I 1 I L,

lo' lO" 5»I0* 10' S^" Ud/c

Figure 4. Variation of maximum amplitude of stack top

versus wind speed and percentage of critical damping.

Fung's power spectrum. For calculating Uiz), it was

assumed that the wind speed increased with height

according to the 1/7 power law:

V{x) = V,{zmY" (8)

where f/o is the wind speed at a reference height of 30

feet.Estimates of the peak deflections y{z) max were

obtained from the relation:

2/(2)max = 3VRJP (9)

where the factor of 3 (3 times the standard deviation)

corresponds to a probability of 0.9973 that 2/(z)max

will not be exceeded; i.e., during a storm, the value

will not be exceeded, on the average, more than 0.27

percent of the time.

The calculated amplitudes pertain to assumed

damping ratios, ^, of 0.001, 0.025 and 0.006. As

expected, the amplitudes increase with an increase in wind speed and are greatest for the smallest damping

ratio of 0.001. For comparison. Figure 4 presents field measurements of the amplitudes for wind speeds up

to 52 fps. These amplitudes are in good agreement

with the theoretical results for a damping- ratio of 0.001, and suggest that the damping in the stack is quite low. Field data (Stack B, Reference 9) for a

steel stack having similar dimensions and free vibration characteristics as Stack A, but having a damping ratio of .006, are also brought into comparison in Figure 4. These data compare well with the

theoretical curve for a damping ratio of 0.006. The experimental data of Figure 4 pertain to wind

speeds at 30 feet in the range of 20 fps to 75 fps. The

Reynolds number, based on the efflux diameter and

wind speed at the top of the stack, increases from

118
1.5X108 to 6X10'' while the Strouhal number

decreases from 0.35 to 0.10. In the range of Reynolds

numbers greater than 3.5 XlO'', which corresponds to the periodic vortex shedding range, there is no

change in the trend of the experimental data and the

theoretical curves based on random excitation match

the experimental data quite well. This is because, in

this range of Reynolds numbers, the Strouhal

number is much smaller than the Strouhal frequency

at which vortices are shed (Figure 1) and a resonant

is eliminated.

It is also noted from Figure 4 that there is no peak

in the dynamic response at a Strouhal number of 0.2, the value at which resonance is sometimes observed

for cylindrical structures. In this case, a Strouhal

number of 0.2 corresponds to a Reynolds number of 2.9X10^ which is in the range where the vortex shedding is random. Power in this range is supplied over a wide range of Strouhal numbers and, as a

result, excitation occurs over a wide range of frequencies.

Scruton [11] observed a similar phenomenon in a wind tunnel test and mentions that: "A model of the

tower for the Museum Telephone Exchange, London,

showed the effect of an aperiodic wake (random

vortex shedding) for SX10'<Nr<3.5X10^. This

cylindrical structure was tested at values of Nr up

to 2.9 XlO^ Oscillations were spasmodic and the

amplitudes increased steadily as velocity was

increased. There was no predominant frequency of vortex shedding, excitation occurring over a wide

range of frequencies."

This phenomenon may seem inconsistent with the

observed behavior of cylindrical towers and stacks

which have exhibited peaked resonant vibrations at a Strouhal number of about 0.2, and which appear to be relatively quiescent at other Strouhal numbers.

However, apart from subcritical values of Reynolds

numbers such peaked vibrations usually occur only

when a Strouhal number of approximately 0.2 corresponds to Reynolds numbers greater than

3.5 XIO^, where the vortex shedding is periodic. For

instance, in 1953, a welded stack of 16 ft. diameter

and natural frequency of 1 cps came to resonance and

failed in a wind of about 50 mph; the corresponding

Reynolds number was 7.3 X 10*' and the corresponding

Strouhal number was 0.22. Similar resonant oscilla- tions at a Reynolds number of about 4 X 10^ were also observed in recent wind tunnel tests at Langley

Research Center, NASA, involving Saturn IB and

Saturn V launch vehicles [10]. On both models, resonance occurred at a Strouhal number of about 0.2.

In connection with the foregoing, it is apparent

that an increase in natui'al frequency of a structure may not be a feasible means of reducing Karman

vortex oscillations, and, in fact, can be detrimental.

This is because an increase in natural frequency is accompanied by an increase in the critical wind

speed; if this critical wind speed corresponds to a Reynolds number in the range where the vortex shedding is periodic, a resonance condition may be

created. However, an increase in natural frequency is advantageous when the critical wind speed is increased to a value greater than the probable

maximum speed for the site.

1.3. Self Excited Response

For supercritical values of Reynolds numbers

A'fl>3.5X108, the vortex shedding is periodic and

there is evidence [10, 11] which indicates that the

associated aerodynamic forces are strongly dependent

upon the motion of the structure. As mentioned

above, instability tends to occur at a Strouhal number

in the neighborhood of 0.2, which happens to be the

Strouhal number of the Karman vortex street at

subcritical Reynolds numbers.

Although a Strouhal number of 0.2 should in general be avoided Tor Nr> 3.5X10'^, estimates of the vortex oscillations for cylindrical structures may, in this case, be computed using an approach advanced

by Scruton [11]. In this approach it is assumed that oscillations will be maintained at constant amplitude rj when the

energy dissipated by positive damping is equal to the

negative aerodynamic damping provided by the wind

stream; that is when:

{5a-\-ds)v=0 (10)

where 5a is the logarithmic decrement of the negative,

aerodynamic damping and 5s is the logarithmic

decrement of the positive, structural damping.

For a flexible structure, the negative aerodynamic

damping can be determined by the integration:

8,= f

p (PK^cj^Hz) dz / 2 f m{z)(t>''{z) dz (11)

•'o / 'o where (^(z) represents the displacement mode of

oscillation and Ka is a non-dimensional parameter

which must be determined from experiment. The

value of Ka is dependent upon the aei'och^namic

shape, the Strouhal number and the Reynolds

number, and the amplitude of vibration. Ka can be

positive or negative and oscillations will be maintained only when it is negative and when the

119
attendant value of 5a is numerically equal to the

positive damping provided by the structure. For a subcritical Reynolds number of about

1.2X10^, Scruton determined the variation of —Ka

with displacement from experiments on smooth,

circular cylinders. Peak excitation occurred at a Strouhal frequency of 0.2 and the variation of —Ka

with 7} at this frequency followed the hyperbohc

relationship

-Ka~ =0.55 (12)

cl

Although Scruton's results were obtained at a

subcritical value of the Reynolds number, similar

results were obtained by Reed [10] for supercritical

Reynolds numbers in the periodic flow regime. These

tests indicate that motion dependent forces, in the

form of negative aerodynamic damping occur at a Strouhal frequency of about 0.2 for Nr>3.5 X 10« and

suggest that Scruton's results are also applicable to Nr in this range. Since Ka and hence 8a are dependent upon

amplitude rj, limiting amplitudes may be obtained by

calculating values of da for a number of values of rj. The limiting amplitude (see Equation 10) is then

determined by the intersection of the — 5a vs. 17 and

Ss vs. r] curves. The structural damping, 5s, will, in general, depend upon amplitude, but insufficient information is available on this variation and 5s is normally taken as a constant. Measurements of 5s made on stacks and towers in

still air have been reported by Scruton [11] and are found to range from about 0.02 to 0.18, the damping

being generally greater for concrete or concrete-lined

construction than for unHned steel construction.

It is interesting to note that, on the basis of Equation 12, it is possible to relate the values of Ka

and Cl, the Karman lift coefficient used by many

writers to express aerodynamic lift forces L as L = y2pU-dCL sin o^t (13)

Using the following equivalence [11] -4^KavS

Cl= ; (13a) a

with S equal to the Strouhal number at resonance

(i.e., 5 = 0.2), then on substitution of Equation 12,

Cx, = 0.27. This value is close to the mean-squared

lift coefficient Cl^ = 0.274 measured by Fung [4] for a

stationary cylinder.

Fung tested up to A^^? = 1.4X lO** and found Cl to be fairly constant for A''/? > 4.5X10''. With decreasing

Reynolds numbers below 4.5 XlO" there is sufficient experimental evidence which shows that Cl increases

to values between 0.6 and 1.0; this range of A^'^e, however, is not important for tall structures.

1.4. Correction Procedures

If calculations show that either excessive amplitudes of Karman vortex vibration are to be expected

or that small but sustained vibrations may occur as a result of a critical wind speed equal to the prevailing

wind speed for the area, several alternatives are available to the design. Since the aerodynamic

stability of a structure depends upon the aerodynamic

shape, the frequency of oscillation and the structural

damping, these alternatives include modifications to one or more of these factors. Modifying the structure height to diameter ratio or taper is usually the first approach to be made; but since this change may not be practical in many cases, alternate procedures are

available. These include:

1. Dynamic Spoilers

2. Utilization of bracing or guying

3. Utilization of frictional or impact damping

devices

4. Addition of an internal gunite or refractory

lining

5. Addition of mass or change in fundamental

frequency

In general, the addition of aerodynamic spoilers is often more feasible and more acceptable than

changes of the natural frequencies or increase of the

structural damping. The purpose of spoilers is to "spoil" the airflow over a body in order to avoid the

generation of vortices with a predominant frequency,

or to break up the correlation of the aerodynamic

exciting forces over its length.

An optimum configuration of spoilers for cylindrical structures was developed at the National Physical

Laboratory [13]. It consists of a three start system of rectangular section strakes of height 0.09d and of pitch 5d. In the case of circular towers and stacks, it

is only necessary to apply this device to the top

third of the structure. Other spoiler configurations which have been found

to be effective in reducing vortex vibrations of cylindrical structures consist of a two or three start system of equally spaced vertical fins arranged in a

helical pattern [14]. The optimum height of these

strakes is about O.ld and the optimum pitch is about

lid. This configuration has also been found to be

effective when applied only to the top third of circular cross section towers and stacks.

120
Although spoilers are effective in reducing Karman

vortex vibrations of cyUndrical structures, they

increase the drag loading. Wind tunnel tests [15] indicate that the drag coefficient for a circular cyHnder fitted with helical strakes is about 1.15 based on the circumscribing diameter. This drag coefficient

is approximately the same at that observed for smooth circular cylinders at subcritical Reynolds

number. A summary of reported drag coefficients for circular cylinders is shown in Figure 5. In the

supercritical Reynolds number range, the range of primary interest for the present problem, the drag

coefficient for a cylinder with spoilers is about twice

as great as that for a smooth cylinder.

For adjacent structures such as stacks, stacks

close to a structure or small stacks, corrections can be

made by bracing or guying. For tall flexible structures, guy wires would appear to offer a

feasible solution provided there is adequate land

space available for guy anchorages. In some cases, guy wires have been used to connect dampers to the

structure [20, 21]. For adjacent stacks or towers near

existing structures, l)racing can bo provided by moans

of trusses or crossed pipes. In general, the spacing

between adjacent cylindrical structures should exceed one and one-half diameters, which is the minimum

distance cited by Landweber [22] for out-of-phase

vibration due to wind perpendicular to a line of cylindrical sti'uctures; bracing can be expected to be

effective only when the spacing exceeds one and

one-half diameters. Cross bracing is less effective in reducing vortex vibrations for wind parallel to a line of cylindrical structures, particularly if the spacing

between the structures is greater than two to three

diameters; such bracing, however, would appear to be effective in controlling dragwisc vibrations due to

buffeting in the wake of upwind structures. The utilization of frictional or impact type damping

devices usually have proven to be an effective means

of controlHng vortex vibrations of flexible, cylindrical structures. As noted above, the dampers are usually

connected to the structure by means of guy wires. However, other types of damping devices, which

require no external connections, have been used or

pi'oposed. These devices consist of acceleration

1.2

I 0

®

I M M M I 0- Slarlock • Slolhtr (8"i4a" Cft. covtr aiHl ••ll4p«»«r)

<S>- SKarlock • St*lli*r (S"<4«" cyl m>—Hi wrt»ct)

iourc* Woodruff (AS.C.E <>ri>c. paptr I70«, Jgly l*S«) (««Mct ratio 5: 1) tmooth cylin^r

I 1 I I I I I

I C>«t«ny > S»r»n»«n (W».C.A TN 303> N»v

Inf. Cy1in4«r v«ry tmMtti tyrfoco

I

I I I I I f) Faf* • WorMp , Infinil* R*ut*i Cylindtr

.

I I M II ® Wtil«lb«f9«r , Infmit Smooth CyliMOf

(7) Clncotto et ol (Infinite Smooth Cylindar)

Figure 5. Drag coefficient versus Reynolds number.

121
(impact) chain dampers [12] and auxiUary mass

(Lancaster) dampers [10]. The acceleration chain

damper, which provides beneficial damping when a

vibrating structure causes hanging chains to impact

against the walls of the structure, has been found to be successful in controlling vortex vibrations of a Wullenwebber antenna [23] and of an unfueled

launch vehicle [12]. In general, both the impact and

Lancaster type dampers become prohibitive for large structures because a relatively large mass for the

damper is required to provide a substantial increase

in damping.

In the case of stacks, a thick internal gunite or refractory lining greatly increases damping. The

addition of a lining acts in two ways that can be

approximated by calculation; first, mass is added to the stack thereby reducing its natural frequency;

second, although refractory lining increases the

moment of inertia of the stack which in turn increases

the natural frequency, it reduces the dynamic

deflection. The change in moment of inertia can only

be expected to occur for a thick lining that is forced

to act integrally with the stack. A change in the natural frequency of a structure

can, in some cases, be a feasible solution to the

problem. For vibrations occurring within the supercritical range of Reynolds numbers, it is recalled that

the vibrations are random when a critical Strouhal

frequency of about 0.2 corresponds to a Reynolds

number in the range, 3XlO'^<A^fl<3.5Xl08. On the

other hand, when a Strouhal frequency of about 0.2 corresponds to a Reynolds number greater than about

3.5X10", a self-excited response phenomena will occur, and the amplitudes, depending upon damping,

could result in a catastrophic failure. It is desirable,

therefore, that the structure natural frequency and/or

damping be such as to avoid the occurrence of this phenomenon.

In cases where it is impractical to increase the

fundamental frequency of a structure to such an

extent that the critical wind speed for and

iVij>3.5X 10'' is raised above the maximum wind

speed likely to be encountered, then consideration

should be given to a reduction in frequency. A

decrease in frequency serves to reduce the wind speed

for vibration instability with the result that the

energy input clue to aerodynamic excitation is lessened. In some cases, a reduction in frequency

would place a Strouhal number of 0.2 in the range of Reynolds numbers where the vortex shedding is random, thereby eliminating the possibility of a

self-excited response; however, this reduction would

tend to augment the random vibrations, although

this may not be important provided there is a

reasonable amount of damping available.

