AD-A203 866 FT E FCE , -- N-1789

November 1988By M. JacobyN O E L Sponsored by Marine Corps Research,

Technical Note Development and Acquisition Command

PRESSURE COEFFICIENTS FORBASIC TENSIONED-MEMBRANE

STRUCTURE FORMS

ABSTRACT This report details FY85 wind tunnel tests on basic ten-sioned-membrane structure forms, data reduction and analysis, andresults. Models of parallel and diagonally-arched structures weretested. Testing was performed at the James Forestal Laboratory windtunnel, Princeton University, and the environment wind tunnel locatedat the Naval Civil Engineering Laboratory (NCEL). All data and resultshave been converted to pressure coefficient form to facilitate their usein wind load calculations. Results are presented in Appendixes A, B,and C. Appendixes A and B give average and peak section pressurecoefficients arranged by model for different wind incident angles, res-pectively. Appendix C shows pressure coefficient contour plots arrang-ed by model for different wind incident angles. The effects of varyinglength, height, wind incident angle, and cross section on parallel-arched structures were measured. Finally, an example wind load calcu-lation using the results is contained in Appendix D.

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REPORT DOCUMENTATION PAGE BFRE COMPLETINORMI REPORT NuMBFR 12 GOVT ACCESSION NOQ 3 RECIPIENT'S CATALOG NIIMBEA

TN-1 789 [0N666386

4 TITLE 'sorO SIIIIII YEOFRP R ERO O EE

PRESSURE COEFFICIENTS FOR BASIC Not Final; FY86TENS IONED-MENBRANE STRUCTURE FORMIS

7AU 1.OR(O. 8 CONTRACT OR GRANT NUMBER(,)

N. Jacoby

9PERFORMING ORGANI ZATION N AME AND ADDRESS 10 PROGRAM ELEMENT PROjECT. T ASKAREA & WtORK UNIT NUMBERS

NAVAL CIVIL ENGINEERING LABORATORYPort Hueneme, California 93043-5003 00178E-4-101

II CGNTROLI.ING OFFICE NAME AND ADDRESS 12 REPORT DATEMarine Corps Development November 1988and Education Command 13 NUMBER OF PA-GESQuantico, VA 02134 90

4 MONITORING AGENCY N AME 6 AODRESS1,I dItrrecr from, co--tt-dnl off,,,) 15 SECURITY CLASS (.1 ISIS leporl

Unclass if ied

TS. DECLASSIFICATION DOWNGRADINGSCHoEDULE

16 GISIRIBUTION STATEMENT (,I 1h', R-Polc

Approved for public release; distribution is unlimited.

IT DIS*TRIBUTION STATEMENT (of hb.e bI ,,et-d -r Bl.ck 20. 1I different from, Report)

8 S,00 EMENTARY NOTES

I9 KEY WORDS IConl-nu on re-ers sd, I/ - -- )sr and Ide,lfy bY block number)

'Wind tunnel, tensioned-membrane structure, pressure coefficients - --r7

20 At-PRA-? 'ConIr-- on -orme a~de it necessry and ldenfrfy by block etnbe)

This report details FY85 wind tunnel tests on basic tensioned-membranestructure forms, data reduction and analysis, and results. Models of para-llel and diagonally-arched structures were tested. Testing was performed atthe James A. Forestal Laboratory wind tunnel, Princeton University, and theenvironment wind tunnel located at the Naval Civil Engineering Laboratory(NCEL). All data and results have been converted to pressure coefficientform to facilitate their use in wind load calculations- eut r presented. .

DO D , j'.RM 1473 EO0 ION OF 1 NOV1 AS IS OBSOLETE UnclassifiedSECURITY CLASSIFICATION OF TIlS PAGE Who, Doa Enteed)

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SECURITY CLASSIFICATION OF THIS PAGE(Whn Dos Entered)

20. Continued

in Appendixes A, B, and C. Appendixes A and B give average and peak sectionpressure coefficients arranged by model for different wind incident angles,respectively. Appendix C shows pressure coefficient contour plots arrangedby model for different wind incident angles. The effects of varying length,height, wind incident angle, and cross section on parallel-arched structureswere measured. Finally, an example wind load calculation using the resultsis contained in Appendix 0.

