F I N A L REPORT
JUNE 1976
ON THE ELASTIC STABIL ITY O F SHELLS
by P . h *
Wilfred H. Horton 3 ,
(NASA-ZO.- 1 4 8 4 8 4 ) 0.1 T H E E L A S T I C STABILITY N76- 3 1 5 6 8 OF S H S L L S F i n a l 3epor t (Georg ia I n s t . of T e c h . ) 86 p H C $5.00 C S C L 13M
U n c l a s G3/39 4 6 7 3 4
School of Aerospace Engineering GEORGIA I N S T I T U T E O F T E C H N O L O G Y Atlanta, Georgia 30332
https://ntrs.nasa.gov/search.jsp?R=19760024480 2018-05-28T16:03:28+00:00Z
SUMMARY
A synopsis of a series of inves t iga t ions i n t o the i n s t a b i l i t y
of a x i a l l y compressed cy l ind r i ca l s h e l l s is given i n t h i s report .
There a r e two prime parts . One which dea ls with s tud ie s which were
made on small s ca l e p l a s t i c vehic les and one which summarizes the
r e s u l t s of t e s t s on l a rge r e a l i s t i c a l l y reinforced aluminum a l loy
c i r cu l a r cyl inders of contemporary design.
The object ive of t he research, which w a s made n t h models, was
t o devise a technique of non-destructive evaluation. The r e s u l t s
presented show t h a t , with models a t any r a t e , success was achieved.
Probing methods which can be used t o determine the loca t ions of
weakness and the per t inent i n s t a b i l i t y load l e v e l s were devised.
The research on la rge sca le s h e l l s was undertaken with a view
t o determining the c r i t i c a l loads under as uniform a circumferent ial
d i s t r i bu t ion of a x i a l compressive fo rce a s possible . It is c l ea r
from the r e s u l t s presented t n a t t h i s ob jec t ive was closely met.
The cornplate in tegra t ion or t he methods developed with small
vehicles i n t o the work on l a rge sca l e s t ruc tu re s was not a t ta ined .
The ~ l f f i c u l t i e s encountered were pr imari ly due t o the mechanical
incompatibili ty o: the loading system and the probing systems.
Studies made i n the f i n a l s tages of t he work showed c l ea r ly t ha t
rhese d i f f i c u l t i e s could be overcome.
Acknowledgements
The work reported was made possible by a grant from
NASA. This support is gratefully acknowledged as are the
many referenced and unreferenced contributions from various
friends and colleagues. Their stimulating discussions and
freely given assistance with thc: experimental program were
invaluable.
Tom Haack, Bud and Marla Skinner nust be accorded a
special ack~~owl.edgement for without their skill and co-
operation the work on large shells would have been m~ch less
successf ul.
? sincere word of appreciation is also due to Nell Blake
who gave much needed help in the preparation of the final
report.
List of Contents
Introduction.
The Model Shell Programs.
General Statement
The Use of the Southwell Technique in Conjunction with
Harmonic Analysis.
An Evaluation Method Based on the Vaziation of Wall
Lateral Stiffness with Axial Load Level.
An Evaluation Nethod Based Upon the Variation of Dynamic
Mass.
An Evaluation Procedure Rased Upon Combined Loading.
Conclusion Drawn From the Results of the Non-Destructive
Evaluation Program.
A Parametric Study on Ring Stiffened Shells.
Tests on Large Scale Stringer & Ring Stiffened Shells.
General. Remarks.
Details of the Shells.
Main Body Construction
Main Body Inspection.
Shell End Machining.
Test Facility.
The Loading and Force Reaction System.
Hydraulic System.
Load Determination.
The Data Acquisition and Processing System.
I n s t a l l a t i o n of t h e Tes t Vehicle ii. t h e F a c i l i t y .
Qua l i ty and Accuracy Achieved i n the Large Scale S h e l l
Program.
S h e l l C i r c u l a r i t y .
Shel: End Q u a l i t y .
Load and Reaction Bearing Surface Qual i ty .
F i t of S h e l l Ends on t h e Load and Reaccion Bearing
Surf aces .
Load Steadiness .
Repea tab i l i ty .
Resu l t s Obtained.
Non-Destructive Evaluation.
Maximum Load Levels At ta ined . Buckling Behavior and Post Buckled Condition.
Load-Strain Rela t ionship .
Line-Load D i s t r i b u t i o n .
Load Displacement H i s t o r i e s .
Conclusions.
L i s t of F igures
Figure 1.
Figure 2.
F igure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
F igure 8.
Figure 9.
F igure 10.
Figure 11.
Figure 12.
F igure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
F igure 18.
Figure 19.
Data Acqu is i t ion System Flow Diagram.
Harmonic Spectrum and Southwell P l o t , S h e l l 1000.
Harmonic Spectrum and Southwell P l o t , S h e l l 1002.
PC, and Psw Compared t o Experimental Loads, S h e l l 10XX.
A Schematic Diagram of t h e S t i f f n e s s Probe.
St i f fness-Axial Load P l o t s f o r Unst i f fened C i r c u l a r
Shel l .
Rectangular Panel - MD vs. F a t 30 Hz.
E l l i p t i c S h e l l - MD vs. F a t 20 Hz.
Rectangular Panel - Minimum MD vs . Corresponding P.
E l l i p t i c S h e l l - Minimum MD v s . Corresponding P.
Load-Deflection P l o t s , Inc reas ing Axial Load, f o r
220 Degrees Angular P o s i t i o n .
C r i t i c a l L a t e r a l Force Behavior Under Axial Compres-
s ion.
Ps, vs. SR, Non-Uniform Rings, S h e l l 09XX.
Psw vs. SR, Non-Uniform Rings, S h e l l 08XX.
Ring and S t r i n g e r Sect ion
End Ring Sec t ion
Block Diagram of C i r c u l a r i t y Checking System.
Schematic of Large S h e l l Tes t ing System.
Large S h e l l I n i t i a l Geometry.
L i s t of Tables
Table I.
Table 11.
Table 111.
Table I V .
Table V.
Table V I .
Table V I I .
Table V I I I .
Table IX.
Table X,
Table X I .
Table X I I .
Table X I I I .
Table X I V .
Summary of the Result of the Wall S t i f f n e s s Variat ion
Study . St i f fnes s P r o f i l e on Unstiffened Circular Shel l Under
Zero Axial Compression.