2. Dynamic Response to Gust Loading

2.1. General

In addition to the effects of lateral vibrations

caused by Karman vortex shedding, it is necessary in the design of exposed structures to make allowances

for the influence of dragwise vibrations due to gust

loading. It is a comparatively well-known phenomenon that the turbulence characteristics of natural

winds are distrubuted randomly in both time and

space and that this turbulence produces a stochastic

dynamic response of a structure. For such cases, it is meaningless to attempt a deterministic solution to the problem; however, power spectral techniques

have proved to be powerful tools for analyzing the response of structures to random inputs and will be

the approach discussed in the remainder of this paper.

Thi'ee elements are involved in determining the

dynamic response (deflection, stress, etc.) of a

structure to random wind loads: (1) the input power

spectrum, defined by the power spectral density of atmospheric turbulence, $/(/) ; (2) the frequency

response function of the structure T{f), defined in terms of the steady-state-load-response amplitude

for a unit sinusoidal gust as a function of the forcing

frequency /; and (3) the output power spectrum

<l>o(/) defined in terms of the response quantity of

interest. The basic relationship between input and

output spectra for linear systems is given by the

expression

:

Mf)= I Tif) <!>,(/) (14)

where \T{f)\'^ is the square of the modulus of the

structure frequency response function. The variance

or mean-square response is obtained by integrating

with respect to frequency; i.e.,

,.00 ^r'=

I Ml) df (15)

0 Under certain simplifying assumptions that the

atmospheric turbulence is locally stationary and

Gaussian, and the shape of the input power spectrum

is invariant with the level of intensity of turbulence,

it is possible to obtain quantities for the probable

peak values of the dynamic response. For example,

Davenport [24] has shown that the ratio, g, between

the probable peak response and the RMS response

( is given by

:

122
g = V2 In j/r+0.57/ V2 In j/T (16)

where T is the averaging period for the mean wind

(usually 1 hour) and where, according to Rice [25]

.= yy-'Mf) df I l\n{f) df^' (17)

The product vT in a sense is a measure of the

effective number of cycles of vibration that the

structure will undergo during the averaging period T. The larger the number of cycles, the larger is the

chance of an extremely large response occurring. The

value of g generally lies in the range of 3.0 to 5.0.

2.2. Application to Tall, Slender Structures

Tall structures, such as towers, can be regarded as

line-like systems, i.e., structures extended in only one

direction. Consequently, all parameters of the

system such as mass, stiffness, deflection, etc., can be

regarded as functions of only one space variable. On

the basis of this assumption, the system will obey, in the linear elastic range, the partial differential equation

,d^y{z) dy(z) d'y{z)

0 ro(2)

dt P{z, t)

(18)

where

z = the space variable measured from the

ground

i = the time variable

y = the displacement of the structure m = the mass/unit length of the structure

6 = the damping/unit length of the

structure

c = the bending stiffness/unit length of the structure

P{z, 0 = the applied load

The load P{z, t) can be written in the form

P{z, t)=Piz)+p(z, t), (19)

where P{z) is the mean load and p{z, t) is the

fluctuating component. Since the structure is linear,

then the total response can be obtained by the

superposition of the response due to P{z) and that due

to p(2, t). The former can be obtained by the

traditional methods of statics whereas the latter requires dynamic analyses and the use of statistical theories. When normal mode analysis is applied to Equation

18 it can be shown [26] that the variance or meansquare deflection of the structure to the fluctuating

load is given by:

<t>n{z)(t>m{z)

EE f H

r H^*if)H^{f)CUf) df (20)

where

c..(/)= f f *^f^y (21)

Jo c{z)c{z')

(t>n(z), <t>m{z) are the n"' and jn*"* mode shapes

Hn{f) is the complex frequency response of the n**" mode

Hn*{f) is the complex conjugate of Hn{f)

Y{z, z', t) is the cross spectrum of p{z, t) and En is the normaUzation constant of the mode

where

m(z)

/ ^<^"'(^) dz

Jo c{z) (22)

All of the necessary properties of the random wind

loading are contained in the term Cnm{f) and the

solution of the problem to gust loading is reduced to the determination of this term in a form useful for design purposes. Unfortunately, C„m(/) depends upon

<j>{z), c{z) and the distribution of area and drag for the structure, and hence any given Cnmif) is specific to the particular structure whose modes and stiffness functions are used to evaluate the integrals.

If one assumes that normal components of the

exciting force are in the form eTM' then one can easily

prove that the complex frequency response in the n^^ mode is

(23)

where 0 is the percentage of critical damping.

The normal mode analysis thus transforms the

problem into a set of single-degrec-of-freedom

systems and the total response is obtained by a superposition of the individual modal responses. The

amplitude of H„(/) represents the magnification

factor, which is defined as the ratio of the deflection

of the system during vibration to that corresponding

to a static condition, and is given by

123
HnU) (24)

+4/3^

This expression tends, as would be expected, to the

value of unity when / approaches zero and approaches

zero at large values of /. At the natural frequency, the

response is maximum and the peak becomes greater

as the critical damping ratio jS becomes smaller. For most structures, the damping is small, and in

this case only the diagonal terms in the summation

(Equation 20) need be considered, i.e.,

1 f \H^{f) pC„„(/) df (25)

where \ Hn{f) \ is given by Equation 24

and Cnnif) is given by Equation 21 with <^„(z') =<j)n{z')

2.3. Evaluation of C„mif)

In addition to the modal, stiffness and basic drag

data for the structure, certain statistical properties

of the wind velocity are required for the evaluation of the integral given by Equation 21. The properties

include the power spectrum of the wind velocity and

its spatial correlation. The former reflects the

distribution of energy among various wave fre- quencies, and the latter indicates how two velocity

components located at two different points in space

are correlated. A spectrum of the horizontal velocity measured by

Van Der Hoven [27] is shown in Figure 6. The curves are seen to be characterized by several prominent peaks.

The region on the high frequency end, commonly

referred to as the gust region, reflects the power

OUST REGION

o' 1 I 1 1 i i i p I I I 1 1 iijil 1 II I I I 1 1 mil I I 1 1 mil ' ' ' 1000 100 10 I 0.1 0 01 .001 PERIOD (HOURS)

Figure 6. Van Der Hoven's gust spectrum.

spectrum of turbulence for strong winds. If the

spectrum, Sv{f), of this region is plotted versus the

frequency, /, on a log-log scale, then the slope at the

high frequency end of the scale would be close to the

universal value in isotropic turbulence of —5/3. It should be mentioned that experimental results are

available only up to a frequency of 3 cps. In

accordance with the theory of turbulence, however,

the spectrum contains very little energy at higher

frequencies.

A region of very low energy exists to the left of the

gust region and is usually referred to as the spectral gap. This gap is very helpful in the measurement of wind, since it provides a means for obtaining meaningful and stable mean velocity measurements. For

intance, if a record of one hour duration is averaged,

the small-scale fluctuations will be averaged out and

a true "mean" is obtained. To the left of the spectral gap, one finds large-scale fluctuations; these, however, reflect weather-map changes whose periods are much larger than the natural periods of vibration of structures and, hence, are of no concern to structural

engineers. The spectral gap, which provides this clear-cut distinction between gusts and weather-map

disturbances, may not exist, however, in certain

extreme weather conditions such as tornadoes. These

conditions are, nevertheless, of such rare and localized nature that they are normally considered as special cases by structural designers.

A generalized gust spectrum was obtained by

Davenport [28] from 100 individual measurements

made in strong winds at several locations all over the

world and at heights in the range of 40 to 500 ft. This spectrum is plotted in Figure 7, and can be

written in the form

:

SAf) (26)

where Sv(f) is the spectrum of longitudinal velocity,

/ is frequency in cps, K is the surface drag coefficient referred to Uo the mean wind speed at a reference

height of 30 feet, and x is defined by

:

x = mOf/Uo (27)

Harris [29] has shown that the Davenport spectrum

dues not fully conform to certain known results of the

equilibrium theory of turbulence, and proposed the

alternate equation:

4KUo'x

7(2+^6 (28)

124
WAVE NUMBER, = (CYCLES / METER)

Figure 7. Spectrum of horizontal gustiness in high winds.

The two equations, however, are almost identical

except in the low frequency range, as can be seen in Figure 7. The energy spectrum has been found to be

independent of height in the height range indicated

above (40 to 500 ft). Recent measurements by Harris

[29] have also substantiated this assertion in the

height range 58 to 598 ft. The spectrum, then,

appears to be nearly universal in this height range

and is only a function of the ground roughness, as

reflected by K, and the square of the mean wind

speed at the reference height. Average values of K

are given in Table 1. These are seen to range from a

value of 0.085 for large cities and very rough, hilly

terrain, to a value of 0.005 for flat, open country.

Interpolations of these values may be used for conditions intermediate to any of these exposures.

Table I. Surface drag coefficients, K and velocity exponents, a

E.xposure Description K a

A Large cities and very rough, 0.085 1/3

hilly terrain. B Rough wooded country, towns. .010 1/4.5

city outskirts. C Flat open country, open flat .005 1/7

coastal belts and grassland.

The other parameter which is needed in describing

random wind loads is the cross-covariance (or

cross-correlation) function. This function measures

the correlation between velocity fluctuations of a

given frequency located at two separate points in space. The process is analogous to that of the random

electrical signal in communication theory. The latter has been extensively investigated by Rice [25] and

others. Davenport [30] has shown that the normalized

correlation coeflficients for the longitudinal velocity can best be represented in the exponential form,

R{^z,f) =e-'-f^^'''(j<'^ (29)

where As is the separation distance and C is an

empirical constant. A typical correlation curve is shown in Figure 8. Based upon experimental data

obtained by Singer [31], the following values for C

may be used

:

Along-wind direction : C = 7.7 Cross-wind direction : C = 23

Vertical direction: C = 7.7

These values of C clearly indicate that eddies are elongated in the direction of wind. This phenomenon

may be attributed to the presence of the ground

surface. The correlation coefficients are normally complex

quantities and are made up of two quantities : in-phase

and quadrature components. In other words, the best

correlation between two points may not necessarily occur at the same time. The parameter expressed by

Equation 29 is then the modulus of this complex

quantity and is also called the square root of the

coherence function. The phase is found to be small

and is normally neglected. In the evaluation of structural response to wind

loading, the load spectrum rather than the wind

velocity spectrum is needed. The former, however, can be obtained from the latter as follows: The drag force on the structure, P(z, t), can be

written as

P{z,t)=y2pCDAU-'{z, t) (30)

0.30 0.»

Figure 8. Typical correlation curve of wind velocity.

125
where p is mass density, Cd is the drag coefficient, A is the projected area and U is the longitudinal component of the wind velocity. Writing P{z, t) and

U{2, t) in terms of a mean and a fluctuating component, Equation 30 becomes

p+P=y2pCDA{u+uy (3i;

where P and U are the mean components, and p and u

are the fluctuating components. Neglecting the term

Equation 31 yields

2Pu

(32)

Hence, the load spectrum, Sp{f), can be written as

4:P'S.if)

(33)

where St,(f) is the velocity spectrum defined by

Equations 26 or 28. In the above derivation, it was assumed that the

drag coefficient, Co, is the static value corresponding

to 17. Experimental results [30], however, indicate

that this coefficient increases with frequency. For

slender, flexible structures, the error derived from

this assumption may be small, largely because of the

fact that at large frequencies, i.e., gusts with small

wavelength, the wind is poorly correlated. In Equation 21, the term Y{z,z',f) (the cross spectrum of the load) can be expressed as the product

of the load spectrum Sp{f) and the correlation

function R{Az,f). However, for a three-dimensional

structure, the spatial correlation in the three direc- tions must be considered. It is reasonable to calculate the correlation between gusts over the flow region

aft'ecting the loading on the structure. This assumption is generally considered to be reasonable [32] and

results in the following expression for spatial

correlation

R{z, z'J)

where

^27-l+e--A /2M-l+e

2y-

(34)

y = n.5fAx/Uo

fjL = 3.S5fAy/Uo

5 = 3.S5//f7o

The first two products in Equation 34 were obtained

by integrating the terms e"'-"^ and e^-" in the crosswind

and downwind directions, over distances Ax* and Ay,

respectively. For slender structures, it is implied in Reference 32 that Ax be taken as the diameter of the

structure and Ay be taken as four times the diameter.

A limited amount of experimental data obtained by

Vickery [33] indicates that the latter assumption may

be unconservative and additional experimental data

are needed to define the limits over which the

correlation should be extended. It is generally

considered to be conservative to assume that Ay is at least equal to the diameter or downwind dimension

of the structure.

If it is now assumed in the most general way that

the mean drag loading P{z) varies with height, then

it is easy to show that C„„,(/) can be written in the

form

C„„.(/)=45„(/) r f

4>M<i>m{z') P{z)P{z')

C{z)C{z') U{z)U{z')

'R{z,z',f)dzdz' (35)

Where S,.{f) is the velocity power spectrum given by

Equation 26 or 28, i?(z, z',f) is the spatial correlation

function given by Equation 34, and P{z) and U{z)

are the mean wind load and wind speed at height z. All of the significant properties of the fluctuating

drag loading are contained in Equation 35. Hence,

once the integration indicated by this equation is performed, the double summation indicated in Equation 20 or 25 is performed, followed by integration with respect to frequencj^, to obtain the variance

of the deflection at any point in the structure. The

variance of other structural quantities of importance

such as shearing forces and bending moments, which

are linearly related to displacement, may then be

obtained using conventional procedures. The equations can be solved straight-forwardly by numerical

integration with a digital computer.

It is generally assumed for gust loading calcula- tions that P{z) and U{z) can be taken as hourly

averages. When wind speed data for shorter averaging

periods are available, the pldt of Figure 9 may be

used to convert these speeds to hourly averages. This

plot was obtained by Durst [34] by means of a

statistical analysis of data taken in strong winds over

flat, unobstructed terrain. In Figure 9, F represents

the ratio of probable maximum wind speed averaged

over time t to the mean hourly speed. For "fastest

mile'' wind speeds the averaging period t is given by

f = 3600/1'/ where t is in seconds and V/ is the fastest mile speed in miles per hour.

The variation of U(z) with height is generally

assumed to follow the power law.