Library Card

Naval Civil Engineering LaboratoryPRESSURE COEFFICIENTS FOR BASIC TENSIONED-MELIBRANE

STRUCTURE FORMS (No+ Final) by M. JacobyTN-1789 90 pp illus Nov 1988 Unclassified

1. Hind tunnel 2. Tensioned-Membrane 1. C0078E-4-101

This report details FY85 wind tunnel tests on basic tensioned-membrane structure forms, data reduction and analysis, and results.Models of parallel and diagonally-arched structures were tested.Testing was performed at the James A. Forestal Laboratory wind tunnel,

Princeton University, and the environment wind tunnel located at theNaval Civil Engineering Laboratory (NCELI. All data and results havebeen converted to pressure coefficient form to facilitate their use

in wind load calculations. Results are presented in Appendixes A, B,and C. Appendixes A and B give average and peak section pressure coef-ficients arranged by model for different wind incident angles, respec-

tively. Appendix C shows pressure coefficient contour plots arrangedby model for different wind incident angles. The effects of varyinglength, height, wind incident angle, and cross section on parallel-

arched structures were measured. Finally, an example wind load calcu-lation using the results is contained in Appendix D.

Unclassif ied

SECUqRTY CLASSIrI C TION OF TWIS PAGE'Wh- D.- F,I.-,d)

CONTENTS

Page

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

BACKGROUND THEORY ............ ........................ 1

TEST DESCRIPTIONS ............ ........................ 3

ANALYSIS .............. ............................. 5

CONCLUSION .............. ............................ 7

ACKNOWLEDGMENT .............. ................ ....... 7

REFERENCES .............. ............................ 7

APPENDIXES

A - Pressure Contour Plots ..... ................ A-iB - Section Average Pressure Coefficients . ......... . B-iC - Section Peak Pressure Coefficients .. .......... C-ID - Example Wind Load Cal ulations ... ............ D-1

Accession For

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INTRODUCTION

The Naval Civil Engineering Laboratory (NCEL) has been tasked bythe Marine Corps to develop an expeditionary shelter system. This systemwill provide environmental protection for command and control, equipmentmaintenance and storage, and other combat support functions. The systembeing developed utilizes tensioned-membrane technology. Examples oftensioned-membrane structures are shown in Figures I and 2. This sheltersystem must withstand wind gusts up to 120 mph. For conventional build-ings, standard guidelines such as NAVFAC DM-2.2 or ANSI A58.1-1982 (Ref 1and 2) can be used to estimate wind loads. However, these guidelinescannot be used on tensioned-membrane structures due to their unusualconstruction. Section 6.4.3 of Reference 2 states that wind tunnel test-ing is "recommended for those buildings or structures having unusualgeometric shapes, response characteristics, or site locations for whichchanneling effects or buffeting in the wake of upwind obstructionswarrant special consideration, and for which no reliable documentationpertaining to wind effects is available in the literature."

FY84 development efforts included wind tunnel testing and compila-tion of data for various geometries and sizes of basic tensioned-membrane structure forms under consideration. The wind tunnel testswere performed by Ocean StrucL. es, Inc., under contract to NCEL.Unreduced data from these tests were turned over to NCEL for reductionand analysis. This report documents these tests, FY85 verification windtunnel testing performed by NCEL, analysis results, and conclusions.

BACKGROUND THEORY

'This section details the basic equations and principles used forbuilding aerodynamics and wind tunnel testing.

The pressure distribution around a body immersed in a moving fluidis primarily function of the local variation in fluid velocity producedby the body.---From Prnoulli's equation, with the subscript o referringto freestream conditions, .

PO 1 2 p 1 (- + g z + -- v -+ g z + Iv 2Po 0 2o p 2

. . . . • . . i I l i l l I I I

where p = static fluid pressurep = fluid mass densityg = acceleration of gravity

z = elevation

v = fluid velocity

For the low velocities encountered in building aerodynamics,compressibility effects are neglible. Assuming constant elevation,

Equation 1 reduces to,

p - p I V 2 (2)o 2 0 (2

Lhe maximum pressure difference from this equation is,

( ) 1 2o max 2 "o V

at the stagnation point where the flow velocity2 is z(to. DividingEquation 2 by this reference value, (1/2) p v , yields the following

dimensionless form of Equation 2,

0 = (v) 21 2 1 -2 o Vo

where Cp is defined as the pressure coefficient. All data and resultsdetailed here are in this form.

