SPACEWOUND COMPOSITE STRUCTURES

'IS CONTRACT DAAJ02-77-C-0016

0FINAL REPORT

JANUARY 1978

BY

DALE ABILDSKOVSAM YAO

SUBMITTED BY: DEC 1978

FIBER SCIENCE, INC.* GARDENA, CALIFORNIA

FOR

U.S. PRMY RESEARCH AND TECHNOLOGY LABORATORIESFORT EUSTIS, VIRGINIA

FIBERI i

: FSI 'sSCIENDE, Inca

Approved for public release

Distribution unlimited

BestI Available

copy

DDC AVAILABILITY NOTICES

1. Approved for public release; distribution unlimited.

2. Distribution limited to U. S. Gov't. agencies only; (state reason indicted in

a, b, c, d or e); (date statement applied). Other requests for thisdocument must be referred to the Eustis Directorate, US Army Air Mobility Researchand Development Laboratory, Fort Eustis, VA 23604.

a. Classified

b. Contractor Performance Evaluation

c. __ Foreign Information

d. Proprietary Information

e. Test arid Evaluation

DISCLAIMER

3. The findings in this report are not to be construed as a n~fia Department'of the Army position unless so designated by other authorized(,documents.

" When Government drawings, specifications, or other data are used for anypurpose other than in connection with a definitely related Government procurement

operation, the US Government thereby incurs no responsibility nor any obligationwhatsoever; and the fact that the Government may have formulated, furnished, or

in any way supplied the said drawings, specifications, or other data is not to be

regarded by implication or otherwise as in any manner licensing the holder or any

other person or corporation, or conveying any rights or permission, to manufacture,use, or sell any patented invention that may in any way be related thereto.

S 5. Irade names cited in this report do not constitute an official endorsement or

approval of the use of such commercial hardware or software.

DISPOSITION INSTRUCTIONS

(6. Destroy this repurt when no longer needed. Do not return it to the originator.

7. When this report is no longer needed, Department of the Army organizationswill destroy it in accordance with the procedures given in AR 380-5.

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE (nonw Date Entered) _________________

REPORT DOCUMENTATION PAGE BEFORE COMPLETING 1-70PJPORT NUMBER 2 OTACSINN.3 EIIN' AAO U E

S5pacewound-pomposite Structures, Final~elt T an-#01oV 79

Dale Ahildskov DA0-7C006

Fiber Science, Inc*.RA&WR UI UBR

245 East 157thi StreeteGardena, CA 90248 E

11. CONTROLLING OFFICE NAME AND ADDRESS

Applied Technology Laboratory, USARTL (AVRADC(M6 I Jana" 378Ft Eustis, VA 23604 .NUMBER OFPAGES

714. MONITORING AGENCY NAME A AODRESS(tV@AWM Controilli Office) 1. SECURITY CLASS. (of this report)

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it DISTRIBUTION STATEMENT (of this Report)

Approved for Public Release, distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, it different frem Report)

IC. SUPPLEMENTARY NOTES

III. KEY WO1406 (Continue on revere side it necessary and identify by block number)

Composites SpacewoundFiberglass Fuselage StructuresKevlar Ballistic ToleranceGraphite Survivabilityai lbooms ________________________________A ASTr (cimitim a revers ebb Nf nesaw an Mni uly by block nube)

The objective of this program was to investigate the potential of the space-wou'it structural concept to provide a ballistic tolerant structure to the highexplcsive proje~ctile. The spacewound structural concept, developed by FiberScience, Inc*, is an open weave wet filament wound composite structural conceptwhich has the potential for venting the blast pressure from the high explosiveprojectile while at the same time providing a multiplicity of redundant load

paths. ~(Continued)

DD JA 73 j ENIOM6OF I NOV 6S IS OBSOLETE Unclassified SLited

__3 8 5 3 SECURITY CLASSIFICATIO14 OF THIS PAGE (V -_6i~nqd

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGK(Sm Date Bne.Q

lock 20. Continued

Twelve 24-inch diameter cylindrical specimens were designed and fabricated byFiber Science, Inc., and were subsequently ballistically tested at the AppliedTechnology Laboratory, Fort Eustis, Virginia. Three materials (Kevlar,Fiberglass, and Graphite), two fiber coverage ratios, and the tse of anexternal fiberglass aerodynamic skin surface were assessed. Based or theresults of these tests, four kevlar specimens with a fiberglass cloth skin,tun with 25% and two with 50% tiber coverage ratio, were selected fnr finaldesign evaluation. Tae final specimens were 16-).Lich diameter cvlirders witha four-bolt ring/frame attachment fitting at each end to facilitate structuraltesting*

The final de gn specimens were subsequently structurally tested both beforeand after high xplosive projectile ballistic tests at the Applied Technologyaboratory. A 'inal report describing the test program and results iscurrently in preparation.,

Mumm I~m hUm O

---i;. i

ILnclassI1ie

Unclassified

SPACEWOUND COMPOSITE STRUCTURES

CONTRACT DAAJ02-77-C-0016

FINAL REPORT

JANUARY 1970

BY

DALE ABILDSKOVSAM YAO

SUBMITTED BY:

FIBER SCIENCE, INC.GARDENA, CALIFORNIA

DDCFOR[gi11l rr

U.S. ARMY RESEARCH AND TECHNOLOGY LABORATORIES ii C 1 197FORT EUSTIS, VIRGINIA H

DApproved for public releaseDistribution unlir.ited

J FOREWORD

This report was prepared by Fiber Science, Inc. in accor-

dance with Contract DAAJ02-77-C-0016, issued by the Eustis

Directorate, U.S. Army Air Mobility Research and Develop-b4, oot

ment Laboratory, Fort Eustis, Virginia*. Mr. Hddle-Been

was the U.S. Army program technical monitor.

The activities reported herein cover the period from

January 1977 to November 1977. The Fiber Science project

engineer was Mr. Sam Yao.

*Redesignated Applied Technology Laboratory, Research

and Development Laboratories (AVRADCOM), 1 September

1977.

SUMMARY

Six configurations of Spacewind cylinders were designed

to a prescribed set of strength and stiffness criteria.

The variables were two levels of fiber coverage and three

reinforcements; glass, Vevlar and graphite. fine cylinder

of each design was fabricated at Fi.'.'r Science and tested

for ballistic tolerance at Fort Eustis.

Four more cyl'r.ders werc fabricated for final testing.

The variable was two levels of fiber coverage. Kevlar

49 was the reinforcement for all four.

TABLE OF CONTENTS

[ Page No.

SUMMARY I

TABLE OF CONTENTS 2

LIST OF TABLES & LIST OF FIGURES 3

INTRODUCTION 4

DESIGN 9

FABRICATION 13

TESTING 15

CONCLUSIONS 20

APPENDIX A 21

SPACEWIND ANALYSIS FQUATIONS

APPENDIX B 31

DESIGN CALCULA2 IONS

APPENDIX C 39

END FITTING ANALYSIS

APPENDIX D 43

MATERIAL PROPERTY COMPUTER PROGRAM

APPENDIX E 49

MATERIAL PROPERTIES, UNITS 1-6

APPENDIX F 56

MATERIAL PROPERTIES, UNITS 7-10

APPENDIX G 67

DRAWINGS

APPENDIX H 69

NOMENCLATURE

2

LIST OF TALES & FIGURES

Table No. e, No.

1 Ballistic Samp]es Tested 15

2 Weight Analysis 19

3 Desiqn Data, Units 1-6 34

4 Design Data, Units 7-10 38

Figure No. P'_e No.

1 Band Damage Data 17

3

I

INTRODUCTION

"Spacewind" is a descriptive term applied to the filament

windiag process used in this contract. Normal filament

winding procedures are very specific in requiring bands to

be exactly adjacent to each other. Spacewind nomencla-

ture for a structure with adjacent bands would be "I.00

fiber coverage ratio." That is, the ratio of surface

area covered by strands to the fotal surface area is 1.00.

Spacowind deliberately requires spaces between roving

bands. The final structure, regardless of wall thickness,

looks like it is made of old fashioned cane or wicker be-

cause thore are holes qeo'netrically arrainged over the en-

tire surface.

A non-standard language has developed to explain the non-

standard filament winding process called Spacewind. The

following definitions will ho!p in reading this report.

Strand A qene ral term 1nd.catiuq an essentially

continuous length of filamentary material,

whether large or small, twisted or un-

twisted.

Band Width A single strand miqht be wound or several

strands might be lathered and wound at one

time. Band width is the width of the total

number of strands wound at one time.

Iqinding Angle Strands are wound onto a rotatinq mandrel

by traversing from end to end of the man-

drel. The angle botwoe a strand and the

4

mandrel axis is the winding angle. It is

both + and - with reference to cartesian

coordinates since the band direction

changes.

F.C.R. Fiber Coverage Ratio is the ratio of man-

drel surface area covered with strands

going in one direction to the amount not

covered, as sketched below. F.C.R. is

used as an easily calculated expression

fer Spacewind.

\ wb'A

W SN axis

F.C.R. W b* b +Ws

F.A.C.R Fiber Area Coverage Ratio is the area

co-ered by fibers divided by total surface

5

area, realizing that bands run both left

and right.

Fiber Volume A second ratio, unrelated to F.C.R., is

the ratio of fiber volume to the total

volume of fiber and resin.

A prior contract, DAAJ02-76-C-0040, administered by the

Applied Technology Laboratory, Research & Technology

Laboratories, Fort Eustis, Virginia, had demonstrated

it is possible to use analytical models in designing

Spacewind composites. This contract was intended to

evaluate the potential of Spacewind as a structure with

built-in pressure relief valves.

Explosive projectile fire directed 3t modern Army air-

craft is often fatal because the overpressure from theI,

blast requires the fuselage to become a pressure vessel.

Fuselages are not designed as pressure vessels because

of a very large associated weight penalty. The result

is structural failure from a blast which might be insig-

nificant in terms of dama(e from shrapnel. Spacewind

was considered a possible solution to overpressure from

explosive projectiles because it has multitudes of btiilt-

in pressure relief vents.