U{z) = Ua{z/SO)'' (36)

where U{z) is the velocity at height z above the

ground, Uo is a reference velocity at a height of

126
I 10 100 1000 IO.0OO tUec) Figure 9. Ratio (F) of probable maximum speed averaged

over period t to that averaged over 1 hour.

usually 30 ft and a is an exponent which depends on

the roughness of the terrain. Average values of a are given in Table 1. Using the concept of gradient height, i.e., the

height at which the effect of ground friction becomes

negligible, hourly wind speed data for a given

exposure may be converted to exposures of different roughness. Average gradient heights are in the order

of 1,500, 1,300, and 900 ft for exposures denoted in Table 1 by ^, B, and C, respectively. Based on a

900-ft gradient height for an open exposure (C), the mean hourly speed in Exposures A and B may be

related to that in Exposure C by

U{z)=imU,,c(^^^ (37)

where U(z) is the mean hourly speed at height z, Uo,c

is the hourly speed at 30 ft for Exposure C, and Zg is the gradient height. Equation 36 is plotted in Figure 10 for the three types of terrain.

z(ft.)

Figure 10. Wind velocity profiles.

It must be cautioned here that the above values

of a and Zg represent only average conditions, and do

not apply in cases where extreme conditions of shielding or channeling prevail.

3. References

[1] Von Karman and T. & H. Rabach, Uber den Mechanis- mus des Flusigkeits und Luftwiderstandes, Phys. Zeits

13(2), 1912.

[2] Milne-Thompson, L. M., Theoretical Hydrodynamics,

Macmillan, New York, N.Y., 1955.

[3] Roshko, A., On the Development of Turbulent Wakes

From Vortex Streets, NACA Tech. Notes 2913, 1953.

[4] Fung, Y. C, Fluctuating Lift and Drag Acting on a

Circular Cylinder in a Flow at Supercritical Reynolds

Number, Shock and Vibration Bulletin Part II, No. 26, Office of Secretary of Defense, December 1958.

[5] Cincotta, Joseph J. et al., Experimental Investigation of Wind Induced Oscillation Effects on Cylinders in Two

Dimensional Flow at High Reynolds Numbers, paper

presented at Meeting on Ground Wind Load Problems in Relation to Launch Vehicles, NASA Langley Research

Center, June 7-8, 1966

[6] Roshko, A., Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Numbers, /. Fluid Mechanics, 10, (3), 1961.

[7] Scruton, C, On the Wind-Excited Oscillations of Stacks, Towers and Masts, paper presented at Symposium on Wind Effects on Buildings and Structures, National

Physical Laboratory, Teddington, Middlesex, England, June 1963.

[8] Hurty, Walter C. and Moshe F. Rubenstein, Dynamics

of Structures, Prentice Hall, New Jersey, 1964.

[9] Nakagawa, Kenji et al. An Experimental Study of Aerodynamic Devices for Reducing Wind-Induced

Oscillatory Tendencies of Stacks, paper presented at Symposium on Wind Effects on Buildings and Structures, National Physical Laboratory, Teddington, Middlesex,

England, June 1963.

[10] Reed, Wilmer H. Ill, Models for Obtaining Effects of Ground Winds on Space Vehicles Erected on the Launch

Pad, paper presented at Conference on The Role of Simulation in Space Technology, Virginia Polytechnic

Institute Engineering Extension Series Circular No. 4, August 1964.

[11] Scruton C. et al.. Wind Excited Oscillations of Structures, The Institution of Civil Engineers, Paper No. 6758,

London, 1964.

[12] Reed, Wilmer, H. Ill, Hanging Chain Impact Dampers,

paper presented at the International Research Seminar:

Wind Effects on Buildings and Structures, Ottawa,

Canada, Sept. 11-15, 1967.

[13] Scruton, C, Note on a Device for the Suppression of the Vortex Excited Oscillations of Flexible Structures of Circular or Near Circular Cross Section, With Special Reference to its Application to Tall Stacks, National

Physical Laboratory Aero. Note 1012, April 1963.

[14] Goldman, R. L., Karman Vortex Forces on the Vanguard

Rocket, Shock and Vibration Bulletin Part II, No. 26, Office of the Secretary of Defense, December 1958.

1^7
Cowdrey, C. F. and J. A. Lawes, Drag Measurements at High Reynolds Numbers of a Circular Cylinder Fitted with Three Helical Strakes, National Physical Laboratory, Aero Report 384, July 1959. Steinman, D. B., Problems of Aero-Dynamic and

Hydrodynamic Stability, Proc. Third Hydraulics Conf. Univ. Iowa Studies in Engin. Bull. 31, 1946. Weaver, William Jr., Criteria for Design Against Wind

Induced Vibrations in Antenna Members, Annals of the New York Academy of Sciences, Vol. 116, Art. 1, June 26, 1964. Guyton B. et al., Maximum Amplitude of Oscillation of a Cylinder due to its vortex wake, Proc. ASCE, Vol. 82 No. HY4, August 1956. Ammann and Whitney, Investigation of Karman Vortex Shedding of Steel Stacks, Prepared for Chemical

Construction Company, New York, August 1968. Boorne, R. A., The Aeroelastics of Tall Stacks, Inst. Aero. Sci., Preprint No. 851, October 1958. Den Hartog, J. P., Recent Technical Manifestations of von Karman's Vortex Wake, Proc. Nat. Acad. Sci. of USA, Vol. 40, 1954. Landweber, L., Flow about a Pair of Adjacent Parallel Cylinders Normal to the Stream, David Taylor Model

Basin Report 485, 1942. Farmer, Moses, G. and Reed, Wilmer H. Ill, Study of Wind Excited Oscillations of High Band Wullenwebber

Antenna, NASA LWP-324, November 1966. Davenport, A. G., The Application of Statistical Concepts

to the Wind Loading of Structures, Proc. Inst. Civ. Eng.

19, 449-472, 1961.

[25] Rice, S. 0., Mathematical Analysis of Random Noise,

Bell System Tech. Jour. 23, 282-296, 1944 and 24, 46-59, 1945.

[26] Thompson, W. T. & Barton, M. V., The Response

Mechanical Systems to Random Excitation, J. Appl

Mechs. Vol. 24, No. 2, 1957.

[27] Van der Hoven, I., Power Spectrum of Horizontal Wind I Speed in the Frequency Range from 0.0007 to 900 Cycles

per Hour, J. Meteor. 14, 160-164, 1957.

[28] Davenport, A. G., The Spectrum of Horizontal Gustiness Near the Ground in High Winds, Quart. J. Roy. Meteor.

Soc. 87, 194-211, 1962.

[29] Harris, R. I., Measurements of Wind Structure at Heights up to 598 Feet Above Ground Level, Electr. Res.

Assoc. Report No. SPI/T31, 1968. (Unpublished).

[30] Davenport, A. G., The Buffeting of Large Superficial Structures by Atmospheric Turbulence, Annals of the N.Y. Academy of Sciences, Vol. 116, Art. 1, 1964.

[31] Singer, I. A., Wind Gust Spectra, Annals of the N.Y. Academy of Sciences, Vol. 116, Art. 1, 1964.

[32] Vellozzi, J. and Cohen, E., Gust Response Factors, Proc. ASCE Vol. 94, No. ST6, June 1968.

[33] Vickery, B. J., On the Reliability of Gust Loading

Factors, Paper presented at Tech. Meeting Concerning

Wind Loads on Bldgs. and Structures, Nat. Bur. of

Stds., Jan. 1969.

[34] Durst, C. S., Wind Speeds Over Short Periods of Time,

Meteor. Magazine, Vol. 89, 1960.

128
SOME DEFICIENCIES IN CURRENT METHODS OF ANALYSIS

R. W. Clough, Chairman

Division of Structural Engineering and Structural Mechanics

The University of California

Berkeley, California 54720

Deficiencies in methods of analysis for structures subjected to wind forces are considered. Areas of similarity between wind and seismic forces and their treatment by current building codes are discussed. Deficiencies include a neglect of the dynamic nature of the wind problem,

a lack of basic information, and an inadequate definition of acceptable levels of risk.

Key words: Buildings; climatology; seismic loads; structural engineering; wind loads; vibrations.

My talk will give us an opportunity to try to get

back on schedule, because I don't have a formal

paper, and I don't intend to take anything like the

allotted time.

As was mentioned, my subject is supposed to be

deahng with the deficiencies in the wind load

problem. I am afraid the principal deficiency that

will show up is my own lack of experience with this problem ! My experience is highly limited in the wind

area. What I want to do is to talk very briefly about a

specific problem that I was associated with. And in connection with this you might keep in mind that

my point of view in working with this problem was as a structural dynamicist working primarily with

earthquake engineering-type problems.

The particular problem that I was confronted with was the analysis of a guyed tower. This was a tower

which was to be a rather monumental structure. It was supposed to support a restaurant at a very high

elevation, and the analysis seemed to pose a considerable challenge as far as my own field of interest was concerned. At that particular time, we happened

to be working on analysis techniques for nonlinear

structures at Berkeley, and this seemed to be a good

opportunity to apply some of our computer programs

to a very practical example. After we got into the

analysis of the problem, it turned out that the

principal question of concern to the design engineer was the dynamic behavior of this structure, which,

of course, was quite a change of direction as far as our

analytical requirements were concerned. But, inasmuch as we had had quite a bit of experience with

earthquake design analyses for dynamic effects, we

felt that we probably could divert our direction, here

also, into the dynamic direction, so we proceeded to

set up a computer program for the dynamic

analysis of this non-linear structure. The program was based on a two-phased operation.

We started by considering the mean static wind load

acting on the structure and treated this as an

iterative solution of the nonlinear problem, successively changing the stiffness properties of all the

structural components in accordance with the forces which they were carrying. After we got the nonlinear

solution, we then proceeded with the dynamic

analysis for which we assumed the structure would

behave linearly, vibrating as a linear system about

the non-linear equilibrium positions defined by the mean wind pressures. This approach seemed reasonable to us, and, of course, it was a fairly straightforward problem to calculate the vibrational

properties for the particular stiffness coefficients associated with the mean wind condition which we

had previously calculated. So we went through the

standard vibration analysis, and then used mode

superposition procedures to calculate the dynamic

wind response. During the time that this analysis was under

way—in other words, while we were setting up the

computer program to do the things which we

thought needed to be done—I had my initiation into

the deficiencies in this whole wind business. Of

course, we needed information about the types of loadings to be applied to the particular structure at the particular location, and very quickly we found

what we thought were adequate data for preliminary

design purposes, describing the mean wind conditions

which we should apply to the structure. But, when we

began looking into the problem of dynamic behavior

of the winds and dynamic variations of velocities or

129
pressures, I was amazed to find that the Weather

Bureau simply didn't make measurements of that

type and had no statistics of any sort which were

directly applicable to our problem. This, of course, completely limits the capability of an analyst with

the kind of approach that we were proposing to take. Fortunately, after a number of inquiries, we were

directed to the NASA group which has been making

measurements at the Cape Kennedy tower, and they were kind enough to supply us with some excellent wind data for their 150-meter tower system which we

felt we could distort sufficiently to serve the purposes

of our own analysis. So, with this information, we

were actually able to make a deterministic study of the behavior of this particular nonlinear structure. About the time we got the data, unfortunately, the

whole project was canceled, and we never did carry out the complete set of analyses that we had in mind.

We had just started making some comparisons of nondeterministic studies—following Davenport's

techniques—to compare with our deterministic

studies. Our original hope was to use our deterministic analysis as a substitute for wind tunnel studies

we thought we could actually introduce specific

winds, study the actual behavior of the structure from a mathematical model of the structure, and, by

this approach, get something equivalent to a wind

tunnel study. Ultimately, of course, we recognized

the need for the nondeterministic study, to get some

estimate of the overall performance to be expected

over a long period of time.

This is the experience that I had. In connection

with this experience, I recognized a lot of deficiencies in the wind load picture, and I also recognized that

there are very definite similarites between the

deficiencies in the wind problems and those which we

recognize in the earthquake engineering field. I thought I might, just very briefly, relate some of my

concepts of these deficiencies. The first deficiency, I think, is in the code

specifications themselves. Both in the case of the

earthquake problem and the wind problem, the code

treats the behavior of the structure as a static problem. The dynamic nature of the problem which

actually exists is essentially ignored by the code. In

this respect, I think the earthquake business is a

little bit ahead of the wind business, because, at

least in the specification of the seismic coefficients,

there is some recognition of the dynamic properties of the structure; the seismic coefficients are presented as a function of the frequency of vibration of the

structure in the typical code approach. Also, I think

that it has become rather common practice now in

these monumental-type structures for rather complete dynamic analyses to be made of the seismic

behavior of structures. Very, very few really large, important structures in seismic regions are now designed without having

rather thorough digital computer studies of their

dynamic behavior under seismic conditions. In both

of these respects the wind load deficiencies seem to be more severe than those in the earthquake area. There

is very little direct recognition in the code of the

dynamic nature of the problem, and I think only in a very few instances, such as the ones which we have

heard about this morning, have we had significant

analyses of the wind behavior, including some

consideration of the dynamic response. Both of these

factors—the improvement of the code, and considerably more actual study of the dynamic behavior of the structure in the analysis phase—are necessary. The second area of similarity in deficiencies between the wind and the earthquake problems is in the lack of information. In the earthquake area, the reason for this shortage of information is quite

obvious. The major earthquakes, which are the

primary hazard to our structures on the West Coast,

are very, very rare occurrences. The Coast and

Geodetic Survey has a network of some 250 strongmotion seismographs distributed throughout the

seismic regions; but, even with this very large

network available, we have very, very few records of important earthquakes. In fact, we have no records

of really major earthquakes of the Anchorage or Chile proportions. This, I think, is not so much a

deficiency on the part of the people interested in making the measurements as it is a fact of life. We

just don't get that kind of information very fre- quently. On the other hand, in the case of wind data,

it seems that wind information is really quite

available; it's just a matter of devising suitable

instrumentation systems and going to work on getting

the information. I think the NASA tower at Cape

Kennedy is an excellent piece of work in this direction; and I think the NBS-ESSA cooperative

progi'am which is being set up here at this facihty is, also, a very good step in that direction. But these are very limited efforts in what should be a very

important area of investigation.

Now, in this regard I might point out that the City

of Los Angeles in its most recent code adopted a requirement that any major structure must include

two strong-motion seismographs in the structure. They put the burden of providing instrumentation on

the owners of the buildings in this case, and I think

there could be some consideration given in the wind

130
loading area to the same type of thing. I think major

j buildings such as the United States Steel Building

and the World Trade Center could very well be

forced by some sort of code requirements to include

in their actual cost of the structure some instrumentation which would benefit the whole profession.

; Finally, the other area of similarity, in the

; deficiencies of the design problem, between earth-

, quake and wind is in the area of defining the risk for which we ai'e actually designing structures. Code

' provisions are established as rather sterile quantities,

with very, very little indication of what kind of risk

• one is accepting—whether it's a hundred-year

j condition or a 10-year condition—and they also say

nothing about the level of damage which might well

j be expected to be associated with that particular

I loading condition. In the case of the earthquake

I problem, the typical designing engineer's philosophy

j is that he wants his structure to perform well—that

is, without structural damage—in relatively moderate

I earthquakes, but he is willing to accept a significant

' amount of structural damage in a major earthquake.