For wind tunnel testing of models, dynamic similitude conditionsmust be met. Dynamic similitude requires the Reynold's number for boththe model and full size structure be the same, i.e.,

Remodel = Reprototype (5)

Strict adherence to Equation 5 is difficult when testing small-scalemodels. Generally, building forms are so angular that viscous effectsare secondary. Reference 3 suggests that for wind tunnel testing of

building forms, dynamic similitude will be met for model Reynold'snumbers in excess of 11,000. As discussed later in this report, all

model Reynold's numbers in this effort were between 170,000 and 950,000.

Finally, consideration must be given to accurately simulatefull-scale boundary layer conditions. The distribution of meanwindspeed with height is described by the power law relation,

2

where Vz = wind speed at height z

= free stream wind speedz = height6 = boundary layer thicknessa = exponent, dependent on boundary layer type

Table 1 lists I different boundary layers and exponents.

Table 1. Boundary Layer Profiles and PowerLaw Exponents (Ref 4)

Boundary Layer Type Power Law Exponent

City 0.34

Urban 0.18

Open terrain 0.17

Figure 3 shows these boundary layer profiles referenced to the NCEL

wind tunnel. These boundary layers can be simulated In the windtunnel by proper placement of flow impediments or screens upwind ofthe wind tunnel test section.

TEST DESCRIPTIONS

Two separate series of wind tunnel tests are described in thissection. The first series was performed by Ocean Structures, Inc.,under contract to NCEL. After receipt of this data, and compilation ofdata on similar structures from other sources, verification testing wasperformed at NCEL.

Wind tunnel testing performed under contract to NCEL was performedat the low turbulence wind tunnel located at the James ForestalLaboratory, Princeton University. Table 2 lists the wind tunnelcharacteristics.

Table 2. Princeton Wind TunnelCharacteristics

Characteristic Specification

Working cross section 3 ft by 5 ft

Maximum speed 120 mph

Maximum blockage 5%

Blockage refers to the ratio of maximum cross-sectional area to testsection cross-sectional area. Pressure measurements were made withpressure taps connected to a 90-tube manometer board using dyed alcoholwith a specific gravity of 0.793. All pressure measurements were

3

referenced to test section static pressure. Velocity measurements were

made with a pitot-static tube connected to the manometer board.Figure 4 shows tube assignments.

Worst case environmental wind conditions are flow across open, flatterrain with few obstructions. Consequently, models were mounted away

from test section walls to minimize boundary layer effects. Model mount-ing details are shown in Figure 5. The Reynold's number for all models

varied between 570,000 and 950,000. Pressure taps wero placed overroughly half of each model's surface. Each model was tested over windincident angles from 0 to 180 degrees in 30-degree increments. Datawere recorded by photographing the manometer board after the readingstabilized. Figure 6 shows a sample data photograph.

Dimensions of models tested at Princeton are .hown in Figure 7.Alodels of both parallel- and diagonally-arched tensioned-memhranestructures were tested. Model groups A, B, and C represent parallel-

arched Clamshell Buildings, Inc., series 50 structures. Models in groupA are of constant cross section and varying length. Models in groups Band C have constant lengths, but different cross sections (Figure 8).

The diagonally-arched model tested was a 1/100-scale model of theSpandome, Inc., structure. All models were made of wood.

Another parallel-arched tensioned-membrane structure under

consideration by NCEL was the Sprung Instant Structure, manufactured bySprung Instant Structures, Inc. This structure is geometrically similarto the Clamshell structures mentioned above. Wind tunnel data on theSprung was provided to NCEL by the manufacturer in FY84 (Ref 5). Prelimi-nary analysis of wind tunnel data on both parallel-arched structures wasconducted. Results showed much smaller negative pressures, or suctions,over the Sprung structure. Due to similarities between both parallel-arched structures, verification testing was performed at NCEL to rectifythe differences. Characteristics of the NCEL wind tunnel are detailed

in Table 3.

Table 3. NET, Wind TunnelCharacteristics

Characteristic Specification

Working cross section 3 ft by 5 ft.

Maximum speed 45 mph

Maximum blockage 5 to 10%

Velocity measurements were made with a Kurtz hot-wire anemometer.Pressure measurements were made with pressure taps connected to a 47channel Scanivalve Corp. valve tree and a Serta Systems 0 to n.1 psid

strain-gauge-type differential pressure transducer. All pressure measurements were referenced to tunnel test section static pressure, measured

at the model roof height. All instrumentation was controlled by a Macsym2 microcomputer. Real-time conversion of pressure measurements topressure coefficient form was also performed with this system.

