NAFL INST. OF STAND &

Aiiiob 'laaTiM

NBSiR 81-2199

Wind, Earthquake, Snow, and Hail

Loads on Solar Collectors

Louis Cattaneo

James Robert Harris

Timothy A. Reinhold

Emil Simiu

Charles W.C. Yancey

I

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

January 1981

-QG

100

.056

1#^ 81-2199

1981

c. 2

Prepared for Department of Energy

''^ice of Solar Applications for Buildings

ice of the Assistant Secretary

Conservation and Solar Applications

shington, DC 20585

NBSIR 81-2199

WIND, EARTHQUAKE, SNOW, AND HAIL

LOADS ON SOLAR COLLECTORS

Louis Cattaneo

James Robert Harris

Timothy A. Reinhold

Emil Simiu

Charles W.C. Yancey

National Bureau of Standards

Library, E-01 Admin, Bldg,

FLB 2 7 1981

POl OlCC 'Ore

Qaoo

a. ^

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

January 1981

Prepared for Department of Energy

Office of Solar Applications for Buildings

Office of the Assistant Secretary

Conservation and Solar Applications

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Jordan J. Baruch, Assistant Secretary for Productivity. Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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ABSTRACT

The Report describes and interprets wind-tunnel, full-scale, and field

studies of wind and snow loads on flat plate solar collectors, conducted

under contract for the National Bureau of Standards, and uses results of

these studies and other data available in the literature to develop information, guidelines, and criteria for the design of flat plate collectors

subjected to the action of wind, snow, and earthquake loads. Also given

in the repopt are data on hail loads, based on information and studies

available in the literature.

iil
PREFACE

This report is divided into four parts. Part I, entitled Wind Loads on Flat~Plate Solar Collectors presents performance requirements for flatplate collectors subjected to wind loads and their supporting systems,

and describes pending revisions to the specification of wind speeds in

the American National Standard A58.1, A description, summary, and

interpretation of recent wind tunnel and full-scale measurements of wind

loads on flat plate collector systems, performed by Virginia Polytechnic

Institute and State University under contract with the National Bureau

of Standards, are presented. The approach employed to develop design

criteria, based on these measurements is described. Wind load design

criteria are presented in detail, and numerical examples are provided.

Part II, entitled Earthquake Loads on Solar Collectors , examines the

relative importance of seismic forces in the design of solar collector

systems and shows that these forces ae generally small compared to those

induced by wind. Information is provided on the design of solar collectors subjected to seismic loads. Part III, entitled Snow Design Criteria

for Flat-Plate Collector Installations , presents performance requirements

for flat plate collectors subjected to snow loads and their supporting

systems, and describes findings of field studies conducted in 1979 under

contract with the National Bureau of Standards. The approach employed to

develop design criteria is described, and snow loading design criteria are presented in detail. Part IV, entitled Hall Loads on Solar Collectors , presents data on hail loads based upon information and studies available

in the literature.

The report is primarily designed to be a source document for use by code

and standard writing bodies in developing minimum design loads for solar

collectors. For this reason, a fairly high level of complexity has been

retained reflecting the influences of various pertinent factors. This is

particularly true in the case of wind loads.

The authors have endeavored to link the guidelines and provisions suggested

in this report to the proposed 1980 draft of the American National Standard

A58.1 produced by the American National Standards Institute (ANSI). This

draft, which is currently being balloted for adoption, contains numerous Improvements over the 1972 version and it is expected that the draft will be

adopted soon. Since the numbering of figures and tables in the final adopted

version will differ from those in the draft (due to a format change), all

figures and tables referenced in this report are referred to by name rather

than by number.

The comments and cooperation of Mr. Robert Dlkkers of the Center for

Building Technology, NBS, and of Messrs. Tieleman, Akins, Sparks,

O'Rourke, Corotls, Dowding, Rossow, and Changnon are gratefully acknowledged. Mr. Emil Simlu served as project leader.

iv
Table of Contents

Page

ABSTRACT ill

PREFACE iv

SI CONVERSION UNITS viil

PART I - WIND LOADS ON FLAT-PLATE SOLAR COLLECTORS 1

LIST OF TABLES 2

LIST OF FIGURES 3

INTRODUCTION

2. PERFORMANCE REQUIREMENTS 4

3. REVISIONS TO ANSI A58.1 5

4. THE VPI & SU EXPERIMENTAL INVESTIGATION 6

4.1 Types of Installations Considered 6

4.2 Wind Tunnel Modeling of Solar Collector Installations

and Simulation of Flow 7 4.3 Comparison of VPI & SU Model Results with Full-Scale

Test Results and Other Model Test Results 8

4.3.1 General 8

4.3.2 Comparison of Price's Fork Model and Full-Scale

Test Results 9

4.3.3 Comparison of Aylesbury Full-Scale and Model

Test Results 10

4.4 Comparison of Model Results with ANSI A58. 1-1980 /Draft

Provisions 11

5. DEVELOPMENT OF DESIGN CRITERIA 12

6. WIND LOAD DESIGN CRITERIA 13

6.1 General 13

6.1.1 Definitions 13

6.1.2 Symbols and Notations 14

6.1.3 Warnings - Limitations of Data Base 16

6.1.4 Analytical Procedure 18

6.2 Wind Loads on Solar Collector Cover Plates - Safety

and Serviceability Requirements 13

6.3 Wind Loads on Individual Collectors - Safety

Requirements 23

v
Table of Contents

Page

6.4 Wind Loads on Solar Collector System Supports - Safety

Requirements 23

6.5 Safety of Buildings and Foundations Supporting

Collector Systems 27

7. EXAMPLES 27

7.1 Collectors Mounted on a Sloped Roof 28

7.2 Collectors Mounted on a Flat Roof 30

7.3 Design of Collector Cover Plates for a Variety of

Installations 33

8. REFERENCES 34

PART II - EARTHQUAKE LOADS ON SOLAR COLLECTORS 44

LIST OF TABLES 45

NOTATION 45

1. INTP JDUCTION 46

2. RELATIVE IMPORTANCE OF SEISMIC FORCES IN THE DESIGN OF

SOLAR COLLECTOR SYSTEMS 46

3. DESIGN OF SOLAR COLLECTORS SUBJECTED TO SEISMIC LOADS 46

4. REFERENCES AND BIBLIOGRAPHY 47

PART III - SNOW DESIGN CRITERIA FOR FLAT-PLATE SOLAR COLLECTOR

INSTALLATIONS 49

LIST OF FIGURES 50

NOTATION 50

1. INTRODUCTION 51

2. PERFORMANCE REQUIREMENTS 51

3. FINDINGS OF STUDIES CONDUCTED IN 1979 51

4. DEVELOPMENT OF DESIGN CRITERIA 54

4.1 The Snow Load Criteria of ANSI A58. 1-1980 /Draft 54

4.2 Development of Criteria Specifically for Solar

Collector Installations 55

5. DESIGN GRITERIA 55

Vi
Table of Contents

Page

5.1 Criterion for the Safety of Flat Plate Solar Collectors 53

5.2 Criteria for the Safety of Buildings Supporting

Collector Systems 56

5.2.1 Building Supporting Flush Collectors 56

5.2.2 Building Supporting Protruding Collectors 56

5.2.3 Surfaces that Receive Sliding Snow 58

5.3 Criterion for the Serviceability of Collector Systems. 58

5.4 Guideline for the Serviceability of Buildings

Supporting Collectors 58

6. REFERENCES 58

PART IV - HAIL LOADS ON SOLAR COLLECTORS 75

LIST OF TABLES 76

LIST OF FIGURES 77

1. INTRODUCTION 78

2. REGIONALIZATION OF THE UNITED STATES 78

3. MAXIMUM HAILSTONE SIZES 79

4. HAILSTONE VELOCITIES 79

5. HAILSTONE DENSITY 79

6. PROPOSED PROCEDURE FOR DETERMINING DESIGN HAIL LOADS ON

SOLAR COLLECTORS 80

7. ACKNOWLEDGEMENTS 80

8. REFERENCES 81

9. BIBLIOGRAPHY 82

vii
SI Conversion Units

Length

1 foot (ft) = .3048 meters (m)

1 inch (in) = 0.0254 meters (m)

1 mile (U.S. Statute) = 1.609347 x 10^ meters (m)

Velocity

1 mile per hour (mph) = 4.470400 x 10 ^ meters per second (m/s) = 1.609347 kilometers per hour (km/h)

Force

1 pound-force (Ibf) = 4.448 newtons (n)

Pressure

1 pound-force per square foot (psf) = 47.880 pascals (Pa)

viii
PART I

WIND LOADS ON FLAT-PLATE

SOLAR COLLECTORS

by

Timothy A. Reinhold

1
LIST OF TABLES Page

Table la. Peak Negative Pressure Coefficients for Top Surface of

Collectors (Cover Plates). Comparison of Price's Fork

Model and Full-Scale Data, S/SL = .062 35

Table lb. Peak Positive Pressure Coefficients for Top Surface of

Collectors (Cover Plates). Comparison of Price's Fork

Model and Full-Scale Data, S/a = .062 36

Table 2a. Peak Negative Pressure Coefficients for Net Loads on

Collectors. Comparison of Price's Fork Model and FullScale Data, S/i = .062 37

Table 2b. Peak Positive Pressure Coefficients for Net Loads on Collectors. Comparison of Price's Fork Model and FullScale Data, S/£ = ,062 38

Table 3. Peak Pressure Coefficients for Top Surface of Collectors

(Cover Plates) Mounted Flat on a Building Roof 39
LIST OF FIGUpiS Page

Figure 1. Solar Collector Systems Mounted on a Sloped Roof 40

Figure 2. Solar Collector Systems Mounted on a Flat Roof 41

Figure 3. Collector Systems In Ground Installations Next to a Building - Berm Units 42

Figure 4, Collector Systems in Ground Installation in Open Location 43

3
i

1 . INTRODUCTION

Although extensive charts and tables have been developed for guidance

in determining wind loads on buildings and other structures, the advent

of solar collectors has led to many situations which are not adequately

covered by existing wind load criteria. While it is reasonable to

expect that roof wind loads are applicable for solar collectors mounted

directly on a roof surface or for collectors which form the roof surface, no direct correspondence is apparent for many of the other common installation configurations. Consequently, a study of wind loads acting

on typical solar collector installations was conducted using wind tunnel

models and a full-scale installation. This report proposes specific

design criteria which are based on recent experimental data reported in

ref. 1 and on the 1980 draft revision of American National Standard

A58.1, "Building Code Requirements for Minimum Design Loads in Buildings

and Other Structures" (ANSI A58.1 - 1980/Draft) [2]*. The criteria

provide for safety and serviceability requirements for solar collector

cover plates, individual collectors and systems of collectors subjected

to wind loads.

In order to design solar collector installations which meet specified

performance requirements for wind loads, information is needed which

prescribes wind loads on cover plates, individual collectors, arrays

of collectors, and supporting systems. The prescription of wind loads

requires knowledge of extreme wind speeds which can be expected at the

site being considered and of appropriate pressure coefficients. Building codes and standards which consider wind loading generally include

both classes of information, as well as the procedures for using that

information to calculate wind loads. The approach followed herein was:

(1) Update estimates of extreme winds for the ANSI A58.1 - 1980/Draft,

(2) Obtain, from wind tunnel tests, additional data on pressure coefficients for use in the specification of wind loads on solar collectors,

and (3) Develop specific guidelines for determining wind loads on solar

collectors which use the ANSI A58.1 - 1980/Draft as a base document

and which reflect the additional information obtained from the wind

tunnel tests.

2 . PERFORMANCE REQUIREMENTS

There are four basic requirements for the performance of solar collector

installations under wind loads:

(a) SAFETY AND SERVICEABILITY OF SOLAR COLLECTOR COVER

PLATES: Collector cover plates should not fracture due

to wind loading and devices used for their attachment

should withstand the wind loads.

* Numbers in brackets Indicate references at the end of each part.

4
Cb) SAFETY OF INDIVIDUAL COLLECTORS: Individual collectors

should not tear loose from their supports due to wind

loads*

(c) SAFETY OF COLLECTOR SYSTEM SUPPORTS: Collector system

supports should not collapse due to wind loading.

(d) SAFETY AND SERVICEABILITY OF BUILDING COMPONENTS SUPPORTING COLLECTOR SYSTEMS: Building components which support

collector systems should not collapse or perform

adversely due to the weight of the collector systems and

induced wind effects.

Two other items are noted for consideration by the designer, although no specific provisions are developed. First, solar collector systems are often designed for a longer service life than most roof membrane systems.

Consequently, care should be employed in designing the collector system

to allow for expected service of the roof membrane. Second, investigations of damage caused by extreme winds have indicated that a significant

amount of damage may be due to low-cycle fatigue. The state of the art

does not adequately provide for the development of specific provisions for

low-cycle fatigue at the present time. It is expected that low-cycle fatigue

will not be a significant problem provided that components of solar collector

systems are designed to withstand the prescribed loads without exceeding

the allowable stresses conventionally used for the materials in question.

3. REVISIONS TO ANSI A58.1

This project provided partial support for two research efforts which

contributed to the development of a new map for extreme wind speeds in

the United States. The map is part of the proposed revisions to the

ANSI A58.1 Standard, ANSI A58.1 - 1980/Draft. In the first study, extreme

wind speeds caused by extratroplcal storms at over 100 primary weather

stations in the United States were considered. A portion of the study

was concerned with the selection of the best probability distribution to

fit the historical data. These distributions were then used to predict

the expected extreme wind speeds for a variety of return periods ranging

from a few years to hundreds of years. Results are reported in ref. 3.

The second study considered hurricane wind speeds along the Gulf and

Atlantic coasts of the United States. Probability distributions of

hurricane climatological characteristics, based on historical data, were used to simulate a large set of hurricanes using Monte Carlo techniques.

Based on the simulated hurricanes, probability distributions of extreme

wind speeds were developed for points at 50 nautical mile intervals along

the Gulf and Atlantic coasts of the United States. Extreme wind speeds

determined from the probability distributions are reported in ref. 4 for

various return periods ranging from 10 years to hundreds of years.

Extreme wind speeds predicted in these studies were used to develop an

updated map which is included in the ANSI A58.1 - 1980/Draft.

5
4. THE VPI & SU EXPERIMENTAL INVESTIGATION

An experimental investigation was conducted for the National Bureau of

Standards by Virginia Polytechnic Institute and State University (VPI &

SU) during 1978-80 to determine wind loads on solar collector panels.

The investigation involved both wind tunnel model tests and full-scale

measurements. Descriptions of the buildings and solar collector configurations Investigated in the model and full-scale tests are presented

together with test results in a three volume report [1]. Also included are descriptions of the flow conditions, instrumentation, test methods

and data reduction techniques. A brief summary of the test program,

major findings and conclusions are presented in the following

subsections.

4.1 TYPES OF INSTALLATIONS CONSIDERED

The model tests were designed to include a cross section of typical

installations. The model configurations can be roughly grouped as roof

installations on low rise buildings and ground installations. Roof

installations are further grouped according to whether collectors are mounted on sloped or flat roofs. These two types of roof installations

are illustrated in figures 1 and 2, respectively. Ground installations

are grouped according to whether collectors are placed against a wall

(berm units) as shown in figure 3, or whether they are placed in the

open, away from buildings, as shown in figure 4.