Comparison of Buckling Loads Predicted From Dynamic
Mass Variation With Those Achieved on Test.
Charac ter i s t ics of the Frames and St r ingers of the
Shel l s Used i n Ford's Parametric Studies.
Charac ter i s t ics of Shel l s With Uniform Rings and
Str ingers .
Charac ter i s t ics of Shel l s With Non-Uniform Rings
and Uniform Str ingers .
Fourier Series Coeff icients f o r Deviation Data.
(Circumferential)
Fourier Series Coeff icients f o r Deviation Data.
(Longitudinal)
Geometric Cha rac t e r i s t i c s of Large Shel l s Tested.
C r i t i c a l Loads and Stresses .
Helght of S t r a in Mea~urement Planes Above Base Plane.
She l l D. S t r a in s (Micro-inch per inch) a t 15% of
C r i t i c a l Load.
Shel l C. S t r a in s (Micro-inch per inch) a t 27.4% of
C r i t i c a l Load.
Shel l A. St ra ins (Micro-inch per inch) a t 75% of
C r i t i c a l Load.
Table XV.
Table XVI .
Table XVI1.
Table X V I I I .
Table XIX.
Table XX.
Table =I.
Table X X I I .
Table X X I I I .
She l l B. S t r a in s (Micro-inch per inch) a t 98% of
C r i t i c a l Load.
Shel l A. Local S t r a in Conditions and C r i t i c a l Loads
Derived From Highest Load Level Data.
She l l B. Local S t r a in Conditions and C r i t i c a l Loads
Derived From Highest Load Level Data.
She l l C. Local S t r a in Conditions and C r i t i c a l Loads
Derived From Highest Load Level Data.
Shel l D. Local S t r a in Conditions and C r i t i c a l Loads
Derived From Highest Load Level Data,
She l l A. Centroidal S t ra ins . Lncal Centroidal
S t ra ins Normalized t o Mean.
Shel l B. Centroidal S t ra ins . Local Centroidal
S t ra ins Normalized to Mean.
Shel l C. Centroidal S t ra ins . Local Centroidal
S t ra ins Normalized t o Mean.
Shel l D. Centroidal S t ra ins . Local Centroidal
S t ra ins Normalized t o Mean.
1. In t roduc t ion
The r i n g and s t r i n g e r s t i f f e n e d c y l i n d e r f i n d s u n i v e r s a l app l ica -
t i o n i n aerospace s t r u c t u r e s , and h a s done s o f o r s e v e r a l decades.
However, i t i s apparent from a review of t h e c u r r e n t l i t e r a t u r e t h a t
t h e r e is a d e a r t h of p r a c t i c a l d a t a obta ined from tests on r e a l i s t i c
s c a l e veh ic les . It i s p e r t i n e n t , too , t o n o t e t h a t t h e a c t u a l load
d i s t r i b u t i o n achieved on t e s t i s q u i t e f r e q u e n t l y n o t c l e a r l y def ined.
I n f a c t , only four cases i n which load d i s t r i b u t i o n neasurements a r e
a v a i l a b l e seem t o be recorded (1, 2 , 3, 4) and of t h e s e only one appears
t o r e f e r t o a l a r g e s c a l e v e h i c l ~ . A s Babcock (5) n o t e s i n h i s review
of s h e l l buckling experiments t h e p r a c t i c e of determining t h e a c t u a l
d i s t r i b u t i o n "is probably no t more widely adopted due t o t h e d i s -
couraging r e s u l t s obta ined i n most cases. ' '
The i n t e n t of t h e work, h e r e i n repor ted , was t o a c q u i r e d a t a
on r e a l i s t i c s c a l e r i n g and s t r i n g e r s t i f f e n e d c i r c u l a r c y l i n d r i c a l
s h e l l s l i a b l e t o genera l i n s t a b i l i t y under a x i a l compression. From
t h e onset t h e g o a l was t o a t t a i n t h e h ighes t q u a l i t y t e s t v e h i c l e s
and t o achieve t h e b e s t p o s s i b l e c i r c u m f e r e n t i a l d i s t r i b u t i o n of
a x i a l load.
R e a l i s t i c s c a l e v e h i c l e s of good q u a l i t y a r e expensive t o pro-
cure and prepare f o r t e s t . Thus i t is d e s i r a b l e t o maximise t h e
amount of information which can be obtained from each specimen. To
t h i s end a secondary program was undertaken - t h e o b j e c t i v e t o es tab-
l i s h a method of non-dest ruct ive eva lua t ion of c y l i n d r i c a l s h e l l s
under a x i a l compression.
The two programs were run i n p a r a l l e l . Both are summarized i n
t h e r e p o r t . They a r e d e a l t wi th i n t h e o rder of t h e i r completion.
2. The Model S h e l l Programs:
2.1 General Statement -
A s expla ined i n t h e in t roduc tory s e c t i o n , model s t u d i e s were
conducted i n an a t tempt t o d e r i v e d a t a which would be p e r t i n e n t t o
t h e main program. I n p a r t i c u l a r , t o develop methods of f a i l u r e pre-
d i c t i o n which would enab le u s t o determine, from r e l a t i v e l y low v a l u e s
of t h e app l ied f o r c e , t h e region of f a i l u r e and t h e c r i t i c a l load.
The s h e l l a which were used i n t h e v a r i o u s s t u d i e s made i n t h i s pro-
gram were cons t ruc ted from p l e x i g l a s s , an a c r y l i c p l a s t i c wi th a
5 modulus of 4.5 X 1 0 l b / i n 2 . I n a l l c a s e s t h e t e , t s were conducted
i n a Baldwin Model 120 CS screwjack u n i v e r s a l test machine of 120,000
l b . capac i ty . Th i s machine was modified so t h a t t h e load i n d i c a t i n g
system gave an e l e c t r i c a l output p ropor t iona l t o t h e app l ied load.
S t r a i n gages, wP,cn used t o check uniformity of load d i s t r i b u t i o n f o r
models were of t h e Hickson s e l f adhesive v a r i e t y and were suppl ied by
Tinsley Telcon Ltd., London, S.E. 25. The displacement t r ansducers
were i n a l l i n s t a n c e s of t h e Hewlett Packard 24 DCDT o r 7 DCDT types .