4

Figure 9 shows dimensions of two of the three models tested. Theparallel-arched models are 1/60 scale. The Sprung Instant Structures

model shown in Figure 9 will hereafter be referred to as model D. Thediagonally-arched 1/100-scale Spandome model used earlier at Princeton

was also tested (Figure 7).The atmospheric boundary layer for open, flat terrain with scattered

windbreaks was simulated. Figure 3 shows the actual boundary layer pro-file during testing. Flow velocities during testing were approximately8.2 meters per second, resulting in test Reynold's numbers of 170,000.For the parallel-arched models, one quarter section was tapped. Measure-

ments were taken for azimuth angles varying over 180 degrees, in 30-degree

increments. During each test run, corresponding to each azimuth angle,every tap was sampled 6,000 times. Data output consisted of average,

maximum, and minimum pressure coefficients for each tap.

ANALYS IS

Comparisons of Princeton and NCEL wind tunnel data on the

1/100-scale diagonally-arched model were made. Results showed goodcorrelation, with an average 3.7 percent difference between tap readingsand a 26 percent standard deviation. Princeton test data were used forsubsequent data analysis and reduction. Figure 10 shows comparisons ofresults on model D for NCEL, Reference 5 tests, and potential flowpredictions. From the graphs, Reference 5 test data underestimatednegative pressures, or suctions. As a result, NCEL data on the SprungInstant Structure model were used for analysis and reduction.

Figure 11 shows the analysis and reduction flowchart. Each majorstep is discussed below. The first step in the data reduction process

consisted of conversion of Princeton data to pressure coefficient form.Data from the Princeton tests were recorded by photographing the mano-meter board after the readings had stabilized (see Figure 6 for example).

Columns 9 and 10 as identified in Figure 4, recorded the total tunneland test section static pressures referenced to atmospheric, respec-

tively. The total tunnel pressure is the sum of the dynimic pressure,and the static pressure,

1 2H S + 2 p v (7)

where pH= total tunnel pressure

PS = static pressure

The dynamic pressure is determined by subtracting the test sectionstatic pressure from the total tunnel pcessure:

1 2 (8)pv PH - PS

5

This pressure difference can be calculated for the manometer boardus ing,

PH Ps = S.G. PH20 (h9 - h1 0) (9)

where S.G. = specific gravity of manometer fluid (0.793)

PH20 density of water

h9 = manometer fluid height in column 9

hlo = manometer fluid height in column 90

The pressure difference between the static pressure at tap x and testsection static pressure is,

Px Ps = S.G. PH20 (h - h1 0) (10)

where h = manometer fluid height in column x.x

At tap x, the pressure coefficient is calculated from,

hx - h0hx h10

Cp h -h (11)h9 h10

Using Equation 11, the pressure coefficients were calculated from thedata photographs.

After data conversion to pressure coefficient form, pressure co-efficient contour plots were generated. This was accomplished with the

DISSPI,A graphics software package from Issco, Inc., on the PRIME 750minicomputer at NCEL. A geometric simulation of the wind tunnel models

was constructed. Inputs were pressure tap coordinates and the corres-

pondence pressure coefficients. Using a least squares weighting tech-nique, contour plots were calculated in user defined intervals and super-

imposed on the model's surface. Appendix A contains top views of thecomputed contours, arranged by model and azimuth angle. These contoursare approximations by nature of the weighting technique. An accuracycheck revealed that the algorithm worked well in the interior of a sur-face, but had trouble accurately resolving contours along boundaries.

This effect was compensated for by mnnually estimating pressure co-

efficient contours along model boundaries.

After contour plot generation, each model was sectioned, as shownin Figure 12. The parallel-arched models were divided up into 12 sec-tions, symmetric ahout the model centerlines. The diagonally-archedmodel was divided into 16 sections. Section avprage pressure co-efficients were calculated using,

Z Cp. AIP . . - (12)

1 1

6

where Cp = section average pressure coefficient

A. = ith area between contours1

thCpi = i pressure coefficient, equal to the average to the

coefficients defining A i

Areas were measured using a Salmoiraghi optical planimeter. Average

section pressure c efficient results are found in Appendix B. AppendixC gives the largest negative or positive pressure coefficients for eachsection, arranged by model.