Six cylinders 24 inches in diameter and 72 inches long

were specified as a vehicle for evaluating thie ballistic

tolerance of Spacewind. Three reinforcements, S-2 glass,

Kevlar 49 and graphite were specified for evaluation.

All six cylinders were to be designed to the following

stiffness and strength requirements.

6

Stiffness: EIy = 2.6 x 109 lb-in 2 (flexural stiffnessabout 'y' axis)

LEz = 2.6 x 109 lb-in 2 (flexural stiffnessabout 'z' axis)

GK = 1.2 x 109 ib-in 2 (shear stiffness)

Limit Load: Mx = 1.37 x 10 in-lbs (bending momentabout 'x' axis)

Mz = 3.87 x 105 in-lbs (bending momentabout 'z' axis)

. .Sz = 1.14 x 103 lbs (shear in the 'z'.,,direction)

NOTE: The x' axis is the longitudinal axis S, cylin-

der.

Following testing of these sections by the Army four

more cylinders 16 inches in diameter by 72 inches long

were designed using Kevlar 49 as the reinforcing fiber.

These specimens included four attachment fittings at each

end to facilitate structural testing. The design criteria

used for these four cylinders were:

*9 , 2Stiffness: EIy = 1.1 x 10 lb-in

EIz = 1.1 x 109 lb-in2

GK = 0.5 x 109 lb-in2

Limit Loads: Mx = 1.2 x 105 in-lb

Mz = 1.53 x 105 in-lb

Sz = 2.84 x 102 lb

Sy = 2.922 x 103 Ib

Following sections give design data and fabrication

techniques for these cylinders. All testing was per-

formed by the Army Air Mobility Research and Development

I * Laboratory, Fort Eustis, Virginia.

I' 8

r.F1

DESIGN

Design equations are given in Appendix A and design cal-

culations based on these equations are given in Appendix

B.

One primary design consideration was whether to design

single wall or sandwich wall structures to meet the sta-

bility requirements. A foam core in a sandwich wall

would not be acceptable because it would block off all

the Spacewind holes which were being considered pressure

relief valves. Honeycomb could be used, though, because

of its constrction. Stability calculations showed that

only the fift -percent F.C.R. graphite specimen required

sandwich wall construction.

The structural requirements given earlier apply to cylin-ders supported at its ends with bending forces applied.

These requirements Are best met by strands wound at a very

small angle to the cylinder axis. A hoop load was also

known to be a requirement to resist overpressure load-.

Its magnitude was unknown, so hoop strength could not be

designated.

Past design experience led to an empirical feeling that

twenty-percent of all strands should be hoop, or circum-

ferential, strands. These strands do not contribute

significantly to the strength and stiffness requirements,

but do contribute to ballistic tolerance. The balance of

strands were calculated to be + 24 degrees to the cylinder

axis.

9

TIt i x cy~ I IidIt, wort,.' AwL~ i ca Lteltl r St. I' iw 1~ I In~ *I c

t tod t rt I : I I.,.; ti,: Kov I I r .1') %%F : ' I ecl e 1:: t lit

i11. I ti 1. t'ilon. t 1-. t i oil %I I wo ere, ma11.14.uk I I c r i[I di .I-

t10 t r in ani v t: ft t i 1tit.' ;otIiie Ove rrir vt li. o.id~

*ind t o havo an mort, !,wvro to.-, I 'Tlit'y a 1 sc) 11ad to hadve

klild t i t i ziqs- .;() t hey col'Id he I ).cded . 1 holldu i 11(l at Ic1lc

t 1110 f t t 0 I L' t OS' t i 11(

Ih: it t -a I c ii I a L oi u~l~ br tIlIo I it-t i -,I-; I areo it Appoilui ix C

Tho nCo* cii ce . omp Lu v'Od h; 0110' 1u-SOt 'ii prv i- US Ly lt F ibe r-

8e eice.it y Ie ue to as; el broom. A broomn r LtIiiqi s

( JI*' rV i MiIS %1/ '(' W01I nd i.n tc .1 (A reti Ill- til i d i roo. icim Iti1

~'.:ekat~ nd t-11011 t riUif Crrcid( Lo it nild (. 'Vlie . virt*Uila:

I ()V Iuf. I wo N tit, ri itia't fn tlt te t) I dt Lo makt, two I i L t. I iy

Best Available Copy10)

end to end, as s~hown below.

*A closire flanqo for the cylinder was desiiqned to back

tit, tho t ittintIs and rovings were wound over it as shown

1 Iow.

The attach fittings were then bonded inside the cylinder

at four places on each end. A force applied to one or

more fittings is transferred to the mounting ring and

thereby to the rovings as well as to the rovings by adhe-

sive bond shear.I

These four cylinders were fabricated and delivered to

Fort Eustis for testing.

1

'I

I

L

I

12

__-

FABRICATION

Cylinders were wound on standard helical filament winding

machines. The machines were programmed to give the pattern

desired and that program was used for all three reinforce-

ments.

Tooling was composed of a steel shaft, steel collars, glaos

composite ends and an ABS sheet cylinder as sketched below.

ABS sheet shaft

/ \ collarend -"

Ends were bolted to the collars, which in turn were bolted to

the shaft. The ABS sheet was bonded to the ends and then

was pressurized at 1 PSI with air to stabilize it. The

outer surface was coated with mold release so it could be

removed after winding and curing the cylinders.

The last four demonstration cylinders had flanged end

plates built in. These plates were made from ten plies

of Style 1581 glass fabric impregnated with epoxy resin.

They fit over the fiberglass tooling ends and were wound

13

over with rovings, which prevented the tooling from being

* removed in one piece.

Glass composite tool ends for these cylinders were cLt in

half and sealed together again before the ABS sheet was

bonded on. After the cylinder was cured, ends were un-

bolted from collars and pushed into the cylinder. They

then were removed in half pieces, ready to be used again.

Fittings were made from glass fibers and epoxy resin by

filament winding around two spools. The windings, before

being cured, were moved to a fiberglass mold and deformed

to the correct shape and then cured. The resulting struc-

* ture was two fittings, formed end-to-end. It was cut in

the middle to yield two fittings.

Properly located holes were drilled in the wound and cured

* cylinders. Fittings were mated to the holes on the inside

of the tank and adhesive bonded into place.

There were no fabrication problems in winding or assembly.

14

ID

- -

TESTING

The first cylinders made were 24 inches in diameter and

92 inches long. These were cut in half (46 inches long)

at Fort Eustis and one-half had a single ply of 181

glass fabric laminated on to simulate the skin on an

aircraft. Twelve variations were tested as shown below.

Reinforcement FCR Skin

Glass .25 & .50 with and without

Kevlar .25 & .50 with and without

Graphite .25 & .50 uith and without

Table 1. Ballistic Samples Tested

Samples were held in a fixture and fired upon. Results

were evaluated by Fort Eustis personnel as follows.

Damage Assessment

1. To assess the relative damage to the specimens as

a result of the 23mm HEI-T ballistic impact tests,

an inspection of the specimens was conducted in

which the number of partially or fully severed fiber

bands was tabulated.

a. The number of severed fiber bands was counted

on the top, bottom, and exit side of the speci-

mens ns shown in Figure 1. The damage on the

entrance side was not considered for the follow-

ing reasons.

(1) The damage is relatively small compared to

the top, bottom, and exit. side damage.

15

(2) The damage on the entrance side is a function

of whether the projectile passed through one

or more bands or through the function plate.

b. The number of hoop bands and + 240 bands was

counted separately.

c. The degree of damage (i.e., porce at of band sever-

ance) was estimated as being 25, 50, 75 or 100

percent.

d. The band damage data are shown in Figure 1. The

damage levels were then weighted to arrive at a"Damage Coefficient". The weights are as follows:

Percent of WeiqhtingBand Severed Fator

25 1

50 2

75 3

100 4

The weighted points were then summed for each

damage location and band direction. Then the

points were summed over all damage locations to

arrive at a damage coefficient for both the 24'

and hoop bands.

2. it should be noted, however, that the loss of a given

band in the 25% FCR specimens is more damaging than

the loss of a band in the 50% FCR specimens in that

the band thickness in the 25% FCR specimens is twice

that of the 50% FCR specimens.

--- (4

4

0

04

I-mm T

Samples were given the following code.

First Character

F = Fiberglass

K = KevlarSG = Graphite

Second Character

* 1 = 25% FCR

2 = 50% FCR

Third Character

A = with #181 glass clothskin

B = no skin

Test results are graphed in Figure 1.S

The effect of a skin is very small and perhaps none at

all. Glass and Kevlar reinforced specimens tested quite

similarly, while graphite was a clear third choice.9

Weights of the various samples are given in Table 2.

1

18

Spacewind CompositeStructures

Ma ter7i-a- FCR WeightCalculated ActualNo Skin No Skin With Skin

S-Glass 25% 29.58 33 35.75

S-Glass 50% 29.04 32 35.5

Kevlar 25% 14.66 17.63 20.27

Kevldr 50% 14.63 15.38 18.25

Graphite 25% 9.4 11.75 15.5

Graphite 50% 10.93 12.63 15.25

Table 2_. Weight Analysis

Kevlar 49 samples are 40-50% lighter in weight than glass.

The final demonstration samples were made from Kevlar rein-

forcement because of weight.

9

19

CONCLUSIONS

Test results indicate a single ply 181 glass covering

over Spacewind cylinders has little, if any, effect on

their ballistic resistance to 23mm HEI-T projectiles.

i B Graphite reinforced cylinders suffer more damage, andperhaps less predictable damage, than glass or Kevlar

reinforced cylinders. Spacewind appears to offer a solu-

tion to ballistic projectile over-pressure damage to

*aircraft fuselage structures.

2

20

APPENDIX A

SPACEWIND ANALYSIS EQUATIONS

I

SPACEWINO ANALYSIS EQUATIONSI

The equations used in the design of the specimens follows:

Relation Between Modulus & Shear Modulus

I = I, 3t

K = 27R3t

E _ (EI)K 2(EI)G (KG)E KG

The above equations were used to establish the helical

winding angle. This was accomplished by first assuming

0 20% of the winds would be in the hoop direction and 80%

would be in the helical direction. The properties of

spacewind composites were calculated using the computer

with various helical winding angles and the helical angle

I'9 which satisfied the above equation (E) selected.