Power f o r t h e displacement t x w d u c e r s was from Hewleti Packard 6227 B
dua l D.C. power s u p p l i e s and t h e s t r a i n gages worked i n conjunct ion
wi th Hewlett Packard power supp l ies .
Crossbar I r------- Scanner 1 I I i I I I I
I r - - - - - - - - J I
----! Vollirre t e r C o q u t e r i 1471 Regis ter
Stiffness Probe and End Shortening Transducers Hickson S t r a i n Gages
1
.
I I
I t7 6 *
Teletype Unit
j
I
- Test Fiat hine Lozd I n d i c a t o r
I
------ Cont ro l Data Flow
. .
F i ~ t r e 1 Data Acq-Lr;'. I. Lon Systca Florr Diagrar, .
The var ious t ransducer s i g n a l s were processed i n accordance
wi th t h e datc: a c q u i s i t i o n system flow diagram given i n f i g u r e 1.
The d i g i t a l computer t h e r e i n referenced was of t h e Hewlett Packard
2115A t m e , whi le t h e d i g i t a l vo l tmete r used and t h e c rossbar scanner
were compatible Hewlett Packard equipment.
A d e t a i l e d account of t h e u s e of such p l a s t i c models f o r
s t r u c t u r a l r esea rch i s given i n r e f e r e n c e 6 , Considerable informa-
t i o n r e l a t i v e t o t h e method of f a b r i c a t i o n is given i n r e f e r e n c e 7.
2.2 The Use of t h e Southwell Technique i n Conjunction With - Harmonic Analysis.
The f i r s t s t e p s i n t h e non-dest ruct ive e v a l u a t i o n pi gram were
taken by Ford (8). He s t a r t e d from t h e observed f a c t t h a t t h e r e i s
a po in t - t h e c r i t i c h l p o i n t - f o r which t h e normal displacement-
load h i s t o r y when analyzed i n t h e Southwell f a s h i o n y i e l d s a reJ.iable.
e s t imate of t h e i n s t a b i l i t y load. However, t h e sea rch f o r such a
s p e c i f i c po in t is a most t ed ious opera t ion . The ques t ion which he
sought t o r e s o l v e was; can a more g r o s s p i c t u r e of t h e displacement
be t r e a t e d i n such fash ion a s t o obv ia te t h e need t o l o c a t e t h e
c r i t i c a l po in t? I n h i s at tempt t o answer t h i s quest ion Ford determined
t h e load-displacement h i s t o r i e s a t a l a r g e number of p o i n t s on a
v a r i e t y of a x i a l l y compressed c y l i n d r i c a l s h e l l s . He found t h a t when
t h e displacements along a genera to r were t r e a t e d a s a who?e t h e r e
was cons iderab le u n c e r t a i n t y i n t h e a n a l y s i s , a l though Southwell p l o t s
could f r e q u e n t i y be developed. However, when t h e displacements
H n r m c n l c J k ~ n i tude M i I n x o n i c Spectrua nnd S o u t h w c l l 31ct, Z h e l l 1000.
F i ~ u r e 3 Harmonic Spectura and Southwell P l o t , S h e l l 1002.
around t h e shell, i n a plane normal t o t h e generators , were consid-
ered a s a family t h e ambiguity could be removed. I n deal ing with t he
circumferent ia l displacements Ford's procedure was t o harmonically
analyze t he displacement pa t t e rn anC then t o t r e a t t he magnitude of
t he predominant harmonic as a displacement. When t h i s was done excel-
l e n t Southwell p l o t s could be developed. Fig. 2 & 3 a r e i l l u s t r a t i v e
of h i s r e s u l t s . These f i gu re s give t y p i c a l examples of t he impulse
spectrums and the Southwell p l o t s derived therefrom. For c l a r i t y t he
impulse peaks f o r t he spectrum have been connected by s t r a i g h t l i n e s
t o form an envelope.
AS noted e a r l i e r t h i s procedure, which i s c lo se ly ak in t o
t h a t suggested by Donne11 (9 ) , adopted by Tuckerman (10) and appl ied
by Craig (111, removed t h e ambiguity i n i n t e r p r e t a t i o n of any pa r t i c -
u l a r s e t of c i rcumferen t ia l displacement da ta . Unfortunatelv, t he
loca t ion of t h e v e r t i c a l s t a t i o n s a t which the da t a should be co l lec ted
and analyzed was s t i l l an open question. For s h e l l s of t h e types
used, the ind ica t ions were t h a t planes i n t h e mid-region were appro-
p r i a t e . Figure 4 gives a comparison of t h e correspondence between
the c r i t i c a l values derived from t h i s procedur?, the a c t u a l i n s t a b i l i t y
load and the predicted va lues f o r a s p e c i f i c family of s h e l l s . Further
d e t a i l s a r e given i n s ec t i on 2 i n which a sununary of t he t o t a l study
ca r r i ed out is presented.
The disadvantages of t h e method a r e c l e a r ; i t involves a con-
s iderab le amount of ana lys i s and i t f a i l s t o give any c l e a r ind ica t ion
1 of t he regions of weakness. Moreover t h e da ta appropriate i s generated I
I b only a t loads which a r e a high percentage of t h e a c t u a l c r i t i c a l . i
ri :: ,,,*,?.. ia .. ir*D-r..;... ...i-rF v.d.l.l'. =
. , .,'*
2.3 An Evaluation Method Based on the Variat ion of Wall La te ra l - St i f fnes s With Axial Load Level.
A s ign i f i can t weakness of the harmonic ana lys i s technique
became c l e a r when consideratic- was given t o daca obtained from
t e s t s on e l l i p t i c she l l s . Another weakness is t h a t the b e t t e r t he
qua l i t y of vehicle the higher t he load l e v e l needed t o generate
per t inent data. Consideration of these two i s sues led t o a search
f o r a more powerful process which could be universa l ly applied.
The f i r s t s tep i n t h i s d i r ec t ion was made by Bank (12). He showed
tha t t he wall l a t e r a l s t i f f n e s s of a s t r inger -s t i f fened c i r c u l a r
cy l ind r i ca l s h e l l decreased a s t he a x i a l load increased and t h a t
there exis ted a t l e a s t one point on the s h e l l wal l f o r which t h i s
change was l i n e a r , and f o r which the in t e rcep t of t he load s t i f f n e s s
l i n e with the load a x i s corresponded t o the a c t u a l t e s t value of
c r i t i c a l load. This observation was made on a s ing le s h e l l .