CONCLUSION

Results detailed in this report are based on rigid models. Withtensioned-membrane structures, structural shape is fabric dependent.The dynamic behavior and total deformation of these structures in heavywinds is unknown. Should these deformations be excessive, the resultantflow about the structures will be altered, and the results presented maynot be accurate. For diagonally-arched structures, fabric flutter maybe a problem due to large expanses of unconstrained fabric. This

represents another dynamic phenomenon not accounted for in the presentwork. Finally, application of results presented in this report isdemonstrated in Appendix D.

ACKNOWLEDGMENT

The author would like to acknowledge Sophia K. Ashley of the NavalCivil Engineering Laboratory, for her experience, assistance, and supportof the work described in this report.

REFERENCES

1. Naval Facilities Engineering Command. NAVFAV DM-2.2: Structural

engineering design manual. Alexandria, VA, Oct 1970.

2. American National Standards Institute. ANSI A58.1-1982: AmericanNational Standard minimum design loads for buildings and other

structures. New York, NY, Mar 1982.

3. Colorado State University. Wind engineering study of One Williams

Center, Tulsa, by J.A. Paterka and J.E. Cermak. Fort Collins, CO,

Dec 1974.

7

4. Naval Civil Engineering Laboratory. Technical Report R-912: Fieldand wind tunnel testing on natural ventilation cooling effects on threeNavy buildings, by Sophia K. Ashley. Port Hueneme, CA, Dec 1984.

5. Babowal Builders and Engineers, Limited. Pressure disLIJbution on aSprung structure measured on a 1:96 scale model in the wind tunnel.Calgary, Canada, Jul 1981.

8

Er

I-

4 0

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C-

cc

CN

Scattered30 Wind tunnel height windbreaks

28 City

26- -- Actual wind tunnel boundary Open, flatlayer profile terrain

24

22-

20-

0" 18-•

0L 16-E

- 14-

!2 12-

10-

8

6-

4-

2-

0 I I • III I

200 300 400 500 600 700 800 900

Velocity (feet/minute)

Figure 3. Atmospheric boundary layer profiles referenced to the NCELwind tunnel.

11

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7-77

> CD

z C-) ,-

__ Er

0D U) U)E Hm) 0 z U) l u

0.2~ Cl C)

=) Z

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1 2

Details of Princeton 31/2' x 5' wind tunnel test section.

X

1 x 36 dia. 30100 tube manifold

60

20

I 42

Figure 5. Princeton wind tunrip 1 test section.

13

Af

414

w Wo

\ ~15

Model L* D* H*H

__Al 24.0 7.98 3.07_ A3 18.0 7.98 3.07

A5 12.0 7.98 3.07A6 9.0 7.98 3.07

B6 11.72 8.53 4.36C6 14.30 9.08 5.65V All dimensions in inches

L

5.40--i

jDoor line-__, '14.4

16.8

Beam shape Fabric sag line

at center

5.40

2.16

Figure 7. Dimensions of models tested at Princeton.

16

7.45-

1.82

"A" 260

1.25-120

7.98 1.29

4 8.53

____ ____ ___ ____ ____ ___9.08

All dimensions in inches.

Figure 8. Cross-sections of model groups A, D, and C.

17

Dimensions of wind tunnel models tested at NOEL.

Configuration "D"

630;, 2.69

_________30___

___t

10

20

4.72

Configuration "A"

___ ___ ___ ___ ___ ______ __10.80

20.20 120

4.60

Figure 9. Models tested at NCEL.

18

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19

Wind Tunnel Data

IfConversion to Pressure

Coefficient Form

Model Geometry I Coordinates

Contour Plot Generation

Contour Plot Igion

Final Average SectionPressure Coefficients

Figure 11. DAta reduction And analysis flowchart.

20

Section definition and wind orientation.

Parallel-arched structures

8 5

1l2 4 1 911 32 10

7 6

Wind direction 00

600900

Diagonally-arched structures90 0

3 600

3 00IFW ind direction

11 12

10 13

2 5

Figure 12. Structure section definitions.