; Of course, he is hoping to avoid any total collapse and

! loss of life in a major earthquake, but the concept of

I accepting damage in a major earthquake is very well

j accepted throughout the engineering profession on

the West Coast. Now, this is a nice philosophy of

I design; I think it's a consistent one in terms of the

I economy of the country, but, associated with that

philosophy, there have been no indications of the

kind of earthquake we are talking about when we

I specify our seismic coefficients—no indications as to

whether these coefficients are supposed to relate to a

10-year earthquake or a hundred-year earthquake, or whether there should be any damage associated with

the structure that is designed according to these

coefficients. This is one of the tremendous deficiencies

in the whole earthquake problem; there has been no

real attention paid to the specification of these Ijasic coefficients. What should be done is to establish the

level of earthquake for which one intends to design

and then establish some sort of recurrence date for which that earthquake would be expected, and have

this clearly indicated in the code provisions.

Apparently the same situation is also true with

respect to the wind problem. There seems to be no

indication of whether the 40-pound pressure which,

apparently, is now specified in New York, is associ- ated with a 10-year return period or a hundred-year

return period, and apparently, there is no indication

of whether the structure is expected to come through

the design loading conditions without damage or whether some significant amount of damage is to be

expected. It seems to me that we can't continually

increase the factors of safety of our structures simply

by increasing the load coefficients one way or another,

without somewhere indicating the kind of risk which we associate with these various factors of safety. And,

I think that very soon in both the earthquake and

wind business, we are going to have to make some

sort of direct attack on this problem of relating the

code provisions to some measure of the risks which we

are taking.

Those are the only comments which I have to make. I thank you very much.

131
I

I

! !
PANEL DISCUSSION

Mr. Edward Cohen, Chairman

Amman & Whitney

New York, New York 10011

Dr. A. Allan Bates

Chief, Office of Engineering Standards Liaison

National Bureau of Standards

Washington, D.C. 20234

Professor A. G. Davenport

Faculty of Engineering Science

University of Western Ontario

London, Ontario, Canada

Mr. H. C. S. Thom

Senior Research Fellow

Environmental Data Service, ESSA

Silver Spring, Maryland 20910

PANEL DISCUSSION

De. Bates:

I am going to inject an unexpected note into this discussion—a note which may sound shghtly ominous

to some of you; actually, it is not ominous, I assure

you. Ed [Cohen] referred to the fact that there is now

in existence an Office of Standards Policy (now office of Product Standards) . This office, while it is located

within the Department of Commerce, has re- sponsibilities which spread far beyond the Department of Commerce—spreading to all the agencies

of the US Government, departmental, regulatory, and otherwise, which are concerned with

standards and matters relating to standards, such as building codes, which are, of course, in large part,

compendiums of standards. This newly established

office is only one part of a general concern of which I am sure you are all aware to some degree. There is a

concern in governmental circles—Federal, State, and

otherwise—over the development of standards in

this country under the traditional organizations,

which have been largely private. Our standards and

codes have evolved from privately introduced,

privately conducted actions; and this has endowed

the United States with one of the richest bodies of standards in the world. It has been a traditional

activity which has served us well but one which has come under increasing criticism in recent years. You're all aware of the concern of the Congress over consumer standards. You're aware of the concern of Congress over standards in general, especially as they

affect the public welfare. Now, if there is anything

that affects the public welfare, it is the standards and

the codes which relate to building and construction.

The two speakers yesterday were complementary

to each other in a most useful way. Professor Maugh

dealt in a very practical way with the bones and

skeleton—and Wayne Koppes with the skin or

exterior. Wayne Koppes showed us some slides—

a

series of pictures of damage, in which steel spandrels

and windows were torn loose by wind and went flying

around the atmosphere, to possible public detriment.

(Wayne's slides might collectively have been entitled

"Gone with the Wind!") The implication of pubhc

concern and public welfare was so great, not only in those slides, but in the remarks which he and

Professor Maugh and others made, that it is quite

certain that we are delving here in a field which is going to be looked into by Congress in the next year

or two. Professor Maugh pointed out, I think, the

primary areas of ignorance. He related them to three

major aspects of our subject, and he started out hy

saying that we need a great deal more information,

which is, I guess, pretty well known—although this

is not to despair over getting it, nor is it to be

derogatory of the vast amount of information we

already have. He related his remarks to frameworks

in the process of construction, that is buildings in the

process of erection, which are perhaps sometimes

peculiarly vulnerable to damage by dynamic forces,

and yet, in which case we have less information than we have for completed buildings. He also spoke of the

necessity of relating the frequency and mode of response in buildings—in high-rise buildings—with

relatively high frequencies, and related that to the

subjective factor, that is to say, how much the

average human being will stand without alarm, in building motion. This is certainly a subjective factor

in the study—the kind which should be studied more

often. He then went on to speak of structures with

relatively low frequencies. This gets us into areas in which both potential danger and ignorance are, perhaps, becoming magnified. Incidentally, in Moscow, a year ago, I stood at the foot of a TV tower

which is, according to my Russian informant, 1,700 ft

tall with a restaurant at the 900-ft level, and he told me, if I understood him correctly, that the structure was expected to sway 3 meters in the wind at the top.

Now, the frequency of that structure is, of course, not very high, and one wouldn't get the feeling of vibration up there. But, this is the sort of thing we

are getting into, and in which our ignorances are becoming magnified as we become bolder in design.

Wayne Koppes pointed out that the frequency of danger and, indeed, the totality of danger—the total summation of danger and of damage—is not so much

with the structure, but with the localized components

of the skin, the windows, the spandrels, and so forth. He emphasized further that the negative pressures

are, in general, apt to be higher than the positive

pressures, and this is, likewise, an area in which

while we are not ignorant—we know much less than we should. He also spoke of the funneling effect, which is obviously very important and of high

potential danger to the welfare of persons. He spoke

of the instance in which, I think he said, persons were—or potentially were—blown into a pond ; while

the pond was shallow enough that the effects were

135
not too damaging, this illustrates what can happen

due to these strange effects. Both speakers repeatedly referred to building

codes, and Professor Clough, this morning, returned

to them most emphatically in emphasizing the

deficiencies of codes. This brings me back to my

opening remarks, that codes and standards have

become of such concern to the public that the

deficiencies which have been so emphasized here

throughout yesterday and today, simply cannot be

permitted to continue. And indeed, they are not

continuing in the same order of magnitude as in the

past. The deficiencies of codes and standards are,

I think, quite certain to be the object of public

attention—a good deal of public attention. I can

refer you to a report, here, by a Congressional

committee which came out only a very few days ago,

in which the recommendation is made that every

voluntary standard, in effect, shall be subjected to a Governmental review, a very extensive three part

Governmental review—one for the legitimacy of the

procedure which has been followed; one for the

technical content, the adequacy and accuracy of the

technical content; and finally, the third review which

relates to what we might call the economic and social

effect of the standard. And, the recommendation is that all private voluntary standards be subjected to that review. Now, literally, this is almost an

impossible task to carry out, and, if and when this comes to your attention, I would suggest you get not

too greatly alarmed, as you might if you took the

language literally—because an impossible task can

be dealt with on the basis of its impossibility.

However, that task can be modified to become

possible, and will have a rather strong effect upon

such organizations as are represented by this group

here today, which are largely private—although not

entirely so. So my principal concern is the codes and standards

as viewed by any and all Governmental agencies,

regardless of their origin—private, Governmental, or otherwise—that these codes and standards shall be

reviewed with due diligence as they relate to the

public concern and the public welfare. Obviously, no

building code can ever be a perfect building code. Wayne Koppes made this point—that the extremely

complex local aspects of wind load and wind damage,

positive and negative, are such that it is almost

hopeless to ever reduce them literally to a complete

code which will take all of the curious aspects of buildings into mind. So, it is not expected that

building codes or building standards can be reduced

to perfect coverage which will assure no possibility

of damage or discomfort or danger within reasonable i ecomonic limits; but it is expected that due diligence

will be exercised—and I'm happy to say, as repre- sentative of this particular office which may have this task, that I am dehghted with the diligence and the

advancement in knowledge which has been shown by

the speakers in the discussions of this session. I think -j it's been a most fruitful session, and I hope it will be j followed by others, extending the vast reservoir of^ private competence and private knowledge which is represented here and in related organizations into

sufficient and proper progress in building codes and

standards.

Professor Davenport:

Mr. Chairman, I felt that probably my most useful task might be just to try to summarize some of the

keynotes that have appeared in some of the valuable

papers we've heard. I'll try to deal with them in not

necessarily the sequence in which they were given,

but rather in a manner more orderly in terms of the

development here. In this instance, I would like to

start with some comments on the meteorological

area, which I feel is the basis of most of our technical

problems.

We saw from Professor Gill's paper some evidence

that the instruments which we use to measure wind

speeds are extremely important. And, there was a

relationship—I felt—between his and some of the

remarks which Mr. Fichtl and Mr. Kaufman made in

their very interesting paper. One of the matters which concerns us is to try to find an adequate means

for referencing wind speed on a national basis or on a

continental basis, if you like. There are several

approaches to this. The Weather Bureau and the

Canadian Department of Transport have used what

are fairly standard measurements—they've used

hourly wind speed; they've used maximum gusts and

in the United States they have used the fastest mile.

And, there are also some upper level wind aero- nautical observations which are becoming extremely

valuable. I feel that there is a very great need to try

to communicate, to the meteorological organizations,

the need for developing a consistent type of measurement. This point was referred to by Mr. Smith. In the

brief discussion this morning, I came out in favor

for technical reasons—of an average which is based on something like a 15 minute average which is justifiable both for structural and meteorological

reasons. There are several difficulties which exist at present.

One is the determination of maximum gusts. As we

saw from Professor Gill's paper, the tj^pe of instruments which are used affects the reading. If you use

136
the fastest mile, you find that the estimate of the

fastest mile from actual records is an extremely

tenuous business when the wind speed gets very high,

for the simple reason that you're trying to measure

very small increments of distance on a chart of paper. There's never been any estimate that I've seen of the

accuracy of the actual data that has been presented.

The use of hourly averages is very much colored by

the method of observation, and in not all cases has

the hourly average been the true average, but has

been, rather, a guess by the meteorologist who's on

duty. These point to the fact that there is a need to improve accuracy in the records; and secondly, a need

to develop some consistent estimate of wind speeds

from which we can build a useful model of what the

wind environment of the structure is likely to be. Sometimes I've felt that we have looked at the

definition of the meteorological problem rather like the motorist in Nova Scotia who asked the way to somewhere from a local, and the local replied that, "If I wanted to get to there, I wouldn't go from here."

I feel that to try to evaluate the meteorological

problem from the vantage point of the surface of the

globe is probably the worst possible starting point to get to the final objective.

I feel very strongly that the kinds of observations

which we have tend to be misleadingly different—due

to entirely local effects—if a town has grown up

around the anemometer, then you're likely to see that reflected in the velocity of the wind. Historically

in the United States, with the coming of aviation,

there was a tendency to move most of the first-order meteorological stations off to airports from their positions in the centers of cities. This itself dramatically increased the estimates of wind speeds, and

hence the wind loads. This was entirely unrelated to a change in climate; it was simply that the instruments were moved.

I feel that there's a tremendous amount of information which is available, both to structural

engineers, and also to people who are interested in this kind of research. We've got the task ahead of us

to unscramble the information that is available, and

I think also, we have a task to improve the nature

of the records which are currently being made.

The value of upper-level winds is very useful in this respect. And, I've been most impressed by the

ICAN—I don't know what that stands for, something

about International Civil Aviation Network—these

types of organizations are interested in winds which

are free from the influence of the earth, and it's surprising how much order seems to emerge from the

chaos which comes from relying on surface

observations.

One factor which hasn't been touched on very

much in the meteorological area is the importance

of tornados. Mr. Thom might have some very useful observations in this connection. I think, though, that

if you were to order the damage in Canada and the

United States as to order of importance per year, I'm sure that tornados would head the list. I .suspect

that they cause more damage on an annual basis,

than do earthquakes—and, probably, more deaths.

Yet, we have extremely few handles by means of which we can get hold of this problem of tornado

action. The second area that I'd like to touch on is the

question of aerodynamics. In Professor Cermak's

paper, the value of wind tunnel techniques was noted.

We also saw pictures of his micrometeorological wind

tunnel at Colorado State University which was the

first effective instrument on this continent which

could handle structural problems in, what I consider

to to be, an adequate way. There is a long history to wind tunnel testing procedures. The evolution has

been, naturally, organized around the availability of wind tunnels. And, the kind of wind tunnel that

developed for aeronautical research was a very

logical one. It was designed, usually to be turbulencefree because the loads on aircraft are turbulence-free.

It was designed to obviate entirely the kind of conditions which really exist at the level of the

structures we're building. The micrometeorological

or boundary layer wind tunnel creates a flow repre- sentative of the wind. I believe it has to be used more

often, and the importance of its use—as distinct from

other types of wind tunnels—has to be emphasized.

Martin Jensen, a very well-known worker in this area, once remarked that he felt that the aeronautical

wind tunnel had already had nine lives in this kind

of problem area—that its inadequacies have been

demonstrated many times, but still people will continue to test in aeronautical wind tunnels, in

spite of quite strong evidence that some of the

problems are inadequately dealt with in this kind

of environment.

We heard from Dr. Simon of the importance of vortex shedding, and this, again, is a highly interest- ing problem with which we have to grapple. His was

the only contribution which dealt really effectivelj''

with this problem—but which was, perhaps, more

associated with the non-turbulent situation. When

we transfer our thinking to turbulent flow, our

experience is that we find a lot of surprises. The paper

by Professor Cermak, I think, very much underlines

the fact that the nature of our aerodynamic problems

is highly conditioned by dynamic influences. This

reality must color a lot of our future developments.

137
I think the question of the state of the integration

of the dynamic aspects into the profession was

highhghted by three papers—one by Professor

Vickery, one by Dr. Vellozzi and Mr. Cohen, and also the paper by Dr. Chen and Mr. Robertson. I think

there were several distinct approaches in evidence

here. I might at this point distinguish between what

I feel is a code approach, which is, inevitably, a

simplified approach—its terms of reference are not

altogether the same as the technical aspects of strict engineering design. It has responsibilities to the

public, which are embodied in the utility of the code.

Five or six years ago, I was asked to contribute a

section on dynamic loading which was usable—or hopefully usable—for the Danish Code. This has now

been in operation for several years. It was found to be

quite usable; engineers are finding that it is a manageable concept to deal with and doesn't stretch the ordinary structural engineer's technical background too far. There have been some points which we have to work with further in the Danish Code.