Calculation of Outside Shell Radius

1 E R4 41 El = (R -R.)

4 1

Calculation of Maximum Bendin9 & Shear Stresses

Mz

°max -2I ii R t

M SMx +-- -

2m i112 t t R t

22I

Calculation of Critical Axial (fendinq) BucklinStress

Solid Wall Constnictiofl

0t

r cc 0 )

R 0+ R.

,1 0.606 -. 546 (1 nf

2 'x Ry

ScInd(wich WcM I Consitructionl

C (FACI)

Not ti V~ACR - I'ibex Ati ('orak't) )IMc 10

Calclat01 ofC1,I t ial Di svt C11we Iletwoon C'm~ia-OVe

~i'he o li t ic'41 Iinth btwon.I vo0aS-O0vo potul t ot the lwli

edIW i lid i 11IS it" Oc I Oki I d t~d by VejW% t i 11 t 110 ICK I i 119 st Vo-a V.

to the comipreaa live at ren jth of tho hol hxa1 windimps.

2 3

Solid Wall Construction

2 E I

Pcr L 2 (pin ended column)cr

cr eacr t 12 Lcr

Eec

* Lcr 12 Fccu

F. e E 2IIe 2

F - cu 11cu

Sandwich Wall Construction

ii 2

Pcr - 2 (pin orded column)crcr

(cc + 2 tf)

12

t ttf 'y

E

F_ 2u 11

cu 2

24

cr = 2 (t t)3

crr

11Ee(tc+t

2 3

TE- (t +tcr 12 F t

C u

When the core is weak in shear

Ge (t~ + tf0cr 2 t ctf

G e G c(FACR)

Note: FACR =Fiber Area Coverage Ratio

Fiber Coverage Analysis

Fiber Coverage Ratio "FCR"

FCR b~~~- (by definition)b +Ws

.Wb

WS

+ c

-~axis

25

W s (FCR)

W b 2 - FCR

Ss in 2 L, s'

Ws L 2 sin a cos atS

The open area between helical bands is

(ws* Open area = WsL = S) os-Y 2 inqc* ci'

The total area including fiber coverage to mid point of

helical bands is92

(Ws + Wb) 2

Total area = --- I o-2 SIMI, cosla

* The fiber area coverage ratio (FACR) is

Otion ArtvaFACR I otilAre- (by definition)

(w )2

FACR 1 -(Ws + Wb) 2

W (FCR)Note: Wb

FACR 2 FCR - (FCR)2

2

~26

FCR FACR

* .250 .4375

.375 .6094

.500 .7500

.625 .8594

.875 .9844

The fiber area coverage ratio for both circimferential

and helical windings is

FACR (F1ACR)h + [1- (FACR)h] (FACR)c

Note:

(FACR)h 2 (FCR)h - (FCR)2

* (FACR)c (FCR)c

(FCR) (FACR),, (FCR) (FACR) (ACR)

.250 .4375 .250 .250 .5781

.375 .6094 .375 .375 .7559

.500 .7500 .500 .500 .37!0

.625 .8594 .625 .625 .9113 N•.875 .9844 .875 .875 .9981

The fiber cross-over area (FCOA) for helical idndingsis

* 2PCOA b

27

The fiber area (FA) is

FA = Total area - open area

FA = (Ws + Wb) 2 _ (Ws)2

2 sina cosa

The fiber cross-over coverage ratio is

A2

FCOA (Wb) WbFA (Ws + Wb)2 _ (WS)2 Wb + 2W

swbs

Noting FCR - Wb

qb +ws

Wb (I - FCR)Ws5 FCR

Wb IFCOA W 2Wb (-FCR) + (1- FCR)FA Wb + FCR FCR

FCR FCOAFA

.250 .1429

.375 .2308

.500 .3333

.675 .4545

.750 .6000

.875 .7778

Fiber Volume Ratio Analysis

In order for the thickness of Spacewind helical windings

28

to be the same at cross-over points and in between the

cross-over areas, the fiber volume ratio "Vf (ratio of

fiber volume to total of fiber p.-us resin volume) at the

cross-over points will differ from the fiber volume

ratio in between cross-over points.S

The fiber volume ratio at and between cross-over points

is,

d 2 (two plies of windings)too - fco

-b-o- (one ply of windings)o Vfbco

Assuming there are no voids,

VfcoStco = t and Vfbco 2

As an example, assume the fiber volume ratio at the cross-

over points V fcO 65,

then between cross-over points the fiber volume ratio would

be,

i =, .65Vfbco .. 6. = .325

The desired fiber volume ratio assuming no resin bleed

out for fiber coverage areas of 25 and 50% are,

FCR = .25

29

FCOA = .1429FA

V f .1429 x .65 + (1 -. 1429) .325 .3714

*FCR .50

FCOA .3333FA

V f .3333 x .65 + (1R .3333) .325) =.4333

f3

APPENDIX B

DESIGN CALCULATIONS

31

DESIGN CALCULATIONS

Units one through six

Design Criteria

ID = 24.0 in.

L = 72.0 in.

Stiffness:

EI = 2.6 x 109 lb-in2

y

El = 2.6 x 109 lb-in 2

GK = 1.2 x 10 lb-in

Limit Loads:

Mx = 1.37 x 10 in-lb

M = 3.87 x 105 in-lbz

3S 1.14 x 10 lbz

Ultimate loads = 1.5 x limit loadsI

Construction -- 20% @ 900 (hoops) and 80% @ + 240

Fiber volume ratio = .50

Fiber coverage ratio (FCR) -- arbitrarily selected at

.25 and .50.

3

32

1'

Analysis

I

The material properties are based on computer analysis

inputting the fiber and resin properties, fiber volume

ratio, fiber orientation and fiber coverage ratio. Appen-

dix E shows the composite material properties for the

various materials. Note the helical winding angle was

arrived at by an iterative process where the relation

between the E and G of the composite satisfied the cri-

teria stiffness.

Table 3 summarizes the calculation for units one through

six. The equations used are shown in Appendix A and all

stresses are for ultimate loads.

33

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OLHH in ~0 kO o w w wLM Ch CL HL0N L 0 0 m mLAL

o r- o o oN 0 v oCooo o r -4o H L N w v -X tn m LA o tL n H in HH .H r-4 oC %oN N4a D m e -r0 . 0

aN HN 1 C 4r C H LA4('7 co-4 r-

C.w

C) n mA 0 CAW0000 v O N N- W O Hr vr- 0 aM0 NninH N CA.D. COCA MN P4 I P-40 %0

cL r4 N N4 N r * H CL'. C4 4-)vJ in H H (4

o4J

4J-

O~ ~ w'00 NN H HO~ 0A 00.'vON OH wv ww 0Xi ini O N 0. N N~ 0 ,C4A4w%'.nc O - 0 H O'. w w

NW H0H 4 H )

E4

*n N n M. NLn LACOWCO Nn O A O M tWt nC ni nL Ln CAm LA L LNCA w'Dn~n.O m Fr .f-N 0 w (

in inN NW4 C- co c Ln n in N N *'-4co N w)

.w rA N 4 H H in LA(' H Cv in U)I

0c(0 4.4

* '.4

4J40

04 toU U) M 0H 04 04 04 '-H U

'.4 w. (n U 4)1 10D .4 0\ 'o *4 Wp M *r C ArH o - 00 C) 04 D4 z r

cdo H H- H- r-i -A%- .14 H.-

>1 U U i L U) u U)~ 4

I' JA

CALCULATIONS FOR SANDWICH WALL CONSTRUCTION

t = .25 in.

tft .0527 in.

Ge .750 x 3000 = 2250 psi

0c = 2250 (.25+ .0527) = 25,847 psi

35

Units seven through ten

Design criteria

IID 16.0 in.1L = 72.0 in.

Stiffness:

$ E1~ - .I x 10 lb-ira2

El 1.1 x 10 lb-in2

GK 0.5 x 109 lb-in 2

Limit Loads:

25Mx 1.2 x 105 in-lb

M 1.53 x l05 in-lb

S 2.922 x 103 lbyS *= 2.84 x 10 lb

Ultimate loads 1.5 x limit loads

Construction -- 20% @ 900 (hoops) and 80% @ + 240

Fiber Volume Ratio -- .65 at cross-over areas and .325

between cross-over areas.

I Average 'iber volume ratio for .2S and .50 FCR are .3714

and .4333 respectively.

o Fiber coverage ratio -- .25 and 50.

36

'ohe nldterial proportion are shown in Appendix F. Table

4 sumarizes the cnlculations for units tsovan throughton.

m,

Proprty____ ________KevIar 4-/Epo:y

* |Vf, % 32.5 32.5

E, l0 psi 6.492 6.492

F.C.R., % 25 50

FACR (hel. only), % 43.75 75.00

" FACR, % 57.81 87.50

EX, 16 psi 1.553 3.156

E ,10 psi .5232 1.119

06 psi .7827 1.6522-,R, in. 8.4081 8.2084

t, in. .4081 .2084

Ri_-,____8.2041 8.1042

0 psi 2659 5337.1 ,psi 1459 2919

I i 18,399 18,259

F # psi 5558 11,241

F psi 1837 3958

F ell 11 11,375 11,375

L ,in. 6.2521 3.1927

Wso in. 4.6462 2.3726

Wb , in. 1.5487 2.3726

* Pc' Ib/IZ 2014 .0231

Table 4. Design Data, Units 7-10

38

APPENDIX C

END FITTING ANALYSIS

39

Frame

IInternal member loads were solved by a computer program

with the following assumptions:

EI = Constant - MX

Loads reacted in a -Q or - distribution

Tho critical loads are summarized below.