21

• ~1 i5I I

Appendix A

PRESSURK CONTOUR PLOTS

A-1

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Appendix B

SECTION AVERAGE PRESSURE. COMMI TENTS

Bl-1

Recommended Section Pressure Coefficients, Model Al

Azimuth AngleSection

0 30 60 90

1 -0.40 -0.70 -1.30 -1.00

2 -0.40 -0.45 -0.65 -0.40

3 -0.35 -0.45 -0.45 -0.40

4 -0.35 -0.60 -0.85 -1.00

5 -0.40 -0.50 -0.80 -1.00

6 -0.40 -0.05 0.40 0.50

7 -0.35 -0.25 0.25 0.50

8 -0.35 -0.40 -0.80 -1.00

9 -0.35 -0.85 -1.30 -1.25

10 -0.35 -0.10 -0.30 -0.65

11 -0.45 -0.65 -0.60 -0.65

12 -0.45 -0.50 -0.55 -1.25

B-2

Recommended Section Pressure Coefficients, Model A3

Azimuth AngleSection

0 30 60 90

1 -0.45 -0.80 -1.20 -1.00

2 -0.45 -0.50 -0.50 -0.40

3 -0.35 -0.50 -0.40 -0.40

4 -0.35 -0.65 -0.85 -1.00

5 -0.45 -0.60 -1.05 -0.95

6 -0.45 -0.10 0.50 0.55

7 -0.35 -0.30 0.25 0.55

8 -0.35 -0.45 -0.85 -0.95

9 -0.35 -0.95 -1.25 -1.15

10 -0.35 -0.10 -0.25 -0.60

11 -0.40 -0.60 -0.65 -0.60

12 -0.40 -0.60 -0.65 -1.15

B-3

Recommended Section Pressure Coefficients, Model A5

Azimuth Angle

Section0 30 60 90

1 -0.60 -0.90 -1.05 -0.85

2 -0.60 -0.55 -0.40 -0.30

3 -0.50 -0.60 -0.45 -0.30

4 -0.50 -0.60 -0.80 -0.85

5 -0.55 -0.80 -0.95 -0.85

6 -0.55 -0.10 0.50 0.60

7 -0.50 -0.40 0.25 0.60

8 -0.50 -0.55 -0.75 -0.85

9 -0.35 -0.90 -1.20 -1.05

10 -0.35 -0.05 -0.20 -0.45

11 -0.50 -0.75 -0.65 -0.45

12 -0.50 -0.55 -0.75 -1.05

B-4

Recommended Section Pressure Coefficients, Model A6

Azimuth AngleSection

0 30 60 90

1 -0.70 -0.90 -0.80 -0.80

2 -0.70 -0.55 -0.30 -0.25

3 -0.65 -0.75 -0.40 -0.25

4 -0.65 -0.80 -0.80 -0.80

5 -0.60 -0.90 -0.80 -0.80

6 -0.60 -0.15 0.50 0.65

7 -0.60 -0.45 9.35 0.65

8 -0.60 -0.75 -0.80 -0.80

9 -0.35 -0.85 -0.90 -1.00

10 -0.35 -0.05 -0.15 -0.45

11 -0.55 -1.00 -0.65 -0.45

12 -0.55 -0.70 -0.70 -1.00

B-5

Recommended Section Pressure Coefficients, Model B6

Azimuth Angle

Section0 30 60 90

1 -0.80 -1.00 -0.75 -0.85

2 -0.80 -0.75 -0.55 -0.45

3 -0.70 -0.85 -0.60 -0.45

4 -0.70 -0.90 -0.80 -0.85

5 -0.75 -0.90 -0.80 -0.80

6 -0.75 -0.10 0.50 0.75

7 -0.65 -0.10 0.40 0.75

8 -0.70 -0.70 -0.80 -0.80

9 -0.30 -1.00 -1.00 -0.80

10 -0.30 -0.10 -0.25 -0.45

11 -0.60 -0.80 -0.80 -0.45

12 -0.60 -0.75 -0.80 -0.80

B-6

Recommended Section Pressure Coefficients, Model C6

Azimuth Angle

Section0 30 60 90

1 -0.75 -1.10 -0.85 -1.10

2 -0.75 -0.90 -0.65 -0.85

3 -0.70 -0.90 -0.80 -0.85

4 -0.70 -1.05 -0.90 -1.10

5 -0.70 -1.00 -0.80 -1.00

6 -0.70 -0.10 0.50 0.85

7 -0.70 -0.10 0.50 0.85

8 -0.70 -0.85 -0.85 -1.00

9 -0.25 -1.05 -1.10 -1.15

10 -0.25 -0.10 -0.30 -0.65

11 -0.55 -0.85 -1.00 -0.65

12 -0.55 -0.85 -0.85 -1.15

A-7

Recommended Section Pressure Coefficients, Model D

Azimuth AngleSection

0 30 60 90

