ITNCHNICAL REPORT

67-54-GP

4 GUIDE FOR ESTIMATING MAXIMUM ANCHOR

LOADS ON AIR-SUPPORTED STRUCTURES

Iby

Thomas C. Strain

and

Ronald F. Tumeinski

RECEIVEDJUL 2 1 1967 March 1967.

G rEq a L

General Equipment & Packaging Laboratory

IDistribution of this reportis unlimited. Release to ADCFSTI is authorized.

TECHN ICAL REPORT

67-34-GP

GUIDE FOR ESTIMATING MAXIMUMANCHOR LCADS ON AIR-SUPPORTED STRUC-PJRES

by

Thomas C. Strain

and

Ronald F. Tumeinski

Project No. IM64210ID503 March 1967

General Equipment & Packaging LaboratoryU. S. ARMY NATICK LABORATORIES

Natick, Massachusetts

FOREWORD

This report was prepared by the Shelters Division, General Equipmentand PaKaging Laboratory, U. S. Army Natick Laboratories, Natick, Mass.The wr,ýk was performed under Exploratory Development Project 1IM642101D503,"Tents and Organization Field Equipment," Task 01, Studies in tne Struc-tural Mechanics ef Tentage, Work Unit 003, Review of Design Manual.

Its contents are based on the technical data contained in the "DesignManural For Ground-Mounted, Air-Supported Structures," prepared by the HayesInternational Corp. Birmingham, Alabama, for NLabs under contract DA19-129-AWC-1209.

The intent of this report is to provide the design engineer with acomplete, concise guide for planrning the ground support and anchoringde-ices required for stabilizing air-supported structures.

The authors wish to acknowledge the guidance, encouragement andsupport of Mr. C. J. Monego of the Shelters Division in the preparation

of this work.

EDWARD A. NEBESKY, Ph. D.Acting Director

General Equipment & Packaging Laboratory

APPROVED:

DALE H. SIELING, Ph.D.Scientific Director

W. M. MANTZBrigadier General, USACcrmanding

ii

TABLE OF CCLrE•TS

List of Figures iv

Symbols v

Abstract vI

1. !ntroductio, 1

2. An.-hor L-2- Calculations 2

a. Forces Creating Anchor Loads 2

b. Definition of Anchor Load Coefficients 8

c. Formilas for Calculating Anchor Loads 9

d. Sample Calculations 13

iii

ILIST 01 YIrIGthES

1. Single-Wall, Spherical

2. Single-Wall, Cylindrical

3. Double-Wall, Cylindrical 3

4. Variation of Impact Pressure 'v~' Air Speed, 6

Sea Level Standard Atmosphere

5. Impact Pressure Correctior Factor, kp, Variation with

Altitude & Temperature

6. Variation of Anchor Load CoeffPc-ent with Shape 10

(Spherical)

7. Variation of Base Anchor Load Coefficient with 11

Shape

8. Variation of Guy Line Load Coefficient with Shape 12

9. Single-Wall Sphere 13

10. Single-Wall Cylinder 15

11. D-W Cylinder 17

iv

!*I

SYMBOLS

Af Floor area, sq ft

A Planforn, area (max. horizontal cross sectional area),sq ft

AL Anchor Loac, lbs

AL Anchor load due to internal pressure, los

BL Base anchor load, lbs

CAL Anchor load coefficient, single-4all

CBL Base anchor load coefficient, double-wall

CGL Guyline anchor load coefficient, double-wall

a Reference length - tent diameter, ft

GL Guyline anchor load, lb

h Teitt height, ft -

Length of tent, ft

P Total anchor load, 16s

P Shelter enclosure pressure, lb/sq fte

q Dynamic (impact) p-essure, lb/sq ft

r Tent radius, ft

U Velocity, ft/sec

W rent vddth, ft

Density of air, Slugs/cu ft

ABSTRACT

This report contains all the graphs, tables, mathomatical formulas.

and design data necessary to estimate the maximum loads on anchoringsystems used with air-supported shelters subjected to winds up to 105 mph.

The design data are presented in non-dimension coefficient form., Sampleproblemsr, are included to illustrate the use of the data and their appli-cation ".o both single and double-wall structures.

vi

I

GUIDE FOR ESTIMATING MAXIMUM ANCHOR LOADSON AIR-SUPPORTED STRUCTURES

1. Introduction

In October 1950, a Design Manual for Spherical Air-Supported

Radomes was published as Cornell Aeronautical Laboratory Repor ! N^.UB-664-D-l.