B V P M

55V -20 lb -2281 lb -1038 in-lb

2100 26 1608 1137S2250 -1265 -3319 740

3150 -1265 -4094 739

Section properties of the frame (E-glass)

22 '

.16 .04 .0064 .0003 -- 3.25

$ .26 1.625 .4225 .6866 .2289

E .42 .4289 .6869 .2289 .08"

- .4289 _1.02 in.42

y = -4 .2i

I = .2289 + .6869 - .42 (1.02)2 .4788 in4

Maximum stresses are:

. 094 739 x 2.23 13,189 psi.42 .4788

x - 4,518 psi| ~max x.42'

40

i 7

Attachment

End Frame Limit Loads:

= 1.2 x 105 in-lb* 105

M = 1.53 x 10 in-lbz

S =2922 lbsy

Ultimate load = limit load x 1.5

zBolt loads -- 4 bolts B

Vt

153,000 x 1.5 591 lbi * P~~~x =2 x 14 cs4 i " ,V

V = 2922 x 1.5= 1095 lb Vtt YV y -4

= 20,000 x 1.5 = 6428 lb - Vy* Vt

Resolving V to the tangential and

radial force components

I Vs = 1095 cos 450 = 774 lb tl

Vt = 1095 sin 450 = 774 lb-- 774 lb

* The combined tangential and -

radial forces are . .

(1774 I1b))b

Vl =6428 +774 -7202 lb lb

VT2 = 6428 - 774 = 5654 lb Vt2

41

Lj

Fitting

Use 1/2-20 UNF boltwith 180,000 psi U.T.S. 8

socket head cap screw

11,591 lb 7207 lb

Fiber stress

~~2 x 119 x 28,977 psi

Bond stress of broom

*1191x 2T 8 x 8 x .4325 = 827 psi

Shear strength =180,000 x .6 x i~(.25) 2 21,205 lb

Bond stress of fitting end 2" x 2"'

(7742 + 72072)1/ -105ps(2 x 2) -(rx 252) =10 s

Bearing stress on metal insert ~ 0"au 01T- .10" S-2 glass

* 0 br - (7722 + 72072/2=1,4 ps OB gaslmnta br (.5) (.4435)1633pigaslmnt

_.204" spacewinding

42 .06" alum 6061-T6

-443

IS

SIliii I

APPENDIX 0

I MATERIAL PROPERTY COMPUTER PROGRAM

I

II,

It

I, i~43

~tiS

MATERIAL PROPERTY COMPUTER OUTPUT

NOMENCLATURE

AF Fiber thermal expansion coefficient, in/in/F°

AFT Fiber transverse tIermal expansion coefficient,in/in/F0

AR Resin thermal expansion coefficient, in/in/F0

AX Composite thermal expansion coefficient in x-direction, in/in/F0

AY Composite thermal expansion coefficient in y-direction, in/in/F0

EF Fiber modulus, psi

EFT Fiber transverse modulus, psi

ER Resin modulus, psi

EX Composite modulus in x-direction, psi

EY Composite modulus in y-direction, psi

FCU Fiber compressive strength, psi

FTU Fiber tensile strength, psi

FXCU Composite compressive strength in x-direction, psi

FXTU Composite tensile strength in x-direction, psi

FXY Composite shear strength, psi

FYCU Composite compressive strength in y-direction, psi

FYTU Composite tensile strength in y-direction, psi

GF Fiber shear modulus, psi

GXY Composite shear modulus, psi

RHO Resin density, Ib/in3

TF Fiber thickness, in

UF Fiber Poisson's ratio

UXY Composite Poisson's ratio

UYX Composite Poisson's ratio

44

PROGRAM SvPR(INPUT,OUTPUT,TAPE5=INPUTTAPE6=OUTPUT)

GOMJ31 REA0J(5929(H_-.ADU(1) ,,1b)0050i5 4 FORMAT(1A51.JCCO15 IF (r-OF95) 10i)94

000036 5 FOkNAT(2F1G..,2E1J3v1I5)OC6036 WRITE(6q7)H-..AD

40L,0447 FORMAT(lHlv,16AS//J006~344 I~K=ER/ (2.(1**UR)06LO50 WRITE-(699)RHORqURvER9GR9AR

00 65 FORMAT (5X916HRESIN PRPRI-S1X4ROFe9X3U=~~rtHR

0908365 WRITE(6913)00O1 0 FORMAT(5X,16HFI93E PROPERTIES//5Xv1a7HNO* ALPHA TF VF

I EF L.FT GF AF AFT 'iF. h HOF FTU FCU C K 1

004^007 Ra1±~jsG OZ? RQ12=6'4

064,072 RQ22:=Je

O~C74RS12='4.

0000~76 S20OCC377 RSb6=.3.a 0c 10a TT=J.

40LIC1 HO=O*Of4C1D3 00 23 I:±..K

C&CUC4 REAO(5,12)A(Ib ,TtIhRHOF(I),UFII),VF(I),@EF(I),EFT(I),GF(I),PAF(I),A*

d~i,141 12 FORMAT(5FlO.4/5EG32F~.4/FI .e4I

Ot'C2LI 14. FORMAT (17,Fb.,22F8.*.,5rZ12.3 2F8.44,2F10.i,1F6.41

GOUO3 FCU(II:FCU(Il4VF(I)00 205 TT1TT+T(I)

066211 =I)5*97OCC 1 3 Sl=SIN(Al&GL 15 S=i*CCL216 S3SS4SZ

0 0 1, 222 c1:03S(M) yQhLI'rl'*

i6OL225 C3:c1~c "Is R

OCvr227 C4=C2**eOCC231 SZ4=SIN(2**A)

OL 245 IC) ZtT I N U

r 45

&L'252 CzS.FTVFIl)OU254 L=-F( D 'VF U) t(1.-VF(1) )!?.P,4L262 EcG=..FT(l)

I Er0) )0<.K(D)GC3 2 UTL=JTLT/L"

OLR5 U=1-ULT4.JTL

Gu324 I~ C ON TI nU6aL324 EL=EF(I)CLS26 _7T=_F(I)LL327 UI-F1

2(Ilzi/+UETCELS44(2. LUTL+4 .*U'GLT)*S2*,C2)00365 3-,() I / 4 ('L L - o :* T ) S 'C + * L * C - 2 * '2

4L 312 ( r) =1 0 /U,, i : -T4s4jGT)*2G+_ *TL (C4tS4.)i416 B167(AT)~i/J = U _T,_*T- UGT S l E-LUL2**LT*IC

c)GC437 L33(I) =1s/ U+ ( :.- +T- *L)(,-Lur_2**LT 3C

C)

~OC473 t-''L/ LLC4..+*5(-L/tLT-2ULT)S2A*S2AI

UJLS24 UI=-4/.*UT-2*I *UTEL,---,/ )S2A*S2A)

IC541 uZ=JZL)i4;C541 M1S2'*( U T+ L/ET-.5 W-. GLT-C2U+I," ULT+EL/ET-L/GLT) )

~L5/L

GL623 32

&L656 8=SAT(VF/3:..5926)

OC-71L AT= (A #a3b+Au'~R* (1 9-35) /ET

WC22 A2=A6*S2MT4'C2GE726 A22~A-UI~

W7 6T1 CL) Z6*T(I/(1.-Ul2'U2I)

EL744 A t'I II-A 12+ 31%/LL,751 42C 1) ~A JEGULL

STm' NoTt1 vUML6ULATIO~NSCL757 L.T=.GL757 ULT=Jo

L£C7b Ij U1 :I

6b763 UJ2.i./( ;*PI (_+.+TL, _UTcT

Ili L E)U--= (o s;. PSi) (--L4T- (L)TL*LULTE) - 4 PSl4'LT)

46 THIS PAE IS BEST QUALITY PRACTICART,L FR~~~om c4Y YU1lSkiwi 1' D.D Q

06 "33 Q12ZA(I I 3*U +U2+J3+U4001&4C 1N(I)=3.4 UttU2.U3*COS(2.*td+U.4 COS'..*A)

6 1057 Q12N(=U1U2-U4COS(4*'A).A~17L12Z*'DI~=3,*U1+U2-U3*C0S(29*.A )+U4*COS(4o+Al

0Gi1C6 Q6b-1(1) =U1+U2-L 4 0OS (4.* A)00111?7 A=*7353 i-A0u112C Q15l=o*lU 3CO(*A+U*O(9A)

(OC1137 Q.aZ() U-U2-U4*COS (4* A I001150 a22S(11=3.*U1+Uz-U3*COS(29*A )+U'.'+COS(4.*A)t001166 Q66S(ID=U1*U2-U 4 &COSf4o*A1001177 2., CONTINIJ;

4&12U~lRHO:iHO/TT

001203 312=19f~0412C4 3822:0

Q012i6 SAI13*601207 SBA2=0*

j 001,713 00 304 I:1,K00L.214 PRH0(VF (I)*RHOF(I)+(1.-VF(I) *RHOR)*T (I)/TT+RHOOO 1225 3811=9311811ui)ru.l001227 382~1+1(*

0012321 Sa22=$35Z2+2(I)*TI

00131+ UXQ12.1&22ITI/TR

0013252 RQ6x=66N(D+1i /T001255 RS.4!=tISDTD/TR1

OC123 2 Z: Cz U2 2(IT T( T+F

QL12 GXY::,266XY/TT (I/TR

001271 SA =3A/ 51(*AB(

IO.136iS3 9 T1 wI(,2 1xuyEYuxGYHx

001SL5 X=rA-61Z3/3HM:8.2/ 5,5H

001355 UX=31/B2

oc.13ISI2i EY=QYTLi 3I X:-B3

) ,, V7 XUFU )(~.LR2- Q2Rj)/01 )aR0ZQ2()k-200O14 6 FYUFU(1 1 2M( *QIQ2(I)* 2

a41425 FSCU=FCU'U(4 ~ S2-SZR1)(QI()R2-QCLI*S2031435 FXY =FSTU/((l.+(FSTU/FSCU)**2+FSTU/FSrU)**.5)/29301446 24. WRIT-'(o,2o)IFATJ,FYTU,FXCU,FYCU,F(Y