1 -0.65 -1.05 -1.10 -0.75

2 -0.65 -0.75 -0.55 -0.10

3 -0.55 -0.70 -0.50 -0.10

4 -0.55 -0.75 -1.00 -0.75

5 -0.60 -0.65 -0.70 -0.80

6 -0.60 -0.35 0.15 0.50

7 -0.55 -0.40 0.05 0.50

8 -0.55 -0.50 -0.75 -0.80

9 -0.70 -1.35 -1.35 -0.90

10 -0.70 -0.55 -0.75 -0.60

11 -0.55 -0.70 -0.70 -0.60

12 -0.55 -0.60 -0.70 -0.90

B-8

Recommended Section Pressure Coefficients, Model F

Azimuth AngleSect ion

0 30 60 90

1 -0.50 -0.60 -0.50 -0.65

2 -0.50 -0.35 -0.35 -0.95

3 -0.75 -0.30 -0.25 -0.55

4 -0.55 -0.50 -0.50 -0.55

5 -0.65 -0.70 -1.00 -0.95

6 -0.65 -0.75 1.05 0.65

7 -0.55 -0.90 0.85 0.70

8 -0.75 -1.00 -0.70 -0.70

9 -0.65 -0.35 -0.40 -0.50

10 -0.65 -0.05 -0.10 -0.80

11 -0.80 -0.10 -0.40 -0.65

12 -0.40 -0.25 -0.10 -0.65

13 -0.60 -0.60 -0.90 -0.80

14 -0.60 -0.75 -1.05 -0.50

15 -0.40 -0.85 -0.80 -0.60

16 -0.80 -1.05 -0.65 -0.60

B-9

Appendix C

SECTION PEAK PRESSURE COEFFICIENTS

c-It

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL Al

Azimuth Angle

Section0 30 60 90

1 -0.80 -1.26 -3.06 -1.21

2 -0.80 -1.20 -2.13 -1.17

3 -0.50 -0.83 -1.08 -1.17

4 -0.50 -0.85 -1.11 -1.21

5 -0.56 -0.89 -0.91 -1.00

6 -0.56 -0.07 (0.18) 0.69 0.56

7 -0.41 -0.32 (0.02) 0.38 0.56

8 -0.41 -0.46 -0.98 -1.00

9 -0.98 (0.78) -1.62 -2.33 -1.77

10 -0.98 (0.78) -0.93 (0.78) -1.76 (0.83) -1.49 (0.45)

11 -0.59 -1.07 -1.36 -1.49 (0.45)

12 -0.59 -0.65 -0.60 -1.77

C-2

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL A3

Azimuth Angle

Section•0 30 60 90

1 -0.80 -1.45 -2.44 -1.17

2 -0.80 -1.30 -1.79 -1.1i

3 -0.54 -0.91 -1.06 -1.11

4 -0.54 -0.91 -1.15 -1.17

5 -0.60 -0.93 -1.09 -1.00

6 -0.60 -0.09 (0.11) 0.69 0.57

7 -0.44 -0.32 (0.09) 0.34 0.57

8 -0.44 -0.41 -0.89 -1.00

9 -0.96 (0.78) -2.04 -2.20 -1.87

10 -0.96 (0.78) -1.04 (0.68) -1.65 (0.83) -1.43 (0.45)

11 -0.61 -0.96 -1.36 -1.43 (0.45)

12 -0.61 -0.85 -0.76 -1.87

C-3

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL A6

Azimuth AngleSection

0 30 60 90

1 -0.93 -1.48 -0.94 -0.82

2 -0.93 -1.20 -0.81 -0.83

3 -0.70 -1.16 -0.78 -0.83

4 -0.70 -1.12 -0.82 -0.82

5 -0.64 -0.87 -0.77 -0.82

6 -0.64 -0.17 (0.06) 0.56 0.67

7 -0.57 -0.43 0.46 0.67

8 -0.57 -0.75 -0.76 -0.82

9 -1.07 (0.76) -1.69 -2.06 -1.57

10 -1.07 (0.76) -0.93 (0.82) -1.06 (0.89) -1.17 (0.59)

11 -0.78 -1.88 -1.33 (0.04) -1.17 (0.59)

12 -0.78 -0.80 -0.80 -1.57

C-5

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL B6

Azimuth Angle

Section

0 30 60 90

1 -1.11 -1.55 -0.83 -0.94

-1.11 -1.32 -0.83 -0.98

3 -0.76 -1.28 -0.96 -0.98

4 -0.76 -1.30 -0.94 -0.94

5 -0.79 -0.91 -0.81 -0.82

6 -0.79 -0.11 0.64 0.76

7 -0.57 -0.13 (0.04) 0.48 0.76

8 -0.57 -0.71 -0.79 -0.82

9 -1.17 (0.76) -2.85 -1.66 -0.91

10 -1.07 (0.76) -0.93 (0.82) -1.06 (0.89) -1.17 (0.61)