One is the question of vortex shedding, and this we're

trying to improve on at the moment.

In his paper. Professor Vickery pointed out that

the basic concepts of this approach are in reasonable

agreement for tall, slender structures with wind

tunnel work. The main influence of such a code, which

embodies the gust factor, is that, rather than change

the level of average loading, if you like, from the total assembly of all structures that we build, the gust

factor approach does not move the average value of the wind loading very much. What it does do is discriminate between structures a lot more than

present static wind loading codes do. For example, it has tended to relieve the loading significantly on such

structures as apartment buildings—which are very

broad and usually relatively stiff. It has tended to reduce the loading required for such structures from

what are our present-day code values. For slender

structures, such as smoke stacks, the loadings have

increased. And, in consideration of the damage rate,

I think this is a consistent development to have

happen—as the damage rate certainly would indicate

that smoke stacks are quite prone to damage under

certain circumstances. So, this has made the question

of wind loading a far more dispersed kind of loading

than it has hitherto been.

This has not as yet been adopted very widely by a number of codes. The French codes consider the

Danish approach regarding the gust loading factor,

and they did adopt a half-way-house, which was

embodied in the Russian Code, but they felt it was

too complex. My own feeling is that this is not the

case. We in Canada are intending to embody the

similar dynamic principle of gust factors.

I think that one of the questions that has to be

dealt with very much in the area of structures and

codes was referred to, both by Professor Maugh and

Mr. Koppes, in their very interesting papers. Professor Maugh referred to construction problems.

I think this is a very real question, and it's being

neglected in codes. Another question is the distinction between the

skin and the bones. I thought that was a very

felicitous phrase. I think it is quite essential that we ' discriminate between the formulation of the load

itself, in the first instance, between the skin and the j bones. The gust factor approach—along the Danish

lines and the new Canadian lines—will be organized

around these two aspects. The gust factor will apply,

in one sense, to the structure as a whole, and there

will be other gust factors entirely for use on the

exterior cladding. The reason is, of course, that the

size of the structure produces a fairly large averaging

effect on the overall loading and it also has resonant

amplification. The skin, on the other hand, is exposed

to very high local pressures—much higher local pressures—which are not averaged out and the resonant characteristics are entirely different. The

characteristics of the structural components are

entirely different from the characteristics of the

structure as a whole.

I think that one other aspect which has been

referred to this morning—perhaps on the philosophical end, but very important to think about—is the measure of the level of risk. We're using once-in-30-

year wind loads or once-in-50-year wind loads, and

these match up fairly well with what we reckon to be

"working loads" from our experience. The background of this is largely conditioned by history. There was a time when wind loads tended to be organized

around the maximum observation on record. Then,

people like jNIr. Thom came along with statistics,

showing that this is not a reasonable basis, because

records only exist to be broken now and again. It so happened—I think this is a fairly historical evaluation—that the once-in-50-year or the once-in-30-year was an average for the period over which we had

records and, therefore, it was logical to match the

wind speeds that were used in design for this kind of return period. But, if you turn to other kinds of loading, such as earthquake loading—as Professor

Clough was referring to this morning—you find that,

if you apply the same logic, you end up with a completely ridiculous answer. If people designed for the expected once-in-30-year earthquake load, they

138
wouldn't bother about earthquakes at all. What is happening, in a sense, is that we have a margin which

is protecting us—which is providing a buffer—between what you might call the most severe incident

that the structural engineer is prepared to entertain.

This buffer, or the safety factor, is keeping us out of trouble, because, really, when you talk about a

once-in-30-year wind load, you expect it to happen

once in 30 years doesn't mean that you go for 30

years without it. There are reasons to think about

this question quite seriously from several points of view. One is that the glass and the structure as a whole do not necessarily deserve to be given the same

return period. Some people may think that the loss of glass in a strong wind is a sort of safety valve. There are a lot of philosophical connotations to this problem which I think are worth trying to differ- entiate between. Another factor here is that for aerodynamic instability where the kind of margin

that you have—represented by the once-in-30-year

load—is not adequate at all. Finally, I would like to endorse the remarks that we should have better criteria to deal with in evaluating wind loads. The question of motion has

been mentioned several times. These, in many cases, are the most complicated problems and the most

difficult problems to overcome. If you can beat these

problems adequately, the structure itself will nor- mally have sufficient capacity to deal with strength

conditions. There's also the question of fatigue. My

impression is that most wind failures, if they do

occur, occur through fatigue. And the question of fatigue is always coupled with plastic action because

you cannot have plastic action without exposing

yourself to fatigue, and to deal with plastic action,

purely and simply, without considering how many

times the structure is bent back and forth—is to meet only half the problem.

Mr. Thom:

Dr. Pfrang asked me to say a little about wind

damage. I have been making some studies on wind

damage, based on data which the Weather Bureau

has collected over many years—since 1916, as a matter of fact. Several interesting points can be

briefly mentioned. Wind damage from large-scale

storms, such as hurricanes, extra-tropical cyclones,

and also including thunderstorms—which, of course, are small-scale storms, but those in which we can measure the wind speeds, at least—damage from this type of storm runs between five and six hundred

million dollars on the average per year. This damage

amount fluctuates violently from year to year, and

can run up to a billion and a half dollars. The damage

from tornados—which are storms in which we cannot measure the wind speeds—runs about one third of the

damage from these large-scale storms and thunderstorms. It runs about $150 million a year, and again,

there are large fluctuations from year to year. Of course, much of this damage is to small

structures, and literally, the figures aren't too

accurate. However, one can draw some important

conclusions from them. At the same time, we've

conducted studies into the mortality—that is, the

loss of life—due to these types of storms. There are some rather interesting facts which I'll be calling attention to in these two studies, and these

arise from probabilistic considerations. In the case

of the large-scale storm, the damage is constantly

increasing from year to year. It is going up ex- ponentially, roughly, as the population increases. This, of course, is due to the fact that the probability

of being hit by a storm of this character is proportional to the amount of area that is covered by

structures which is proportional to the population.

So, this damage has increased from year to year and

will go on increasing—perhaps with some little reduction, maybe due to design (I don't know what

can be done along these lines). Anyway, the fact is that it's increasing, and it must increase based on

this increase in probability of structures being struck

by such storms. Now, as far as the loss of life is concerned in these

large-scale storms, this has been greatly reduced

because of the warning system that's been put into

effect in the last 20 years or so. You have observed

this yourself; the loss of life in hurricanes, for example, has been reduced to almost no loss of life at

all, as compared to 20 or 30 years ago. This, possibly,

will increase some along with the probability of being

sti'uck by these storms, but, as the warning systems

improve—which they, no doubt, will—this will probably keep the loss of life at some reasonable level. One other thing to consider here, of course, is that

the area of the country along the East Coast, where

the major part of the population is concentrated, has

the largest probability of high winds. So, this contributes a great component to this damage. In

the Mid-West, where the population is much more

spread-out, the probability of damage is less. On the

West Coast, where the population is large—becoming

larger and larger all the time—the probabilitj^ of high

winds is generally ver}^ low, so the risk of damage is low.Now, in the case of tornados, the damage has also increased, because you can't take a house in when

there's a warning of a tornado—you can't hide it

139
somewhere; it's going to be struck by the tornado

if this is the inevitable consequence. The loss of life in tornados also has been greatly reduced by

improved warnings. The wind damage, however,

continues to rise. It rises in a somewhat different manner, because the high probability of tornados in the United States is in the Mid-West, where the

population is, more or less, spread out. But, we can

see in the statistics, that, as a result of the migration

from farms to cities—which has been large over the

past 30 years—the chances of striking urban areas have also increased. Hence, this has been a considerable factor in increasing the damage loss in tornados

•—that is, the chance of the storm's striking an urban

area is much larger than it's striking a single

farmhouse. Here again, the situation with respect to the probability is a little different. In the area along

the East Coast, where we have the main concentration of population, the probability of tornados is relatively small. On the West Coast, the probability

of a tornado is practically zero. So, fortunately,

where we have the most sparse distribution of population, we have the high probabilities.

Enough of that .... The striking thing is, I think,

that this damage is increasing. And, by the nature of the probabilistic situation, it must constantly

increase, except for what can be done in the way of design against this damage.

Now, to actually get to the program: I got the

impression from Professor Gill's presentation, that

the instrumentation is in pretty good shape. He

showed that we have instruments that can be used to measure most of what we anticipate measuring at the

present time, and that, if we need to go to higher

frequencies, development of such instrumentation

could take place—which would take care of the

problem. So, I think this is in very good shape

thanks, to a large extent, to Professor Gill, himself,

who has designed and built many of the instruments

that are in use today. In the second paper by Mr. Singer and Mr. Smith,

I thought that a very pessimistic view of things was

given. I don't feel that things are quite that bad. It seems apparent, at least, that the wind problem—and

the mechanics problem also—divides itself into two

parts. One is what might be called a macro-wind—the

kind of winds that we now produce for design data. And, superimposed on this is a gust which we

determine theoretically and, in some cases, have been

able to measure. It's apparent, also, I believe, that

the gust is a scale change on the macro-wind, and this

is a rather happy set of circumstances, because it makes the statistical theory somewhat simpler. So,

if we can determine the gust factors with some degree

of accuracy and then superimpose this on a macrowind, I think we would have an estimate which

would have a standard error—or relative standard

error—that was certainly well within the accuracies

of the mechanical design.

I would say another word here—based on some of my own experience. We have used the fastest mile

largely because there was record available, and it's the best record we had available—available for a

considerable number of years, a requirement for a

valid statistical analysis. We might have made a

better choice if we had been in a position to start with

other instrumentation and we could then have

chosen a better measure of the wind. But, one must

not forget that this is a climatological problem

where, in order to determine probabilities and design

values with respect to wind, one must have a fairly

long previous record. So, one can't say today, let's change the observation and have a design value

tomorrow. If we changed the record, we would have

to wait quite a number of years before we could make

some reasonable estimate of the probabilities. Now,

as to the validity of the present data : we have checked on numerous occasions where there were reports of high winds, in other cases where we were able to add

a considerable amount of data to the previous

records—and we've found that, in a large percentage

of the cases, the records were stable, and that the

addition of extra records simply served to enhance

the accuracy of the estimates, and did not change the

climatological features, namely the statistics of the

distribution.

Now, a word about the return period—I don't

really like the term "return period;" I like to use "mean recurrence interval" because it explains

really what the term means. Mr. Cohen brought up

this question this morning, and the question also was

raised in Ottawa. No answer has been given to this,

and I don't know whether there is an answer to it or

not. But, certainly, I think everybody would agree that a 50-year mean recurrence interval is not a measure of the probability as it applies to the

structure. As was pointed out by an Austrailian^—

I

think it was Professor Joubert—in Ottawa, that if this were so, there would have been a large number

of structures which would have failed over the past

hundred years. Well, we haven't experienced this. So,

what apparently is happening, and I think this can

be demonstrated if one considers a rather simple

structure—is that we have enormous factors of safety on the mechanical side. Otherwise, this 50-year

design wind just wouldn't be safe. And, we're pretty

140
sure that the wind speeds cannot be that far wrong

nor can we be that far off on relationship to the static load. Certainly, there are random errors in both, but

they couldn't be as far off as this probability must be. So, I think that—as Mr. Cohen said this morning

we should get to a more realistic consideration of the

overall probability. As somebody said the other day,

we're going to design buildings no matter how much

we know, and this is what's gone on in the past. I think a 50-year mean recurrence interval just came

to be something that everybody sort of liked. It's been going on for a long time, and if you try to change this in any standard or code, you're going to run into a lot of difficulty. So much for that . . . Mr. Fichtl and Mr. Kaufman gave a very interest- ing paper which provides a good bit of information on

the fine-scale structure of the wind. I think that we

need a lot more of this kind of work, particularly at high wind speeds. Most of the spectra that we've had

in the past have been determined at low wind speeds

by people who are interested in air pollution, and

these may not be adequate for the higher speeds. But,

I don't think that they're very far off either, because we have other checks with respect to the gust factors,

which makes them appear to be rather reasonable.

Finally I would like to comment on wind damage

as it relates to the complexity of the structure. I think it is, as Professor Davenport pointed out, if you

look at the mechanics of the problem, you'll find that

the probability of a concentrated load on the cladding

will be much higher than the probability of a load

which causes a collapse of the building. The building

is made up of a series of components which interact

with each other and which produce a convolution of probabilities which makes the chance of failure of the

whole structure an extremely small probability. If this weren't so, then we would have much greater

collapse damage from wind.

The statistics we get on wind damage are, admittedly, not very good. I don't think anyone can get

very good figures on wind damage, but we do l.lie best we can. We've had a lot of criticism about the.se figures. Some insurance companies want to do onething with them, and other insurance companies want

to do the opposite. For one person, our estimares are too high; for another per.son the estimates are too low .... What these figures do show is what's

inevitable in the probabilistic model—that these are

increasing ... So, I say in both of these studies that

the principal use of these estimates is to show the

relation from year to year, rather than anj' al^solute value. From my examination of the data, I would say

that a major part of the total consists of a large

number of small damages—that is, mainly on the

cladding of the buildings. (I'm now talking about

thunderstorms, extra-tropical cyclones—the kinds of storms that you would experience, let's say, in Minnesota—excepting tornados.) Now, as far as tornados are concerned, the situation is entirely

different. As you know, few structures will withstand

a tornado. When a tornado strikes a building, that's usually the end of it, unless it happens to be a

reinforced concrete structure or some similar strong

structure; but, even there, there have been cases where a tornado causes a collapse by failure in some

particular area of the building. By and large, I would

say that, for the large-scale storms, the damage is mainly to the cladding or to relatively small

structures.

I remember a Bell Laboratory man saying to me

that of 1,500 microwave towers his company had

constructed, it had lost three. If you consider the

probabilities in this situation, you would expect a lot more failures than that. In other words, those towers

are designed to be strong enough to carry the loads. I've wanted to look into those three failures for I have

a sneaking suspicion that tornados did the job of destruction.

141

APPENDIX

Note: The following papers were submitted

after the formal program was established.

COMBINING A WIND TUNNEL ANALYSIS WITH A THREE-DIMENSIONAL

ANALYTIC BUILDING ANALYSIS

Gary C. Hart

Assistant Professor of Engineering

University of California

Los Angeles, California 900^4

A three-dimensional computer oriented stiffness representation of a liigh-rise building is described. Statistical quantities obtained from aeroelastic models in a boundary layer wind tunnel

are combined with the three-dimensional analytical building model to obtain a probabilistic

description of the building's response. The response is expressed in terms of the mean and co- variance of floor displacements and stresses in the structural members. The procedure is intended

to provide a more realistic combination of the aerodynamic and structural behavior of a high-rise

building.