As can be seen in figures 1 through 4, the number of parameters required

to describe the various configurations is quite large. Consequently, it was not possible to run an exhaustive series of tests where all parameters were varied Independently. Instead, a series of representative

cases were investigated involving some 63 configurations and well over

1500 individual tests. The roof overhang and the length to width ratio

of model buildings (see figure 1) were not varied systematically because

earlier investigations [5,6] indicated that roof pressures were not significantly influenced by variations in these building characteristics.

Tests of collector installations on buildings with sloped roofs included cases where the collectors were mounted directly on the roof surface,

mounted parallel to the roof surface but with an open gap between the

roof and the back of the collector, and mounted at an angle to the roof

surface. Such configurations are described by the parameters shown in

figure 1.

Tests of collector installations on buildings with flat roofs, figure 2,

included cases where the collectors were mounted with various angles of

inclination to the roof. Tests were conducted on models with and without parapets. Parapet cases included vertical parapets, 3 =90°, and

inclined parapets, 3 = 60°. Installations with multiple rows of

collectors were also studied.

6
Berm unit tests, figure 3, Included a single row of collectors mounted

against a building wall. One and two story buildings with flat or sloped roofs were used in the tests. The collector array was mounted

at various angles of inclination to the horizontal.

Solar collector systems consisting of single or multiple rows were

included in the tests of general ground installations, figure 4. The

collector arrays were mounted at various angles of inclination to the

horizontal.

4.2 WIND TUNNEL MODELING OF SOLAR COLLECTOR INSTALLATIONS AND SIMULATION

OF FLOW

The buildings and solar panels were modeled in the wind tunnel at a geometric scale ratio of 1/24. This scale ratio was chosen in order

to provide models which would be large enough to facilitate pressure

measurements and also to reduce the possibility that the pressure coefficients would experience Reynolds number dependence [1]. However, the

wind tunnel flow was originally designed for use in testing tall buildings at a model scale of 1/400 to 1/600. For the testing of low-rise

buildings, emphasis is placed on modeling the lower portion of the boundary layer. Thus, if the ratio of turbulence integral length scales for

model and prototype is considered at roof elevation, the proper geometric scale ratio is probably on the order of 1/200 to 1/300. This

results in a discrepancy by a factor of about 10 between the geometric

scale of the structural model and the geometric scale of the

longitudinal component of turbulence.

With regard to the discrepancy between model scale and scale of the

longitudinal component of turbulence, the ANSI A58.1 - 1980/Draft

states that wind tunnel tests will be considered properly conducted

only if;

"The geometric scale of the structural model is not more than

three times the geometric scale of the longitudinal component

of turbulence."

It is clear that these model tests would not satisfy this criterion. On

the other hand, the ANSI A58.1 - 1980/Draft also notes that due regard

should be given to the dependence of pressures on Reynolds number. Consequently, while the tests do not fit the scaling requirements of ANSI

A58 . 1-1980 /Draft , the results would have been questionable because of pos

sible Reynolds number dependence if the scaling requirements had been

satisfied for the given flow conditions.

The scaling requirements in the ANSI A58.1 - 1980/Draft for acceptable

wind tunnel tests can probably be considered conservative. The current

state of the art of x^lnd tunnel testing does not allow a clear assessment

of the consequences of discrepancies in modeling velocity profiles,

turbulence intensity profiles, or geometric scales, especially when such

discrepancies occur simultaneously for several of these parameters.

7
There are indications that correct m9deling of the intensity of the

turbulence is one of the most important considerations [5,7], Furthermore, comparisons of wind tunnel and full-scale results would suggest

that point pressures can be adequately reproduced in the wind tunnel

provided that the scale of the longitudinal turbulence component is at

least as large as the largest model dimension [5],

In the experimental investigation of wind loads on solar collectors,

the length scale of the longitudinal turbulence component was 2,5 to 3,0

times as large as the length of a collector [1] but was smaller than the

largest building dimension or the length of a row of collectors. Furthermore, the pressures reported are averaged over given areas (as

opposed to point pressures). Area averaged loads or pressures were chosen rather than point pressures and corresponding loads because it was felt that the area averaged pressures more closely represented loads

on collector panels or their supports. The effects of distortions in the

scales are likely to be more pronounced for area averaged pressures

than for point pressures. However, as mentioned previously, the effects

of the distortions cannot presently be quantified.

Two possible solutions to this dilemma are available. The first is to

compare model test results with those obtained from full-scale tests.

The second is to compare results for collectors mounted flat on a roof

with design values for roof loads which have been shown by other tests

and past experience to be adequate. This second solution represents

essentially a calibration of the test results to current practice.

Both solutions have been pursued and will be discussed in the following

sections.

Other features of the flow simulation are described in ref, 1, The

flow is considered to compare favorably with that of Exposure Category

B in ANSI A58, 1-1980/Draft, This is based primarily on a comparison of

turbulence intensities of the simulated flow at model roof height with

expected Intensities for full-scale exposure conditions. The mean velocity

profile actually corresponded more to a profile characteristic of Exposure A than Exposure B since the power law exponent was 0,37 for the

wind tunnel flow. However, as noted earlier, the intensity of the turbulence is considered to be a more important parameter to be simulated.

Furthermore, normalization of pressures by means of local velocity pressures (as was done in this work [1]) tends to remove the dependence of

pressure coefficients on the mean velocity profile,

4,3 COMPARISON OF VPI & SU MODEL RESULTS WITH FULL-SCALE TEST RESULTS

AND OTHER MODEL TEST RESULTS

4.3,1 General

Evaluation of wind tunnel model tests must always center upon questions

concerning how well the model results reproduce full-scale conditions.

The answers to such questions ultimately depend upon comparisons of

model and full-scale test results, although some Insights can be

8
obtained from comparisons of different model studies. For these reasons, the test program included a series of full-scale tests conducted

at the VPI & SU Price’s Fork Research Station, and model tests of the

Price’s Fork building and solar collectors. Additional tests were

conducted on a model of the full-scale experimental house at Aylesbury,

England for which extensive full-scale and other model test results are available. Consequently, it has been possible to conduct comparative

studies of model and full-scale tests on the Price's Fork building and

on the Aylesbury building. In addition it has been possible to compare

results obtained from model tests conducted at VPI & SU and at the

University of Western Ontario (UWO) to assess effects of differences

in model scales and flow simulation. These comparisons are presented

in detail in ref. 1 and 8 and will be summarized in subsections

4.3.2 and 4.3.3.

4.3.2 Comparison of Price’s Fork Model and Full-Scale Test Results

It is noted that the conclusions that can be drawn from the comparison

between model and full-scale tests should not be regarded as definitive,

owing primarily to the following basic difficulties. First, it was not

possible in this project to reproduce the topographic features of the

terrain surrounding the full-scale site. The actual site, although

typical of many possible sites, differed significantly from the uniform,

homogeneous terrain used in the laboratory simulation. Second, while

the procedure for estimating peak loads adopted in ref. 1 to compensate for filtering problems in the original tests was satisfactory on

the average, there were individual situations where estimates based on

the procedure deviated significantly from the actual peak loads. One

of these situations consists precisely of the Price's Fork model. The

deviations in this case are shown in tables 1 and 2. Owing to the factors mentioned above, judgement should be used in attempting to draw

conclusions from the comparisons between model and full-scale

measurements on the Price’s Fork configuration.

Based on comparisons of model and full-scale test results, the following

conclusions were drawn in ref. 1:

"For nearly stationary data records local mean pressure

coefficients agree reasonably well, while local rms pressure

coefficients and the magnitude of local peak pressure

coefficients are approximately twice as large for the full-scale."

These conclusions are suggested for both pressures on a single face of a collector and net pressures on a collector. On the other hand, the

comparison of model and full-scale results shown in tables 1 and 2 suggest different conclusions which are listed below. The pressure coefficients presented in tables 1 and 2 are based on mean hourly wind speeds

as opposed to fastest mile wind speeds which are used by ANSI A58,l~

1980/Draft.

9
(1) Coefficients shovm in table l.a indicate that the fullscale peak coefficients for negative pressures are usually

1.5 to 2.0 times larger than corresponding coefficients

for predicted peaks based on the model test results.

(2) Comparison of coefficients listed in table l.b indicates

that model and full-scale results are essentially equal

for wind directions of 0 and 360 degrees where the mean

pressure was also positive. The coefficients also agree

within experimental scatter for the other wind directions

listed, where the mean pressure was negative. The probability . distribution of positive peaks for cases where the mean

pressure is negative has not been studied [1].

(3) Coefficients for peak net negative pressures shown in

table 2. a indicate a significant discrepancy between

predicted and measured peak values for the model tests.

The predicted peaks from the model tests are generally

equal to or larger than the peak coef f iciencs obtained

from full-scale measurements.

(4) Coefficients for peak net positive pressures shown in

table 2.b indicate the same conclusions listed above

under item 3.

Consequently, while the comparison of model and full-scale results

presented in ref. 1 might suggest that model coefficients for peak

pressures (both for a single face and net on a collector) should be

doubled, the comparison shown in tables 1 and 2 would suggest that predicted net pressures should not be increased. Owing to the discrepancies

illustrated it is difficult to suggest any systematic corrections to the

coefficients obtained from the wind tunnel tests.

4.3.3 Comparison of Aylesbury Full-Scale and Model Test Results

A detailed three-way comparison between full-scale pressure measurements

on a two-story building at Aylesbury, England, and pressure measurements

on models of the Aylesbury building which were conducted separately at

VPI & SU and UWO are contained in ref. 8. Based on that comparison,

ref. 8 suggests the following conclusions:

"... that model mean, rms and peak pressure coefficients are generally in agreement with full-scale results if;

(1) Local pressure coefficients are used.

(2) The streamwise turbulence intensity is modeled adequately

for at least two building heights.

(3) The streamwise turbulence integral scale is at least as large as the largest model dimension.

10
(4) Gross features of the upstream terrain such as mountain

ridges and changes in nearby surface elevation are modeled adequately.

(5) The full-scale data records do not exhibit a nonstationary character such as low-frequency components

and/or short-duration gusts."

There are several facts which preclude the use of these conclusions to

justify the numerical values of pressure coefficients for solar collectors as measured in the wind tunnel tests. First, the VPI & SU model

of the Aylesbury building was constructed at a 1/50 scale rather than

the 1/24 scale used in the solar collector tests. As a result of this

scaling, the longitudinal turbulence integral length scale was at least

as large as the largest model dimension. As noted previously, the integral length scale in the solar collector tests was larger than the

length of a collector but not larger than the largest model dimension

or the length of an array of collectors. Second, only point pressures

are considered in the comparison of the Aylesbury building and the

appropriate model tests. Consequently, it is speculative to apply these same conclusions to the solar collector work where area averaged

pressures were measured.

4.4 COMPARISON OF MODEL RESULTS WITH ANSI A58, 1-1980/DRAFT PROVISIONS

Since neither of the comparisons of model versus full-scale test results

proved completely satisfactory in resolving questions about the model

test results, it is important to compare the model results against what

is used or specified in current practice. The ANSI A58.1 wind load provisions are a logical benchmark for comparison since the provisions

have a historical basis which suggests that they are adequate. Several

of the solar collector installations included collectors mounted flat on the building roof and it is reasonable to compare the cover plate

pressure coefficients with ANSI A58.1 roof pressure coefficients for

similar slopes. Rather than use the 1972 edition of ANSI A58.1, which

is the latest adopted version of the standard, it was decided to compare

pressures with ANSI A58.1 - 1980/Draft because it includes advances in

the state-of-the-art of wind load definition and because it is expected

to be adopted in the near future without substantial changes.

A comparison of cover plate pressure coefficients and ANSI A58. 1-1980/Draf

c

roof pressure coefficients is shown in table 3. In the comparison, if a collector was located in more than one zone it was assumed to be located

in the higher zone if more than 30 percent of its area projected on the

roof fell in the higher zone. As a result, the end collectors on the

Price’s Fork building are located in zone 2 (see ANSI A58.1~1980/Draf t)

since they are placed near the edge of the roof. On the other hand,

the solar collector arrays on the other model buildings were shorter

than the length of the building and consequently the end collector was some distance away from the roof edge.

11
All coefficients presented in table 3 are for use with fastest mile wind

speeds since that is the usual ANSI convention. However, the ANSI A58.1-

1980/Draft coefficients are intended for use with Exposure C wind speeds

while the model conditions are believed to correspond more closely to

Exposure B conditions. Based on comparisons of wind pressures and presssure coefficients reported in ref. 6, it can be shown that peak pressure coefficients for Exposure B are as much as 1.5 to more than 2.0

times higher than peak pressure coefficients for Exposure C conditions.

However, owing to the reduced wind velocities at low elevations for

Exposure B conditions as compared to Exposure C, the design pressures

for Exposure B are actually equal to or slightly lower than those for

Exposure C. Consequently, the peak pressure coefficients obtained in

the model tests should be about 1.5 to 2.0 times larger than the ANSI

A58. 1-1980/Draft values.

In general, the values of the model and ANSI coefficients presented in

table 3 are comparable. This is not consistent with the expected results

as outlined in the previous paragraph. It can therefore be concluded

that the peak surface pressures measured in the wind tunnel are between

about 1.5 and more than 2.0 times lower than the surface pressures

specified in current design practice.

5. DEVELOPMENT OF DESIGN CRITERIA

The first consideration in developing design criteria which would reflect

the information obtained from the VPI & SU wind tunnel tests was to

decide what corrections if any should be made to the pressure coefficients. Based on the comparisons with the full-scale measurements and

with ANSI A58. 1-1980 /Draft provisions it was concluded that use of the

pressure coefficients obtained from the wind tunnel tests with wind

speeds for Exposure B would yield design pressures which would be unrealistically low, whereas their use with wind velocities for Exposure C

would provide reasonable design pressures. The correction, which amounts

to an increase in the pressure coefficient of between about 1.5 to 2.0

times the wind tunnel value, is consistent with the correction suggested

by some of the full-scale data.

The second consideration in developing the design criteria was to make

the criteria compatible with the provisions of ANSI A58. 1-1980/Draft.

In the course of developing the guidelines for use with ANSI A58.1-

1980/Draft an effort was made to use the ANSI tables as much as possible.

This effort produced several relationships which are intuitively appealing.

For example, as the collector is mounted at angles of inclination to the

roof slope, the collector array begins to act as a roof ridge, and it

would naturally be expected that the end collector would experience pressures more nearly characteristic of zone 2 than zone 1 (as defined in

table 3 and figure 1) even though the end collector might be well away

from the edge of the roof. This trend did appear in the data. Consequently, the guidelines for determining pressures on end collectors when

the collectors are mounted on sloped roofs at an angle of inclination

12
to the roof, suggest that the end colljector be designed for zone 2 pres”

sures even if it lies within roof zone 1. A second interesting trend is

that when the collectors protrude above the roof ridge, the peak pressures

on end collectors tend to increase abruptly when more than half of the

collector extends above the ridge height. This abrupt change occurred

in the negative peak pressures on the cover plate and negative net loads,

and corresponded to winds blowing over the roof ridge diagonally from

the rear, i.e., since collectors face south, winds from the Northwest or Northeast directions. This trend could be explained by the effect of

the accelerated flow over the roof that would begin to strike the upper

part of the collector.

Reductions in pressures for collectors that account for trends such as those discussed above are reflected in the guidelines suggested in sec- tion 6, In some cases the trends are based on only a few data points

but their consistency and the fact that most could be explained intuitively led to the conclusion that the guidelines should Include provisions to account for the variations in pressure coefficients. It is

recognized that design of many installations may not warrant use of the

detailed reductions in pressure coefficients presented. In those cases

the designer should simply Ignore the allowed reductions. It is also

noted that if uniform strength is desired, all collectors should be

designed to resist the pressures specified for end collectors.