After its publication, the radome was adopted as standard by the military

on many ground-mounted radar installations. Hundreds were built and consid-

erable experience with their design and operations had been gained in the

field.

In March 1956, the Ccrnell Design Manu~al was revised to incorporate

information accunrulated since its original publication. This revised

manual, is designated as: "Design Manual for Spherical Air-Supported Radomes

(Revised) Report No. bB-909-D-2."

Air-supported shelters were being di'veloped for the military, varying

in shape from spherical radomes to cylindrical structures with spherical

or flat ends. Although the spherically shaped radome had been subjacted

to aerodynamic testing, no studies were made for other shapes. The design

of other configurations was based on fragmentary Jnformation available from

various sources. The need for reliable design information was obvious.

To obtain aerodynamic data on flexible, cylindrical, air-supported

structures, a limited wind tunnel study wa- conducted at the Massachusetts

Institute of Technology on a one-tenth scale model of the Army's standard,tent, air-supported, single-wall, nike-hercules, aboje-ground launcher.

As a result, a final report was prepared by Raffi J. Bicknell entitled,

"Wind Tunnel Test on an Air-Supported Tent Model" Report No. 1024, Department

if Aeronautics and Astronautics, Wright Brothers Wind Tunnel, MIT, June

1963.

Beginning in July 1963, the U.S. Army Natick Laboratories contracted

a program with the Hayes International Corp. for extensive wind tunnel

studies on spherical and cylindrical single-wall* structures and cylindrical

double-wall** structures.

*Single-Wall - A flexible structure consisting of a single membrane usually

in the shape of a spnere or cylinder. It is supported by a continuous flow ofhigh volume, low pressure air enclosed between the membrane and mounting

surface.**Double-Wall - A flexible structure consisting of two membranes usually in theshape of a half cylinder. The two rembranes form an envelope containing air,

which resembles an air mattress bent into a "U" shape. The structure issupported by a flow of low volume, high-pressure air.

This program consisted of analytical and wind tunnel stdies on 26 scalemodel air-supported structures. This contract resulted in a Lesign maiualentitled, asign Manual for Ground-Mounted Air-Supported Structures."It provides design criteria to facilitate engineering of aerodynamicallystable air-supported structures. Included in the design manual are datafor estimating maximum anchor loads to be exptcted in winds up to 106mph.The contents of the prasent report are based on the data contained in theI•ayes report. It is prepared for the convenience of engineers whose primaryinterest is the anchoritig of military shelters.

2. Anchor Load Calculations

a. Forces Creating Anchor loads

Faoric shelters subjected to winds of high velocity can experienceaerodynamic forces of conbiderable magnitude. In order to estimate themagnitude of these forces, twentý six single and double-wall shelter modelswere tested in a wind tunnel with winds up to 105 miles per hour. Theaerodynamic force data obtained, were reduced to non-dimensional coefficientform by dividing the force data by a reference area and the dynamic pressrure.

Several very important facts should be emphasized at this time.The aerodynamic force data used here were maximum values so that the anchorloads calculated by techniques in this report will be maximum loads. Thesecond fact is that no attempt has been made to ascertain the effect ofwind gusts. The impact pressure used is for a wind of constant velocity.

The tent planform area Ap was selected as the reference area andis defined as the maximum cross sectional area in a horizontal plane.Planform areas are given by the following expressions for common tent types:-

Sphere

,% (= ,. , )22

Cylinder with spherical ends:

Ap = IT (Y ? w (l - W)2 h

2

Figures 1 through 3 are exan4j1es of air-supported structures.

Figure 1. Single-Wall, Spherical

figure 2. Single-Wall, Cylindrical

Figure 3. Double-Wall, Cylindrical

3

Cylinder with flat ends:

Ap = W 1

where:

Ap = planform area, sq ft

W = width of tent, ft

1h = length of tent, ft

The planform areas for tents with radii up to 80 feet are shain inTable I.