Singhal (13) extended the work and demonstrated i t s v a l i d i t y
f o r a wider range of t e s t vehicles .
The s i x add i t i ona l types were a s follows:
(1) An uns t i f f ened c i r cu l a r .
(2) A longl tudina l ly s t i f f ened c i r cu l a r .
(3 ) A longi tudina l ly and circumferent ial ly s t i f f ened c i r c u l a r .
(4) An unst i f fened e l l i p t i c .
(5) An unst i f fened e l l i p t i c with cut-out.
( 6 ) A s p i r a l l y s t i f f ened c i r cu l a r .
Special details of these shells and that used by Bank are
Given in Table I.
For a1.l of Singhal's tests the normal force used for wali
J.:rteral stiffness determination was limited to a level which at zero
:.ompression deflected the wall no more than one third its effective
thickness and which under load did not cause displacements greater
than one half this thickness. The probe used was as shown schematically
: n Figure 5. Investigation stations were spaced 1.0 inches apart in
0th the longitudinal and circumferential directions. Singhal was able
t:o show the applicability of the method for orthodox shells but not for
spirally stiffened shells.
Figure 6 and Table I1 give typical data. The minor discrepancy
in stiffness values quoted in the table and given on the curve is due
to some very slight slop in the turntable bearing.
The advantages of the method are readily apparent.
1. FP orthodox reinforcement the cross-sectional shape does
not influence the result.
2. It enables the investigator to locate the areas of weakness
and to make reliable estimates of critical load from data
obt,~ined at relatively low levels of applied end load.
TI .- disadvantages are equally clear.
1. A considerable amount of test time is involved.
2. Special arrangement must be made for the stiffness determina-
tior.. These involve arrangements for the application of the
side force needed and neans for determination of the wall
displacement, unadulterated by any rigid body motion of the
test vehicle.
Ill
TAB
LE I..
SUM
MAR
Y O
F TH
E: R
ESU
LT
O
F TH
E WALL
ST
IFF
NE
SS
VA
RIA
TIO
N STUDY
b S
peci
mcn
N
We
r
0 1
2 3 4
/-
5 6 " Thc
i
T
Ac tu
al
Bu
clrl
ing
Lo
ad
(lb
)
40
50
1375
1080
20
00
371
191
34
00
Pre
dic
ted
D
uc1c
ling
Loa
.d
( 1-b
42
00
13
90
1060
19
50
36
0
180
4700
in t
his
ca
se
b
Sh
ell
C
ou
st;r
uct
ion
Str
ing
er
Sti
ffe
ne
d
Cir
cu
lar
Uns
tif
f en
ed
Cir
cu
lar
Str
ing
er
Sti
ffe
ne
d
Ci
rcu
lar
Rin
g
and
S
trin
ge
r S
tiff
en
ed
C
irc
ula
r
Un
stif
f en
ed
Ell
ipti
c
Uns
tif
f en
ed
Ell
ipti
c W
ith
A
C
uto
ut
Sp
ira
l S
t iff en
ed
Circular
dif
fere
nti
d.
Lcve
l of
S
ide
F
orc
eU
scd
ra
ms )
454.
-n
200
&
500
500
75
75
60
0
sti
ffn
es
s was m
casu
rcd
' E
rro
r
+3.7
-leg
-2.5
'3 *O
-5.8
4-38.2
Rcmark
. Bank'
s
pL
ied
Ela
sti
ca
lly
Bu
ckle
d
Ela
sti
ca
lly
I
Bu
ckle
d
Ela
sti
ca
lly
Bu
ckle
d
and
Cra
cked
. B
uck
led
E
las
tic
all
y
Bu
ckle
d
Ela
sti
ca
lly
Bu
ckle
d
and
Cr
acke
d
Slotted 'H' Section Nylon Thread -\
I Steel Base
U
PLAN -
Figure 5. A Schematic Diagram of t h e Stiffness Probe
12 i : m -. .. ,"
Table I1
Sti
ffn
ess
Pro
file
of
Un
stit
'fen
ed C
ircu
lar
Shel
l [J
ndcr
Zer
o A
xia
l Compr::csion.
r
Ccn
era2
or
1
2 3 4 5 6 7 8 9 10
ll
12
13
1 4 15
16
17
18
19
20
21
22
2 3
2 4 2 5 26
27
2a
29
39
31
32
3 3 - 3 . .&
2 5
36
Nor
mal
Sti
ffn
ess
(lb
/in
ch)
Dis
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....
....
....
....
....
....
....
....
....
....
... Scn
m o
f Ll
lc S
he
ll -
Data n
ot a
rqu
irc
d,
.- --
An Evaluat ion Method Based Upon t h e V a r i a t i o n of Dynamic Mass.
I n t h e p r i o r s e c t i o n a method of e v a l u a t i o n based on w a l l
s t a t i c s t i f f n e s s was descr ibed and observa t ions made r e l e v a n t t o t h e
problems assoc ia ted wi th i t s a p p l i c a t i o n . I n t h i s s e c t i o n a v i b r a t i o n
method which t o some degree reduces t h e s e d i f f i c u l t i e s i s discussed.
The concept of s tat ic w a l l s t i f f n e s s v a r i a t i o n and t h e concept
of dynamic mass v a r i a t i o n are cl-osely akin. Thus Nassar (14) under-
took a s tudy t o determine whether o r n o t t h e later v a r i a t i o n could
be l ikewise used.
I n vicw of t h e p r i o r resea rch on t h e a s s o c i a t i o n of v i b r a t i o n a l
behavior and i n s t a b i l i t y (Discussed i n more d e t a i l i n Refs. 14 & 15)
a column and a f l a t p l a t e were included i n t h e t e s t program.
The shaker system cons i s ted of a MB Vibramate E x c i t e r (Model PM 25)
d r iven through a MB power a m p l i f i e r (Model 2125) by a PAR s i n u s o i d a l
output o s c i l l a t o r (Model 110). Th i s was mounted i n such a manner a s
t o ensure good p o s i t i o n a l c o n t r o l and t o enable t h e shaker system t o
apply s u f f i c i e n t normal f o r c e preload t o mainta in con tac t wi th t h e
specimen s u r f a c e dur ing t h e e x c i t a t i o n cycle . The shaking f o r c e and
t h e r e s u l t i n g a c c e l e r a t i o n were measured a t t h e e x c i t a t i o n po in t .