* L1466 CONTINUE4 C01471 GU TO 1

CG-73 E ND

Tois PAGE is Usn! QUATATY PRLTCIO

48

is

- APPENDIX E

iiMATERIAL PROPERTIES, UNITS 1-6

49

S-GLASS/EDOXY

- -R40= PR0412IE UR= .3500 ER= 4*70--E+05 GP= i*7GiE4U5 AR= 4.010E-0

FFRPROPFRTIES

NO. ALPHA TF VF EF EFT GFAr

1 9100O e2000 05003 i.26GE+G7 i.26E+07 4eOjCE+a5 292GUCE-6 ---2

2 24.00 09000~ 0.00 i.260E+07 I .260E+07 4.CCCEafl5 2.23tE-0~6 2

CO?4PISITE PROPERTIES

-EX= 89536E+05 UXY= .-4794EV= 1*957E+fl5 UVX= .2222GYY= i.961E+CS RHO= .0164

--- AX= -3*826E-06AYz 1*533E-05

NO* FXTU FYTU FXCU FYCU FXY

1 20800 0,382 13760 5545 37352 - 20M0i -- 6782 -. 13760C.-- 5545 33

MAt O0L-X 7,=JSMi TO DDO -

50

I 17-4iE4O S AR= 4. CE-0 5

GF AF AFT UF RHOF FTU FCU CK

-4.~)E+--~2O~-Q--Z.2-~ -. 20~*C900 -325001 2i5G(,*3 925GO4.CQ0GE+t05- MOU-06 2.20JE-06 *22GG .I290 325000 215OGG *25C0

fXY -- ------

735

1 P---13-i- . - ----.--.-..---

1~~..--~ e ~~--

5-GASSEPOXY

--- ,RESIN FROPERTIES - -

RHO= e0412 UR= .350f ER= 41,70DE+G5 GR= 1*74iE405 AR= 4.t3MJ-05

FIBER 1OR11PERTIES

NO* AL~FlM TF VF EF EFT GF AF £ AFT

190.130 .2000 .5000 L.260E+Q7 i s260E+&,7 4*G0OE4C,5 2.20E-6 222 24#13 98060 *503i0 i*260E+0? iZ60F+ 7 4 CBS'.E+C!; 2*21DE-V6 2e20

CCIPOSIT PROPERTIES

* --EX=- i,774E+06 UXY= 44677EYz 9.287EO05 UYX= *24.44GxY2 d.236E*os RHO=0.0328AX= 7*622E-D7AYlm l194E-D5

NO. FXTU FYTU FXCU Fycu FXY

I 423E4I 17271 28C.25 11426 811

2 -42364 17271 28025 l1426 83C6

NdS P AU 18 5I=2 QUALT A=AAXXZ

I 51

~7i4S AR= 4 O-r

GF AF AF UF PM0FFTU FCU CK'

*GOOEtGS4- 2*20TE-E)6 2*2G E-0l6 .220 32560C. 215000 *5:v;.0~ECI2.2ODE-P6 2.203 E0-6 .22LZC93 25 l 21500C *50M~

0606

1454

~CVL4 49/, :jXy

NO- ALP4As TFF VF AFAF1 9 J L .2 . 1 j 5 ' ,.~ EFT Gr A2 j L 9, AF

C OiPOS I TrPJ~-TZ

X. Yz 2 , 4633

AY: 5

NO. xT FYrU cu FYou1 '41~ 215i3X

2 r$. 762

I. PflIBS PAUJ IS BEST QUALITY 4M

MWe OWXP MWISHO TO DWA

52

GFAF AFT UF RH OF FlU FCU C K

a E + 5 -.44 C 6 3.6LGE-CS .22CO .0524 '380C00 ~ O *5

O4E~5~ 3*44EZ-. 3*30OE-05 *2200 .0524 380000 70000 .2500)

lk)

4EtR'9/EPOXY4i

--- RESIN -PROPERTIES -

RHO= *041? UR= .350 0 - ER= 4.7-CCE+05 GR= i.7441E+05 AR= 4.013OE-05

FIBER PPOPERTIES

NO* ALPHA TF VF EvEFT GF AFAFT

2 t4.00 .8000 0500a i.900E+07 .ocoOE+06 34C00E+15 -3v440gAU6 3.0

COMPOSITE PROPERTIES

- ~ EX-2*529E+06 UXYz .4707EV= l.100E+C6 UYY= 02063GXY= So804E+05 RHOz .0234AXu -1*103E-05AY= 5*396E-06

NO*- - FXTU FYTU FYCU FYCIJ FXY

1 48792 l9702 8988 3e2q 3256

2 48792 19702 4986 3629 3256

53

74!E45 AR= 4.C33E-05

GF AF AIFT UF RHOF FTU FCU CK

.OCCCE+05 -3944CE-66 3*0,Eu *0 9C524 31U, 70OU .5os~*CCDE+' 5 -3. 4 40:-tjL6 3.20E- 5 .22cC .C4 7CO 5C

6

IV6V

...hOREL3030/EPOXY

---~-~RE~tPRPERTIES-

RHO0= .0412 UR= .3500 ER= W.OE405 GR= 1.741E+05 AR= .O-i

FIBER PROPERTIES

NO. ALPHA TF VF EF EFT GF AF

S1-90*00 *2040-- 95000 39400~E+07 i*3COE+06 -- 7.5CCE+fL6 .-- 2*404E- 7----2'4t 24.060.8000 .5000 3*400EG07 I*300E+06 3*5rVE+C6 -2*400E-7 2

COIOPOSTIE PROPERTIES

-2.20 3E+06 -- UXY= *4781EVA 9.*10 3E 05 UYX= .1975

-GXY= 4*968E+CS RHO= .0131AXm - '8.847E-06A'V= 3.;277E-06

N-ws ----- FXTU .FYTU FXCU FYCU FY

120696 M34 03691 5500 36128266- - 314 - -13691 - 5500- 3612

)5

*741E+05 AR= 4,)I-1

GFAF AFT UFP HOF FTU F rCu CK

S.CCE+L6 -- 2,*40E- )7- ---296E-06 .Z22irC *636 ---325064 21SCIV 92;

3.5'CE+C6 -2.lOOE- 37 2096!E-06 .22C- OL636 32500C 2100 *25uQ

1212

~41

4

J~iOR~L 30/EPOXY -

:,*ESI , PROPERTIES-

4140= *0412 .UP,= *35i30 ER= 4.?OE+05 GR= 1,741F+035 AR:; 4., -US-

8I~ PROPERTIES GFA -,-A

Nb. ALPMA TF FE EFT FA

1.- 90.01 -. 2000 45000 3*400E+07 134CEO-06 -3.500E+C6 -2.40OEin4 2.2 24,30 46000 450 Z*400E*07 io3VCEU6 3*50eE+C6 ~2940E-of 2.

COM~POSITE PROPER'TIES

SSY 4*484E+66 UXYz *4607EYx 1*91AE*Cfi UYX= $1969GXY= 10039E+06 RHO= .0262AXm -L'.869E-06A Y. 3*107E-C6

.-. No* FXTU FYTU FXCU FVCU FXV

1 4196? 17003 27759 li?48 787'_241962 174C3 27759 11248 7P?7

MOT

741F05 AR= 4.IOE-05

*CEC .. E- .6E26 .36 35h Z5JGF I AF AFT UF RHOF FTU FCU CK

7

A

''A

Ws14

4. .~ ,-''t4 ~ -,4 - - - -- - _ _ _ _ _ _ _ _ _ A s ,-

''A*R

I

APPENDIX F

MATERIALS PROPERTIES

UNITS 7-10 1

56

I

ii 56

CI

-4

K EVLA4P 49,iPOXY

PESIN FPROPC.RTIC-'

RHO3= o C UR= *Y :7, 4*7Ci +'5 GR= 1*74iE+C5 AR: 4,6&&E-05

FIBER PRPEIRTVS

NO. ALPHA" TF VF EF EFT GF AF AFT

1 aCc a.,hc q5uv, is9)cE*Z7 iscC%.E+C6 7.W+5. ~ ''

2 24.~, ;) *60 1*9OC*a+ 7 1 0 C- + U"6 0 +.~C3 j 5

COMiPOSITE PROPERTIES

EXz 15 5 3-::+ 6 UXY: 415977EY= 5*232E+(5 UYX= *21GXYz 3,571'-+C5 R$4Oz #.20AX= -2,12.E-C5

NO. FXTU FYTU FXCU FYCU FXY

± ~ ~ 73 5~5 ~ 17E5 ~ 2

2 3 0 5

57

41E+G'S AR= 4*6&&E-05

GFAF AFT UF RHCF FTU FCU CK

C. c+ 5 3*44(7.-C6 3.uU03E-5 ,22CO *0524 33U0U TOM13 025DO0 r -3944E-36 !*OUCE-zro 222t. 0 052 380000 70000 02500

FKEVLAR 49/EPOXY

RESI'4 Kl~PiRTITES

RHO= .14,12 UR= '351,0041 ~.0 GR= i.7L41F+5 AR= 4.CO E-5

F19ER PROPERTIES

* NO. ALPH-A TF VF EF EFT GFAF AFT

I 9 3 O.5sP *5lz1 1.9Z.OE+07 i.crc~E+L63c ~ +5 4~6 3.00

2 24 *6500 1.9 n0E+37 ±.0C~t6 3.100E+u5 .3 440t~ 30

COMPOSITE PROPERTIES

EX= 3*156E+C6 JXY: 9576~2EYz 1*119E4-t6 UYX= *244GXY= 7*34EtS RHO= .0241A~z -1e168E-Q5AYm 5*739w7- ~l

Noe FXTU FYTU CXCU 1"YCU FXY

1 6~'1ii424' 3640 3958

2 V3 S 36~81 40C3

'4I 58

741F+fl5 AR= 4.O02?E-05

GFAF AFT UF RI40F FTU FCU CK

O*C C+ 3 5 -344tE--u6 3.OJOE-351 *22C5) .0524 3 SIM 7coo0 15E000. -~2+05 i-3*440E-06 3oOODE-05 .220O 0 0524 38DO 70000 *50co

'(EVLA.' 49/EPOXY

RESIq' PROPRTI -S

RHO= *0-.12 UFk= *350 47.. GP= AR7=Ei5 V 4.5V 5

FI;3'P FRPEPTI:s

No, A~LPHA TF VF EFEFT GF AF AFT

2 24.J *JI. .LEO7L~~ 1,0)Ec+05 .3#44Ci-36 3.GJOOE-!3'