The dynamic pressure, q, due to wind velocity is defined by thefollowing expression:

q 1= U U2

2

where:

q dynamic pressure, lb/sq ftU = wind velocity, ft/sec

density of air in (slugs/cu ft), 1 b - sec2

ft

= .00238 for a stzndara day atsea level

The variation of impact pressure with wind speed at sea level and59'0F is shown in Figure 4. An impact pressure correction factor as afunction of pressure altitude and temperature is shown in Figure 5.

In single wall shelters, the lift due to internal pressure must beadded to the aerodynamic lift. The load on the anchors due to internalpressure can be calculated from the following expression:

AL P A*Ae e

ALe anchor load due tc 4 ternal pressure, lbs

4

Table I

TENT PLANFOR.M AREA, Ap

SPHERICAL AND CYLINDRICAL TENTS ,WITH HEMISPHERICAL EIqD.

Tent Planform Area, AP, Sq. Ft.Tent Radius ..... ...___ _ _ _ _ __ _ _ _ __ _ _

r Ft. Spherical Cylndrlcal Cyllndrical Cylindrical

1/2 - W/lh 1/3 - W/lh 1/4 = W/lh

10 314 714 1114 151412 452 1028 1604 218014 615 1399 2183 296716 804 1828 2852 387618 1017 2313 3609 490520 1256 2856 4456 600622 1520 3456 5392 732824 1809 4113 6417 872126 2123 4827 7531 1023528 2463 5599 8735 1187130 2827 6427 10027 1362732 3216 7312 11409 1550534 3631 8255 12879 17503

36 4071 9255 14439 1962338 4536 10312 16088 21864

40 5026 11426 17826 2422642 5541 12597 19653 26709

44 6082 13826 21570 2931446 6647 15111 23575 3203948 7238 16454 25e70 34886

50 7853 17854 27854 3785452 8494 19310 30126 4094254 9160 20824 32488 44152

56 9852 22396 34940 4748458 10568 24024 37480 50936

60 11309 25709 40109 54509

62 12076 27452 42828 58204i 64 12868 29252 45636 62020

66 13684 31108 48532 6595668 14526 33022 51518 70014

70 15393 134993 54593 7419372 16286 I 37022 57758 7849474 172803 39107 61011 82915

S 76 1814*5 42964ý53 18745778 19113 43449 67785 92121

80 1 20106 5706 71 ( 71306 96906

5 60

44-;

7--4

6*ý . .. . . . . .

T+91KI71jc..t -

06

4J

*~ ~ ~~~~~~~~\- A--------------+----

C.)

-4*Fo, #74 .2VF4f -7

IP e = internal pressure, lbs/sq ft

Af = floor area, Eq ft

To summarize, the total force that must be resisted by tne shelteranchoring system is created ty the:

(1) Aerodynamic load for double wall shelters(2) Aerodynamic load PLUS internal pressure for single

wall shelters.

b. Definition of Anchor Load Coefficients

The general definition of an anchor load coefficient dve toaerodynamic forces is:

CAL

where:

AL = anchor load, lbs

C AL= anchor load coefficient

In double wal± shelters the anchor load is carried by anchors at

the base of the shelter, as well as, by anchors securing the guylines.The coefficients associated with these two loads are:

CBL - BLqAp

CGL .L.qA

p

CBL = Anchor load coefficient for base of shelters.

rGL = Anchor load coefficient for guy lines.

BL = Anchor load on base, lbs.

GL = Anchor load on guy lines, lbs.

q = Dynamic (Impact) Pressure lbs/sq ft

8

Anchor load coefficients as a function of width/length and

height/diameter ratios are plotted in Figures 6, 7 and 8.

c. Formulas '>r Calculating Anchor Loads

Using Figures 6, 7, and 8 it is a simple matter to estimate themaximum anchor load on an air supported structure. The problem resolves

itself to geometry and substivtution into formu•as. The items of information

required are:

Shelter geometryDesign wind speedEnclosure pressure (single wall only)

(1) Single Wall Shelters

Total Anchor Load PAL = CALqAp + Pe Af

(2) Double Wall Shelters

BL = CBL qAp

GL = CGL qAp

Total Anchor Load PAL = qA (CBL + CGL )

The way the calculated load is distributed is a matter for the tent

designer. If the anchoring system consists of individual anchors equally

spaced around the shelter and the holding capability of the anchor isknown, the total load divided by the anchor holdi.ýg power will determine

the number of anchors to be used. If the shelter is to be continuously

held down along the floor perimeter, the total load divided by the shelter

perimeter determines the load/foot.