The t ransducer was a BK Impedance Head ( type 8001). The t ransducer
output s i g n a l s were condi t ioned wi th MB Line Dr ivers and MB N 400
s igna l amplifying un i t s . The conditioned outputs were fed i n t o a
SD 101 B Dynamic AnalyserITracking F i l t e r of 1.5 Hz band wtdth tuned
t o the exc i ta t ion frequency. The f i n a l l i n k i n the da t a acquis i t ion
chain was a HP 2115 A computer and a HP 2402 A i n t eg ra t ing d i g i t a l
voltmeter. These l a t e r elements were combined with a crossbar scanner
t o form the universal da ta acqu i s i t i on and processing system used i n
the p r io r referenced t e s t s .
It was found t h a t the dynamic mass a t any point was sens i t i ve
t o the l e v e l of t he exc i t a t i on force used. However, f o r a f ixed
exc i t a t i on frequency and a constant a x i a l load the dynamic mass
varied smoothly with the l e v e l of exc i t a t i on force. Figures 7 h 8
show typ ica l r e l a t i onsh ips between dynamic mass and average exci ta-
t ion force f o r var ious values of a x i a l load. It is c l e a r t h a t each
curve has a d i s t i n c t minimum. h%en the minimum values of dynamic
mass f o r a given frequency a r e p lo t ted against the appropriate a x i a i
load l e v e l a l i nea r r e l a t i onsh ip r e s u l t s , a s s h o ~ q i n Figures 9 & 10.
It is t o be noted t h a t t h i s l i n e in t e rcep t s t he load a x i s a t a point
which is common f o r a l l frequencies and which corresponds t o the
c r i t i c a l a x i a l load value.
A complete summary of the r e s u l t s obtained i s presented i n
Table 111.
It should be noted i n connection with t h i s method tha t the
acquis i t ion of data i s a l i t t l e ea s i e r than i s the case with the
1 lb.
30 13
Figure 8. Rectangular Panel - % vs. F at 30 Hz.
F i g n e 10. E l l i p t i c S h e l l - Minimun MD vs. Corrrsgor.di3g P .
Ta
ble
I
Sp
ecim
en
I
Un
stif
fen
ed
C
irc
ula
r S
he
ll
Un
stif
fen
ed
E
llip
tic
Sh
ell
W
ith
A
Rec
tan
gv
la
r C
uto
ut
,I.
Co
mp
aris
on
o
f t
ac
kl
in
~ lo
ad
s p
red
icte
d
fro
rn
dhnru
nic
mas
s v
ari
ati
on
-
wit
h
tho
se a
ch
iev
ed
on
te
st.
I
Lo
wes
t P
red
icte
d
Ac
tua
l B
uc
kli
ng
$
Err
or
Rem
ark
Bu
ck
lin
g L
oad
( l
b)
Ac
tua
l b
uc
kli
ng
lo
ad
was
d
ete
rmin
ed
by
S
ou
thw
ell
Met
ho
d.
Ac
tua
l b
uc
kli
ng
lo
ad
was
d
ete
rmin
ed
by
S
ou
thw
ell
Met
ho
d.
Ac
tua
l b
uc
kli
ng
lo
ad
is
th
e l
oa
d a
t w
hic
h
sna
p o
cc
ure
d.
(~
uc
kle
d ~la
stic
ally
)
Lo
ad o
ffs
et
to
pro
du
ce
ins
tab
ilit
y
away
fr
om
the
cu
taw
ay
reg
ion
. A
ctu
al
bu
ck
lin
g l
oa
d i
s t
he
lo
ad
at
wh
ich
sn
ap
oc
cu
rre
d.
(~
uc
kle
d ~l
as
ti
ca
lly
)
G~
mn
eral
Note
:The
sh
ell
s u
sed
f
or
th
e v
ibra
tio
n s
tud
y w
ere
the
sa
me
as
th
ose
fo
r s
tati
c s
tiff
ne
ss
stu
dy
. T
he
dis
cre
pa
nc
ies
in l
oa
d c
arr
yin
g c
ap
ab
ilit
y
are
du
e to
va
ria
tio
ns
i.n
th
e a
pp
lie
d
loa
din
g d
istr
ibu
tio
ns.T
he
S
ou
thw
ell
met
ho
d w
as
use
d f
or
the
co
lum
n a
nd
pla
te to
av
oid
'a
mb
igu
ity
in
de
fin
itio
n o
fth
e a
ctu
al
bu
ck
lin
g l
oa
d.
i
-
wall stiffness method but the lnterpretation of the data is some-
what more involired.
2.5 An Evaluation Procedure Based on Combined Loading. -
Duggan (16) and Craig and Duggan (17) investigated the issue
from a somewhat different viewpoint. Circular cylindrical shells,
both stiffened and unstiffened, under axial load are imperfection
sensitive structures. Similar bodies, however, when loaded by
forces normal to their surface are not. Such forces nevertheless
are destabilizing.
Thus the above referenced investigators studied the behavior
of a monocoque right circular cylindrical shell of 16" in length,
11.2" diameter and 0.030" wall thickness under the action of a point
load normal to the shell wall and a uniform axial compression. They
discovered that for fixed levels of axial load the normal force - wall deflection history was initially linear but subsequently became
hyperbolic, (Figure 11). Data from tt:ir loading combination were
analyzed, in the Southwell manner, for different levels of applied
compression. The result was an interaction relationship which was
essentially linear. Thus it was simple to extrapolate the curve of
critical lateral force versus axial compressive load and so deduce
the critical compressive load for zero lateral force. Their result
is shown in Figure 12.
The general validity of their approach cannot be denied but it
A - 700 lbs.
L a t e r a l D e f l e c t i o n
Fi&ire 11. b::d - Deflect ion Plo ts , I n c r c a c i s g h i e l . Jjd, for 220 Degree Angular Position.
must be pointed out that experimental confirmation was made on one
shell only. Moreover, the approach is a little more time consuming
than the direct stiffness approach because of the labor involved
in computing the critical lateral forecs from the displacement data.