Key words: Buildings; dynamics; gust loads; matrix analysis; mode shape; probability theory;

wind loads.

1. Introduction

This paper presents a systematic procedure for combining an aerodynamic high-rise building model

with a three-dimensional computer oriented stiffness representation of the building. The building's response is expressed in terms of the mean and

covariance of the floor's displacements and structural member's stresses. A boundary layer wind tunnel is used to model the

wind's structure and the topography surrounding the

building. Various wind speeds and angles of attack can be studied. During all such studies the aeroelastic

model is allowed to translate in two orthogonal

directions and corresponding time histories of response are recorded. These two orthogonal motion

time histories are assumed to be approximations to the actual building's first two normal coordinate

response-time histories. The means, variances and

covariance of these two time histories are calculated. Then, these statistical quantities are combined with an advanced three-dimensional analytical building

model to obtain a probabilistic description of the

building's response. The procedure has assumed that

the response of the building's third and higher modes

does not significantly influence the response and

therefore can be neglected.

The proposed procedure has the following important characteristics: (1) the aerodynamic forces acting on the building are considered in the response,

(2) the structural behavior of the building's beams

and columns can be modeled using "state of the art" techniques, and (3) the in-plane rotations of the

building's floors are approximately calculated by

using the building's actual first two modal vectors.

It is believed that the presented wind design

procedure more realistically combines the aero- dynamic and structural behavior of a high-rise

building. Also, by virtue of the separate modeling of the structural stiffness and the aerodynamic response

this procedure is particularly well suited to con- tinuously use new future developments in each of these areas.

2. Dynamical Equations of Motion for

the Building

The first phase of a dynamical analysis of a

high-rise building involves determining the structure's equations of motion. In such a formulation we must

first define the building's independent generalized

coordinates. Figure 1 shows a simplified building and

its assumed generalized coordinates. In general, there

will exist three independent rigid body floor displacements per story—two translational and one rotational

degree of freedom. For the buildings that are the

main concern of this paper, the translational

displacements of the floors are assumed to be large

when compared to the floors' rotational motion.

However, this rotational motion can still be expected

to significantly affect the structure's stresses in the

outside frames. Several methods exist for formulating

the stiff"ness matrix of the building [1, 2, 3],* and it should be emphasized that the accuracy of the

entire wind design procedure depends on the

formulation of the structure's stiffness matrix.

* Figures in brackets indicate references at the end of the paper.

145
(•^1 th STORY

2nd STORY

1st STORY

/77S777

Figure 1. Generalized coordinate (floor) displacements of a

building.

If the generalized coordinates of the building are located at the center of mass of each floor, then we

can write the building's dynamical equations of motion as

Now, if we define the building's normal coordinates

as !Q}-m-Mg! (2)

then the dynamical equation of motion in each

normal mode (coordinate) is Qi+2^M^+^^''Q, = F,, i=l,2, 3, -..iV (3)

When high-rise buildings are modeled in a wind

tunnel, only the first two translational {X and Y)

modes of the building are modeled. In general such

modes will correspond to the first two normal

coordinates of the structure. For future discussion it

is here established that the X and Y translational

modes correspond to the first and second normal

modes, respectively. It is also assumed that the

building's motion in its other normal modes does not

contribute to its response and are assumed to be

zero. Therefore, we obtain

Ch +2^,^A+WQi = F, (4)

Q2+2^'M2+^iQ2 = F2 (5)

Q, = 0; f = 3, 4, --.iV (6)

which completely defines the deformed configuration

of the building.

Because of this normal coordinate truncation the

relation between the generalized and normal

coordinate displacements, Eq. (2), simplifies to

9i

{qN}

*11 <J'l2

*22

^'21 *22

IN Q2

< 0-

,0.

(7)

Therefore, from Eq. (7) we see that a knowledge

of the first two normal mode displacements enables us to completely define all of the building's generalized

coordinate displacements. Also, the eigenvector

matrix used to relate the normal and generalized

coordinate displacements is calculated using the

building's stiffness matrix. This matrix is obtained by

using the most recent building models and can include

such important internal degrees of freedom as column

vertical displacements and beam-column joint

rotations [2, 4]. Knowledge of the generalized coordinate (floor) displacements enables one to completely define the

deformed position of the building. From such a deformed shape the stresses in the building's beams

and columns can be expressed in terms of the

generalized coordinate (floor) displacements. Let such

a relation l)e written as

(S)

The preceding formulation establishes the neces- sary equations to relate the structure's normal mode

displacements to its generalized (floor) displacements and stresses. It is important to emphasize

the fact that while the knowledge of the first two

normal mode displacements is sufficient information to completely characterize the structure's deformed shape, the error associated with such a shape depends on the validity of the assumption

that the contribution of the third and higher normal

modes is negligible. This means that the designer146
analyst must first establish what it is that he wants

to caluclate, then calculate the building's eigen- vector matrix and decide whether or not the results obtained using only two normal modes are within

his desired accuracy criteria.

3. Wind Tunnel Response of Building

Present procedures for modeling the wind-excited

motion of a high-rise building in a wind tunnel at- tempt to model the building's first two translational

mode responses. Figure 2 shows a simplified diagram

of the building's wind tunnel model. This model is allowed to move parallel to its two principle axes. This motion is resisted by a physically created spring

stiffener and a viscous damper at the base of the

model. The dynamical equations of free vibration

for the wind tunnel model are

lox&x +CxOx + «Sa-^a- = 0 (9)

(10)

It should be noted that the wind tunnel model is assumed to be a rigid body supported at its base

and the spring stiffness at the base is the only elastic restraint. Upon studying Figure 1 and Eq. (7), we see that

under certain conditions the generalized coordinates

of the wind tunnel model, dx and dy, are exactly

equivalent to the building's first two normal coX-DIRECTION MOTION

B

Y- DIRECTION MOTION

8x

UNOEFORMED

POSITION

ordinates, Qi and ^2- These conditions arc: (1) the

fundamental mode shapes of the building in its X

and Y directions are straight lines, and (2) the ele- ments of the first two modal vectors corresponding

to the floor rotations are zero. This is shown graphically in Figure 3 for a three-story building. However,

in general, these criteria are not exactly satisfied and dx and dy only approximate the structure's

first two normal modes.

The spring stiffnesses and viscous damping constants of the wind tunnel model are selected such

that dx and dy approximate Qi and Q2, respectively.

With such a selection the time histories of building response in the wind tunnel [i.e., dx{t) and dy{t)] are approximations to the actual time histories of first and second mode displacements [i.e., Qi{t) and

^2(0]- The accuracy of the approximation can be

studied by expanding Eq. (2) for the three-story

building in Figure 3,

Qiit) =ynqi{t) +ynq2{t) +ynqs{t) H {-ym^it) = 7n9i(0 +yuqdt) +71797(0 (X-Direction)

+71292(0 +71595(0 +71898(0 (^-Direction)

+71393(0 +71696(0 +71999(0 (Rotation)

If the Y-translation displacements and the rotational displacements are zero and if the terms 711, 7i4 and 717 plot a straight line "mode" shape, then

Qi{t) is exactly equivalent to dx{t). Otherwise, the

displacement measured in the wind tunnel, 6 (<), is an approximate measure of Qi{t). Now we must

define what properties of these wind tunnel time

histories must be calculated in order that we can

accurately describe the behavior of the structure.

First we must calculate the mean response of the

first and second mode displacements. This is ac- complished by using temporal or sample averaging

techniques. The mean displacements of the first and

second normal coordinates are

/ % . / 7

/

/

^^2 /

/

Figure 2. Wind tunnel representation of building. Figure 3. Linear mode shapes of example building.

147
^[Qi(0]-^C^x(0]= ~ f exit) dt (11) =

1 f'' E[_Q,{t)^^Eldy{t)^= - / dy{t) dt (12)

where the length of the time history is denoted by

T, see Figure 4. Second, the variance of the coordinate displacements is of practical engineering importance. This

statistical quantity is a measure of the variation

about the mean structural response. By taking the

square root of the variance, we obtain the standard

deviation. A large standard deviation to mean

displacement ratio denotes a very oscillatory behavior whereas, a small ratio indicates a nearly static response. To calculate the variance of the first and

second normal coordinates, we use the equations

Var (Qi(0)== Var (dxit))

= ^ f (exit)-Eldx{t):\ydt (13)

^ •'o Var (Qiit))^ Var {dyit))

eY{t)-E[_ey{t)']ydt (14)

Third, the covariance between the first and second

normal mode displacements gives an indication of the correlation between the two modal displace- ments. If the two motions are not very correlated

then the covariance term has a small magnitude.

The covariance is calculated using the following

equation

:

Gov (Qi(0,Q2(0)- Gov {ex{t),ey{t))

=

\j^ {ex{t)-Elexm)

{ey{t)-Eley{t)^) dt (15)

The variances and covariance can be collected into a 2 X 2 matrix called the covariance matrix, it is

"Var(Qi) Cov(Qi, Qs)'

Gov (Qi, Q,) Var {Q,)

The three previously-mentioned statistical quantities enable us to establish the probability associated

with a certain value of building response; (i.e., displacement, shear, or moment). If the building's

motion has a Gaussian probability distributed about

its mean response, then these statistical quantities

completely define the distribution. However, even

if the response does not have a Gaussian probability

distribution, we can still obtain valuable information about the probability of any response by using

Chebyshev's inequality [5].

4. Probabilistic Response of Analytical

Building Model

In the previous section we calculated the building's

mean, variance, and covariance response in its first two normal coordinates. Physically these normal

coordinates can be approximated in the wind tunnel

;

however, from the designer-analyst's viewpoint,

they are only a convenient mathematical quantity.

The real items of his concern are the shears and

moments in the building's beams and columns be- cause it is these generalized forces which determine

the building's stress level. Therefore, we must now

relate the statistical quantities we can calculate to the building's generalized coordinate displacements

and forces. In order to completely define the deformed shape

of the building, we must completely define the dis- placement of all normal coordinates. This is indeed a major task. However, as previously noted, it is sometimes possible to calculate the building's re- sponse with a "fair" degree of accuracy by only

using two normal modes. In other words, the response

of the higher modes is assumed to be zero. It is important to realize that such a two normal mode

description of the building's response is only an

approximation and may be in error when higher

modes significantly contribute to local shears or moments.

Equations (7) and (8) relate the first two normal

coordinate displacements to the building's generalized coordinate (floor rigid body) displacements

and its stresses. Repeating these equations, we write

(7, repeated)

and

Figure 4. Modal response of wind tunnel model. [ ^

! = [5] 1 3 } = { Q I = [L] ! Q ! (8, repeated)

148
The statistical properties of the normal coordinate

displacements calculated as defined in Eqs. (11)-

(15) can now be used to calculate the corresponding

properties of the generalized coordinate displacements and stresses. The mean values of these quantities are

^tlg!] = [i^M{Q)] (16)

and

^[{<rn = [LM{Q)] (17)

It can also be shown that the corresponding co- variance matrices are [F"]=m[F^^][AT (IS)

and

m= [.LjyQj_Lj (19)

The means and covariances calculated as described

in (16)-(19) can now be used to completely define

the Gaussian probability distribution or Chebyshev's

inequality.

Special attention should be paid to the following

items: (1) only two normal modes are used and,

therefore, [V^\ is a 2X2 matrix; (2) the building

matrix is a separate part of the analysis and can be

obtained using "state of the art" techniques; (3) the

rotational motion of the floors in the actual building

are approximated by using such rotations as they

exist in the first two normal modes.

5. Conclusion

The procedure outlined in the preceding pages of

this paper is intended to help improve the wind

design of high-rise buildings whose dynamical behavior is only slightly asymmetric and whose first two normal mode shapes are nearly linear. By using

the building's first two actual modal vectors with the

approximate time histories of normal coordinate response we can impi'ove the accuracy of the computed structural member stresses. Separate modeling of the aerodynamic response

calculations and the building stiffness characteristics

enables us to utilize the continuously improving

techniques of each. The validity of the procedure for design of highrise buildings which possess the dynamic characteristic assumed herein must be proved by future

design and full scale measurements. Such studies are very strongly recommended.

6. Nomenclature

[q] = vector of building's generalized coor- dinate displacements

[yl/] = diagonal inertia matrix

[C] = damping matrix

[S] = building stiffness matrix

{A} = forces corresponding to the generalized

coordinates

{Q} = vector of building's normal coordinate

displacements

[$] = normalized eigenvector matrix = inverse of normalized eigenvector matrix

/3, = damping in i^^ normal mode

fli = natural frequency (rad/sec) of i"' normal

mode

Fi = force corresponding to the ^"' normal co- ordinate

N = number of generalized displacements for the building, three per story

{a} = vector of stresses that exist in the building's beams and columns

[B] = transfer matrix relating generaUzed dis- placements and member stresses lox, IoY= mass moment of inertia of the wind

tunnel model about an axis passing

through the centroid of the base and

parallel to the X- and F-axis, respectively

Cx, Cy = viscous damping of wind tunnel model in the X- and F-direction, respectively

Sx, Sy = rotational spring stiffness at the base of the wind tunnel model in the X- and Fdirection, respectively

[K]^ = transpose of the matrix [/v]

7. References

[1] Clough, R. W., and I. P. King, "Analysis of Three- Dimensional Building Frames," Publications, IA BSE,

Zurich, Switzerland, Vol. 24, 1964.

[2] Weaver, W. W., and M. F. Nelson, "Three-Dimensional

Analysis of Tier Buildings," Jour, of the Struct. Div., Proceedings of the ASCE, Vol. 92, No. ST6, December

1966.

[3] Hart, G. C, "Response of Thrcc-Dimensional Buildings

to Multiple Random Wind Forces," Stanford University Technical Report No. 92, Dept. of Civil ICngineering,

Stanford, California, July 1968.

[4] Rubinstein, M. F., and W. C. Hurty, "I^ffect of Joint Rotation on Dynamics of Structures," Jour, of the Engr. Mech. Dir., Proceedings of the ASCE, Vol. 87, No. EM6,

December 1961.

[5] Parzen, K., Stochaatic Processes, Holdcn-Day, Inc., San

Francisco, California, 1962.

149

THE ENGINEERING INTERPRETATION OF WEATHER BUREAU RECORDS

FOR WIND LOADING ON STRUCTURES

S. C. Hollister

Cornell University

Ithaca, New York 14850

This paper utilizes the records of the fastest mile as published by the United States Weather Bureau from data obtained at their airport stations, to develop wind loadings on engineering

structures. It analyzes gusts and shows how gust loadings should be dealt with in structural

design. Roughness of terrain and extent of cover in rural and urban localities are systemized for engineering purposes. Occurrence of extreme winds, as studied by the Weather Bureau, is extended

to a stage where a practical code may be written. Finally, designing for a given structural life and for a desired level of risk is discussed.

