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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)
Unclassified
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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0* V 'I r- r- N M LO CA 0 r, in H- rA0~~~ q0 COIDU N 'OD w m Amim r-r-- 0a
a M 0 0 0 00 Hl 00 0 o in 0 Ln ('* r- r- 03 N r- r'-0 tn ic n Ln v in %o . H 0 C14 r, r N- N rN
* H4
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mr m r-Nr- c)in w0 cmH 0- N N- oo %4 0 ( a7 o HH i- - n in wD H- cn in H r4 in Coo o m n LA H 0 H Co H H 0D o) c, 0 %oD N o co c 0
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SI
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
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-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 =
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9 oC 6PELE+ fi 7 0 5 1F 6 517 81 ~391 a7 3311 21.
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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
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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
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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
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[ 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
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-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
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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
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7 ? 1 1 7 o ,- I )* 8 - '
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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
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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,
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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
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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
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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
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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
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~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~
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8? 29621.2 5496,.? )1'7 be5 2Z24.1 11 3)5.9 -7,3'.5c-:6 2 o' 3-5
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p9? 2317q,6 7329.6 ~62,1 2257. 1246:..9 -6o 977:1.-39F6
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:~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
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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.
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I I ," 1 ,5 . -- _+ E 7 - + r .+ T. 126 89g.7 7 r-7+ r 4 ±2.1.
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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.,
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+ A b" 5 " r6 1 •5:6 19l 5 ,.'. 11 981 3,9 Z 7164 7 t
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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
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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
1458 9 633,6 1! .45o2 28474.2 91+53.3 3,387.-36 i.8~0
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2 2& u 2 19F .71 Zo 2 59,16 1 i6:5 6In5 2o92?5: -6 i195E-C3
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9 3594*1 L 44. r) R.S!2 .4 25 r 3 8 . :817.a9 2,76)E-16 1 a 9 9 E 5
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728 Ft3%.8 7! 02 66373*5 22545*4 24I2 3, 2.o27t;:-" I i.20>
69±1.9 549.J~2V.1 2~?O 416.6 2.!-537-- 6 1.2lE-05
65599 01 599544 595.i.4 21452.2 25186.7 2(54-:-06 i*±98E- Q
622,9e.9 65"1.6 5615)o2 2, 894e5 26Er' 5 t*945E-36 1.195>2-5
8917 7.7(-o55 2 7.. 2ob 23 3 3.s5 27143.1l 1 084 ;E -2 3 02-3
5 )0q 7661. 9 49372.6 *-q772. , 9 Z174*7 l.73SE-5c6 I.,18 3-0
5293%3.5 R2 7 9 46-5 701 449 Z±E 0 29,25 o '. i*6'.5E-:6 l!74=-.15
5n124*q 8929.2 ~d5 2 ,5 '1 .E 7 1 3 aX4 4 13 1.563L-~ 1.63
40177*4 11892 r 1 _7 2 ?3 1663 T 1 33357,8 i 453- £. *79iE-05
379c6eC 1273241 23941s.3 169,3665 33996,1 4. o525E-36 lo..46E-C5
5qL 2.I 3 5 26 7- 2 o2 15012- 34524.4 1*643:-46 1. E-5
.. 392105 14'54 4. 20-; 1 09 15E39T 35153.7 t.824>27-6 9*628E>T
3 2 3 8 , 15 '224.? 22c~s"-3 7 15-'.1P.9 35655.. 2. L 7 5 o 941187-06
3 *,,8 .5+a. 2120 7:5 15212.1 36111.2 2 , "? 6 80 4r
Z 15j, 71b76 7-o1 1 7. 5s7 1 53', 0 3o733,9 3*2951---6 7,255>-C'O
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2 2 5 *7 12r-t 9 i6'3?i905 !62,)r .4 ]t7--933 54143:.-6 5014SE-Co,
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
0.O 973E+6 .64E'5 .2 E+ 0 285L .6224. 162500.0 o .3 X%10 40 9.28E+%t6 7648E+0.5 2*216E+CS .2 161975.1 4.7 34
2 q q.7 6E +i,6 7*64!E+05 2*4.3-+C5 .2996 .a36 l6j419o4 0 ~.i 3
3.30 90670E+06 7.b3lE+05 2d340E+ a'w"317251 154887.9 '1 j74.0 3~too 3c 9,61 8E+ C C 7*618E+O S 2*734+*.5 o3433 o6272 146. 47 35630 9.551E+CG ?.bG2E+u5 Zr,8 3E+3,: *3757 .0299 1531267.2 116.I 14
6.40 9.46?E+06 7*582E+05 ;,o. 4~" o4149j 0 G 3 145413.2 1 '
7.00 9o366E+C6 70555E1+25 7 . 63 AE+~ ". r 6.~6 .0372 140344.9 23G.o S
8.3C 9*24bE+C6 7*53!.E+Ci 4..35E+05 .5124 s 41 134289.7 3ji.2
940C 9.±u6E*06 7050i14tQ5 4,48,tEKS' .570i .C47w 12927600 3R2*4 3
10.00 3*947E4C6 1*467E+v.5 4*983E+ujF .6326 .052A 122118#7 473~7 3
11400 80766E+L6 7,4.31E- 5~.2~0 v tie9 1~ 8 68* $112*Ci 8.563E4L6 Is 39;E.S 604~91E+05 .7756 *066!) 109758. 687.' 3)"13.00 81339F+Oc6 7934iE+ 5 6*71 E+CS .v.4s 904 10379*4 ft103 3
14.00 8oJ93E+L6 7. 3' E"U' 7 ,36 5c+,l5 .019b 048%~ 97823.4 9144*1 21
15*06 7*825E+CE 7.252E+aJ5 A9647 *05 o.9 957 e ,2 92144i.9 1089.6 21
1690 7 *5.37F + C6 7*.2E+Or25 e ,75 6E C 5 1.0 7.j9 *1L23 866903.1 12460? ? 1
17.00 7*230F+r6 7.o.49E+w5 9.4q1E+t'5 I t144Z .1131 $148A90 1415.7 2
Issue~ F6.907C40 7s09'.E+45 lo..25E+ub 1.2143 1li47 76548,F) 1i097 0 2!