COMPOJSITE PROPEiTIES

EX= 9*65;E*%5 u~v *i7;EY: 5ol6.E+C5 UYX= .2337GXY= Z-*.j--+CS PHO= s.1114

AYz 5*58sbF-Cb

NO* FX TI l FYTU FX<CU F Y CL FXY

966 3441 7612 -3 374 95 u 3--105 1.751 l

59

17 1 E + 15 AR=.d2EE

GF AF AFT UF RHOF FTU FCII CK

C -3*44cz-te 3,13'43-,45 .0220 .0524 3aoocG M0O0 .2500

1 -53 +05 -3.*.iC-- 395aE 05 *22C .0574 38E000 7000C .2500

I;

KEVLA'R 49/0POXYV

RESIN PR OF .T IE S

RkOt= .41 ti- 93515 ;-R= 497[-%.fiEK35 GR= 1@741E'C05 ARZ 4, 00'E-cs

FIV3 R, PROP$EP R IES

NO* ALPHA TF VF EF EFT GF A AFT

± 95J 3 19i0.070 .OO-+ s -3*44CE-- 6 30112 24.~u 803 *,3323 1.9 GE+07 1*6G&E:.-6 7.4 +5 -34dE -3~

COMPOSITE PROP-ERTIES

EX= 2Z41--+V6 XY= *4213Ey: i@1C4--:+Vb UYX= s2176GXY: 5o1.8E+C5 RHG= e.L231AX= 1~EECAY= 5o256E-CG

NO* FXTU FYTU FX(;U FYCU FXY

I t+-1 19677 794S 3625 29232 4*283) 19FI32 7699 3598 2qcG2

oft

60

I 1-EC5 ARZ 4. gOCE-05

F F AFT UF R F FT' FCU c CK

~OV+ 5 -3.a.4 4CE - 6 ~22C,0 oC5?4 3s0c0 7U0 0C0+OQ03+5 -3 *44.-Z 3.30GE-05 ?2 3 C524. 383000 70C&C 05000

5IwoI

-r rufir~ .ni-~r~~u h8 PAGS IS MWi QAl? IIAXA

F16'cR VOma-T17S CC"SIN PROPECTVrS Compo"

VF ", 5 E F r + A;, = 5~7 5, EP t4,7 f;+ 5 RHO=~4 tF T= WR = R 4.%CFAR r FTUZ

R~'= Cj524 741"+~ HOP= .:U2 UP .35!' FrtJ:F1'U =325'PC.r AF -?Lc- FSU FSU

UF =

AI')HA EXv FY XY UVX FXTLI FYT F)

69 ~49'3ZE+ E, 6*qE45 2,:88F+C. **tr 7i *0* CP" 2. 2 2£. r 69?+ .'+ .34 '3'5 1L5375.5 I !Z

L-u 6~. 1 4~ 64992E*LS z,i~lFK5 *-let -^3L4 i C4 6 33 a33o r)*449E~f~6 608r1 7 .252-.C S .3?1k * C 7Lr-;5'.L 41 o4 7 3 2t. C 6.41 I!P +O, 6.97iE;+Ce5 1779T+ r 0149! * 739 j,17 5 *9 66. 4 Us.c z 6,,3? 2E +(1 6056E+C5 a5 4 " F* i5 .37ei .4' 99694.3 11349 221

6.U'L 6.3i3E+16 6 0 ? F -+~ 2o73AE.,- .3999O .43 T72'73 o5 149.0 225 T~!iE + 9 6,9.9IE+r~ 4. 2 3 , r L. 7 94546eq '4, 1 220

9 oC 6PELE+ fi 7 0 5 1F 6 517 81 ~391 a7 3311 21.

110~ 4.9 R 9E+, 6 0 37 C*M7 r ?.7E+. "t Z2 P5161809 42 1 7-115.2 478qE~tvE S a 790 +5 7,26'E-+. .%3 .Ti 97 148*5 Sij I. I

5iO ?.1;4E + C6 E) 0.~ ' 6 gr28 +t' C, m 6 .g+ r'64 \ n I~~~3.2~~~~1 . 7817t6 6'?+~ .e4 4*37 2-3. 1

2 1 .~~~~~~~~~~~~L~- 9ci~ ~ 6 1 ~ t ~ 3 E ~ :.. 3 j 7 . FI

r5. C 11I4<t 1."i(p' 67797E 66.t I* 3.C 1.%. .6~r 5.riE :.6r. t.4S 12~t 64443* 6

f* 6 6 + , 7 ;+ S44. 7, '~ '~ 7.C 3c ~ *~'12 9~L& *72 1z85, 5 447.

o,, .75q + 6 6 49 -- ' 7 26 1 4-T,611

4 . F P+ r F, r,4, 7+ F 7,,7----E L - .6 15 74 1

AR PHO J o, I-~~~

FTU= 1

8:138 AS It IS ? QUAIT P OZO

3t~4 FV~j -

e cu

46±56 3~-c 3 4yJ-

2 73 5.

"7 4 6.7., IZ54,

(17 172 1:,6?.

945460 14, 9*4.

R39 . 6 242.1

2-129 -816485 4 4.59

'KEVLAR 49/c FOo) 00 rg IPS6 9M QUAMY lraMMIT4ld

VF~~F = r5,EFT= ±.vp: = IE COErfF . 5 = 3 . CfE 5 AR = 4 .3 .J;97_CUFTUq AF FS u=AFu -=O = -3412

3 .3= .3:UF = 22IDAT 5FU

ALPHA EX EY Gxy UyFXt ~ t

4,8 a~! i 5 ! * 72 6 4 E + V 2 * 4 7 6 E + C 5 - 2 6 5 5 # 17 -7 5 z 1l? mJ O4 51 *2,4 E ,C7 8* 4 E+p -283 *PJ87 2; V 4 .* ?' 4 514.~ O 1.Z~ L+ 7 8 2 ! , 3 .C5? ,j -V5~ .224 198957,C)1 45.9iE0i1 1. '1.~ 9 .7 E r.3746 # l~ 9 6 1 21 7 45'7 0 2 1. 31 E C w. 9~ ~ 9 7 7 0 ,E + C . 4 2 1 8 ~ 8 1 5 7 . 1 2 7 q 4 4 .:Be~ 80!69E + s 4- 2 2 81 +& * .4769 1 8 5775, 5 ?3.L 3 4 3'~ lsl 43L7 8 7 E ~ . 7E + -46 9~ *L3? 1!'744 . F ± j12.3~ l.~~ Fj+~ 7 7.9~ 3?E4 7. '2E+ J5 * i9 Cff;i ~ 4~ 47 ~ ' 4

2~o 3 ? 4E 46 38 - 4 1 1 '

RoiZ (+ jc . 7E+ ch 4. 5 76 3 rO 1&26 . r, P. 1 .o J ':c~ 4 ' . 9 8 7E + ~E .. .5 4 -5 4 6z 1 4 9 87 , 1.3 ?

14 A.

9~ SaE 7* -E~~j

k 62E-?

-CV'IP03 ITE DMI7TTICS

= '4.TCRHO= 9 C.4115AR FTU= i125,.0o

1 UP FCU= TO5."

FXTU FYTU FX CU FYCU FXY AX AY

2% 416,41 47 9 452? ,'. 297.,3 193.P -1 *529 -. - 6 2,4 . -29E25

21 9 8957. q g 7 45 ). 29 l, 197ro.5 -1.668E-3 2,25'-C5

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52-.1? o2. 7 2q?.? 4357,9 -316.-.1 2q 12-9S

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-1 t -19 7 -2o'7'

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8 96523.5 7 3j,5 4 237,5' 27PA.? 6195. -2-997-'6 ?12E-05

7 3 5937 -4458- , r -. 45 -E-(5

5 738ZV.. ?43'.91, 2:'7 . CF ?734.t3 8qj2.7 - 9 :-, 2.767"-J )

6 ,%7a .- 26, 6 2.35.3 26 , 9617.CT -5.6.2C-'6 Z.79"D7 1372o 297-, 2 ?3544. 67i,3 1)332.6 -5,95-.166 29 ?28--9

7 61 75?,. 2L. ,..) 237.6 175o.9 -6.'5.--06 "I 53*. , L-3. :".6a- , 2 '.9. :73 *47 ,7- 2.49 S "7051 , 91.0, 1 1 4 o,' 3 :, 6 k A74 o7 -4,29 -3 2, 6 E -1

;17,9 26 4. Z53 55*6 3 2I, 61, 4 96 * 6,,-. 2 5 3,.- ,7 - ' 2. 7 E

7 63479. b?35 9372.1 "1354 E7.L1 .7 -. 715.-26 2, 67 - 5

63 774 1 , 262,170- 1 7 9

79 3,. 194 26- s r; .2 o5 -7,533 --- 6 -?-LC S?1 25.Z_5 r 31 F. 576 , 2Z .r. . 1 4 5 4 -7,3 50-1

72 2134.7 5..'K. s .q 'ie. -1.465-. 7 6 E Z

S 2}'2 S . 3'i.2 1 .9 . 3. 7 169 o 5, --, A -

;'? 3 ?79 4 ? 7., ,5 9374* 2. 3 ., 2 , o.F 0 -!. 76-3 5.6f'-

75 15"2 o. 7 4 7' ?r 3t . ,5T . p 1757,4 -3,912- 6 A 47 - 5 '

[ KVLM 49~(~Y"is PaLPI I= QUMATKEVAP49rOVY " vjj a 1WS113 TO DDO -

FF-RRDOTSPEST N P" -P;kTTS cdoo~

VF *31 1. is f u-+7 VP *2A6 P z 4.71 CE+&5v R H f

WC .42903 EFT= i.VEG'+! = *57L.R ..- SL FTU: I

P *ti 5 . 23? GF ., , UF +-C RHIR= *,412 FCU=FT 75 ,3o AF =-2,.XO-E~ 06 SU Al FSU=

FCU = NC-* AFT= 7.3Z'.AE-05UF = 2 r

EYH = GYY UXY thY FXTU FYTU X

7, ?352E-+LF, '164E~u 5U~E~ 3117 -^9 1207(15,L -0?' 2593'

i~ 7 .347F*CE 7 16 E+ 5 2.a 1 E+C 3 ,46297 j2CI99q 4*3 2 5 9 8

2 ot '7 3-RE+ .; 7lr7-C7 7*2E4 ll 1L 145 P7l 251'

-t r r 7 3- E+i S 7!48E+Z5 Z s7 27+. F 1328 1 C3!92299 27E9 248

4, 7,A17(' 7, 1- F-,+ u 24471 *E~ ,2?5 *37 .74 115839*4 s51. 25

5 01 r 7,1 E# 1 697+L 656;:4+ 1 - ;6 11 258~ ~ 9 . 1V?9.3 5 2 5

3f 4oF:u+ F, b . ,+ So 142E o 44,, A .6 V5 ~. o169

40 3.3j , 6.?S+ %.774 27!' q 296. 3258.5",

C.r 6 : * ; +1 c 994'2E4K 6 7 L+ . 41 3E465 , -7 . 17?5 0 '736Z.4 45 i1 2 15

o 4 2E+ CS l 6' 9E4 ~L54K :.E6... .h 9111E.2 4128.6 ?'