It is recognized that manufacturers may want to design collectors or collector cover plates that can be used in any type of installation in

certain geographical areas. It is possible to use the guidelines presented in section 6 to define broad categories by selecting the worst

pressure coefficients for certain types of installations. Then knowing

the design pressure for which the cover plate is certified, it is possible to establish limits on allowable wind speeds. An example of the

application of this approach is presented in section 7,

6. WIND LOAD DESIGN CRITERIA

6 . 1 GENERAL

Recommended provisions for the determination of wind loads on solar

collector cover plates, individual collectors, and systems of collectors

are described in the following sections. The provisions are presented in

the form of criteria followed by specific guidelines for using tables

contained in ANSI A58 . 1-1980 /Draft to obtain wind loads. Use of these

wind loads in the design process will lead to systems which meet the

criteria of sections 6.2, 6.3, 6.4, and 6,5.

6.1.1 Definitions

The following definitions apply to the provisions for wind loads on solar collector systems and system components.

13
DESIGN PRESSURE ON COVER PLATE , p - equivalent static pressure

to be used in the determination of wind loads for solar collector

cover plates. The pressure is assumed to act normal to the sur- face, either as a pressure directed toward the surface or as a suction directed away from the surface. A positive value of a pressure coefficient indicates a pressure directed toward the

surface; a negative value indicates a suction.

DESIGN PRESSURE ON AN INDIVIDUAL COLLECTOR , p - equivalent static

pressure to be used in the determination of wind loads for supports

of individual solar collector panels. The pressure is assumed to

act uniformly over the surface of the collector and in either

direction normal to the plane of the collector. A positive pressure

is one directed toward the surface with the cover plate; a negative

pressure is one directed away from the surface with the cover

plate.

DESIGN PRESSURE ON A SYSTEM OF COLLECTORS , p^^^ - equivalent static

pressure to be used in the determination of wind loads for supports

of an array of solar collector panels. The pressure is assumed

to act uniformly over the surface of the collector array and in

either direction normal to the plane of the array. The design

pressure is the largest of the negative or positive pressures

acting in either direction normal to the plane of the collectors.

ZONE IN WHICH A COLLECTOR IS LOCATED - a collector mounted on a roof or against a wall is considered to be located in a designated

zone if 70 percent or more of its area, projected on the roof or wall, falls within that zone. If a collector is located in more

than one zone, it is assumed to be located in the highest zone where more than 30 percent of its projected area is located. The

projection is taken normal to the plane of the roof or wall. The

various zones on a roof or a wall correspond to the areas indicated in the table, "External Pressure Coefficients for Loads on Building Components and Cladding" of ANSI A58. 1-1980/Draft.

6.1.2 Symbols and Notations

The following symbols and notations apply to the provisions for wind

loads on solar collector systems and system components. Symbols which

apply to collector installations are further illustrated in figures 1 through 4.

a: Distance from edge of roof or wall defining boundary between

pressure zones and equal to 10 percent of minimum building

width or 0.4 h, whichever is smaller, but not less than either

4 percent of minimum width or 3 ft, ft

A: Tributary area, sq ft

14
A'; Fraction of collector area extending above roof ridge " h2/A8in(9 + 3 )

B: Width of solar collector row, ft

ji collector in i**^ row of collectors

D: Horizontal center to center spacing between rows of collectors

in multiple row installations, ft

GCp : Pressure coefficient to be used in determining wind loads

on solar collector cover plates

GCpijJ Pressure coefficient to be used in determining wind loads

on Individual solar collector panels

^CpNs* Pressure coefficient to be used in determining wind loads

on a row of solar collector panels

GCp^; Internal pressure coefficient to be used in determining

wind loads on solar collector panels or components

h: Average height of roof, equal to ridge height plus eave height divided by 2.0, ft

hj: Reference height for velocity pressure to be used with

pressure coefficients: (1) For roof installations hji = mean height of collector (see figures 1 and 2); (2) For

berm units hi = mean roof height (see figure 3); (3) For

other ground installations hi = top edge of collector

(see figure 4), ft

h2

: Vertical distance between roof ridge and highest edge

of collector (see figure 1) extending above ridge, ft

H: Parapet height above roof level, ft

I; Importance factor

K2

: Velocity pressure exposure coefficient at height z for terrain

exposure C obtained from table with same name in ANSI A58. 1 - 1980 /Draft

1: Length of collector, ft

p: Design pressure to be used in determining wind loads on solar

collector cover plates, psf

p^: Design pressure to be used in determining wind loads on individual solar collector panels, psf

15
Design pressure to be used iij determining wind loads on an array of solar collector panels, psf

q: Velocity pressure, psf

Velocity pressure evaluated at height z = hj^, psf

S: Spacing between roof and nearest edge of collector (measured

perpendicular to roof - see figures 1 and 2) or spacing

between ground and nearest edge of collector for ground

installations (see figure 4), ft

V: Basic wind speed from map with same name in ANSI A58.1 - 1980 /Draft, mph

w: Width of individual solar collector, ft

z: Height above ground level used in ANSI A58.1 - 1980 /Draft and

equal to hi, ft

• e: Angle of inclination of solar collector relative to roof

slope for roof mounted collectors and relative to ground for

ground mounted collectors.

<|): Slope of parapet measured from horizontal, degrees

0: Slope of roof, degrees

©= Zone 1 for wind loads on central portions of flat or sloped

roofs; after ANSI A58 . 1-1980/Draft (see figures 1 and 2)

©= Zone 2 for wind loads on edges of flat or sloped roofs; after

ANSI A58 . 1-1980/Draft (see figures 1 and 2)

Zone 3 for wind loads on corners of flat or sloped roofs;

after ANSI A58 . 1-1980/Draft (see figures 1 and 2)

©: Zone 4 for wind loads on central portions of walls of

buildings; after ANSI A58 . 1-1980/Draft (see figure 3)

®= Zone 5 for wind loads on end portions of walls of

buildings; after ANSI A58 . 1-1980/Draft (see figure 3)

.1.3 Warnings: Limitations of Data Base

A. Multiple Row Installations

The tested configurations of multiple row collector

installations Included only cases where the system formed a rectangle, i.e., no lateral offset between rows in a direction

16
parallel to the rows. Consequently, no reductions in loads

should be taken for systems which do contain lateral offsets.

B. Berm Units

The berm configurations tested included only cases where the

collector array was shorter than the building wall on which

they were located. The peak loads may increase significantly

on the cover plates, individual collectors and on the system

as a whole if the array protrudes past or above the wall of

the building.

C. Arrays on Sloped Roofs

(1) Collector arrays which are not parallel to roof ridge

The tested configurations of collectors on sloped roofs

included only cases where the array was parallel to the

roof ridge. Consequently the coefficients developed apply

only to these cases. However, it is conceiveable that in some installations on existing structures, which do not

have a roof slope with a southern exposure, the collectors

will be oriented in arrays of 1 or 2 collectors skewed

with respect to the ridge. Caution should be employed in

designing cover plates and support systems for collectors

which are mounted in such a skewed fashion.

(2) Collectors mounted on the northern slope of a roof

It is conceivable that a row of collectors could be placed

on the northern slope. No such configurations were tested

in the wind tunnel and the pressure coefficients provided

in the criteria do not apply to such installations. Wind

loads on the cover plates and on the collectors may be

greatly Increased for such installations and caution should

be employed in designing such systems and their supports.

(3) Collectors mounted on hip roofs

No tests were conducted using collector arrays on hip roof

buildings. However, it is considered appropriate to assume

the same pressure coefficients for arrays on hip roofs as are used on gabled roofs provided that the end collectors

do not extend laterally past the end of the roof ridge.

If the end collector does extend past the end of the ridge,

this condition should be considered similar to that of

the collector extending above the ridge roof, so that the

collector should also be considered to be In zone 2.

17
6.1.4 Analytical Procedure

It is recommended that design wind pressures for SOLAR COLLECTOR COVER

PLATES . INDIVIDUAL COLLECTOR UNITS , and ARRAYS OF COLLECTORS be determined in accordance with the appropriate equations, given in sections

6.2, 6.3 and 6.4 respectively, using the following procedure;

(1) Select the appropriate VELOCITY PRESSURE EXPOSURE COEFFICIENT , K2 J for height above ground h]^ and Exposure C from the table

in ANSI A58. 1-1980/Draft.

(2) Determine the appropriate IMPORTANCE FACTOR , I, from the

table in ANSI A58. 1-1980/Draft. Importance factors for

Category I structures shall be used for determining the

velocity pressure in the equations for sections 6.3 and

6.4 of this document. For velocity pressures used in the

design of cover plates, section 6.2, importance factors

corresponding to Category IV structures shall be used.

(3) Determine the basic wind speed for the site in question

using the BASIC WIND SPEED MAP contained in ANSI A58.1-

1980/Draft

(4) Calculate the velocity pressure for height h]^ using

the equation given in the section on VELOCITY PRESSURE

in ANSI A58. 1-1980/Draft.

6.2 WIND LOADS ON SOLAR COLLECTOR COVER PLATES - SAFETY AND SERVICEABILITY REQUIREMENTS

CRITERION : Cover plates for flat plate solar collector systems and the

devices used for their attachment shall withstand the wind loads based

on the following analytical procedure and guidelines without exceeding

the allowable stresses that are conventionally used for the material in

question.

RECOMMENDED ANALYTICAL PROCEDURE ; Wind pressures for use in the design

of solar collector cover plates shall be determined in accordance with

the following equation;

where GCp^ = ± 0.25, whichever creates the worst loading case.

GCp is obtained from the ANSI A58. 1-1980/Draft table "External

Pressure Coefficients for Loads on Building Components and

Claddings for Buildings with Roof Height h<60 ft", using

the following guidelines.

18
GUIDELINES FOR USING ANSI A58. 1-1980/DRAFT TO OBTAIN PRESSURE COEFFICIENTS

FOR SOLAR COLLECTOR COVER PLATES:

I. Collectors Mounted on Sloped Roofs, 0 > 10“-^ - (see

figure 1)

A. Collectors parallel to roof slope, 3-0®

1. Pressure directed toward the cover plate surface

(positive pressures)

For any collector in an array, use GCp corresponding

to the positive pressures given for 30® < 0 45®

.

2. Pressures directed away from the cover plate surface

(suctions - use negative values in tables)

(a) For end collectors in an array or individual

collector systems:

Use GCp corresponding to angle 0 and the roof zone in which the collector is located

(b) For interior collectors in an array:

Use GCp corresponding to angle 0 and zone 1

B. Collectors inclined to the roof slope, 3 > 0®

1. Pressures directed toward the cover plate surface

(positive pressures)

For any collector in an array, use GCp (corresponding

to the positive pressures given for 30® < 0 < 45®)

2. Pressures directed away from the cover plate surface

(suctions - use negative values in tables)

(a) For end collectors in an array or individual

collector systems:

GCp = GCp for angle 0 and zone 2

where 0 < 20®

,

use values from table for

10® > 0 > 0 ®.

\j For roof slopes in excess of 45®, use values for 45®.

19
For A’ >0.5; GCp = GCp - 0.5^^

EXCEPTION ; For A' <0.1, use GCp corresponding

to the angle 0 and the roof zone in

which the collector is located.

(b) For Interior collectors in an array:

Use GCp corresponding to zone 2 negative values

given for 30° < e ^5°

EXCEPTION ; For A' < 0.1, use GCp corresponding

to the angle 0 and roof zone 1

II. Collectors Mounted on Flat Roofs, 0 <_ 10° - (see figure 2)

A. Basic cover plate loads for collectors on flat roofs

1. Pressures directed toward the cover plate surface

(positive pressures)

For any collector in an array, obtain the magnitude

of GCp from the table values for zone 1.

GCp = -[GCp for zone 1]

2. Pressures directed away from the cover plate surface

(suctions - use negative values in

tables)

a. For end collectors in an array or individual

collector systems;

GCp = 1.2 [GCp for zone 2]

GCp = 1.2[GCp for zone 2] - 0.5^ of S > 0

b. For interior collectors in an array:

GCp = 1.1 [GCp for zone 1]

B. Flat roofs with parapets - allowable reductions to basic cover plate loads

jy Note that GCp for suction pressures is a negative number.

20
Suction pressure coefficients on cover plates for end

collectors in an array or for individual collector

systems may be reduced as follows:

GCp = [GCp from 6.2-II.A.2.a] {1.0 - [3(H-S)/jlsin6 ]}

but the magnitude of GCp shall not be less than

GCp for zone 1.

C. Multiple rows of collectors on flat roofs “ (no lateral

offset between rows in direction parallel to rows) “ provided D < 2,5 i ; see figure 2

Negative pressure coefficients (suctions) on cover

plates for end collectors in an array may be reduced

as follows:

1. For end collectors on interior rows:

GCp = [GCp from sec. 6.2-II.A.2.a] [1.0-(-^||^) (0,15) ]

but the magnitude of GCp shall not be less than

GCp for zone 1.

2, For end collectors on last row - (see figure 2);

GCp = [GCp from sec. 6.2-II.A.2.a] [1.0-(-^^) (0.10) ]

but the magnitude of GCp shall not be less than

GCp for zone 1.

III. Collectors Mounted on Ground Installations

A. Collectors placed next to a building wall ~ berm

units (see figure 3)

1. Pressures directed toward the cover plate surface

(positive pressures)

For any collector in an array, use GCp corre- sponding to the positive pressures given for

walls. Note that the values in the table apply

for zones A and 5.

2, Pressures directed away from the cover plate

surface (suctions - use negative values in

tables)

Use GCp corresponding to the negative pressure

given for walls and the appropriate wall zone.

21
B. Single row of collectors mounted close to ground and not

leaning against a building,

1. Pressures directed toward the cover plate surface (positive pressures)

For any collector in an array use GCp corre- sponding to the positive pressures given for

walls. Note that the values in the table apply

for zones 4 and 5.

2. Pressures directed away from the cover plate

surface (suctions - use negative values in

tables)

(a) For end collectors in an array or individual

collector systems.

Use GCp corresponding to wall pressures

in zone 5.

(b) For interior collectors in an array

Use GCp corresponding to wall pressures

in zone 4,

C. Multiple rows of collectors mounted close to ground and

not leaning against a building (no lateral offset between

rows in direction parallel to rows) provided D < 2.5 see figure 4.

Pressure coefficients on cover plates are obtained using

the guidelines in section 6.2 - III.B and may be reduced

as follows;

1. For collectors in interior rows:

GCp = [GCp from sec. 6.2-III.B] [1.0 -(2^)(0.15)]

but the magnitude of GCp shall not be taken less than

40 percent of the unreduced value of GCp.

2. For collectors in the last row - (see figure 4):

GCp = [GCp from sec. 6.2-III.B] [1.0 - (-^j^) (0. 10)

]

but the magnitude of GCp shall not be taken less than

60 percent of the unreduced value of GCp.

22
6 . 3 WIND LOADS ON INDIVIDUAL COLLECTORS - SAFETY REQUIREMENTS

CRITERION ; Support brackets for individual flat plate solar collectors

shall withstand the wind loads based on the following analytical procedure

and guidelines without exceeding the allowable stresses that are conventionally used for the material in question#

ANALYTICAL PROCEDURE ; Design wind pressures for individual collector

panels to be used in determining net loads on individual collectors shall

be determined in accordance with the appropriate following equation:

A. For collectors which are not an integral part of the roof, i.e. are placed on top of the roof or are actually separate from the

roof surface

Pjg = (GCpn)

B, For collectors which are an integral part of roof, i.e., such

that their back surface is effected by the internal pressure of

the building

%

"" (GCpjj) - %j(GCp^)

where: GCpj[^ =± 0.25, whichever creates the worst loading

case.