19.0C 6eS69E4L6 7ou383E+05 1itu2E4C6 1 9 2'7 98 .1371 71871.5 1791.6 Z
20.00C 2.21 E + C6 6 8 "E +C5 1 .1 1E + 0 1 -1397 .1 s 67456o7 1999.2 Z2
21*00 5o865E+#. 6*122?E05 1*26'J+Lb i%392q o1644 6329*oq 2220o7 Z,
22.0C0 5*505E+06 b~64E+L'5 143k z+0' 16436~5 a179,# 593932 245S6*5 2i
Z3*&G 5 *l45E+4.6 6 8 6FQ,+ 05 1*4?lrt.b 1.4759 .1953 55720. 273?.m! 1
24,00 4*788E+C6 6 .749Ej ;. %I E+, 6 1.bC'.6 .21244. S2?79*S 2973.4
i5900 4o438E+ubc 6 1693E+ 415 1,58CL+76 1,5245 .2299~ 41054*2 3255OR
2 6 0 0t 4o399E+i46 6,64...+j 1,659E+dL. 1.5355 .2487 46u32 3 25. 1
27001 SoM7E+C6 6 059 CE + U 1*736E+u6 1.5379 *2686j 432v-4ol~ ?2~S
2803 3*463E+L6 6 s545E+~) 1.E'12E+Lo 1.53?1 *286 4055io1 4237o3 2.
z 9 aa 3*17;E+06 b*S53E4w'5 1.8"5E+r~ 1.5188 *3117~ 38074.6 4562.9 1
30.00 2.896E+Db 6 *47 2E + .5 41.9r E+ v6 4,49 8o5 *3?4 35751.5 g' 1
31.00 2*641E406 6*447E~u5 2o C2 4E+ Z; 1.4721 .3590 '33575.92 53350i
32.00 2*406E+L6 6 ,432E+;. 5 .L9]E+06 lo4L ,; *38516 3153i 08 5754*1
33.00 ?.19.JE+C6 6*4ZgE+45 2.151F+Thj 1 4C 4L 4 141 2963.85 6198.34.03 1.995E+c6 6*44.E+05 2. 9E +C6 103,139 2 74i.S 666.
* 35.05 i*.',7E+C6 6 *461SE Q 5 2 o26 314( 6 le.208 .47(1' 14. 7161.3
36.6c leC53E+C6 F,515E+-JS 2,312E+Cb. 1,2754 651 11 2'.563oQ 12637.00 1*51C6E+C6 b,584E+Or, ? ,,)5 7 1+ C' 1*.UA o.6~36 203~ 3.
3 8.o00 1*389Et+tj 6,b78i+t5 Z.397E+Zo 1.18uS * 5675 216801 82
* 39,09 1*276E* Cb 6*03EJ do43 IE+3b 1.1315 46C30 2a377,4 943747
4) ~0 C 1 171E+C6 b *961F*tU5 2,4(3CLP 1'2A !99 1911,42 U
141ie0 0 i~u9IF4C'6 7. 15 OE+ 5 2 ?418 1 r+ c 6. 1c 3t9 6~' 1 ± 798.o I17I1 .
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45*3u. 3.'o45I-E *L 5 8 ,4 54.E + Q5 2 ,53 246 7--+, E, 14~. F,4 , 5.63966 ob
t 66
CO"9003TTE r-O'EJRT!S
=4*7k +05 R14'= *C468AR = 4.04 FTU= 16M '
OSR = *35Q ~ FCIJ=
FXTU FYTU FVCtJ FYCU FX Y A Ay
15786749 4 2'. 3' 791*7 ?727,7 il)47.2 -.- ' .5:~
154476.0 74: -P 3*4 6? be 2E%3 179 *I -1 o' 21 r 2 .4 5"1 05
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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
Recommended