I~ 497'TCq 9677 .,32 46597. 631.' 28

IA '+ 69.v+ L.65~K r;4)C '7 49 829, 74 s 4 227z

4.7rr6 66 Er . L 5 5P7+ r 5 o .? F ~ 611:.* 1415 5C 19

8!; 63 ,-+L 01 6i13, 7rt

~:S COVAQO7 TT PROPERTTES

Yy FYTU FYTU iC FYCU NY ( A

Z9 1 207[.59 1239,3 -1 2i

37 19453* 7 17.t 25930,5 ?F11".6 1180.4 -3.41+-

K2 21.~i1722.o 38.S 2=34 5.2 2SC797 1479.1 .86? *q

34O1 1115839.4 6807 2572 4,4 ZCF 3 .6 1582,2 -44SE0 2,994-'-C5

~i~.3~8.3 ~ 7.5 5~6.5 2496,4~ 1693. -5.6~~ *9~q

i -,8,3 117.S ?425 0b 7 21. .,75 - .7~~

. 4 -1 ' 9 1 1 2 8 .2 5 5 0. Z 53 -- q . a ? k " . - 1 2 9 5 -6 ' 6 F 3 7? q 5 , C

1 8957.1 1l~ 25:1. ? 3 2L4 2i72.7 .. 1 5E -~b 29~O

6329.9 i.5.9 ~ 2.+; .5 467 23. 439.6~ .745Z-6 .73-

1 0F 6 56 Z.9 13 . 165 32. o5 7, 3"3.:~ ?

AF J t . 256.1 37 Po 24446.5 3 66.7 *q 1)~

72 8 6977 63'.79g 1 0 7 2 41 66517 .9 4 9.-) 4.3E-

C; 52 74~. 2744.4 139'q.. 3.32.8' -1.694--

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2 c- 25?85. 38I. 3-4.6 26~ 81S.2 -!-5j 2 O7-

9F,~ 33616. ICI .59. 2:15'8R6 1 1.F 2*49 <

7 93. !44 '1; 2 3~.? ?. 9-r 27"? 41.6 . 4J!3

49 27721.9 1 ?'4- 2±.5 37Q~ q 675~~ .. 147E

14 - 98C. 8 &E-7 * 14 4 .2 2, -? : 5'13o 3 # 2,373 L

I. t,6i 5 15 ! '.5 9" i8 .3 17 6,(. . 5 2 3255'. j4 .7 -. 5346 L K ~ 2

17 E3-7* z4 5 . CA, . 252. 513. 7 164>;- 6.7 5.44 ~? 7'79E

E44 F- 27 13' 7. 225ioi 58 qo2663.b 162o7~

21 F' 44 5 . 2,1 - 13 7 q4 2 7 .? s-?? ?- . 5~

7 ? 1 1 7 o ,- I )* 8 - '

KrEVL n t.

F~~ IIO con luit TsT S Pr-SIN PPOP-'Y TTFS o,

EPF43 1.'QUF#!7 VP =.5W6 RHO

- ~ . : 412UP z 35OUPCPO = 12 S-2Cc2EAF FSU PICC1 Fsu=

ALPHA EX EV Y UYY llYX F'XTU FYT F

f.'X 'I49'E+ b 7*392E+OF 2211F+K'5 9?977 * 5 1408M25 02 3i310, #9 E+ 7. 1"+05 *213E~5 29 '58 140411,2 4..5 11

2.0 c .474r+C 6 7.15T+G5~ 2*.317E+t V !5 0 M76? 13919VIO6 1701 3a23*~~~~~ 4..?Er -.7~D 37?.E+. -41 .32 137199.6 40.2 30i

a,, Ao*g5qc4( 7.j4O E +~c *03Z F j;7+, 44 r"34499o5 71. s 1

60(" 1.26EEtCm' 7,TpPp+6= 'T 735+Cs5 .41or C-6 1273C2*0 1610A 20~

9. 7 9 F6 E + t 7 25,E.t+5 4 , II7:r+ r5 o.54 9 2 .c 113458.4 366. 5 at!

o1~2 !.6~r .PIE+ C5 1:2 F+A .6C-5 c .C2. 1t 29 551.3 ?fI?, , r z 4941+-,f; 'I 4 +, 5 ro 1-2 7 o695 98176.6 658.7 27L4!:+; '.446 74 Z r15 E,'47E+-r .795,4 .C ?7 911P911 776.4 464

$ 14.O 7onEr 7oL57E+05 6 E. +E(15 * 8r42 .':F59 88142.3 9L'4o? 25,

169f- ?P.+ b,9SlE+v 7o P!7E+6 1 9 17 i:± z 7A64A*8 1194,1 ?4117., o 6S6qE+(6 6.091 :E+C S 6.454Er+115 i n8 A 016^ 74!69.1i 13 5 5 09

23 *OC 51, Z* L6 So 74AE+05 A LF7 26 *?!CB .1 61936.4 19143 zo0

2?.)1 449!2z+m6 6.6V lo A5~E+. A 3.4 .13i8 54 D6 a8 Z35101 181236VC 41 5E-+r6 6 o 57 9:+ o .?5 4Etr, 1 32 .1976 5157945 259 C. 5 161

25.,> 4 s ' IE +C6 6 ,47?1z+ 0 1 4 9 rL'+ 6 :h4 41 61q 1: 45564.8 6i.. 14'2.0 6. *3+0F 6, 4E, + 5 i ,.44e 25 ^: 6. 4 284C s7 349(o 3 13

2s oF9 F+ 1±5 7E+. fEO2YE+.5 t*93+ o. 4~ 31874.? 4.22*8 1129 a !F~1+ F) 6. -,9E+t5 I A: E'Co ±*43P 356 1 3 Q 436±. 2 1.13" .0c ?6 (-1+ r- 60z5FE+41 1 o7±.' t F+ *279 V1Z4J 's. 5 1,710A,9 9

6i.O+ n s 7A+ 6.iM i :46~ 5 s> 71495,6 5C961~ 1 83?* ic '2 7F+ 1 C 6 0 1 ,1E +Ql5 lo e 345+ifF !iS799 .'5 546. s334 C, ?3!-Et-2 6.,?!4r-4s5 1*887--4: 1,1'.87 etl1~ 7.... 591±7 q 734, C 1086' , .r6 6224r+C5 1 49",7:-7+ 6 i.3! 36 .4TC ?6 2f3. Z '6 3.1 6

I.E'S C, i0"- L f 4 1. 24645.4 6 ,

1'. 0 L? 7* .56 6*"4J 2.i5E+ r6 lop1 2? 218 r-7 53 5

~3.X 1 , 7E. -^ 9 2-13!E4L6 F82 . 7 19278,r 8992.2,4~. 0 , 7 EZ, 46- E CO 05+:~ E 45571 b,4 9 F--;91 4

42, r,,' 90. 15+ 3 7*12,:+' 0 .0~FL f 9C6. *7 1 f 16 1 1A± 4 -C5 .9 3440 1.55;Et:5 7*O7*+^r o"2 5-rA+6 *pr. .7014 1429 1 f-L.i 3

o +r - . ------- - - - - - -

Coml~o:1TT Po'oprRTIES

EP = RHO= n461 5 RHO .046AP~ 4.~E5 rTU= 140822:5

UP = 5cu= 'to: !331115;FSU: 8~r.

FXTU FYTU F'(CU FYCU FY AX AY

£5 40822*5 3w 33 1 o 2619.o9 1£301,4 -6.,833 -7 2*379E--Z

±40411.2 4.5 ':)SI.1.2 2619.! 1!76*7 - 9921=.-37 2*978E-2'3

6? 1 3919,46 ilel 132Z5107 2 617.o5 1463.1 -7 0 j-7- -7 2,976E-01;

.82 137199.6 40.2 30£3 1. 4 2f614.'- 1562,C -7 o5 8 7 -)' I? 976 -1 5'f 49. 7-. 3!J 2. (A1L. 167'..? -89170-)J? 20375E-05

£31697 1?~ 98226!04,7 £802.A -Ss.q)j?-37 ?.q72E-CS5

63 1273C2.0 15£.9' 295A 9.6 25938.5 1946.6 -9*837E*-07 2*ql7; -35

. 1 22q3 23"7 259C*2 2148*5 -Ir,92:-.6 2 l 0I-B 113348.3 288.7 289 2s7 258192 2?89*5 -1.213E-06 2*92c-115

CC 113458.'. 366.5 185 8 2. 25"11. 1 2 49'.6 -ioS6:E- 6 2.5 7E-s a 5 515. , 43eq 231' 3.8 2F5909 271$1- 14"