2.6 Conclusions Drawn From the Results of the Non-Destructive -- Evaluation Program.
It was concluded from the results, which are sunmtarized in the
previous sections that, unless t?ie large scale vehicles have character-
istics which seriously deviate from those of the models, it should be
feasible at low levels of axial force to accurately determinn the
areas of weakness of the large shells and their probable critical
loads. It was recognised, however, that some difficulties could be
experienced because of the scale of the vehicle and in view of the
difference in load application method.
2.7 A Parametric Study on Ring Stiffened Shells.
The results which were generated in the study summarized in
Section 2.1 led Ford (8) to make a parametric study on ring stiffened
shells. To this end he investigated 6 different longitudenal stil-
fening arrangements and 41 different ring arrangements. The character-
istics of the prime components of the shells which he used are sum-
marized in Table IV and the results which he obtained are delineated
in Tables V and VI.
TA
BL
E IV
CH
AR
AC
TE
RIS
TIC
S O
F TH
E FR
AM
ES
& ST
RIN
GE
RS
OF
THE
SHE
LL
S U
SED
IN
FO
RD
'S
PAR
AM
ETR
IC
STU
DIE
S
L
Sh
ape
I
T
Zr
n
lay
ers
M
Str
ing
er
Ty
pe
A B
no
t u
sed
C
-
D E
F
Fra
me
Ty
pe
A
no
t u
sed
Bn
C
no
t u
sed
no
t u
sed
no
t u
sed
Are
a ins2
0.0
63
0.0
32
0.0
07
5n
0.0
33
0.0
40
4
0.0
20
6
0.0
17
7
Shell
Fam
ily
03
00
0
40
0
05
00
06X
X
08X
X
09X
X
lOX
X
07
01
08X
X
09X
X
lOX
X
Ce
ntr
oid
Height
0.1
25
0.1
58
0.0
15
n.
0.1
23
0.1
10
0.2
09
0.0
74
2
10
3.
I
ins
. 4
0.3
25
0.1
7
---
0.1
3
0.2
0
0.1
5
0.0
78
10
4. J
in
s. 4
0.4
6
0.6
0
---
0.2
8
0.7
4
0.0
51
7
0.0
38
1
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C i i m
8
For a particular longitudinal stiffening the various types of
external multilayer ring stiffened shells were made by successive
modification of one basic shell. This was simply done since the
individual layers of which the rings were made were very flexible.
The added layers were glued to the prior layers by capillary gluing.
One very great advantage of this method was that the process could
be carried out with the specimen installed in the test machine. Thus,
the distribution of line load for each shell of a family was sub-
stantially the same as chat for all other members of the family.
The results for all rings of equal stiffness offer no surprises.
They do, however, demonstrate conclusively that end restraint effects
are of considerable importance in longitudinally stiffened shells
which have relatively light ring stiffening, and thus completely
support the work of Peterson (18).
Perhaps the most interesting quantitative data acquired is
that relative to instability Ec!iavior when all rings do not have
equal stiffness. These results are portrayed graphically in Figures
13 & 14.
Ford also p0ioi.s out in his thesis that both longitudinal and
circumferential waves appear in the pre-buckling deformations of
axi~lly compressed, imperfect stiffened shells. This observation is
in full agreement with those reported in References 19, 20 and 21.
He notes also that these pre-buckle deformations are such as to
Un
ifor
m
Rin
g
So
uth
we
ll
a N
on-U
nif
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l i n e a r theory development (22)
3. T e s t s on Larpe Scale S t r i n g e r dnd Ring S t i f f e n e d She i l s . -
3.1 General Remarks- -
A s noted i n t h e in t roduc tory remarks t h e prime purpose of
t h e progran repor tcd h a r e w a s t h e s tudy of l a r g e s c a l e , r e a l i s t i c a l l y
re in forced c i rc .u la r c y l i n d r i c e l s h e l l s l i a b l e t o genera l i n s t a b i l i t y .
It was t h e i n t e n t t o a c q u i r e s h e l l s of h igh q u a l i t y and t o t e s t
t h e s e under as uniform d i s t r i b u t i o n of a x i a l load a s could be
a t t a i n e d . To meet t h e s e d e f i n i t e o b j e c t i v e s s p e c i s l s h e l l s were
designed at t h e Georgia I n s t i t u t e of Technology and manufactureti by
Skinner Aviat ion, Miami, F lo r ida . These s h e l l s were t e s t e d i n a
f a c i l i t y s p e c i f i c a l l y cons t ruc ted f o r t h e purpose. I n t h e s e c t i o n s
which fol low d e t a i l s of t h e s h e l l s , t h e method of p re7ara t ion f o r
t e s t , the t e s t f a c i l i t y , t h e ins t rumenta t ion and t h e ma;or r e s u l t s
a r e ou t l ined .
3.2 D e t a i l s of t h e S h e l l s . -
3.2.1. - Xain Body Construction.
A l l t h e s h e l l s used i n t h i s program were made , ~ f alunir.um
a l l o y (Spec. 7075-T6) and had i d e n t i c a l o v e r a l l dimensions.
They were 74.5 lnches i n diameter anii 108 inches long. Each
s h e l l was made from 6 i d e n t i c a l panels . These panels had a
nominal sk in th ickness oL 0.0253 inches and were re in forced
3 2
by a m u l t i p l i c i t y of 2-shaped s t r i n g e r s which had t h e c ross -
s e c t i o n a l shape shown i n Figure 15. Orte edge of each pane!.
was joggled, and two s t r i n g e r s were r i v i t e d a long each j o i n t
l i n e with 0.125 ~ n c h diameter r i v e t s a t 0.75 inch p i t c h . The
rena in ing s t r i n g e r s were a t t ached t o t h c shee t - - i th adhesive
FM 126-2.
The ends of t h e s h e l l s were re in forced wi th a 0.040 inch
t h i c k doubler p l a t e of 7C?5-T6 m a t e r i a l . They were held
c i r c u l a r by means of heavy r o l l e d C s e c t i o n frames. These
frames had t h e cross-sectior, dep ic ted i n Figure 16. They
were loca ted i n such fash ion t h l t 0.125'' cf r e i n f o r c e d s h e l l
w a l l procr~idsd beyond t h e i r extreme f a c e a t each end of the
s h e l l .