GCpjj is equal to GCp as given in the ANSI A58.1-

1980/Draft table, "External Pressure Coefficients for

Loads on Building Components and Cladding for Buildings

with Height h ^ 60 ft", using the following guidelines.

NOTE ; Obtain GCp from the negative values in the tables but

recognize that the loads can act in either direction

normal to the collector.

GUIDELINES FOR USING ANSI A58. 1-1980/DRAFT TO OBTAIN NET PRESSURE COEFFICIENTS FOR INDIVIDUAL SOLAR COLLECTORS ;

I. Collectors Mounted on Sloped Roofs, 0 > 10°i>^ (see

figure 1 )

A. For collectors parallel to roof slope, 3 =: 0°:

GGpN = ± [GCp for the angle 0 and the appropriate zone]

GCpjj = ± [GCpjj - 0.5] if S > 0^

For roof slopes in excess of 45", use values for 45".

2 / Note that GCpjj used for net loads is a negative number.

23
B. Collectors Inclined to the. roof slope 3 > 0"

1. For end collectors In an array or individual

collector systems:

GCpN = - [GCp for angle 0 and zone 2 ]

GCpj^ = ± [GCpjj - 0.5] if A’ > 0 , 5

^

GCpjj = ± [GCpjj - 0.5] if S > 0^

Note: GCpjj = ± [GCp^ - 1.0] if A' > 0.5 and S > 0-^

2. For interior collectors in an array:

GCpN = ± [GCp for 30" < 0 ^45” and zone 2]

GCpN = ± [GCpjj - 0.5] if S > Oi/

II. Collectors Mounted on Flat Roofs, 0 10" - (see

figure 2)

A. Basic net loads on individual collectors

1. For end collectors in an array or individual

collector systems:

GCpN = ± 1.5 [GCp for zone 2]

2. For Interior collectors in an array:

GCpN = ± [GCp for zone 2]

B. Collector mounted on flat roofs with parapets

No reduction is allowed in obtaining the net loads on an Individual collector.

C. Collectors mounted in multiple rows on flat roofs (no

lateral offset between rows in direction parallel to rows)

- provided D < 2.5 A, see figure 2

No reduction is allowed in obtaining the net loads on an Individual collector.

III. Collectors Mounted in Ground Installations

u Note that GCpj^j used for net loads is a negative number.

24
A. For collectors placed next to a building wall - berm units

(see figure 3):

GCpN = - [GCp for appropriate wall zone]

B« For single row of collectors mounted close to ground and not

leaning against a building:

Use GCpfj equal to the sum of the magnitudes of the negative

pressure coefficient and 70 percent of the positive

pressure coefficient, each for the appropriate wall zone.

GCpN = |neg. GCp I + 0.7 |pos. GCp|) for the

appropriate wall zone

C. Multiple rows of collectors mounted close to the ground

and not leaning against a building (no lateral offset

between rows in direction parallel to rows) - provided

D < 2.5 see figure 4

Pressure coefficients on individual collectors are obtained

using the guidelines in section 6.3 - III.B and may be

reduced as follows:

1. For collectors on interior rows:

90~6

GCpjj = [GCpjg from sec. 6.3-III.B] [l.O-(-j^) (0.15) ]

but the value of GCpjg shall not be taken less than

40 percent of the unreduced value of GCp.

2. For collectors in the last row:

GCpjj = [GCpjj from sec. 6.3-III.B] [1.0-(-^^) (0.10) ]

but the value of GCpjj shall not be taken less

than 60 percent of the unreduced value of GCp.

6.4 WIND LOADS ON SOLAR COLLECTOR SYSTEM SUPPORTS - SAFETY REQUIREMENTS

CRITERION : The support brackets and frames for holding the collector

array shall withstand the wind loads based on the following analytical

procedures and guidelines without exceeding the allowable stresses that are conventionally used for the material in question. The frame shall

be designed in such a manner that it is capable of transmitting the

prescribed wind loads to the ground or to the roof or walls of a building without experiencing distortion or displacements in excess of the

strains corresponding to the allowable stresses for the material in

question.

25
ANALYTICAL PROCEDURE ; Design wind pressures for an array of collector

panels to be used in determining net J.oads on the array should be

determined in accordance with the appropriate following equation:

A. For collectors which are not an integral part of the

roof, i.e. are placed on top of the roof or are actually

separated from the roof surface

PnS - q (GCp^g)

hi

B, For collectors which are an integral part of the roof, i.e.

the back surface is effected by the internal pressure of the

building.

(GCpj)

hi hi

where: GCpi = ± 0.25, whichever creates the worst loading

case

GCpNS is obtained from the ANSI A58. 1-1980/Draft table

"External Pressure Coefficients for Loads on Building

Components and Cladding for Buildings with Height

h < 60 ft", using the following guidelines.

NOTE : Obtain GCp from the negative values in the tables

but recognize that the loads can act in either

direction normal to the collector.

GUIDELINES FOR USING ANSI A58. 1-1980/DRAFT TO OBTAIN NET PRESSURE COEFFICIENTS FOR A SOLAR COLLECTOR ARRAY (2 or more collectors)

I. Collectors Mounted on Sloped Roofs, 0 > 10°!/ see figure 1)

A. For collectors parallel to the roof slope, g = 0°:

^^PNS “ - [^Cp for zone where majority of collectors

are located]

B. For collectors inclined to the roof slope, g > 0°:

^^PNS “ - [^f'p for 30° < 0 ^45° and zone 2]

II. Collectors Mounted on Flat Roofs, 0 ^

10° - (see figure 2)

A. For basic net loads on an array of collectors:

1/ For roof slopes in excess of 45°, use values for 45°.

26
GCpf^S “ - zone 2]

B. For array of collectors mounted on a flat roof with

parapets:

No reduction is allowed in obtaining the net load on an array of collectors.

C. For multiple arrays of collectors (no lateral offset

between rows in direction parallel to rows) - provided

D < 2,5d - (see figure 2):

For interior rows only:

GCpNs ~ - [GCp for zone 1]

III. Collectors Mounted in Ground Installations

A. For an array of collectors placed next to a building

wall ~ berm units (see figure 3):

GCpNS - [GCp for zone where majority of collectors are located]

B. For a single array of collectors mounted close to ground

and not leaning against a building (see figure 4);

GCpNS “ - [GCp for zone 5]

C. For multiple arrays of collectors mounted close to ground

and not leaning against a building (no lateral offset between

rows)

No reduction is allowed for interior rows.

6.5 SAFETY OF BUILDINGS AND FOUNDATIONS SUPPORTING COLLECTOR SYSTEMS

CRITERION : Buildings and foundation systems supporting elevated or ground

mounted collector arrays shall resist the appropriate loads and moments

transmitted by the collector array frame as defined in section 6.4 of this

report. For roof or wall mounted collectors, a path must be provided for

transmitting the wind loads to the structural frame.

7. EXAMPLES

In the following three subsections, examples are presented to illustrate

the use of the design criteria and guidelines given in section 6. Wind

loads will be computed for both end and interior collectors, although it

is recognized that in most cases all collectors should be designed to

withstand the larger loads experienced by the end collectors.

27
7.1 COLLECTORS MOUNTED ON A SLOPED ROOF

Consider the case of an array of eleven collectors mounted on the sloped

roof of a one story building as shown in figure 1. The building is to

be built in Omaha, Nebraska and is 32 feetiJ wide by 50 feet long. The eave height is 10 ft and the ridge height will be 15.5 ft since the roof

is symmetric and has a pitch of 20 degrees. The solar collector installation is characterized by the following parameters illustrated in fig- ure 1: $ = 25®, j, = 8 ft, w = 4 ft, B = 44 ft, cj = 4,5 ft and a = 3.2

ft. Also, the bottom edge of the collector is to be raised 3 ft above

the roof level, S = 2.8 ft, so that snow will slide off the collector.

In this example it is assumed that each collector has a tributary area,

A, of 32 sq ft and the entire array has a tributary area of 352 square

ft. Because the collector is elevated to allow snow to slide off and is

mounted at a slope which is considerably steeper than the roof slope, hj

is equal to 17.4 ft which is greater than the roof ridge height and h2

is equal to 4.7 ft. Consquently, A* is equal to 0,83, From figure 1 it can be seen that collectors Cl.l through Cl, 10 are in zone 1 and that

collector Cl. 11 is in zone 2 (more than 30 percent of Cl. 11 is in zone 2).

Using this information, the wind loads are computed following the

guidelines given in section 6. The procedure is as follows:

Calculate Velocity Pressure : from section 6,1.4

(1)

Velocity Pressure Exposure Coefficient:

^z =

^h. = K(17 ft) = 0.83

(2)

Importance Factor: I

I (collector) = 1.00

I (cover plate) = 0.95

(category I)

(category IV)

(3) Basic Wind Speed: V = 80 mph

(4) Velocity Pressure: q^

q^ (collector) = q^^

(collector) = 0,00256 [0,83] [(1,00)(80)]^

q^^ (collector) = 13.6 psf

q^ (cover plate) = q^^ (cover plate) = 0,00256 [0.83] [(0.95)(80)]‘

q^^

= (cover plate) = 12.3 psf

U For conformity with the American National Standard A58, 1-1980/Draft,

English units are used throughout Parts I, II, and III of this report.

For conversion to SI units, see p. vili.

28
Wind Loads on Cover Plates: from section 6,2

p “ q (GCp) - q (GCp^)

hi hi

positive pressures : from section 6,2,I,B.l

GCp = 1.2 and since GC„, = ± 0,25

Pi

p = (12.3)(1,2) - (12.3)(-0,25) = 17.8 psf

suctions : from section 6.2,I.B,2

a) End Collectors: Note that A* >0.5 since

h]^ > ridge height

GCp = -2.5 - 0.5 = -3.0

p = (12.3K-3.0) - (12.3K0.25) = -40.0 psf

b) Interior Collector:

GCp = -1.55

p = (12.3)(-1.55) - (12.3)(0.25) = -22.1 psf

Wind Loads on Individual Collectors: from section 6.3

= q^^(GCpN)

Note that pressure coefficients are obtained from the

negative values in the tables and are assumed to act in

either direction normal to the collector.

From section 6.3.I.B

(1) End Collector: Note that A’ >0,5 since

hi > ridge height also S > 0.0

GCpN = [GCp for angle 0 and zone 2] - 1.0

GCpN ~ —2.5 — 1,0 = —3,5

p^ = (13.6)(-3.5) = ± 47.6 psf

Wind load = ( ± 47,6)(32) = ± 1523 lbs

(2) Interior Collector: since S > 0.0

GCpjj = -1.55 -0.5 = -2.05

29
Pjj = +(13.6)(-2.05) = ± 27.9 psf

Wind load = (±27,9) (32) = ± 893 lbs

Wind Loads on Solar Collector System Supports: from section 6,4

Note that pressure coefficients are obtained from the

negative values in the tables and are assumed to act in

either direction normal to the collector.

From section 6,4.I.B A = 352 sq ft

GCpNS -

p^g

= ± (13.6)(-1,4) = ± 19.0 psf

Net wind load = ( ± 19,0)(352) = ± 6688 lbs

7.2 COLLECTORS MOUNTED ON A FLAT ROOF

Consider the case of three arrays of eleven collectors mounted on the

flat roof of a one story building as shown in figure 2, The building is

to be built in New Orleans, Louisiana and is 40 ft wide by 60 ft long.

The eave height is 10 ft and there is a 2,5 foot high parapet, (H = 2.5

ft and (j) = 90°) around the edge of the building. The solar collector

Installation is characterized by the following parameters illustrated

in figure 2: 3 = 30°, 1 = S ft, w = 4 ft, B = 44 ft, D = 10 ft and

a =4 ft. The bottom edge of the collector is raised 2.0 ft above the

roof level (S = 2,0 ft) for service of the roof membrane [9], Therefore,

hi is equal to 14,0 feet. It is assumed that each collector has a tributary area of 32 square feet and that each array has a tributary area of 352 sq ft. From figure 2 it can be seen that all the collectors

fall within zone 1 except for Cl. 11, C2.ll and C3.ll which fall within

zone 2 (more than 30 percent of Cl. 11, C2.ll and C3.ll is in zone 2),

Using this information, the wind loads are computed following the

guidelines given in section 6 , The procedure is as follows:

Calculate Velocity Pressure : from section 6,1.4

(1) Velocity Pressure Exposure Coefficient :

= K(14 ft) = 0.80

(2) Importance Factor: I

I (collector) = 1,05 (category I)

I (cover plate) = 1.00 (category IV)

30
(3) Basic wind speed: V = 100 mph

(4) Velocity Pressure:

(collector) = (collector) = 0.00256[0.80] [(1.05)(100)]^

qjj^ (collector) =» 22.6 psf

q^ (cover plate) =

q^^^ (cover plate) = 0.00256[0.80] [(1.00)(100)]^

qhj (cover plate) = 20.5 psf

Wind Loads on Cover Plates : from section 6.2

P = (GCp) - (GCp.

)

positive pressures : from section 6. 2. II. A.

1

GCp = -(-1.3) = 1,3 and since = ± 0.25

p = (20.5)(1.3) - (20.5)(-0.25) = 31.8 psf

suctions : from section 6, 2. II, A.

2

a. End Collectors: Note S > 0

GCp = 1.2[-2.1] - 0.5 = -3.0

p = (20.5)(-3.0) - (20.5)(0.25) = -66.6 psf

b. Interior Collectors:

GCp = 1.1[-1.3] = -1,4

p = (20.5)(-1.4) - (20.5)(0.25) = -33.8 psf

*Allowable reductions to suction on end collectors

due to parapets: from section 6,2.II,B

GCp = 1-3.0] {1.0 - [3(H-S)/ I sin 3]}

GCp = [-3.0] {1.0 - [3(2.5-2.0)78 sin 30°]}

GCp = [-3.0] [.63] = -1.9

p = (20.5)(-1.9) - (20.5)(0.25) = -44.1 psf

*Allowable reductions to suction for end collectors on interior rows of multiple row installation: from

section 6,2.II.C.l

31
GC„ = [-3.0] [1.0 - ( 90-30 )(0,i5)]

P

. 15

GCp = -1.2

However, GCp for zone 1 = -1.3

.*

. GCp = -1.3

p = (20.5K-1.3) - (20.5)(0.25) = -31.8 psf

*Allowable reductions to suctions on end collectors on last row of multiple row installation: from section

6. 2. II. C.

GC^ = [-3.0] [1.0 - ( 90-30 r 0. 10 V] P 15

GCp = -1.8

p = (20.5K-1.8) - f20.5)(0.25) = -42.0 psf

Based on these calculations a reasonable approach would be

to design the cover plates for the end collectors to withstand 44 psf and the cover plates for the interior collectors

to withstand 34 psf. A more practical approach might be to

design all the cover plates for 44 psf.

Wind Loads on Individual Collectors: from section 6.3

Pn " 9h^(<3CpN>

From section 6.3. II.