The U.S. Army uses several types of anchoring systems such as concrete

pads with metal hold down bolts, steel hold down rings on towers and arrow-head ground anchors. The arrowhead anchors, as described in MIL-A-3962A,

Anchors, Ground, Arrowhead, 4", 6" and 8" with Auxziliary Equipment, are

generally used for field installations. Considerable work is being doneby the Natick Laboratories to determine the holding capabilities of the

4" arrowhead anchor in various types of soil. This work will be reportedseparately after it is completed. To give an indication of the order of

magnitude of the holding power, 4" anchors, whc*n driven to their full depth

of 28" will hold about a 1000 lbs in sand and about 2000 lbs in sandy gravel.

9

~~-*-~ ---------- I -

.A .~4- ....- ....-.

--I-

Figure 6. Variation of Anchor Load Ccreffic~ent with Shape~

10

4 4:M-0 24....+re4 +-.-

-. ~~~. ~ 2.... .....

t~

4 -

I I t . ._ _ _ _ _ ._._._._._.

t 'D ---- V-* I

Figure 7. Variation of Base Anchor Load Coefficien.t.-Shape

-IT-

+4 I

120I,0

IAnotner fact of interest is that for anchors driven 28-30" the minimum"distance between anchors should be at least 30 inches. These figuresare presented for illustrative purposes only and will indicate the typeof information required concerning the anchoring system to be used onthe shelter being considered.

d. Sample Calculations

(I) The following calculations are for the slngle-wall, sphericalshape (Fig. 9):

2r h

Figure 9. Single-Wall Sphere

Width = W = 30 ft = 2rHeight Ih = 22.5 ftSea levelTemperature expected + 60 to -30OFWind velocity = 9) knotsEnclosure pressure 1- q

gometric Consideration.

Length of chord = 2y - 2T r 2 - (h-r) 2

y =ý2hr : hy2 Z 2(22.5) (15) - (22.5)2= 169

y - 13 ft

Af = 1y 2 = 169T= 531 Sq ft

Perimeter = 27ry = 2 7r (13) = 82 ft

Ap = ?T r 2 = Tr (15)2 = 709 so it

13

Determining impact pressure, q

Figure 4 - at 90 knots, q (standard) = 27 psf (lb/sq ft)

Figure 5 - max correction factor = 1.21

Actual q = 1.21 (27) = 32.7 psf

Anchor loads

Aerodynamic load

h/d = 22.5/30 = .75

,*/Ih = 30/30 = 1.0 (sphere)

Figure 6 - CAL 1.5

Wind load = CAL qAp = 1.5 (32.7) (709)

= 34,700 lbs

Inflation pressure load = Pe Af

= (32.7) (531)

= 17400 lb

Total Load = 34700 - 17400 = 52,100 in

Distributing Anchor Load

Assume an anchor holds 1500 lb

No. of anchors 52100 3= 351500

Anchor spacing 82 = 2.34 ft

35

14

(2) The following calculations are for the single-wall,cylindrical shape with spherical ends (Fig. 10):

W

Figure 10. Single-Wall Cylinder

Width = W = 50 ft = 2r

Height = h = 25 ftLength = 1h = 100 ft

Sea level standard atmosphere

Wind velocity - 105 mph

Enclosure pressure = q

Geometric considerations

Length of Chord 2y = 2A r 2 - (h-r) 2

y2 = 2hr - h2

y2 = 2(25) (25) -(25)2 = 625

y = 25 ft

Af = Ir y 2 + 2y (h - 2r)

- 625 7r - 50 (100-50)

Af = 1962 - 2500 = 4462 sq ft

Perimeter = 50f - 100 = 256 ft

Ap I r 2 2r (ih -2r)

- 625 Ir - 50 (100-50) = 4462 sq ft

15

IIn this example the planform area equals the floor area which is notalways the case.

Determining impact pressure, q

Figure 4 at 105 mph, q = 28 psf

Anchor loads

Aerodynamic load

h/d = 25/50 .5

W/lh = 50/100 .5

Figure 6 CAL = 1.6

Wind load = CAL qAp = 1.6 (28) (4462)

= 200,000 lbs

Inflation pressure load = Pe Af

= 28 (4462)

=125,000 lbs

Total Load = 200,000- 125,000 = 325,000 lbs

Distributing Anchor Load

Assume an anchor holds 2000 lbs

No. of anchors 325,000 - 163 anchors2000

Anchor spacing - = 1.57 ft.1-j3

This spacing is quite close :or o 4" arrowhead anchor system but might

be suitab~e or other types. If arrowheads are needed, larger anchors,dec per emplacement or pairs of 4" anchors could be used to increase -nacing.