The in te rmedia te frames were r o l l e d from t h e s t r i n g e r
s e c t i o n . They were a t t ached e i t h e r t o t h e ou te r s k i n w ~ r l l
r i v e t s , whose p i t c h was i d e n t i c a l t o t h e s t r i n g e r p i t c h , o r
t o the l i p f l a n g e s of t h e l o r g i t u d e n a l s t i f f e n e r s . I n a l l
cases i n which t h e i n t e r n a l frames were used a n t i - p e e l r i v e t s
were d r iven i n t h e s k i n and s t r i n g e r base ad jacen t t o the
i n t e r n a i r i n g .
3.2.2. blain Bo?y inspec t ion . - A l l t h e t e s t v e h i c l e s were thoroughly inspected be fo re
t e s t . Tn every case the bonded j o i n t s appeared t o bc of good
I
ALL RADII @I
Figure 15. Ring and Stringer Sectio~.
Figure 16. End ning Section
q u a l i t y . Tes t coupon j o i n t s made a t t h e t ime of f a b r i c a t i o n
and us ing t h e i d e n t i c a l process were always f u l l y c o n s i s t e n t
and s a t i s f a c t o r y . A l l r i v e t e d seams and j o i n t s were w e l l made
and t i g h t .
C i r c u l a r i t y and generator s t r a i g h t n e s s was checked on a l l
speciments, bu t a d e t a i l e d s tudy was made on two only. For
t h i s purpose s t i f f end p l a t e s , wi th c e n t r a l bear ings , were
a t t ached t o t h e specimen. The specimen was then mounted, wi th
i t s a x i s h o r i z o n t a l , i n a heavy framework i n such fash ion t h a t
i t could be r o t a t e d about i t s a x i s . The s h e l l was r o t a t e d about
t h i s a x i s and t h e v a r i a t i o n of p r o f i l e recorded a t i n t e r v a l s
a long t h e l eng th c f t h e s h e l l . A s i n g l e l i n e a r v a r i a b l e d i f -
f e r e n t i a l t ransformer was used a s t h e displacement t ransducer
f o r a l l displacement measurements. To e s t a b l i s h a known measure-
ment re fe rence , a t e n f o o t p r e c i s i o n s t r a i g h t edge was pos i t ioned
o u t s i d e t h e s h e l l and Y a r a l l e l t o t h e a x i s . The LVDT was then
a t t ached t o t h e s t r a i g h t edge i n such a manner t h a t i t could
be posi t ioned along t h e specimen a x i s a s d e s i r e d . An e l e c t r o -
o p t i c a l system was used t o t ransduce t h e angular p o s i t i o n . A
block diagram of che o v e r a l l system i s given i n Figure 17.
The method of a n a l y s i s of t h e d a t a acquired i s given i n Reference
16 and Reference 24. Computer programs p e r t i n e n t t o t h e a n a l y s i s
a r e l ikewise given i n t h e s e documents.
Integrat ing
S i g n a l C a d i tioner 1 S c ~ u e r c ~ r
tl 3igi:al
--L--- ~ o n p u ter
if \ag. Tape
Figure 17. Block Diagram of C i r c u l a r i t y Checking System.
3 . 2 . 3 . S h e l l End Machining.
The d e s i r e d uniformity of l i n e load around t h e s h e l l
ends cannot be achieved u n l e s s a v i r t u a l l y p e r f e c t mating
between t h e s h e l l ends and t h e loading p l a t e s can be assured.
A a j o r i s s u e w a s t h e r e f o r e t o d e v i s e means of accomplishing
t h i s . To meet t h e o b j e c t i v e a s p e c i a l machine was designed.
(This i s f u l l y desc r ibed i n Reference 7 ) . However, no machine
can be made t o perform t h e t a s k of trimming t h e ends f l a t
u n l e s s t h e f r e e e x t r e m i t i e s of t h e many s t r i n g e r s a r e thoroughly
s t a b i l i z e d . Th is w a s done i n two ways: 1 ) by s e t t i n g t h e
s t r i n g e r ends i n a m a t r i x of low mel t ing p o i n t a l low and 2) by
s e t t i n g t h e s t r i n g e r ends i n a mat r ix of automobile body pu t ty .
The latter approach turned o u t t o be by f a r t h e most econom-
i c a l and s a t i s f a c t o r y . With t h e automobile p u t t y t h e c u t t i n g
t o o l remained sharp throughout t h e opera t ion .
3 .3 . Tes t F a c i l i t y . -
The s h e l l s were t e s t e d i n t h e School of Aerospace C y l i n d r i c a l
S h e l l t e s t f a c i l i t y , which is descr ibed i n d e t a i l i n Reference 23.
The s t r u c t u r a l test complex h a s two main components, 1) t h e
loading and f o r c e r e a c t i o n system and 2) t h e d a t a a c q u i s i t i o n and
process ing system.
3.3.1. The Loading and Force React ion System. -
The b a s i c p r i n c i p l e of t h e load ing and f o r c e r e a c t i o n
system is i l l u s t r a t e d i n Figure 18. The compressive load
was app l i ed by a m u l t i p l i c i t y of h y d r a u l i c a c t u a t o r s
pos i t ioned around t h e base of t h e s h e l l . For one s h e l l
( s h e l l B) 72 a c t u a t o r s , Enerpac RC 1010, were used. For
t h e o t h e r s h e l l s 18 , OTC No. YS Shorty Type, w?re employed.
The a c t u a t o r s were a t t a c h e d t o a heavy r e t a i n e r r i n g v i a
r a d i a l l y a d j u s t a b l e base p l a t e s . They were ar ranged s o
t h a t t h e i r c e n t e r s of t h r u s t l i e on a c i r c l e whose diameter
matched t h a t of t h e c e n t r o i d a l l o c u s of t h e s h e l l under
i n v e s t i g a t i o n .
The f o r c e provided by t h e j a c k s was f e d i n t o t h e t e s t
s t r u c t u r e v i a a bea r ing p l a t e o r s t r u c t u r e . (The bea r ing
p l a t e was used w i t h t h e 72 j acks and t h e bea r ing s t r u c t u r e
wi th t h e 18 j acks ) . Under no load cond i t ions t h e bea r ing
dev ices were c a r r i e d on a d j u s t a b l e suppor ts . These were s o
trimmed t h a t t h e upper bea r ing s u r f a c e l i e i n a h o r i z o n t a l
plar.2 whi le t h e lower s u r f a c e c l e a r e d t h e jack pads. B a l l
j o i n t s were provided between t h e j a c k heads and pads. (See
D e t a i l B.)