(1) End Collector:

GCpN ~ ± 1.5 [—2.1] = ± 3.2

p„ = (22.6 psf)( ± 3.2) = ± 72.3 psf N

Wind load = ( ± 72.3)(32) = 2314 lbs

(2) Interior Collectors:

GCpN = ± [~2.1] = ±2.1

p^

= (22.6 psf)( ± 2.1) = ± 47.5 psf

Wind load = ( ± 7.5)(32) = 1520 lbs

Wind Loads on Solar Collector System Supports : from section 6.4

32
A = 352 sq ft

NS

= q

From section 6. 4. II,

A

p^g = (22.6 psf) ( ± 1.5) = ± 33.9 psf

Net wind load = ( ± 33.9) (352) = 11,933 lbs

*Allowable reduction for interior rows

^Sns " -

Pj^g = (22.6 psf) ( ± 1.2) = ± 27.1 psf

Net wind load on interior array =

( ± 27.1) (352) = 9539 lbs

7 . 3 DESIGN OF COLLECTOR COVER PLATES FOR A VARIETY OF INSTALLATIONS

Consider the case of a glass manufacturer who is producing solar collector

cover plates which he has certified to withstand 55 psf wind loads. It is

possible to use the criteria and guidelines contained in section 6 to define

categories of installations for which these cover plates would be suitable.

The largest pressure coefficients for cover plates assumed to have an area of 32 sq ft in any of the installations covered by the provisions is

-3.25. This is true for collectors mounted on sloped or flat roofs or on ground installations. Noting that p = ± 55 psf = q^ GCp = q (-3.25),

q, = 16.9 psf

hi

Also for areas which are not subject to hurricane winds,

q^

= 16.9 psf = 0.00256 ]0.95 V]^

or K V

z = 7315

K =

z 1.13 at z = 50 ft

K =

z 0.87 at z = 20 ft

for K =

z 1.13 > V = 80.5 mph

for K =

7. 0.87 9 V = 91.7 mph

Consequently, these cover plates would meet the design criteria outlined

in this report for any collector installation located within map regions

having a basic wind speed less than 80 mph and mounted at elevations

33
less than 50 ft or located within map, regions having a basic wind speed

less than 90 mph and mounted at elevations less than 20 ft.

Similar general provisions could be derived for individual collectors,

mounting brackets or entire arrays. Further provisions could be made

restricting use of the collectors in configurations which carry a wind

load penalty such as those which extend well above the roof ridge.

8. REFERENCES

1. Tieleman, H. W. , Akins, R. E., and Sparks, P. R., "An Investigation

of Wind Loads on Solar Collectors, With Appendices I and II," Virginia Polytechnic Institute and State University, VPI-E-80-1,

Blacksburg, Virginia, January 1980. (Available from NTIS, NTIS access numbers BP80158744, PB80158751, and PB80158769 respectively).

2 . Building Code Requirements for Minimum Design Loads in Buildings and

Other Structures , American National Standard A58. 1-1980/Draft

American National Standards Institute, New York, 1980.

3. Simlu, E., Changery, M. J., and Filliben, J. J., "Extreme Wind Speeds

at 129 Stations in the Contiguous United States," National Bureau of

Standards, Building Science Series 118, Washington, D.C., March 1979.

4. Batts, M. E., Cordes, M. R. , Russell, L. R. , Shaver, J. R. and Simiu,

E., "Hurricane Wind Speeds in the United States," National Bureau of

Standards, Building Science Series 124, Washington, D.C., May 1980.

5. Tieleman, H. W. and Reinhold, T. A., "Wind Tunnel Model Investigations

for Basic Dwelling Geometries," Virginia Polytechnic Institute and

State University, VPI-E-76-8, Blacksburg, Virginia, May 1976.

6. Davenport, A. G., Surry, D. and Stathopoulos, T. , "Wind Loads on Low-Rise Buildings, Final Report of Phases I and II," University

of Western Ontario, BLWT-SS8-1977 , London, Ontario, Canada, August

1977.

7. Marshall, R. D., "A Study of Wind Pressures on a Single-Family

Dwelling in Model and Full Scale," Journal of Industrial Aerodynamics, 1 (1975), pp. 177-199.

8. Tieleman, H. W., Akins, R. E. and Sparks, P. R., "A Comparison of

Wind-Tunnel and Full-Scale Wind Pressure; Measurements on Low-Rise

Structures," Proceedings of the 4th Colloquium on Industrial

Aerodynamics, Aachen, Germany, June 19-20, 1980.

9. Mathey, R. G. and Rossiter, W. J., "Guidelines for Installation

of Solar Components on Low-Sloped Roofs," National Bureau of

Standards, Technical Note 1134, Washington, D.C., September 1980.

34
TABLE l.a

Peak Negative Pressure Coefficients* for Top Surface of Collectors

(Cover Plates). Comparison of Price's Fork Model and Full-Scale Data,

S/l - .062

Model Test Data Full'-Scale Test Data

Coefficients from Coefficients from

Wind Predicted Peaks, Data Predicted Peaks, Corrected Wind Coefficients from

Direction Filtered at 50 Hz 10 Hz Filtered Data Direction Measured Peaks

360 - .8** - .7** 1 - .9 0 - .9** - .9** 4 - .7

30 - .7 - .7

60 - .6 - .6 74 -1.0

90 - .6 - .6 74 -1.2

172 -4.1

180 -1.3 -1.4 173 -2.9

200 -2.2 204 -4.5

210 -1.7 -2.7 212 -4.1

220 -2.6 214 -3.8

230 -2.4

240 -2.3 -2.6 246 -4.3

250 -2.8 247 -3.5

253 -3.8

260 -2.6 259 -4.6

263 -5.1

264 -4.0

270 -2.2 -2.5 269 -4.5

274 -4.4

282 -4.2

283 -4.4

300 -1.2 -1.9

* Coefficients are based on mean hourly wind speeds. (Divide by - 1.61 to convert

to coefficient for use with fastest mile wind speed)

** Positive mean pressure coefficient.

35
TABLE l.b

Peak Positive Pressure Coefficients* for Top Surface of Collectors

(Cover Plates). Comparison of Price's Fork Model and Full-Scale Data,

S/1 = .062

Model Test Data Full-Scale Test Data

wind

Direction

Coefficients from

Predicted Peaks, Data Filtered at 50 Hz

Coefficients

Predicted Peaks,

10 Hz Filtered

from

Corrected

Data

Wind Coefficients from

Direction Measured Peaks

360 0.9 0.9 1 1.1

0 1.0 1.0 4 1.0

30 0.5** 0.5**

60 0.2** 0.2** 74 0.2

90 0.2** 0.3** 74 0.0

172 0.1

180 0.2** 0.4** 173 0.1

200 0.5** 204 0.2 210 0.0** 0.7** 212 -0.1

220 0.6** 214 0.0

230 0.4**

240 0.1** 0.6** 246 0.5 250 0.6** 247 0.1 253 0.2

260 0.5** 259 0.2

263 0.0

264 -0.1

270 0.6** 0.6** 269 -0.1

274 0.7

282 1.0 283 0.7

300 0.8** 1.4**

* See note on table l.a.

** Negative mean pressure coefficient.

36
TABLE 2.

Peak Negative Pressure Coefficients* for Net Loads on Collectors.

Comparison of Price's Fork Model and Full-Scale Data, S/l - .062

Model Test Data Full-Scale Test Data

Wind

Direction

Coefficients from

Measured Peaks, Data

Filtered at 50 Hz

Coefficients

Predicted Peaks,

10 Hz Filtered

from

Corrected

Data Wind Coefficients from

Direction Measured Peaks

360 .1 - .5 1 - .2 0 0.0 -1.0 4 - .5

30 - .1 - .5

60 - .1 - .6 74 - .3 90 - .2 - .7 74 - .6

172 -1.3

180 - .3 -1.4 173 - .9

200 -2.0 204 -1.1

210 - .4 -2.4 212 -1.9

220 -2.3 214 -1.6

230 -2.1

240 - .5 -2.7 246 -1.1

250 -2.5 247 -1.1

253 -1.7

260 -2.5 259 -2.1

263 -2.1

264 -1.5

270 - .5 -2.5 269 -1.6

274 -2.1

282 -1.6

283 -1.7

300 - .1 -1.6

* Coefficients are based on mean hourly wind speeds. (Divide by ~ 1.61 to convert

to coefficient for use with fastest mile wind speed)

37
TABLE 2.b

Peak Positive Pressure Coefficients* for Net Loads on Collectors.

Comparison of Price's Fork Model and Full-Scale Data, S/l • .062

Model Test Data Full-Scale Test Data

wind

Direction

Coefficients from

Measured Peaks, Data Filtered at 50 Hz

Coefficients from

Predicted Peaks, Corrected

10 Hz Filtered Data

Wind Coefficients from

Direction Measured Peaks

360 1.9 1 2.5

0 1.9 2.3 4 1.9

30 1.6 1.2

60 1.1 0.9 74 0.9

90 0.6 0.8 74 1.1

172 0.7

180 0.3 1.3 173 0.5

200 1.6 204 1.5 210 0.5 1.7 212 1.4 220 1.6 214 1.1

230 1.5 240 0.5 2.4 246 2.8

250 2.0 247 1.5 253

260 2.0 259 2.4 263 2.0

264 1.8

270 0.7 2.2 269 1.8 274 1.9

282 2.1 283 2.0

300 1.4 2.3

* See note on table 2. a.

38
Peak

Pressure

Coefficients*

for

Top

Surface

of

Collectors

(Cover

Plates)

Mounted

Flat

ona

Building

Roof Ii

>>2U<o

•o

T3

cduu<oocu

(0uQo00ON

00

0^

COoH

•Ic •K

OJco

ts3

CduQoCO

ON0)

<0oH

•le0) coN

(d 4^ oo u

xj (U •H OU 0) o

04• u o o z ^

tn

O

U

O -u 05 iH

Pk

CM CM • I • I CM• I

CM ON CM 00 r*^ • • • • • ^ o -- I I I

ON o 00 00 -oo 01 0 o1 m \o ^ oI

CMI

fOcMCOCM rO CM CM w I I ^ ^ ^ ^ CNJ I I I

CM vO CM CM O' NO II40«^0 «-40*^0 II rH f—4 f-4

O *^0 II I CMOI ^ ^ ( CM CM z (0 0) 0 0 0) 0) 0 0> (U 0) (U 0 0) 0> 0) 0) 0) OQ > > > > > > > > > > > > > > > u 0) *r-( •H •H •H •H •H •H •H •H •H •H •H •H •H •H •H 0 U 4-t 4J 4^ *J 4J 4J 4^ 4J 4^ 4J 4J

Cd •H Cd •H Cd •H Cd •H Cd •H Cd •H Cd Cd •H 00 (0 00 03 oc (0 00 00 00 CO 00 CO 00 CO 00 CO > a> 0 0 0 0 0 0) 0 Q) 0 0) 0 o> 0 0) 0

•H z pH z PL4 z 04 z Ph Z pH z Ph z Ph z PL4

Cdu ovO ooXo

(£4 3

(bo

Pu

0)0) CLO

CJ

39

**

Roof

zone

after

ANSI

A58.

1-1980/Draf t;

Ifa

collector

is

located

in

more

than

one

zone

It

is

assumed

to

be

located

in

the

highest

zone

where

more

than

30

percent

of

its

projected

area

is

located.
Figure 1 Solar Collector Systems Mounted on a Sloped Roof.

40
a

- <— ®i ® i® a

1

1

1 t

!

1 ^1.1^

/ / / y'/ ^C3.1^

1

1

1

1 / / / / > / / ^ /

yy,

1

1

1

1 '/y.

/ //

/C3.3/

1

1

1 ///

/Z\A' /C2.4/

/ / j

/C3.4/

/ / /

1

1

///

/C1.5^

/ / y

’ //'

/C2.5^

/ / / 0

/C3^5/

1 ®

/C1.6^

/ / /

1 ^2p /C3.6^

/ / /

1

!

1 / / /

'^C2.7^

1/ / ^

4

w

t

/ / y 'X3.7''

1

1

1

1

1 / / /

^C2.8^

/ / 7

,C3.8 J ^ / /I

1

1

1

1 / / /

^C2.9 > C3.9^

7/7

1

1

1

1 Cl.lOy X2.10/ ,C3.10/

/

1

®i V / .

/ / /

/C2.11>

/ / > / //

/C3.11>

/ / > im

1

< a

PLAN

1st row 2nd row last row

ELEVATION (end)

Figure 2. Solar Collector System Mounted on a Flat Roof.

roof

41
i

PLAN

Figure 3. Cuilector Syscems in Ground Installations Next to a Building - Berm Units.

42
B

cu

Cl,

Cl,

3

Cl,

Cl,

5

C1,6

Cl,

C1,8

C1,9

Cl,10

T

w

±

C2,1

Cl,j

C3,1

i=row; j=collector in row PLAN

1st row 2nd row 3rd row

C4,1

last row

ELEVATION (end)

Figure 4. Collector Systems in Ground Installation in Open

Location.

43
PART II

EARTHQUAKE LOADS ON

SOLAR COLLECTORS

by

Charles W.C. Yancey

44
LIST OF TABLES Page

Table 1. Horizontal Force Factor "Cp" for Solar Collector Systens ^8

NOTATION

Apt Force multiplier which accounts for amplification of motion

experienced by the supporting structure.

Cpi Horizontal force factor to be used in obtaining the ANSI

equivalent static lateral force.

T^: Natural period of solar collector panels and their support

system, seconds.

4 '5
1

.

INTRODUCTION

This section presents Information applicable to the design and evaluation

of new or replacement solar collectors and their supports when they are to

be subjected to seismic loads. This information is based upon current

seismic design practice for mechanical and electrical elements as incorporated in building codes and standards. Where necessary, the code and

standard provisions are adapted to reflect the specific characteristics

of solar collector systans.

2. RELATIVE IMPORTANCE OF SEISMIC FORCES IN THE DESIGN OF SOLAR

COLLECTOR SYSTEMS

In the event of an earthquake the components of solar collector systems

would be subjected to inertial forces that are directly proportional to

their mass. Since the self weight of solar collectors is relatively

small, it is inferred that the seismic forces applicable to these elements are also relatively small. For example, in the case of flat plate collectors, the unit weight is of the order of 10 psf- . Using the equivalent

static force approach specified in the 1980 draft revision of American

National Standard A58.1

[1]*

* each square foot of flat plate collector

panel would experience a lateral seismic force of about 5 lb. Upon comparing this order of magnitude with current code and standard design

loads for wind and snow, it is concluded that seismic forces would seldom

govern the design of solar collector components and supports, even in

the most highly seismic zones of the United States.

3. DESIGN OF SOLAR COLLECTORS SUBJECTED TO SEISMIC LOADS

In general, assemblies consist of standard-sized collector panels which

are positively attached to triangular-shaped or diagonally-braced supports,

that are in turn anchored directly to roof supports, a supporting slab, or footings. These assemblies would be categorized as "rigid" and "rigidsupported." All of the components of rigid and rigidly-supported solar

collector systems, their supports and their connections to buildings or ground-supported members shall resist seismic forces as specified for

parts and portions of structures in the 1980 draft revision of the ANSI

A58.1 Standard [1]. The values of the factor C to be used in obtaining

the ANSI Equivalent Static Lateral Force, consistent with ref. 1, are listed in table 1. The importance factor, I, shall be that which applies

to the building being supplied by the solar collector system. The system

shall resist the derived seismic forces without incurring failure or excessive deflection of the supporting and connecting elements.

- For conformity with the American National Standard A58. 1-1980/Draft,

English units are used throughout Parts I, II, and III of this report.

For conversion to SI units, see p. viii.

* Numbers in brackets Indicate references at the end of each part.