Key words: Buildings; climatology; extreme value theory; gust factors; structural engineering;

wind loads; wind profile.

1. The Wind Records

Wind records in other countries, and older records

in this country, simply give the highest velocities observed, without at the same time describing either

the terrain or the roughness of cover, or the capability

of the instrument; and usually without the duration

of the reading or the location of the instrument above

the ground. Such a record is nearly useless for engineering purposes, since it is not capable of

analysis. Responsiveness of the instrument must be

known to evaluate accuracy in recording gusts. Time

of measurement of gusts is required to deal with gust

content. Knowledge of elevation of anemometers

above ground is necessary to compute a profile of pressure against a structure. A careful description of the terrain and of the cover along the axis of the

principal fetch for a distance of 10 miles is necessary

to evaluate the nature of the oncoming windstream,

and to compute the relation of velocity and pressure

to elevation above ground. In this country in recent years, records have been

made at airports of extreme winds, recorded as the

average in miles per hour for the fastest mile of windstream. Such records infer character of terrain

and degree of smoothness (although it would be

incorrect to assume that the profile of the fetch

uniformly justifies use of the seventh-power law). The

use of the mean velocity over the fastest mile of wind

involves distance and time as well as velocity, and

thus gives immediately the opportunity for gust

analysis. The Bureau also standardizes the reported

observations as at 30 ft above the ground, so that

they may be compared statistically with data

similarly reported from other places, making possible

preparation of probability isotachs and estimates of extreme value forecasts. Thus, such records make

possible for the first time the engineering interpretations necessary for designing to resist wind.

This paper deals with the means by which the

information needed for rational design may be

obtained from the fastest-mile records published by

the Weather Bureau.

2. The Occurrence of Gusts

A record of wind velocity consists of a more or less rapidly waving line inscribed on a moving tape. Each

oscillation is a gust. Means over an interval of one hour do not reveal gusts, but give the velocity of a steady background wind. The ratio of the mean

velocity over a short period, as one second, to the

hourly mean gives the gust factor F„ for that period.

Measurements by Giblett, et al. [1]* in 1927-30 at Cardington, England; by Sherlock and Stout [2] in 1933 at Ann Arbor, Mich.; and by Huss [3] in 1946 at Akron, Ohio, clearly show that the intensity of gusts

is greater for shorter than for longer durations; and

that for heights to 225 ft, at least, the gust factor Fg is not a function of height above ground.

Figure 1 shows a plot of the results of Giblett's

observations, as further studied by Durst [1], and of Sherlock's study of gusts [5]. Giblett used a Dines

anemograph, which according to Scrase [6], loses accuracy at intervals below 10 sec. (The 5-sec. value

plotted on Figure 1 shows the tendencj'' to read low on

* Figures in brackets indicate literature references at the end of this paper.

151
az 0.S I 2 5 10 30 60 100 300 900 1000

Gust Duration, sec Figure 1. Relation between gust intensity and gust

duration.

short intervals.) Sherlock and Stout used a pressureplate anemometer of their own design, with a

response of 0.15 sec. [7]. Huss used a cup anemometer

with a response of 1 sec. or more. One value of Huss's

is shown on the figure.

Figure 1 indicates that a fastest mile with a mean

velocity of 60 mph (hence lasting 60 sec.) would have

a gust component of 12 mph. Some longer period of time, say 1 hr., would then have no gust component;

and if it included the 60-sec. period just mentioned,

would have a mean velocity of 48 mph. The fastest 5-min. duration of the hourly period, according to Figure 1, would have a gust factor of 1.09; or a gust

of 9% of 48 mph, or 4 mph, making a total mean

velocity of 52 mph.

Figure 2 shows the relation between the observed

fastest mile and the hourly mean of which it is a part.

Thus, an observed fastest mile of 100 mph would be

a part of a fastest hourly mean of 77 mph.

The form of the curve in Figure 1 for gust

durations greater than 300 sec. is not known

accurately; it may well curve to the right and

become tangent to Fg = 1.0. In any case for a 10-min.

average wind, the gust factor would be little more

than 1.05; and an hourly average would be devoid

of gusts. This justifies the concept of the wind being

made up of a steady component represented by the

hourly average, to which is added fluctuations, or

gusts, both positive and negative, these fluctuations

30 " ^ ^ 1 ^ L 1 30 40 50 60 80 100 150 Hourly Mean Velocity, mph

Figure 2. Relation between observed velocity for fastest

mile, fastest tenth mile and fastest 100 ft of wind.

being more intense the shorter their duration.

The equation for the curve in Figure 1 is, when t is the gust duration,

/^,= 1.73 A' -2 (1)

or in a more convenient form for computing:

log = 0.23805 -0.07935 log < (la)

The present writer knows of no study of probability

of occurrence of winds of shorter duration than the

fastest mile. If it is assumed that the frequency of the

fastest 1^ mile or the fastest 100 ft are the same, one

could use the two lines so marked in Figure 2 for design purposes. Thus, an observed fastest mile of 90 mph would be assumed to contain a fastest 100 ft of 126 mph, while the hourly average would be 70

mph. It would be hoped that the Weather Bureau

could mount instruments at a few chosen stations,

alongside those recording the fastest mile, to deter- mine whether the many factors causing extreme gusts

would cause them with the same frequency as those

of the fastest mile. Such gust frequency might also be

different from that of the fastest mean hourly

velocity. Information on these factors would have use

152
in the economical design of structures. In the

meantime, we must infer that gusts as shown in Figures 1 and 2 have the same probabiUty of occurrence.

3. The Variation of Wind Velocity with

Elevation

It is seen from the foregoing discussion that an

instantaneous profile would have gusts distributed

along it and hence would not be a smooth curve. From

Figure 1 it is concluded that a mean velocity of 10

min. or more is necessary to obtain a smooth profile.

To such a profile an envelope of gusts may be added,

thus producing a synthetic profile of extreme velocities that looks smooth.

Before proceeding further, it is necessary to consider the pattern of wind variation well above the

ground. Omitting the effect of the roughness of the

earth's surface on the wind velocity near the ground,

the pattern of velocity occurrences is shown in Figure 3 for the windiest and the calmest areas of the

United States to altitudes to 130,000 ft. The lower

portions of the curves are seen to be concave downward, from near the ground to about 35,000 ft, where

strong jet streams are encountered. These curves are envelopes, and hence are synthetic profiles. It is the

form of these curves that is important here rather

than the extreme velocity, except to note that the

velocities increase at an accelerating rate. As air moves over a surface, it is restrained

depending upon the roughness of the surface. Turbulence is caused not only by the roughness, but

by thermal currents rising from the surface ; but these

currents are less significant in high winds. Let Z be

the distance from the surface measured normal to it,

0 so 100 150 200 250 300 0 50 100 150 200 250 300

Wind Speed in ft/sec Wind Speed in ff/sec

Synthttlc Wind Spitd Prollln EicMd«il 1% Synthetic Wind Speed Prodlei EicMded %

9%,IO%,20%<ind!0%ot the Winter for the WIndleet 5%,l0%,2O%<»«' 50% ol the Winter for the Colmeet Areo(Northeoettrn Port) o( the United Stolee. Areo ( Northoeetern Port) of the United Stotee.

Figure 3. Synthetic probability profiles to 130,000 ft (From

USAD handbook').

and V the velocity of the wind at Z. If the velocity Va

is known at Za, the velocity Vn at Z/i is

v^ = Va{Zu/Za)"'^ (2)

where n is a function of the roughness. This is known

as Hellman's equation [8]. When the terrain is a

plane, either level or very gently inclined, with no

trees, shrubs or structures, the experimental evidence

gives re = 7. Large airports at which there is a long

unobstructed fetch over level terrain achieve this condition. (Some airports, with cities up.stream, may

not achieve this smoothness.) As the roughness

increases, by addition of trees, structures, or irregular

terrain, the value of n grows smaller. As the lower parts of the profiles of Figure 3 meet

the ground, they are affected by friction so that the

profile schematically has the form shown in Figure 4. At the junction T of the "free air zone" with the

"friction zone," there is a certain velocity Vi, and a

slope a of the tangent to the profile at T. Below T, the form of the profile is given by Hellman's equation,

Eq. (2). The junction of the free-air profile at T with the

profile of the friction layer imposes two conditions at

0 V

Figure 4. Schematic junction of synthetic profile in friction zone with sj'nthetic profile in lower troposphere.

153
Figure 5. Schematic effect of cover on boundary flow.

T: Vi and a are the same at T for both curves. These

conditions become important as the wind is followed

from the relatively smooth conditions, say, at a large

airport, to a rougher terrain and cover, say, over a

small town (Fig. 5) [10]. At the airport, shown at the left of Figure 5, we

assume n = 7 in eq. (2), and consider (arbitrarily)

that T is at 1200 ft. above the ground. The velocity

30 ft. above the ground is v^, and from this and

Eq. (2), v/ may be found. As the wind moves from

left to right, encountering undulating terrain with

trees and' buildings, turbulence builds up in the

friction layer, and at the same time it rises, so that

if C is the thickness of the undulations with cover, the

boundary of the friction layer at the airport being at a height oh' above the ground, rises to oh" at the

small town. A study of data taken over varying

roughnesses seems, for engineering purposes, to

justify the empirical relation

oh" = oh'+4C (3)

Since v/ and a are the same, both at T and T", it is possible to compute the profile oT", and thus to determine n" and Vso"- Sherlock [16] and Davenport [10] proposed attaching the friction curve (Fig. 4) to the gradient wind.

Sherlock used the Ekman spiral [17] to describe the

profile below T. Both Lamb [18] and Taylor [19] had

also studied the Ekman problem, which was that of generating vortices in a body of water over the free surface of which wind was blowing. Huss [3] shows

that Ekman's, Lamb's and Taylor's work coincided.

Sherlock simply inverted the spiral of Ekman.

But the profile oT, Figure 4, is not an instantaneous

profile. Rather, it must be considered to be an

envelope of the gusts that may occur over the same

height, and, through the relationship shown in Figures 1 and 2, this envelope is related to a mean

hourly curve over this height. The concept here is that the Hellman curve is attached at T with a smooth continuity to an envelope of the gusts

occurring in the lower troposphere; and by having at T constant vlues of Vt and a, for various values of n, an interrelated family of curves for the friction layer

is derived.

Figure 6 shows the profile with n = 7 and f3o=100

mph carried to 1,200 ft above the ground, where

^(=169 mph. It also shows a family of profiles for various values of n from 7 to 2, each having the same

Vi and a at T (Fig. 4). The slopes at T were made

similar (nearly) by making the chord of the top

100 ft have the same slope, so that (vi — Va-wo)) was

the same for all other curves as it was for (2^1200 —i'lioo) when n = 7. The value of n was determined from the

equation

154
0 I —1 1 1 0 50 100 150 200 Wind Velocity , mph

Figure 6. Family of Hellman's curves based on mean

fastest observed mile of 100 mph 30 ft above

ground at airport (n = 7)

.

logVt- log z;(,_ioo)= - (log/l(- log -100)) (4) n

Figure 6 may be used for locations where v^o is other

than 100 when n = 7, by using a simple multiplier

that is easily determined. Figure 7 shows two

profiles having the same value of n, but with different values of Va. From Eq. (2), at any height h,

«ft = Wol-) ; " \a)

hence,

VhVh='Va/Va

whence

h

a

0

-* Vq

Figure 7. Relation between two Hellman's curves of same

value of N but different values of Va.

Vh=Vh — (5)

In other words, Figure 6 may be used for a city

where vaoT^lOO and n = 7 by multiplying the abscissa

of all curves by the ratio of the value of ^30 for that

city to 100. Hence, if for a given city, 1^30 = 90 mph,

Figure 6 may be used by multiplying any abscissa

by 0.9.

4. The Occurrence of the Extreme Fastest Mile

The Weather Bureau has established at airports

instruments for measuring the fastest mile of wind,

and reports the observations, adjusted by Hellman's

seventh power law to the elevation of 30 ft above the

ground, by months and by years. The data may be

obtained from each station by applying to that

station. In 1954 Thom [11] published a method by which

annual extreme wind data could be used to estimate

the frequency of such winds. In 1960 he published [12] isotach maps for the 48 states, for 0.50, 0.02 and 0.01 quantities of annual extreme winds 30 ft above the

ground. Using a maximum-value probability

paper [12] (Fig. 8) with Fisher-Tippett Type II distribution [13], a curve could be constructed for a

locality by plotting the values read from the isotachs.

155
995 990 _ 960 ~ 960

900

2500 2000

1000 500

200 ^

100 3

50 I

2' S

,0 1

0 50 60 70 80 90 KX) Wind Velocity, mph

200 250 300

Figure 8. Extreme value probability plotting paper, Fisher-Tippett Type II distribution (after Thorn. [11, 12]).

Such a curve (a straight Une) would make possible

the estimation of the velocity of an extreme wind of any selected mean occurrence interval for the given

locality.

The separate annual extreme mile values for a given station may be plotted on the paper of Figure 8 by using the plotting order

p = m/ (n+1) (6)

in which m is the order of a given observation,

counting from the smallest to the largest observed

value (equal readings are arranged serially), n is the

total number of observations, and p is the probability

Fix). In his 1954 paper, Thom chose the Type II distribution function

Fix) -(.t//3)-7 (7)

to express the probability of a wind speed being less than X. The method of maximum likelihood was used

to determine the parameters /S and 7. The mean recurrence interval R is given by

/e=i/[i-f^(x)] (S)

The probability paper [12] shown in Figure 8 thus

shows Fix) on the left margin and R at the right,

while the velocity v is shown as the abscissa. In 1966 Thom [14] published revised isotachs,

giving 0.50, 0.10, 0.04, 0.02 and 0.01 quantities, and

the corresponding mean recurrence intervals of 2, 10,

25, 50, and 100 yr. for extreme winds in mph

(Figs. 9-13, respectively). The revisions took into

account six additional years of records, bringing the

average total to 21 and improving the accuracy by

about 15 percent.

Based on Thom's method of extreme values and

his latest isotachs, the extreme wind probabilities of 83 representative cities have been studied. Figure 14

shows the risk attendant upon the likely occurrence

of a wind having a mean recurrence interval once

within the expected life of the projected structure. Thus, for an expected 100-yr. Ufe, there is a 10% risk of one occurrence of a storm of an intensity of a

1,000-yr. mean recurrence interval. Using the paper

shown in Figure 8, a straight line plot for a given city,

using the isotachs of Thom in Figures 9-13, can be

projected to forecast the velocity of a wind having

1,000 yr. By using Figure 2, the hourly mean may

be determined, corresponding to the 72 = 1,000 wind.