24 1b.l20* 539 f?34 2F76 25* -1 95 44'0

9 5 98176.6 65 8.7 2 7 19. 2 534.4 3225.2 -ls887E-'j6 2o 3 6E - 4

74 911 p9 61 776o~4 64"8 .9 2 5 7. 1 3515.9 -2o 95--6 2.927a-P5

59 e8142o 3 914o7 257)2o2 25J5 4 3829*9 -2*322--,*6 .1-J

~52 $3313.1. rl' 14. 249R903 24-19 0 4166.9 -2.567---" * ?4:-

5?r 78648.8 1914.1 ?402ol 247203 42. 5)C .E~

1 7 ' 698P6.4 1529.6 ?2 2 7 , 2L36 o8 5317. L - 3?8 6-. E 2o8i5E--.5

68gO 1715.5 ?i.2i50 5 ?4 1 ,.,3 5 72 4.6 -3 6m7.- , 2 o834c- C

61936.4 19-14.3 219'),4 27-99.4 6157.3 i3%~: 2031 'E-15

5 8 2V~ 2125.* 5 Olt 39 23RO -3 66C ?. 2 -4. 3J 8 E -5C 2 .7 8 3 -5

81 ~ 85.735. 116± Z'~. 7^560 -4.635E-. 4 6 2o752-5

976 5157905 2F90*6 169, 8.7 234?.2 7515.3 -. 6F6 E77-3

14 4861. 124. b8"3,1 2 323 .' 7976.4 -3J 2-6 2 . 67 7;--J

45564.8 7114's6 1',7t '. 0 235.5 8 35 of -5*633E-36 2o633zi-G5

42840. 30C. 16C..2 2238.4 8889,1 -5.957;--.6 .8-

717 4OP81 S~ 37 12 , .16 70? 2Z72*4 9333.3 -6s26BE-36 o.525-i

9!. 37874*2 46 22.8 1 .'...0 2257.9 976413 -6,55SE-3 2.462;-O-5I)b 35613,Q 4361.2 i11b; 11 2 245o.4 11183 o4 *6of2-Jh-3 2.39 ~

3 F3 1349-05 471A.9 97q.? 2 2Z A 5 o j1 '0577. 3 -7.u47:7-46 2.o3 1 E -'

71 ~ 493516 5 c9 61.1 894841 2227.9 46 Z953s 1 -7,225:--.1 2 . 2 3

8? 29621.2 5496,.? )1'7 be5 2Z24.1 11 3)5.9 -7,3'.5c-:6 2 o' 3-5

1. t 27859,4 59i7. R 74.5 5 2 224. 11~.i-.9E~ ~th

24645,4 683 -t 1 25.4 4.4 12 ?1? ,2 -7*2?il'2& ..?1-

p9? 2317q,6 7329.6 ~62,1 2257. 1246:..9 -6o 977:1.-39F6

Ti 7>37 5 t 26".' ,- 77 5 ,4 2415.6 139. 3be:h 8~rI

:~t.112 F~1. 51?7. o% 13387.8 12~i~ 6 *35E3 6

S GL 4SS/F DPYY XHSPG ET ULT AlAM V cODP 1 T ES CON

FI07.R PROPERTES

=VF = ,537Rj + = 7 VP = .5'C EP = 4.7CLE+C:; RHO

WF = .6 'T = 1.26rE+.7 W = ,311. AP = 4*,,iE-5 rTU

RHF .9 Gr = + rHor= .L12 UR = 35CG FCUFTU = 35. A = 2."-6 FSU 0EJ .C FSU

FCU = Z152, AFT= •2G- 6UF = ,22:C

ALOHA Ey C y UXY UYX FXTU FYTU

4; •5 05bsi z+L£ 6 Z•51 5 •Zb'5L C 795 162C.4Z o1 l aj i

5 3,: 6 . --+r I , q 2.- + c~ .b 5!E*+ 5 . P61 •7CI8 16219391 Be I290 F,5 , -117*L +. 81 9E+, : 8." E+. 9 E •bt8 161278.8 344,09 1

3.C 6•4q , + ' 3 5 159775,i 71.d IL4 r•o 6 61 L C, , 3. . ' ' 5 , L 3 of. 84 1 5 7 7 11 *4 1 2 7 .• I

5 r 6 9 4+ LE + M 6 .e7 9 ±55125.9 ~Ji1I6 U' 636 qE. e 7q 6 "* $7E + •15 ., 6 152.68.7 E886

, 7•' c ,.36 q +- 1, 1 .782E£, + , 3, 7.3F+,. 5 • 3 9,- r • 959 46589.98 ,9306 V.

' 6•?3 E+ iO77 -'+6 ,3 54E6. 5 1 1c 14,+747,: 515. ". j9.. 6 L . 1 *75C+J, 6 . 6EJ •..745 .1 6,9. 1u598•9 654I, ±

.. ~~~~ ".~E~r L.92E - .13 1 ;! 0 , C- 1 5 ?, 6 -- +. 1 z 75.£+ 5 ;- _+ ,1 45 a'"' 3 [ , ! 3 3 78 9,

I I ," 1 ,5 . -- _+ E 7 - + r .+ T. 126 89g.7 7 r-7+ r 4 ±2.1.

9~~~ + 1268 3* 6L?~93o74, 3L4r i

7!- =3• E;. +I + ._3 5 .4.5%; .L,', 12 Z':q ; •! 138 ,

1 2 . •C 4.6 12E) E+ i 7 ?£ 7 e7 -+ 5 .944 4E . •1 v 724,7 561.,

15 0 " F .7 1 ;5_ 3 + L-•5+" + -. 5 4, F~ •l 6 112392.5 1857r41.C. •. o 61'. -+ Fz 7. E+ " .1 • r 57.5•s 212 3 3" 3. o E+~ .-+ 1 797 1 .8 6 = 1-. •1• 24, 9t 3

+ A b" 5 " r6 1 •5:6 19l 5 ,.'. 11 981 3,9 Z 7164 7 t

-9. 4 • .24 E+2-., - + E 6L6! 2., "•9'+1 ,L79 7 3L 4 L.,

" . ' "5 .1 555 +97t,96.t + 771- 2.E6 .1973 5.9 8

4 b 1 7~-U +.iE~ ,2&) 40C2 3 ft 5 C 217 2

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3 ~~~~~ " '- i•,7+ ,61 o 4g ? 5, 745 ,L 9614,.1

3' .3 ". 44,1 '-3 I 35q,+ +. + -.v . e .L? 4+g 2&, 1 , 7 93 7

.3 0c 1 !r,, 4 17 *

S • + . L,. ...5

+, 37oI :.5, 5 +. r•,.3 .I C- C? + 5 r 9,1F a5.

78 , 2 . + 2 - ,.", 177 A:- + 9 Z 9 7 6 11 3 3 9 2l •5 1 -'54 4 . 9

19 . i": i•31 3E 15 9•i 0£;7 :•7 .£ 9 6 -697 5z , 15 2 2, 2

4Z.+., ~; ., "-++. 2 a - : + 8r4 - . 6c- ":+ -•2: . 85"6> * . .9 .4 16767 -42 L,,[ I• 2 +' .• 347=--+.-Q 7,h ' 2F , , T - ZS6 J(.•o b7 I96 ,

14 : P• 3 + 5 7 4:- -. 0. .+ + = , 2 7 7 2 3 9 2 8 •* 7 2 1 , 1. 14 ,

65 =65

C0M003 iTE POOPERTUcS

ER 4,70LE+CF RHO= 254- = r TU= -to.

UR * 35CL FCU= 7 5,j 9 ,FSU= 8.12.0

PXTU FYTU F<CU FYCU --YAX AY

1'- :7 5 3.2 29489.2 5435oC 3*553-E-36 i.±?5E--05

162193.t Be 1'74~34*4 29476*7 56950 39557E-06 i 7E~

j59775.I. %ld. 11L69 707 29776.2 6 31.Q0 3954DE-16 10176--5

15512509 '4.L58..505 29175o,4 7. 35-6 iI7EG

-~& 1390i Z9,3"795 7671*9 3o483E-= 6 i*178E-05

46 589 *8 3. 6 1'.4212.4 2887406 32i5.03 3.456-16 1.79

44,77 515.1 1 -3212. 0 28ES6*8 8811.7 3.424,:-06 1.18C2-05

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A1

KE.VLAP '.9/EPOXY SM MTAU MO

FIBER PROPERTIES rRPTIS

.50 .0t~7 VP = *5500 -R=4.? CS 14

WF .5q98 EFT= I.CJDE+06 WR z 44i 2 AR = 4.035 FTURHOFt .0524 GF z3*V030E+05 F4HOR= * = FC

FT 2000 AF =-2.*jOUE-06 FSU 89J .uoo 0

FCU t 05030C AFT= 393040*E-05UF = .2290

ALOHA EY E GXY Uxv Uvx PT YI

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2 q q.7 6E +i,6 7*64!E+05 2*4.3-+C5 .2996 .a36 l6j419o4 0 ~.i 3

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t 66

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APPENDIX G

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APPENDIX H

NOMENCLATURE

69

NOMENCLATURE

A Area, in 2

B Angle, deg.

C Buckling coefficient~c

Ee Modulus of elasticity, psi

F Allowable stress, psi

FA Fiber area per unit

FACR Fiber area coverage ratio

FCR Fiber coverage ratio

FCOA Fiber cross-over area ratio

G Shear modulus, psi

I Moment of intertia, in4

10 Moment of inte ia about netral axis, in

I0 Inside diameter, in.

K Torsional constant, in4

L Dimension, in.

M Moment, in-lb

n CoefficientP Load, lb

Q Moment area, in3

R Radius, in.

R Mid wall radius, in.

S Shear, lb

t Thickness, in.

V Volume ratio

W Dimension, in.

y Dimension, in.

a Winding angle, deg.

p Density, lb/in3

o Unit stress, psi

T Unit shear stress, psi

70

SUBSCRIPTS

b denotes band

bco denotes between cross-overs

c denotes composite or core

co denotes cross-over

cr denotes critical

cu denotes compression ultimate

e denotes equivalent

f denotes fiber

fco denotes fiber cross-over

fbco denotes fiber between cross-overs

i denotes inside

max denotes maximum

0 denotes outside

su denotes shear ultimate

x denotes "x" direction

y denotes "y" direction

z denotes "z" direction

11 denotes direction parallel to fibers

71