46
If in the judgement of the engineer, the solar collector system does not

warrant being classified as rigid or rigidly-supported, the appropriate

values of Cp shall be determined with consideration given to the dynamic

properties of both the solar components and the building or structure on which they are placed. In any case, the values of Cp shall not be less

than those listed in table i. The natural period of the collector panels

and their support system determines whether the assembly is to be con- sidered rigid or flexible. (As a guide, an assembly should be considered

flexible if its natural period > 0.05 seconds).

In lieu of a rigorous dynamic analysis, flexible or flexibly-mounted

collectors may also be analyzed by the Equivalent Static Force method.

However, the force obtained by using the ANSI formula should be modified

by the multiplier Ap, which accounts for the amplification of the motion

experienced by the supporting structure. Published values for Ap have a range of 1.0^Ap^5.0 [2].

4.

REFERENCES AND BIBLIOGRAPHY

1 . Building Code Requirements for Minimum Design Loads in Buildings and

Other Structures , American National Standard A58. 1-1980/Draft,

American National Standards Institute, New York, 1980.

2. Seismic Design for Buildings , TM 5-809-10, NAVFAC P-355, AFM 88-3,

Chap. 13, Departments of the Army, the Navy and the Air Force,

Draft: January 1979.

3. Uniform Building Code , 1979 Edition, International Conference of

Building Officials, Whittier, California, 1979.

4. Intermediate Minimum Property Standards Supplement for Solar Heating

and Domestic Hot Water Systems , 4930.2, 1977 Edition, U.S. Department

of Housing and Urban Development, Washington, D.C. 1977.

5. Yancey, C. W. C. , and Camacho, A. A., "Aseismic Design of Building

Service Systems: The State-of-the-Art , " NBS Technical Note 970,

National Bureau of Standards, Washington, D.C., September 1978,

6. Tentative Provisions for the Development of Seismic Regulations for

Buildings , Applied Technology Council (ATC), ATC Publication

ATC 3-06, National Bureau of Standards Special Publication 510,

National Science Foundation Publication 78-8, U.S. Government

Printing Office, Washington, D.C., 1978.

47
TABLEil. Horizontal Force Factor "Cp" for Solar Collector Systems

Part of System Direction of

Horizontal Force

Value of

S

Roof^supported flat plate and

concentrating solar collectors

any direction 0.30

Ground-supported flat plate and

concentrating solar collectors

any direction 0.20

Anchorages and supports for solar

collectors and storage tanks

any direction 0.30

Storage tanks connected to or housed within the building

any direction 0.30

Transfer liquid pipes and storage

tanks resting on the ground

any direction 0.20

48
PART III

SNOW DESIGN CRITERIA FOR

FLAT-PLATE SOLAR COLLECTOR INSTALLATIONS

by

James Robert Harris

49
LIST OF FIGURES Page

Figure 1. Light Snow Cover on Collectors During Snowfall 60

Figure 2. Light Snow Cover on Collectors After 6" Snow 61

Figure 3. Melting and Sliding of Snow 62

Figure 4. Snow Sliding off Steep Collectors 63

Figure 5. Snow Retention on Shallow Collectors 64

Figure 6. Obstruction Below Steep Collectors 65

Figure 7. Ice Dam at Gutter and Icicles Below Collectors 66

Figure 8. Building with Multiple Rows of Collectors 67

Figure 9. Drift between Parallel Rows of Collectors 68

Figure 10. Drift between Parallel Rows of Collectors 69

Figure 11. Basic Snow Loads from ANSI A58. 1-1980/Draft 70

Figure 12. Unbalanced Snow Loads from ANSI A58. 1-1980/Draft 71

Figure 13. Drift Surcharge Load from ANSI A58. 1-1980/Draft 72

Figure 14. Definition of Clear Height H 73

Figure 15. Definition of Sliding Surcharge 73

Figure 16. Load Patterns for Protruding Collectors Close to the Roof 74

NOTATION

C^: coefficient for exposure to wind

C : coefficient for slope

C^: coefficient for thermal properties

H : actual clear height of collector above roof

He: nominal clear height for avoidance of drifting

h^: height of balanced snow load

h^: clear height from top of balanced load to top of obstruction

h^: depth of drift

I : coefficient for level of risk

i : length of obstruction

Pjj: drift surcharge load

Pfi flat roof snow load

Pg: ground snow load

Pg: sloped roof snow load

W : width of drift

Y : density of snow

50
1. INTRODUCTION

Flat plate solar collectors are becoming an increasingly common building

component, both for new and existing structures. Most solar collectors

are located on building roofs, and there is a need for more specific

design criteria to provide safety in the event of large snowfall. This

report summarizes the findings of studies of snow accumulation around

solar collectors conducted during the winter of 1978-79 and proposes

specific design criteria. The structural loading criteria are based on

the use of the 1980 draft revision of American National Standard A58.1,

"Building Code Requirements for Minimum Design Loads in Buildings and

Other Structures" [1]*. The criteria address the functioning and serviceability of solar collectors and buildings as well as safety against

structural failure.

2. PERFORMANCE REQUIREMENTS

There are four basic requirements for solar collector installations with

regard to their performance in case of snow;

***SAFETY OF COLLECTOR SYSTEMS: The collector systems should not

collapse due to the weight of snow.

***SAFETY OF BUILDINGS SUPPORTING COLLECTOR SYSTEMS: The building

should not collapse due to the weight of snow and of the collector systems.

***SERVICEABILITY OF COLLECTOR SYSTEMS: The collector systems

should not suffer prolonged loss of operation due to snow cover.

***SERVICEABILITY OF BUILDINGS SUPPORTING COLLECTOR SYSTEMS: The

building should not be adversely affected by the moisture and

ice associated with snow accumulation around solar collectors.

It is pertinent to note that a collector system will alter the position

and amount of snow retained on a roof. In view of this fact and of the

second requirement, caution is needed in retrofitting collector systems

on existing buildings.

3. FINDINGS OF STUDIES CONDUCTED IN 1979

Two studies were conducted for the National Bureau of Standards during

the winter of 1978-79, one in the vicinty of Albany, New York, [2] and

one in the Chicago area [3]. Twenty-six sites were studied, including

a wide variety of configurations of flat plate collector systems. In

addition, four sites in the Washington, D.C., area were observed by NBS

personnel, and summaries of those observations are also included in this

report

* Numbers in brackets indicate references at the end of each part.

51
There are two items of interest in the study of snow on and around solar

collector systems: the amount (both volume and weight) of snow on the

collector itself, as related to the amount of snow on the ground, and

the difference in the amount of snow on the building from what would

exist if no solar collectors were present. The basic physics of the

problem includes the mechanics of falling and drifting snow around solar

collectors and the melting and sliding of snow from solar collector sur- faces. The studies addressed these issues in a qualitative manner,

although some quantitative analysis was carried out on the data collected

around Albany.

In most cases where observations were made during or shortly after

snowfall, some snow was retained on the collector surfaces. This accumulation was generally small in comparison to the amount retained on other

portions of the roof. Figures 1 and 2 illustrate light snow cover on the collectors following a snowfall of approximately six inches. It is

apparent that such snow cover would prevent the operation of a solar collector, and that it would Impose some load on the collector unit itself.

Intuitively, it could be expected that the snow would quickly melt and

slide off the collector surface. If this were consistently true, the

short loss of operation would not be serious, and the maximum weight on the collector would be that of a single storm. Observations both confirm

and deny this intuition, depending on other cirumstances. Figure 3,

taken within a few minutes of figure 2, shows the anticipated melting

and sliding, even on an over-cast day. The circximstances preventing the

melting and sliding are of Immediate interest.

Observations made in the Washington, D.C, area by the National Bureau of

Standards, as well as observations recorded in ref. 3 serve to define

necessary conditions for dependable shedding of snow from collector

surfaces. Of first importance is the slope of the surface; only those

collectors at a steep angle, more than about 50® with the horizontal,

could be counted on to shed snow. Of nearly equal importance is the

presence of obstructions in the path of the sliding snow; only those collectors completely free of obstructions were completely uncovered by

sliding. Figures A and 5 both show collectors that are flush with the

roof and have no gutters below, only the slopes are different. Most of

the snow has slid off the steep collectors in figure 4, although about

four inches of snow had fallen in the 24 hours before the photograph was taken. Considerable snow covers the collectors in figure 5, even though

only one and one-half inches had fallen in the 24 hours before the photograph was taken. The two photographs were taken only one day apart in

similar locations in the Chicago area.

For collectors that are mounted flush with the roof surface, the most

dependable way of assuring slide-off is to extend the collectors to the

bottom edge of the roof. A flattening of the roof slope beneath the collector, a change in the sliding resistance of the surface down the slope

from the collector, or even a gutter may prevent the sliding action.

Figure 6 illustrates the effect of a flatter slope below the collectors:

those upper collectors above the lower roof are partially covered while

52
the remaining upper collectors are clear. Figure 7 shows the Influence

of a gutter below the collector in forming an ice dam and preventing

sliding.

Interviews with owners in the Chicago area revealed that collectors

with unfavorable situations for clearance by sliding were out of operation

for extended periods, up to two months in some cases, unless the snow was manually removed.

One further observation regarding the sliding of snow from solar

collectors is that any structures beneath the solar collectors that might

catch the sliding snow must be strong enough to carry the Increased load.

Measurements of snow accumulation on flat roofs beneath protruding

collectors in the Albany area indicated that well over twice as much

load existed there as at other locations on the same roof.

Collectors that protrude from the surface of the roof alter the air

currents that carry both falling and blowing snow. The effect is much

like that of a snow fence. Several interesting observations were made

concerning this effect. The presence of a row of protruding collectors

oriented normal to the wind tends to reduce the effect of the wind in

removing snow from the roof. Depending on the amount of clearance below

the protruding collectors, they can also serve to Initiate drifts. The

presence of several parallel rows of protruding collectors creates a situation comparable to a "sawtooth" or "northlight" roof, in which the

valleys tend to fill in with snow. Figure 8 shows a building with many

such rows of collectors. Figures 9 and 10 show the drifting effect on this same building, with snow depths well over four feet (1.2 m)

following in eighteen inch (450 mm) snow accompanied by a significant

wind.

Protruding collectors mounted with a significant clear space between the

roof surface and the bottom edge of the collector were observed to have

less of an effect on the formation of drifts. Also, because this clear

space presented no obstructions to sliding, such collectors were less

likely to remain covered by snow.

One last observation is that the presence of solar collectors seems to

promote the growth of icicles and ice dams. Once a portion of a solar

collector becomes clear on a sunny day, meltwater is produced even when

the ambient temperatures are well below freezing. This water then

freezes upon crossing cold surfaces or dripping into the air. An example

is shown in figure 7. It is not unusual for roof leaks to be caused by

such accumulation of ice and water, even without solar collectors, however some reports in the Chicago area indicated a possible correlation

with the presence of solar collectors. The potential for damage to gutter

systems is obvious.

53
4. DEVELOPMENT OF DESIGN CRITERIA

Although little quantitative work has been done specifically for snow distribution on and around solar collectors, it is possible to develop

more specific design criteria from the findings of the referenced

studies by relying heavily on the draft revision of ANSI A58.1 [1], A

very brief summary of the ANSI A58. 1-1980/Draft provisions is appropriate

in order to fully appreciate the criteria for solar collector installations

4. 1 THE SNOW LOAD CRITERIA OF ANSI A58 .1-1 980 /DRAFT

The basic parameter for determination of design loads for snow is the

weight of snow expected to accumulate on open ground at the building

site. ANSI A58. 1-1980 /Draft contains maps that give the value for this

parameter for much of the United States. (Note that the new edition of

A58.1 does contain a somewhat different map than ANSI A58, 1-1980 /Draf t)

.

Areas where rough terrain or bodies of water create extreme local variation in snow accumulation are not included on the map, but procedures are described for establishing the ground snow load from reference publications

The basic roof design load is taken as 70 percent of the ground snow load,

and further refinements are made by multiplying by three multiplicative

coefficients, as follows:

i) Cg for exposure, varying form 0.8 for roofs exposed on all sides

in windy areas to 1.2 for densely forested areas.

ii) C|- for thermal effects, varying from 1.0 for continuously heated

structures with poor insulation to 1.2 for unheated structures.

iii) I for risk, varying from 0.8 for unimportant and uninhabited

structures to 1.2 for essential structures.

Each of the coefficients has a value of 1.0 for average conditions.

The basic design load is further modified for sloped roofs depending on the slope, the slipperyness of the surface, and the thermal properties of

the building. For roofs and portions of roofs sloped more than 70° with

the horizontal, the design load is reduced to zero. Figure 11 summarizes

the basic snow loads.

The effect of wind is incorporated into ANSI A58. 1-1980/Draft in several

ways. The unbalanced condition caused by removing half the snow load

from any area is Included for all roof types. Further unbalanced loading

conditions are defined for hip, gable, arched, multiple folded plate,

sawtooth, and barrel vault roofs. Drift surcharges are defined for tlte lower level of multilevel roofs and for roofs with vertical obstructions,

such as mechnical equipment screens. Figures 12 and 13 show the unbalanced

loads and the drift surcharges.

54
Another surcharge added to the basic load Is the snow that might slide

from high sloped roofs onto lower structures. Finally, a five to eight

pounds per square foot surcharge for Intense rain is recommended for

certain climatic zones.

4.2 DEVELOPMENT OF CRITERIA SPECIFICALLY FOR SOLAR COLLECTOR

INSTALLATIONS

The next section of this report contains specific criteria for design

considering snow loads. The criteria for the design of collector systems are a relatively straightforward application of ANSI A58. 1-1980/Draft [1].

The criteria for the design of roof structures of supporting buildings

are more complex and more tentative, because the snow retention phenomenon

is more complex and is not as well understood. The criteria have been

developed to meet the basic performance requirements, once again making

heavy use of ANSI A58 . 1-1980/Draft. Further study of the problem is

warranted, both because the studies forming the basis of these criteria

were so limited and because increasing use of solar flat plate collectors

on roofs of buildings is forecast for the future.

5. DESIGN CRITERIA

5.1 CRITERION FOR THE SAFETY OF FLAT PLATE SOLAR COLLECTORS

CRITERION; Flat plate solar collector systems shall support the basic

uniform snow load specified in ANSI A58. 1-1980/Draft without exceeding

the allowable stresses that are conventionally used for the materials

in question.

COMMENTARY; With respect to the application of the ANSI A58. 1-1 980 /Draft

provisions in this situation, several items deserve comment. First, in

those regions where the design snow load represents a winter-long

accumulation of many snowfalls rather than a single large storm, the

criterion is likely to be conservative because of the tendency for snow

to disappear from collectors more rapidly than from the adjoining roof.

But because snow has been observed to remain on collectors for months

at a time during a severe winter, it does not appear appropriate to base

the design of the collectors on statistics for a single large snowfall.

Should the design of collectors prove to be expensive because of this

criterion, which seems unlikely in view of the wind loads that such

systems must withstand, further study of the problem would be warranted.

Second, the coefficient for thermal effect, C^-, should be taken as 1.3, the

maximum value, for collectors that protrude from the roof, because they

will generally be cold until the snow is at least partially removed.

The thermal coefficient for flush collectors would depend on the insulation and thermal characteristics of the inoperative collector, t1ie structure, and the space below.

Third, the modification for slope given in ANSI A58 . 1-1980/Dr if t should be

applied using the "unobstructed slippery surface" curve only if the path

55
of sliding snow is truly unobstructed. Collectors placed in locations

likely to be involved in large drifts or to receive snow sliding from

sloped surfaces above should be designed to resist the appropriate

surcharges, as defined in ANSI A58 , 1-1980 /Draft and the following

criteria for supporting structures.