Having done this plotting for each of the 83 cities,

it was found that they could be grouped into nine

classes, as shown in Table I. Table II gives the same

information with the cities arranged alphabetically.

The mean hourly velocities for Classes I-IX

correspond to fastest mile velocities of 100, 105, 115,

125, 135, 145, 155, 170, and 190 mph, respectively.

These are the 1,000-yr. mean recurrence interval

velocities estimated from plotting the isotach values on the paper shown in Figure 8. These classes are also based on mean hourly velocities (see Fig. 2) of 77, 81,

83, 95, 102, 108, 115, 125, and 128 mph, respectively,

likewise at a mean recurrence interval of 1,000 yr. These values are for the airport station at each city at 30 ft above the ground. The effect of terrain and

cover within the city itself is not included. Variations

in conditions within a given city are likewise matters

that must be included in interpreting the basic data

given in Tables 1 and 2. During the life of a large building, the cover may

be materially changed from time to time. As the city

gains in the number of tall buildings, the height of cover is increased; and from Figure 6, it is shown that n is reduced and the average wind velocity acting on

a building is likewise reduced. Some cities are undergoing considerable alteration, with the removal

of large buildings, altering the exposure and in not a few instances increasing the exposure of a given

remaining structure. Thus, in fixing a value for code

purposes, it is necessary to provide for such possibility

by including the effect of such alteration in city

planning.

5. Determination of Extreme Velocity

for Design

From Figure 1 it is seen that the gust factor Fg

depends on the duration of the gust. The response of a structure to the gust cannot develop fully unless

the gust deviation is long enough to establish the

particular regime of the response. The only data

available bearing upon the time required to establish

156


159

161
Table I. Cities grouped by classes according to extreme

fastest mile at 1,000-yr. mean recurrence inter oal

Class I (Extreme fastest mile 100 mph; fastest hourly mean 77 mph;

Birmingham T •

i. T> « 1 Little Kock

Bismarck Los Angeles

Dallas Memphis

El Paso Phoenix

Ft. Worth San Diego

Great Falls Shreveport

Class II (Extreme fastest mile 105 mph; fastest hourly mean si mpn;

Albuquerque Las Vegas

Baltimore Philadelphia

Burlington, Vt. St. Louis Chicago Spokane

Concord, N.H. Springfield, 111. Duluth Springfield, Mass.

Hartford Wilmington, Del. Jackson, Miss.

Class III (Extreme fastest mile 11.5 mph; fastest hourly mean 83 mph)

Amarillo New York City

Buffalo Omaha

Cheyenne Pendleton Denver Pocatello Des Moines Rapid City Fresno Roanoke

Kansas City Sacramento

Lincoln Salt Lake City

Milwaukee San Francisco Minneapolis Washington, D.C.

Nashville Wichita

Newark

Class IV

(Extreme fastest mile 125 mph; fastest hourly mean 95 mph)

Boston Louisville Charleston, W. Va. Madison

Cincinnati New Haven

Cleveland North Platte Detroit Raleigh Green Bay Richmond

Houston Seattle Knoxville

Class V

(Extreme fastest mile 135 mph ; fastest hourly mean 102 mph)

Atlanta Pittsburgh

Indianapolis Providence

Mobile

Class VI

(Extreme fastest mile 145 mph; fastest hourly mean 108 mph)

Atlantic City Portland, Oreg.

Portland, Maine

Class VII

(Extreme fastest mile 155 mph; fastest hourly mean 115 mph)

Charleston, S.C. Norfolk New Orleans

Class VIII

(Extreme fastest mile 170 mph; fastest hourly mean 125 mph)

Jacksonville Savannah

Class IX

(Extreme fastest mile 190 mph; fastest hourly mean 128 mph)

Key West Tampa

Miami

St. Petersburg

Table II.

Wilmington, N.C.

Cities in alphabetical order with

class designation

City

Albuquerque

Amarillo Atlanta

Atlantic City

Baltimore

Birmingham

Bismarck

Boston

Buffalo Burlington

Charleston, S.C_-. Charleston, W. Va

Cheyenne

Chicago

Cincinnati Cleveland Concord, N.H

Dallas Denver Des Moines

Detroit Duluth

El Paso

Fort Worth

Fresno Great Falls Green Bay_

Hartford Houston

Indianapolis

Jackson, Miss

Jacksonville Kansas City

Key West

Knoxville Las Vegas

Lincoln

Little Rock

Los Angeles

Louisville Madison

Memphis

Class

II IIIV

VI

II

II IV

III

II VIIIV

III

II IV

IV

II

I III

III IV

II

I

I III

I IV

II IV

V

II VIII

III IX

IV

II III

I

I IV

IV

I

City

Miami

Milwaukee

Minneapolis

Mobile

Nashville Newark

New Haven

New Orleans New York City Norfolk North Platte Omaha

Pendleton

Philadelphia

Phoenix

Pittsburgh

Pocatello Portland, Maine

Portland, Oreg

Providence

Raleigh

Rapid City

Richmond

Roanoke

Sacramento

Saint Louis

Saint Petersburg

Salt Lake City San Diego San Francisco Savannah

Seattle Shreveport

Spokane

Springfield, 111 Springfield, Mass Tampa

Washington, D.C

Wichita

Wilmington, Del

Wilmington, N.C_--

162
the regime are due to Farren [15], from research

\i conducted on airplanes. He found that the time

required to achieve the regime was that needed by

the windstream to pass through a distance equal to

eight times the greatest width of the structure. Suppose a building 500 ft high is to be constructed

in Chicago with a life of 100 yrs., in an area where the

undulations of the terrain together with the envelope

of average building heights is 220 ft (C = 220 in Eq. (3) and in Fig. 5). Then, fromEq. (3), o/i" = 2,080

ft, and we will choose, from Figure 6, n = 4. From

Table 2 it is noted that the wind velocity for design is in Class II, with the mean fastest mile of 105 mph.

To determine the gust factor, we use Farren's rule

of eight times the largest dimension of the building,

or 8X500 = 4,000 ft of windstream, which at 105 mph

(154 fps) will pass a point in 26 sec. From Figure 1 we

find at a gust duration of 26 sec. a gust factor of 1.33. From Figure 2 we find the mean hourly velocity

corresponding to an observed fastest mile of 81 mph;

and this multiplied by 1.33 gives gust velocity of 108

mph for the fastest 4,000-ft wind within the mean

fastest mile of 105 mph. This is the velocity at the

airport at 30 ft above the ground. At the site we may

use the curve for n = 4 in Figure 6, by multiplying its abscissas by 1.08. The pressure produced by this velocity in standard

air, q, is (in psf)

g = i^V391 (9)

The velocity at the site is 1.08 times 58 mph (n = 4. Fig. 6) or 63 mph. At 500 ft elevation, it is 69 X 1.08 =

75 mph. The corresponding pressures are 10 and 14

psf distributed up the building in accordance with

the curve n = 4. Figure 6. At leeward corners of buildings negation pressures

are experienced equal to the velocity pressure but of opposite sign (suction). Some buildings have lost windows, blown outward. Gusts of short duration can

cause loadings of impact suddenness. A window 8 ft high, by Farren's rule, would require 64 ft of wind,

which, at 100 mph (or 147 fps) would pass in 0.44 sec. From Figure 1, we find a gust factor of 1.84. The

fastest mile of 100 mph would have a gust factor of 1.30 (Fig. 2) ; hence the short gust would have a gust

factor 1.42 larger. Since the pressure q varies as v'^ (Eq. (9)), the velocity pressure is doubled.

6. Selection of Appropriate Gust Factors

for Design

Consider a chimney 800 ft high, with a mean

external diameter, d, over the top quarter of its height of 25 ft; and a mean cover of 200 ft. Let the

3

\*

N

NO/'

Nx \

V

1,000 900 290 100 90 29 10 9 3 2 I Expected Life of Project, yrs Figure 14. Risk of occurrence of winds of various mean

recurrence intervals, within the expected life of the project.

location be a Class I city (Table 1). For a 100-yr.

life, we choose from Figure 14 a value of R of 1,000

yr., for which ^30= 100 mph. From Figure 6, we find that with 4X200+1,200 = 2,000, n = 4, about, when

^30 = 58 and ?^8oo= 134 mph. To estimate the overturning moment, a wind load due to these velocities should be distributed from base to top. The actual

velocity pressures, in psf, vary from 9 psf to 45 psf,

before taking into account the shape factor. The collapsing pressure distributed around the

ring at, say, the 700-ft level, is due to a fastest-mile

wind of 130 mph (Fig. 6, n = 4). If we consider a

length of tube of 3d, or 75 ft, and multiply this by 8, we have a down-wind travel of 600 ft. Since 130

mph = 176 fps, this wind would traverse 600 ft in 3.4

sec. A gust of this duration, according to Figure 1, gives a gust factor Fg = 1.57. From Figure 2, a fastest mile of 130 mph corresponds to an hourly mean of 98

mph, which, when multiplied b}^ 1.57, gives a speed

of 154 mph for the gust. We must now make a second

163
approximation of the gust factor. 154 mph = 226 fps,

which will traverse 600 ft in 2.67 sec. From Figure 1 we correct the gust factor to 1.60, so that the mean

gust velocity will be 1.60X98=157 mph. This gives a velocity pressure of g = j;2/39i = 1572/391 pgf (iq)

This is the velocity pressure intensity at the stagnation point on the circumference of the cylinder.

Having this pressure, the bending moment in a ring

1 ft high may be computed from

M=±0.5qr'-

in which r is the mean radius of the ring.

ii:

7. Setting Stresses for Wind Loads

Figure 15 shows the plot from the isotachs for the

cities Chicago, Jacksonville and Los Angeles. Consider a structure with a life expectancy of 20 yrs. From Figure 14 we see that there is a 10% risk of a wind having a mean recurrence interval of 200 yrs. occurring once in the life of the structure. There is an 18% risk of a 100-yr. storm occuri-ing and only a 4%

chance of a 500-yr. storm occurring. Figure 15 shows

that for 100-, 200- and 500-yr. storms, the extreme

velocities at 30 ft above the ground at the airport

would be 82, 90 and 100 mph. Suppose the design is based on 82 mph and a 90 mph wind occurs. Then

there is an increase of from 100 percent to 110%;

and since the pressure increases as the square of the

velocity (Eq. (9)), the wind load is increased to 121%.

If a 500-yr. storm should occur, the wind load would

be increased to 149%. With this information, the

design stress for wind can be set to allow a certain

encroachment on the factors of safety for the possible rare occurrence of the higher loading.

The flatter curve for Jacksonville produces greater

intervals. A building with a projected life of 100 yrs. has a 10% chance of a 1,000-yr. wind and only a 4%

chance of a 2, 500-yr. wind occurring in its life. If the

1 I \y 1111 1 M 1

998

.995

,990

.980 960

900

.500

.010

t d

y

c f/

1. L,L1 1 1 1 I

1000 500

D 50 60 70 80 90 100 Wind Velocity, mph

200 250 300

Figure 1.5. Plot of probability curves for three cities, from

isotachs, for extreme velocities at 30 ft above

ground at airport.s.

design stress for wind is based on a 1,000-yr. wind, „i the higher wind would cause an increase in velocity

from 100% (at 161 mph) to 125% (at 202 mph), with

a pressure increase of 57%.

8. References

[1] Giblett, M. A., et al, The structure of wind over level country. Meteorological Office (Brit.), Geophy. Mem.

No. 54, London, H.M.S.O., 1932, 119 pp., 21 pis.

[2] Sherlock, R. H., and M. B. Stout, Wind structure in winter storms, Jour. Aero. Sci., vol. 5, pp. 53-61, 1937.

[3] Huss, P. O., Relation between gusts and average wind

speeds, Daniel Guggenheim Airship Inst., Univ. of Akron, Akron, O., Rept. No. 140, 1946, for U.S. Weather

Bureau, Contr. No. Cwb-6103. (Mimeo.)

[4] Durst, C. S., Wind speeds over short period of time, Meteor. Mag., Meteor. Offc. (Brit.), vol. 89, no. 1056, pp. 181-186, July 1960.

[5] Sherlock, R. H., Gust factors for the design of buildings,

Int. Assn. Bridge & Struct. Engrg., vol. 8, pp. 207-230,

1947.

[6] Scrase, F. J,, Some characteristics of eddy motion in the atmosphere, Meteor. Offc. (Brit.), Geophys. Mem.

No. .52, London, H.M.S.O., 1930, 16 pp.

[7] Sherlock, R. H. and M. B. Stout, An anemometer for the study of wind gusts, Engr. Res. Bull. No. 20, Univ. of Mich., Ann Arbor, Mich., May 1931, 36 pp.

[8] Hellman, G., Uber die bewegung der luft in den untersten

schichten der atmosphare, Meteorol. Zeit, vol. 34,

p. 273, 1916.

[9j Handbook of geophysics for Air Force designers. Geophys.

Res. Directorate, A. F. Camb. Res. Comd., USAF,

Lst ed., 1957, pp. 5-17, 5-41.

[10] Davenport, A. G., Wind on structures, Natl. Res. Counc.

of Canada, Div. Bldg. Res., Tech. Paper No. 88, Ottawa, Mar. 1960. (No attempt was made to connect the

separate curves as has been done in Figs. 4-6.)

[11] Thom, H. C. S., Frequency of maximum wind speeds,

ASCE Proc, vol. 80, 1954, 11 pp.

[12] Thom, H. C. S., Distributions of extreme winds in the United States, ASCI': Trans., vol. 126, 1961, pp. 450-466.

[13] Fisher, R. A., and L. H. C. Tippett, Limiting forms of the frequency distribution of, the largest or smallest member of a sample, Camb. Phil. Soc, Proc. vol. 24, 1928, p. 180.

114] Thom, H. C. S., New distributions of extreme winds in the United States, Jour. Struct. Div., Proc. ASCE,

paper no. 6038, July 1968, pp. 1783-1801.

[15] Farren, W. S., Apparatus for measurement of twodimensional flow at high Reynolds numbers with

application to growth of circulation around wing started impulsively from test, Proc, 3rd Int. Cong. .\ppl. Mcch.,

1930, p. 329, fig. 8.

[16] Sherlock, R. H., Variation of wind velocity and gusts with height, ASCE Proc, Sep. No. 126, April 1952, pp. 1-26.

[17] Ekman, V. W., On the influences of the earth's rotation on ocean currents, Arkiv f. mat., astron, etc., Stockholm,

1905.

[18] Lamb, Horace, Hydrodynamics, 5th ed., Camb, Univ.

Press, 1924, p, 655.

[19] Taylor, G, I., Eddy motion in the atmosphere, Phil. Trans. Roy. Soc. Lond., Ser, A,, Vol. 215, 1915, p. 14.

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