16

I!

(3) The following r-alculations are for the double-wall,cylindrical shape with flat ,.nds (Fig. 11):

it..... .JL...iW'Ii.riIFigure 1i. D-W Cylinder

Width z W = 10, ft

Height = h 50 ft

Length zlh = 200 ftSea level, standard atmosphereWind velocity -105 Taph

Geometric cOns iderations

Lengthi of apruhored sides 2(200) 400 ft

A z W/h

1 100 (200) = 20000 sq ft

Deternining_ Lact jressure.__ _

Figure 4 at 105 mph q = 28 psf

Anchor loads

h/d = 50/100 = .5

W/lh = !CO/200 = .3

Figure 7, CBL = 1.08

Figure 8, C _ .44GL

17

Total Anchor Load PAL + qAp (CBL - CGL )

P = 28 (20000) (1.08 - .44)

AL

= 856000 lbs

BL F 1.08 (28) 20,000 = 607,000 lbs

GL = .44 (28) 20,"00 = 249,000 lbs

Two points to be noted are the extreme forzes possible on an air-supporteld structure and the fact that the base of the shelter requiresthree times as much anchoring as the guyllnes. The latter factor is

contrary to common belief but has been indicated caisistently in thewind tunnel studies performed on model double-wall shelters.

Distributing Anchor Loads

Assume an anchor holds 4000 lbs

No. of Base Anchors 607000 = 1524000

No. of Guyline Anchors 249000 = 624000

Spacing along base 400 = 2.63 ft

152

Spacing of guyline 400 = 6.5 ft62

18

Secunty ClassificationDOCUMENT CONTROL DATA ,R&D

(S.c~w~tv CI8,- r2 01 rtfle bo~dy *I abelecr and tldwx,,,E am.,at- bo at ben 6.oet d l.A.. the ct.. 1 v~po~t . 00#110ld)

4I ORIGINATIN 0 ACITV"'V 'Corp'i.-at s*h,f') 12a REPORT SXCIA,?V C .ASS'FCATION

UnclassifiedU.S. Army Natick Laboratories abGRQ

Natick, Hissachusetts

3 REPORT TITLE

Guide for Estimating Maximum Anchor Loads on Air-Supportect Structures

4 DESCRIPTIVE NOýIES (Typ of ,por, and inli does

5 AUITIOR'5) 'La.I nb,.q str,9 mA4O ,f.1)

Strain, Thor.as C. and Tumeinski, Ronald F.

6 EPRTDAE7. TOTAL NO0 OF PAGES 7b NO OF REFS

March 1967 18So CON'RACT OR GRANT O 9. ONIGINATO;RS1 REPORT N'UMBER(S)

6 7-54-GPb PROJECT NO 11M642101D503

O6 OYTiER REPORT NO(S) (Auiyacornonberw that may be aselod .

I0 A V A IL A9,LJTY LIMITATION NOTICES

Distribution of this report is unlimited. Release to CFSTI is authorized.

I I SUPPL EM2WTARY NOTES 12 SPONSORING MILITARY ACTIVITY

U.S. Armv Natick LaboratoriesNatick, Mlass.

13 ABSTRACT

11his report cor~tains all the graphs, tables, mathematical formulas, and designdata necessary to estimate tle maximum loads on anchoring systems u~sed withair-supported.pheiters subjected to winds up to 105 mph. The design data arepresented in non-dimensional coefficient form. Sample problems are included

to illustrate the use of the data and their application to both single and

double-wall structures.

D D 2 1473 Unclassified

Se'-unty Classification~

Unclassified

Security Classification

14. LINK A LINK 8 LINK CKEY WORDS

ROLM WT ROLE WT ROLE WT

b

Data 8Estimation 8Loads (Forces) 9

Load distributions 9

Anchors (structural) 9

Inflatable structures 9

Radomes 9Tents 9

Structures 9Air-supported 0Cylindrical 0Spherical, 0Desig manual,

S~o

Trab ,hs 0_

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