5.2 CRITERIA FOR THE SAFETY OF BUILDINGS SUPPORTING COLLECTOR SYSTEMS

Four criteria are necessary to satisfy adequately the second basic

requirement, one for collectors mounted flush with the roof, two for

collectors protruding from the roof and one for surfaces that may receive snow sliding off collectors;

5.2.1 Buildings Supporting Flush Collectors

CRITERION; A building supporting collectors mounted flush with the roof

shall resist the appropriate uniform and unbalanced loads specified in

ANSI A58 . 1-1980/Draft as any other roof with a slippery surface.

COMMENTARY; Collectors that are flush with the roof surface do not

appreciably affect the total snow retention and distribution when

compared to any other slippery surfaced roof of the same configuration.

5.2.2 Buildings Supporting Protruding Collectors

H is the clear height between the roof surface and the lowest obstruction

presented by the solar collector system (see figure 14).

a) CRITERIONA building supporting protruding collectors that have a clear height H of more than (defined subsequently) shall resist the

appropriate uniform and unbalanced loads from ANSI A58, 1-1980 /Draft

plus the sliding surcharge defined subsequently without considering

drifting due to the collectors.

For determination of the loads from ANSI A58 . 1-1980/Draft , the coefficient

for exposure, Cg, shall be modified as follows; for building and sites

that would indicate Cg values of 0,8 to 1.0, take Cg as 1.1, and for

buildings and sites that would indicate Cg values over 1.0, take Cg as 1.2.

a.l) DEFINITION; is three feet unless the ground snow load is over

60 pounds per square foot, in which case it is;

He = pg

. Ct • I / 25

—/ For conformity with the American National Standard A58. 1-1980/Dratt , English

units are used throughout Parts I, II, and III of this report. For conversion

to SI units, see p. viii.

56
where and I are the coeffleicnts for thermal and risk characteristics In

ANSI A58. 1-1980 /Draft and pg is the ground snow load in pounds per square foot.

a. 2) DEFINITION: The sliding surcharge shall be taken as a uniform load

applied as a strip at the foot of the collector row with a width equal

to one“half the horizontal projection of the collector row. The total

load shall be equal to the design load for the sloped collector, modified

for the slope factor (see the criterion in section 5.1 and see figure 15).

b) CRITERION: A building supporting protruding collectors that do not

have a clear height H of more than shall resist the appropriate

uniform and unbalanced loads from ANSI A58 , 1-1980/Draft with the

modifications to Cg specified in section 5,2,2a plus the following

loads to account for drifting and sliding of snow: 1) a single row

of collectors shall be treated as a vertical obstruction with the

drift surcharge as specified in ANSI A58 ,1-1980/Draft ; 2) parallel

rows of collectors shall be treated as a modified sawtooth roof by

considering the toe of the collector as the valley of the equivalent

sawtooth and the top of the collector as the ridge of the sawtooth

(see figure 16),

COMMENTARY; Protruding collectors alter the air currents that carry

falling and blowing snow, much like a snow fence. The increase in Cg

coefficients over those specified by ANSI A58 , 1-1980/Draft is Intended to

account for this. The increase in Cg is attractive intuitively and seems justified based on the limited data from the studies [2, 3J

,

Protruding collectors tend to be more free of snow as the clear space

between them and the roof increases, particularly if they are high enough

to avoid any involvement with drifts on the roof. The definition for

minimum clear space Hg is tentative, due to the limited studies made so far, and it should be the subject of further study. One pertinent source

of information is the design of "blower type" snow fences (snow fences

designed to use the wind to keep an area clear of snow by funnellng wind

across a surface at a higher velocity). Such designs are based on a minimum clear space of four feet [4]

,

Also, it appears reasonable that

the minimum clear height depends on the anticipated height of snowpack

for the maximum ground load at the location.

Protruding collectors that do not have a high enough clear space tend to

become involved in drifts. Not enough data exists to confirm for solar

collectors the distribution or the magnitudes of drift loads specified in

ANSI A58 , 1-1980/Draft , but the loads appear to be adequate for design purposes, until more information is available. The common situation of several

parallel rows of collectors tends to cause a load distribution similar to

that specified for sawtooth roofs in ANSI A58. 1-1980/Draft . Once the drifts

begin to form, the geometrical difference between rows of protruding collectors on a flat roof and a sawtooth roof begin to disappear. For the design

of structural members that are normal to the rows and have spans longer than

the row spacing, the sawtooth load distribution may be replaced by a uniform

distribution equal to the average of the peak and valley loads.

57
5.2.3

Surfaces that Receive Sliding Snow

CRITERION; Surfaces located such that they would receive snow sliding

from solar collectors shall resist the appropriate loads from ANSI

A58 . 1-1980/Draft plus the sliding surcharge defined in section 5. 2, la. 2.

COMMENTARY; The sliding surcharge is based partially on observation and

partially on intuition. Observations confirm the existence of the load

and for the limited studies conducted, the magnitude. Further studies

should focus on this in order to better define the magnitude and

distribution of the load.

5.3

CRITERION FOR THE SERVICEABILITY OF COLLECTOR SYSTEMS

The third basic requirement is not a structural concern, but a criterion

is offered based on the findings of the studies;

CRITERION; Any collector sloped less than 50® or without a clear space

below at least equal to shall be designed to account for extended

loss of operation due to snow cover or provision for manual removal of snow shall be made.

COMMENTARY; The criterion is really a system design guideline, and

obviously depends on the probability of significant snowfall. Manual

removal of snow involves consideration of dumping areas, accessibility,

and the resistance of the solar components and the roof surface to damage.

5.4

GUIDELINE FOR THE SERVICEABILITY OF BUILDINGS SUPPORTING COLLECTORS

The fourth basic requirement involves more than structural concerns, and

the structural concern is relatively minor, since the maximum ice loads

usually occur after the maximum snow load, not simultaneously with it.

The following guideline is offered;

DESIGN GUIDELINE; The ice and meltwater caused by the presence of solar

collectors shall be accounted for by assuring the adequacy of the moisture barrier under adverse conditions and by avoiding details likely to

promote the accumulation of large quantities of ice or likely to be

damaged by the weight or expansive action of ice.

6. REFERENCES

1 . Building Code Requirements for Minimum Design Loads in Buildings and

Other Structures , American National Standard A58. 1-1 980 /Draft,

American National Standards Institute, New York, 1980.

2. O'Rourke, Michael J., Snow and Ice Accumulation Around Solar

Collector Installations , National Bureau of Standards, GCR 79-180,

August 1979.

58
3, Corotls, Ross B., Charles H, Dowdlng, Edwin C. Rossow, Snow and Ice

Accumulation at Solar Collector Installations In the Chicago Metropolitan Area » National Bureau of Standards, GCR 79-181, August 1979.

4, Mellor, Malcolm, Blowing Snow, Cold Regions Science and Engineering,

Part III, Section A3c, Cold Regions Research & Engineering Laboratory,

November 1965.

59
60

Figure

1.

Light

Snow

Cover

on

Collectors

During

Snowfall
Figure

2.

Light

Snow

Cover

on

Collectors

After
62

Figure

3.

Melting

and

Sliding

of

Snow
Figure

4.

Snow

Sliding

Off

Steep

Collectors
64

Figure

5.

Snow

Retention

on

Shallow

Collectors
65

Figure

6.

Obstruction

Below

Steep

Collectors
Figure

7.

Ice

Dam

at

Gutter

and

Icicles

Below

Collectors
67

Figure

8.

Building

with

Multiple

Rows

of

Collectors
Figure

9.

Drift

between

Parallel

Rows

of

Collectors
Figure

10.

Drift

between

Parallel

Rows

of

Collectors
WHERE:

FLAT ROOF SNOW LOAD,

Pf = 0.7 Ce Ct I Pg

Cg = COEFFICIENT FOR EXPOSURE TO WIND

Ct = COEFFICIENT FOR THERMAL EFFECT

I = COEFFICIENT FOR IMPORTANCE OF STRUCTURE

Pg = GROUND SNOW LOAD

SLOPED ROOF SNOW L 0 A D. p^

WHERE Cg IS DETERMINED FROM THE FOLLOWING GRAPHS (a SPECIAL

EQUIVALENT SLOPE IS DEFINED FOR CURVED ROOFS)

3 4 I 8 12 on on on on on 12121212 12

WARM ROOFS, Ct 1.1

3 4 6 8 12 on on on on on

12 12 12 12 12

Figure 11. Basic Snow Loads^from ANSI A58 . 1-1980/Draft

70
HIP AND GABLE ROOFS

Balanced Load:

Unbalanced Load:

l.i 1-5 Rs/ c. (to be applied to either side; applies only when roof slope exceeds 15°)

SAWTOOTH, MULTIPLE FOLDED PLATE, BARREL VAULT ROOFS

Balanced Load:

Unbalanced Load:

Notes:

* The slope factor is defined to be 1.0 for this type of roof. ** The snow surface at the valley (assuming a density of 20pcf) need not

be higher than the snow surface at the ridge, thus the peak load may

be less than 3p^/C . e

Figure 12. Unbalanced Snow Loads from ANSI A58. 1-1980/Draft

71
h|^ = height of balanced snow load = p^/y or p^/y

h = clear height from top of balanced load to top of obstruction

(to edge if the obstruction is a higher roof)

h^ = depth of drift = 2 I p^ / y 1 h^

II -J 4.U j -£4. (3 h. for il<50 feet

W = width of drift d

14 h^ for a >50 feet

if W exceeds the width of the roof, the drift surcharge shape

becomes a trapezoid, truncated at the edge of the roof.

Pj = drift surcharge load = Y

y

= snow density in pounds per

square foot, per table:

Pg = ground snow load, psf

under 30 30 to 60 over 60

15 20 25

I

>10 feet

Figure 13. Drift Surcharge Load from ANSI A58. 1-1980/Draft

72
FLAT ROOIF SLOPED RGOF

Figure 14. Definition of Clear Height H

L.k If iZIO^ pj

Figure 15. Definition of Sliding Surcharge

73
CU d) 4-

4-> CD

O

O S- C fd 1/1 sz <u •" U "O CO S- •!- o

S- Q.

s-o

to

s-(U

+->

-l-> fO Q.T3

fOo

CD

(U

i-rjCD

U. i• I 1I1 i

7A
PART IV

HAIL LOADS ON SOLAR COLLECTORS

by

Emil Simiu

and

Louis Cattaneo

75
LIST OF TABLES Page

Table 1. Diameter of Expected Maximum Size Hailstone as a Function of

Geographical Region and Days with Hail Per Year 86

Table 2. Design Hailstone Velocities 86

76
LIST OF FIGURES Page

Figure 1. Hall Regions (Ref. 4) 87

Figure 2, Average Annual Number of Days with Hail (Ref. 4) ...87

Figure 3. Total Number of Days with Hail in an Average 20-year Period

for the Central United States (Ref. 8) 88

77
1 . INTRODUCTION

This report presents proposed hail loads to be used in the design and

evaluation of solar collectors exposed to hail impact. These loads are based upon information that was, in part, not available at the

time of the development of earlier criteria (e.g., NBSIR 76-1187 [1]*,

HUD 4930.2 [2], NBSIR 78-1562 [3]). Much of this information is included

in two extensive documents devoted to hail damage risk prepared for the

Department of Energy by the Jet Propulsion Laboratory (California Instittute of Technology) in 1977 [4] and by Altas Corporation in 1979 [5],

and in a comprehensive hail climatology review published in 1977 by

S. A. Changnon, Jr. of the Illinois State Water Survey [6]. (It is noted

that a large body of data and information used in reference 4 and 5 was provided by the Illinois State Water Survey.)

The proposed loads should not be regarded as definitive. Rather, by

incorporating recent additional information, they represent an improvement upon the earlier criteria. However, the writers feel that uncer- tainties in the area of hail loading statistics continue to exist, some

of them affecting the information presented herein, and that additional

research is required if such uncertainties are to be reduced in the future.

Where experience indicates that the performance of solar collectors

subjected to hail loads is generally satisfactory, laboratory tests for

resistance to hail loads need not be conducted. Nevertheless, for cases

in which previous experience is insufficient or may not be regarded as a reliable guide, laboratory testing is recommended. The information

presented herein is offered for use in such testing.

2. REGIONALIZATION OF THE UNITED STATES

From the standpoint of hail damage risk, the contiguous United States

is divided into three geographical regions designated as Regions I,

II and III represented in figure 1. The regionalization is based on studies by Changnon and the Illinois State Water Survey [6, 7] (see also

ref. 4, page 3-2). These studies have been conducted on a national

scale on the basis of crop and property losses due to hail effects [6].

Further, the contiguous United States is divided into areas characterized

by the average number of days with hail. This division, shown in figures

2 and 3, is based on climatological data and estimates given in ref. 7 and 8, and cited in ref. 4. For certain sections of the United States

where large amounts of data make greater refinement possible, more detailed

maps may be available and should be used if they are based on reliable statistical studies (e.g., [8]). (Note that the numbers in figure 3 represent

the total number of days with hail in an average 20-year period and should

be divided by 20 to obtain the average annual number of days with hail.)

* Numbers in brackets Indicate references at the end of each part.

78
3.

MAXIMUM HAILSTONE SIZES

Maximum sizes of hailstones assumed, for design purposes, to hit an installation depend upon: (a) geographical region, (b) average number of days with

hail, (c) size of area exposed to impact, and (d) design life which, in

turn, determines the mean recurrence interval of hailstone hits considered

in design. It is recommended that hailstone sizes considered for design

purposes correspond to a 20-year mean recurrence interval. Estimates of

mean recurrence intervals of hailstone hits on a i6 sq ft (1.5-sq m) area

are presented in ref. 4 (page 4-11).

According to the statistics reported in ref. 5, the estimates of ref. 4

appear to be, generally, somewhat conservative. For example, according to

ref. 4, in areas with 3 days of hail per year in Region II the maximum

hailstone diameter corresponding to a 20-year mean recurrence interval of

hits on a 16 sq ft (1.5-sq m) exposed surface is about 1 5/8 in (41.3 mm).

According to ref. 5, the maximum hailstone diameter corresponding to the

same exposure classification (Albuquerque, NM) varies betv/een 28.0 mm and

40.0 mm, depending upon the assumed hailstone size distribution used.

Information on maximum hailstone sizes for various mean recurrence intervals

of hits on exposed surfaces of 10 sq m, 50 sq ra, and 100 sq m is found in

table 3 of ref. 5.

Proposed maximum hailstone sizes corresponding to a 20-year mean recurrence

interval are given in table 1. Note that the probability of occurrence of

a collector hit by a given maximum hailstone size and of a horizontal wind

speed of 66 ft/s (20.1 m/s) (see section 4.) acting in a direction perpendicular to a horizontal edge of the collector is lower than the probability of

occurrence of a hit by that hailstone size regardless of horizontal wind

speed and direction. This fact was taken into account in the development of

table 1.

4. HAILSTONE VELOCITIES

The estimates of hailstone impact velocities listed in table 2 are given in

ref. 9 in which it is assumed that the hailstones are spherical, of clear

ice and have a smooth surface. These velocities represent resultants of

vertical terminal velocities due to free fall [10] and an assumed horizontal

velocity of 66 ft/s (20.1 m/s) due to wind speed [9,15].

5. HAILSTONE DENSITY

TV\e specific gravity of hailstones proposed herein for design purposes is

0.9, i.e., the specific gravity of solid ice. It is believed that this

proposed value for the mean specific gravity of whole hailstones (which is

adopted for practicality in test procedures for the evaluation of collectors)

is not overly conservative [11-13] even though lower values of local specific

gravity have been measured in natural hailstones containing varying proportions of trapped air [14].