11 -0.78 -1.23 -0.83 -1.15 (0.61)

12 -0.78 -1.17 -1.74 -0.91

C-6

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL C6

Azimuth Angle

Section0 30 60 90

1 -0.96 -1.74 -0.91 -1.54

2 -0.96 -1.42 -1.26 -1.46

3 -0.72 -1.37 -1.12 -1.46

4 -0.72 -1.46 -1.14 -1.54

5 -0.69 -1.02 -0.83 -1.05

6 -0.69 -0.09 0.56 0.90

7 -0.71 -0.29 (0.10) 0.64 0.90

8 -0.71 -0.89 -0.90 -1.05

9 -1.32 (0.76) -2.56 -2.20 -1.85

10 -1.32 (0.76) -1.34 (0.94) -1.63 (0.96) -1.65 (0.46)

11 -0.74 -1.50 -2.85 -1.65 (0.46)

12 -0.74 -1.27 -0.90 -1.85

C-7

PEAK PRESSURE COEFFICIENTS IN EACH SECTION, MODEL D

Azimuth AngleSection

0 30 60 90

1 -1.36 -3.04 -1.23 -0.88

2 -1.36 -2.54 -1.63 (0.04) -0.60 (0.48)

3 -1.06 -1.32 -1.20 -0.60 (0.48)

4 -1.06 -1.41 -1.34 -0.88

5 -0.78 -0.74 -0.73 -0.78

6 -0.78 -0.39 0.22 0.60

7 -0.58 -0.67 -0.22 (0.28) 0.60

8 -0.58 -0.43 -0.72 -0.78

9 -1.36 (0.38) -3.04 -1.74 -1.71

10 -1.36 (0.38) -2.54 -2.11 (0.22) -1.76 (0.47

11 -1.06 -1.00 -1.08 -1.76 (0.47)

12 -1.06 -1.05 -0.93 -1.71

0-8

Appendix D

EXAMPTYF WIND LOAD CALCUJATJ,)NS

. ..... . ...

PROBLEM:

Find wind and anchor loads on the center section of a series 50clamsmeter w/7 bays as a function of velocity. Assume 90-degree azimuthangle.

SOLUTION:

From NAVFAC DM-2.2, wind loads on structures are calculated from,

2q = 0.00256 Ch Cp

v

where: q = load (in lb/ft )

Ch = height correction factor ( I for h

These are plotted in Figures D-1 and D-2.

The total section loads are found from,

fT = q A

where fT = total section load

A = section area

for this structure,

Section Area (ft ) Ft (ibs)

1 894.25 1.26V2

2 2794.75 -2. 86V 2

3 2794.75 -7.15V2

4 894.25 -2.17V2

These loads are plotted in Figure D-3.

To calculate anchor loads, the section loads per foot of length aregiven above. These can be resolved to concentrated loads acting at themidpoint of each section, or shown in Figure D-4 (assuming the frame ispinned on the windward side and simply-supported on the leeward side.)

Ef = 0 =- h + 0.0142 - 0.0143v2 + 0.0364v

2 + 0.0240v2x1 _

h 2h1 0.0601v

IF = 0 = - 0.003v2 + 0.0294v 2 + 0.0746v 2 + 0.0051v -

v 1 + v2 = 0.1061v2

EM = 0 = (0.003)(1.06)v2 + (0.014)(4.99)v

2 - (0.0143)(17)v2

a

- (0.0294)(16.48)v 2 (0.0746)(44.52)v 2 + (0.0364)

(17)v 2 (0.0051)(5 .94)v 2 + (0.0240)(4.99)v 2 + 61v 2 ;

Fm 2 0.058lV]from (2),

v1 = 0.0480v2

D-3

On the windward side,

VT = [(0.0480v2)2 + (0.0601v2)2] 1/2 = 0.0769v2

The total anchor loads are,

VT (windward) 6.7288v2

VT (leeward) = 5.0838v2

These are plotted in Figure D-5.

The total required anchor capacities are plotted in Figure D-6.

D-4

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8.-.4

U-

ill C

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IN_ \__ - 011

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D-10

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