79
6. PROPOSED PROCEDURE FOR DETERMINING DESIGN HAIL LOADS ON SOLAR

COLLECTORS

The d^jsign hail load shall be assumed to be caused by the perpendicular

impact of falling hailstones with diameters and velocities specified in

tables 1 and 2 (unless it can be determined on the basis of available

data and statistical study that hail of smaller maximum diameter should

be expected to occur). The diameters listed in table 1 are given as functions of hail region and number of days with hail as determined from

maps shown in figures 1 and 2 or 3, respectively. The velocities are given in table 2 as a function of hailstone diameter. The specific

gravity of hailstones shall be assumed to be 0.9.

Evaluation will be based on analysis using known information about the

physical characteristics of the system components or on physical simulation and testing using appropriate hail resistance test techniques or

the hail resistance test techniques described in ref. 15.

In cases where protective measures are provided to prevent impact of hail on system components, such as the use of screens or deflectors, these

protective measures shall be included in the test specimen.

In proposing the design loads given herein, it is not intent ed to completely

prevent punching or local cracking of nonstructural elements such as cover plates of collector panels under hail impact, but rather to control damage

by keeping it at a level which would not cause a major curtailment in the

functioning of the system, a premature failure, or hazards Cteated by

excessive shattering of glazed elements.

The hailstones diameters in table 1 were selected using, as a guide, the

statistical studies reported in ref. 4 and 5. These diameters correspond

approximately to a 20-year mean recurrence interval of a hit on a solar

collector unit assumed to have an exposed area of approximately 16 sq ft

(1.5 sq m) , and are modified for the probability of a concurrent horizontal

wind speed acting in a direction perpendicular to a horizontal edge of the

collector. Calculations based on ref. 5 suggest that exposed areas of 10 sq

m, 50 sq m, and 100 sq m may be expected to be hit during an average period

of 20 years by at least one hailstone having a diameter larger than that

specified in table 1 by a factor of approximately 1.12, 1.25 and 1.30 for

the respective exposed areas. The velocities of table 2 are based on theoretical studies reported in ref. 10 and an assumed horizontal wind speed

of 45 mph (72.4 km/h) cited in ref. 9 and 15.

7. ACKNOWLEDGEMENTS

The writers wish to express their appreciation to Stanley A. Changnon, Jr.,

Chief of the Illinois State Water Survey, for his valuable comments and

suggestions

.

80
8.

REFERENCES

1 . Interim Performance Criteria for Solar Heating and Cooling Systems

In Commercial Buildings , NBSIR 76-1187, National Bureau of Standards,

Washington, D. C. 20234, November 1976.

2. Intermediate Minimum Property Standards Supplement, Solar Heating

and Domestic Hot Water Systems . HUD 4930.2, U. S. Department of

Housing and Urban Development, Washington, D. C., 1977,

3. Interim Performance Criteria for Solar Heating and Cooling Systems

in Residential Buildings , Second Edition, NBSIR 78-1562, National

Bureau of Standards, Washington, D. C. 20234, November 1978.

4. Gonzales, C., Environmental Hail Model for Assessing Risk to Solar

Collectors , JPL 5101-45, Jet Propulsion Laboratory, California

Institute of Technology, Pasadena, CA, December 1977.

5. Cox, M. and Armstrong, P. R., A Statistical Model for Assessing

the Risk of Hail Damage to Any Ground Installation , ALO/4291-1,

Altas Corporation, Santa Cruz, CA 95060, September 1979.

6. Changnon, S. A., "The Scales of Hail," Journal of Applied Meteorol- ogy , Vol. 16, No. 6, June 1977.

7. Farhar, B. C., Changnon, S. A., Swanson, E. R., Davis, R. J., and

Haas, J. E., Hail Suppression and Society , Illinois State Water

Survey, Urbana, IL, June 1977.

8. Stout, G. E. and Changnon, S. A., Climatography of Hail in the

Central United States , CHIAA Research Report No. 38, Crop Hail

Insurance Actuarial Association, Chicago, IL 60606, February 1968.

9. Mathey, R. G. , Hall Resistance Tests of Aluminum Skin Honeycomb

Panels for the Relocatable Lewis Building , Phase II, NBS Report

10193, National Bureau of Standards, Washington, D. C. 20234,

April 1970.

10. Bilham, E. G. and Relf, E. F., "The Dynamics of Large Hailstones,"

Quarterly Journal of the Royal Meteorological Society, Vol. 63,

pp. 149-162, 1937.

11. Macklin, W. C., Strauch, E., and Ludlam, F. H. , "The Density of

Hailstones Collected from a Summer Storm," Nubila , Vol. 3,

pp. 12-17, 1960.

12. Browning, K. A., Ludlam, F. H. , and Macklin, W. C., "The Density

and Structure of Hailstones," Quarterly Journal of the Royal Meteor- ological Society , Vol. 89, No. 379, 1963.

81
13. List, R., Cantin, J. G. , and Ferland, M. G. , "Structural Properties

of Two Hailstone Samples," Journal of the Atmospheric Sciences . Vol. 27, pp. 1080-1090, October 1970.

14. Prodi, F., "Measurements of Local Density in Artificial and Natural

Hailstones," Journal of Applied Meteorology , Vol. 9, No. 6, 1970.

15. Jenkins, D.R. and Mathey, R.G., Hail Impact Testing of Solar

Collector Covers . NBS report in preparation. National Bureau of

Standards, Washington, D.C., 20234.

9. BIBLIOGRAPHY

Arenberg, D. L. , "The Formation of Small Hail and Snow Pellets,"

Bulletin American Meteorological Society , Vol. 22, No. 3, 1941.

Auer, A. H. , "Distribution of Graupel and Hail with Size," Monthly

Weather Review, Vol. 100, No. 5, 1972.

Bailey, I. H. and Macklin, W. C., "The Surface Configuration and

Internal Structure of Artificial Hailstones," Quarterly Journal

of the Royal Meteorological Society , Vol. 94, No. 399, 1968.

Baldwin, J. L. , Climates of the United States , National Oceanic and

Atmospheric Administration, Washington, D. C., 1973.

Changnon, S. A., "Method of Evaluating Substation Records of Hail and

Thunder", Monthly Weather Review , Vol. 95, No. 4, 1967.

Changnon, S. A., "Note on Hailstone Size Distributions", Journal of

Applied Meteorology , Vol. 10, No. 2, 1971.

Changnon, S. A., Solar Energy Information and Data for Illinois , Illinois State Water Survey, Urbana, IL, 1978.

Changnon, S. A., Farhar, B. C. and Swanson, E. R, "Hail Suppression

and Society", Science . Vol. 200, No. 4340, 1978.

Changnon, S. A., and Morgan, G. M. , Design of an Experiment to

Suppress Hail in Illinois, Illinois State Water Survey, Urbana, IL,

1976.

Clift, R., Bubbles, Drops, and Particles . Academic Press, New York,

NY, 1978.

Eng Young, R. G. and Browning, K. A., "Wind Tunnel Tests of Simulated

Spherical Hailstones with Variable Roughness", Journal of the Atmospheric Sciences , Vol. 24, No. 1, 1967.

82
Foote, G. B. and Knight, C. A., Eds., Hail; A Review of Hall

Science and Hail Suppression, (Meteorological Monographs Vol. 16,

No. 38), American Meteorological Society, Boston, MA, 1977.

Friedman, D. G., Texas Hailstorms , Research Department Report, The

Travelers Insurance Companies, Hartford, CT, 1965.

Friedman, D. G. and Shortell, P. A., Prospective Weather Hazard Rating

in the Midwest with Special Reference to Kansas and Missouri , Research Department Report, The Travelers Insurance Companies,

Hartford, CT, 1967.

Gokhale, N. R., Hailstorms and Hailstone Growth , State University of

New York Press, Albany, NY, 1975.

Greenfeld, S. H., Hail Resistance of Roofing Products , Building Science

Series, No. 23, National Bureau of Standards, Washington, D.C. 20234,

1969.

Grlngorten, I. I., Hailstone Extremes for Design , AFCRL-72-0081 , Air

Force Cambridge Research Laboratories, Bedford, MA, 1971.

Harting, A., The UTIAS Precipitation Wind Tunnel , Technical Note No.

181, Institute for Aerospace Studies, University of Toronto, Canada,

1972.

Hoerner, S. F., Fluid-Dynamic Drag , Published by the author. Midland

Park, NJ, 1958.

Houghton, H. G., ”0n the Physics of Clouds and Precipitation," Compendium

of Meteorology , Ed.: Malone, T. F., American Meteorological Society,

Boston, MA, 1951.

Imperial College of Science and Technology (London), Final Report;

Research on Characteristics and Effects of Severe Storms , AFCRL64-531, Air Force Cambridge Research Laboratories, Bedford, MA,

1964.

Knight, C. A. and Knight, N. C., "The Falling Behavior of Hailstones",

Journal of the Atmospheric Sciences , Vol. 27, July 1970.

Knight, C. A. and Knight, N. C., "Hailstones", Scientific American,

Vol. 224, No. 4, 1971.

Laurie, J. A. P., Hail and ITrmEffects on Buildings , Bulletin 21,

National Building Research Institute, Pretoria, South Africa, 1960.

List, R., The Aerodynamics of Hailstones , Research Transl. TG-244,

(Z. Angew. Math. Phys. , Vol. 10, No. 2, pp. 143-159, 1959), Air

Force Cambridge Research Laboratories, Bedford, MA, September 1965.

83
Lbf, G, 0, G, and French, R. R., Hall Resistance of Solar Collectors

with Tempered Glass Covers , Preprint: SERI Conference at Colorado

Springs on Solar Heating and Cooling Systems, Solar Energy Research

Institute, Golden, Colorado, November 1979,

Ludlam, F. H., "The Hall Problem", Nublla , Vol. 1, pp. 12-96, 1958.

Macklln, W, C. and Bailey, I. H. , "On the Critical Liquid Water

Concentrations of Large Hailstones", Quarterly Journal of the Royal

Meteorological Society , Vol. 92, No. 392, 1966.

Macklln, W, C. and Ludlam, F, H., "The Fallspeeds of Hailstones,"

Quarterly Journal of the Royal Meteorological Society . Vol. 87,

No. 371, 1961

McDonald, J. E., "An Aid to Computation of Terminal Fall Velocities

of Spheres", Journal of Meteorology , Vol. 17, pp. 463-465, 1960,

Moore, D, and Wilson, A., Photovoltaic Solar Panel Resistance to

Simulated Hall , Report 5101-62, Jet Propulsion Laboratory, California

Institute of Technology, Pasadena, CA, October 1978.

Morgan, G. M. and Towery, N, G., Micro-Scale Studies of Surface

Hallfall . Final Report, Illinois State Water Survey, Urbana, II.,

March 1974,

Morgan, G. M. and Towery, N, G., "On the Role of Strong Winds in

Damage to Crops by Hail and Its Estimation with a Simple Instrument",

Journal of Applied Meteorology , Vol. 15, No. 8, 1976,

Plat, D, , "Etude Experlmentale des Grelons en Chute Libre", Journal

de Mecanlque et de Physique de L* Atmosphere , Series II, Vol. 4,

No. 1 3, 1962.

Prodi, F., "X-Ray Images of Hailstones", Journal of Applied Meteorology , Vol, 8, June 1969,

Roos, D. V. d. S., "A Giant Hailstone from Kansas In Free Fall",

Journal of Applied Meteorology , Vol. 11, September 1972.

Roos, D, v.d. S. and Carte, A. E., "The Falling Behaviour of Oblate

and Spiky Hailstones," Journal de Recherches Atmospherlques , pp. 39-52,

197 3.

Schllchtlng, H., Boundary Layer Theory , 7th Ed., McGraw Hill, New York,

NY, 1979.

Schumann, T, E, W., "The Theory of Hailstone Formation", Quarterly

Journal of the Royal Meteorological Society , Vol. 64, pp, 3-21, 1938.

84
Smith, M. L., Hall Testing of Solar Reflector Panels , Preprint:

Workshop at Denver on Solar Reflector Materials Technology, Texas

Tech University, Lubbock, TX, 1978.

Thom, H. C. S., "The Frequency of Hall Occurrence", Archlv fur

Meteorologle, Geophysik und Biokllmatologie, Series B, Vol. 8, No. 2,

1958.

Towery, N, G, , Changnon, S. A. and Morgan, G, M., "A Review of HailMeasuring Instruments", Bulletin of the American Meteorological

Society , Vol. 57, No. 9, 1976.

Towery, N. G. , Morgan, G. M. and Changnon, S. A., "Examples of the

Wind Factor in Crop-Hail Damage", Journal of Applied Meteorology , Vol. 15, No. 10, 1976.

Willis, J. T., Browning, K. A., and Atlas, D., "Radar Observations

of Ice Spheres in Free Fall," Journal of the Atmospheric Sciences,

Vol. 21, No. 1, 1964.

85
Table 1. Diameter of Expected Maximum Size Hailstone as a Function

of Geographical Region and Days with Hall Per Year.*

Diameter of Expected Maximum Size Hailstone, Inches (mm)

Days with Hail

per year

Region III Region II Region I

1 7/8 (22.2) 1 1/8 (28.6) 1 (25.4)

3 1 (25.4) 1 1/4 (31.8) 1 (25.4)

5 1 1/8 (28.6) 1 3/8 (34.9)

9 1 1/2 (38.1) 1 1/2 (38.1)

* For 20-year mean recurrence interval

Table 2. Design Hailstone Velocities

Hailstone Diameter, Inches (mm) Resultant Velocity*, ft/s (m/s)

7/8 (22.2)

1 (25.4)

1 1/8 (28.6)

1 1/4 (31.8)

1 3/8 (34.9)

1 1/2 (38.1)

95 (29.0)

98 (29.9)

101 (30.8)

105 (32.0)

108 (32.9)

112 (34.1)

* Resultant of terminal vertical velocity and horizontal velncit) of 66 ft/s

(20.1 m/s) 19J

86
Fig! re .verage Annual Number oi Day ; wi "h 1 ai 1 (Ref. ')

87
Note: Numbers on this map should be

divided by 20 to obtain the

average annual number of days

with hail.

Figure 3. Total Number of Days with Hail in an Average 20-year

Period for the Central United States (Ref. 8)

88
U. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 81-2199

slop No,

'Mm

4. TITLE AND SUBTITLE

Wind, Earthquake, Snow, and Hail Loads on Solar Collectors

5. Publication Date

Orseiii^ation Code

3

7. AUTHOR(S) Louis Cattaneo, James R. Harris, Timothy A. Reinhoid

Emil Simiu, and Charles W. C. Yancey

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rsfreof. City, State, ZIP)

Department of Energy

Office of Conservation and Solar Applications

Washington, DC 20545

13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

i I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-wordl or /ess factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here,) The report describes and interprets wind-tunnel, full-scale, and field studies of

wind and snow loads on flat plate solar collectors, conducted under contract for the

National Bureau of Standards, and uses results of these studies and other data available in the literature to develop information, guidelines, and criteria for the

design of flat plate collectors subjected to the action of wind, snow, and earthquake

loads. Also given in the report are data on hail loads, based on information and

studies available in the literature.

17e KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Earthquake loads; hail loads; solar collectors; snow loads; structural engineering;

wind loads.

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I I For Official Distribution. Do Not Release to NTIS

I I Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

r~l Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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