Load r e a c t i o n was v i a a s p e c i a l upper r e a c t i o n r i n g which
was t i e d t o t h e j ack suppor t r i n g by 36-1" diameter s t e e l
I~k:t- ,r: ~~,~J(~GLI,ITY OF TIIE 1 i i , . i t i , .. dl\!, 1' iG;E I6 POOR
Guide Structure
Section A
Figure 18, Schemrtic of Large Shell Terting Syrtam
-,,,,,,,, ,,.,. . . .. ,_- -- .--. .. . "..* . - .. +.*. . . ~ a 4 , ~ ~ l ~ b , h ~ g
tie bars. A direct tie bar system would give rise to
considerable trim difficulties and so high quality hydraulic
load cells were fitted between the tie rod transfer beams
and the upper surface of the reaction ring, Detail A. These
reaction cells were in~erconnected to form a closed system.
3 .3 .2 . Hydraulic System. - The hydraulic power for the l ~ s d actuators was provided
and controlled via a servo-control system of orthodox character.
All load jacks were interconnected and fed from this common
source.
3 . 3 . 3 . Load Determination.
Load was determined from the pressure applied to the
loading actuators. The pressure generated in the reaction
cells was used as a check. These hydraulic pressures were
read on precision pressure gauges manufactured by Heise.
3 . 4 . The Data Acquisition and Processing System. - -
The data acquisition and processing system used in the
study was the Aerospace Struct.. es Laboratory facility. The
essential elements of this system are delineated in Section
2.1 and a data acquisition flow diagram is presented in
Figure 1. (For more specific details see Keference 23).
3.5. I n s t a l l a t i o n of tlie Test Vcllicle i n t'lr F a c i l i t y . -- -.-----.
The t e s t v c l ~ i c l e was i n s t a l l e d i n t h e io l lowing manner:
(1) The lower j a c k s wcre accurate1.y s e t i n a c i r c l e of
a p p r o p r i a t e d iameter .
(2) The s h e l l was h o i s t e d i n t o the r i g and suspended
above t h e j ack system.
(3) The lower load t r a n s f e r s t z ~ c t u s e \:cis s l i d i v t o
p o s i t i o n and t h e b e a r i n g pad 31.:izilei w i t 1 1 t h c
load ing jacks.
( 4 ) The s h e l l al.igmnent g u i d e s were a t t ~ c l l c d t o t h e
load t r a n s f e r r i n g .
( 5 ) The s h e l l was lovered i n t o p o s i t i o n .
(6) The r e a c t i o n pad, wi th upper load c e l l s attached,
was placed i n p o s i t i o n and a l i g n e d .
(7 ) The t i e - r o d s and b r i d g i n g s t r u c t ~ i l - e s w r c p l aced
i n p o s i t i o n .
(8) The t i e - r o d s wcre s e t v e r t i c a l .
(9) The rcncti1:n r i n g g u i d c sysccm was i r s t n l l . c d .
(10) Mien t h e a p p r o p r i a t e p o s i t i o n s of a l l e lements
had beec e s t a b l i s h e d , tlie rnatinz of t h e Inad and
r e a c t i o n p l a t e s with t h e ends of t11e s h e l l ~a.as
i n v e s t i g a t e d . Th i s was done by scparrltin;: tlic
s u r f a c e s (;ka) a n d i n s t a l l i n g p l a s t ir,ay,cs , ,:I))
between them a t c l o s e l y spaccd i n t e r v a l s . Thc
mating s u r f a c e s were then brought i n t o c o n t a c t and
a smal l a x i a l force a p p l i e d . A f t e r t h i s s l i g h t
colnpressjon t h e s u r f a c e s wcre aga in separa ted and
t h e q u a l i t y of f i t dctermincd f r o n ~ t1:c degree of
f l a t t e n i n g of t h e gages. Except i n t h e develop-
lne l l ! oi Lilt2 ~ l ld~ l i in i l lg p rocess it: bds i ~ v ~ Lodi~:
necessa ry t o remove t h e speci.nen and ma!:e any
changes a s t h e r e s ~ l t of t h i s checl;. In a11 c a s e s
t h e gap between t h e mating s u r f a c c s was cons. idcrably
l e s s than 0.001 inches and this m i s f i t ~ z a s over
ve ry smal l l o c a l i z e d a r e a s .
(11) I n some c a s e s R t h i n l a y e r of llevcon, a v i s c o i : ~ s t c e l -
f i l l e d cpoxy, w a s sprctnd bctwecn tlrc a;lt ill;, S I I ~ ~ : : C ~ : ; .
The mating surraccs wcre t l ~ c n sr1:lcezcd toy,r!t;licr 'cgit-!i
a subs tn r . t in1 conpress ion. (kc )
Spec is1 KotQS-
(*a) Due t c t h c f ; lct t h a t i t was nccess; lry t o s t - a b i l i z n
t h e f r e e ends 01 t11e s t r i n g e r s pri.or r o enti t r i m i n ; ,
and the f a c t t h a t tilis m a t e r i a l l..~;ls riot rcmovecl ;if- t-er
t h i s o p e r a t i o n was comp!ct.c, p lane s u r f a c c s c x i s l c d
a t t h e ends of t h e s h e l l s .
(*b) P l a s t i g a g e s a r c srnnll diameter rot15 of s p e c i a l pl.:i:;t- i c
m t e r i a l . ?'hey 2rc coi;:n;onl.y c m p l u y e d f o r ( l e t c,rr:. i ; ; . t Ir>ri
of haft-bearing s lop , e t c . They are made by
P e r f e c t Circle, Hagerstown, Indiana.
(*c) Despi te t h e l i b e r a l use of t h e a p p r o p r i a t e p a r t i n g
compound, some Devcon became a t t ached t o t h e bear ing
p l a t e s . I n view of t h e time and expense involved
i n r e s t o r i n g t h e s e s u r f a c e s t o t h e i r o r i g i n a l p r i s t i n e
condi t ion, and t h e ve ry s l i g h t improvement i n d i s t r i b u -
t i o n r e s u l t i n g from its use , t h e p r a c t i c e was d i s -
continued, Devcon is a product of t h e Devcon Corpora-
t i o n , Danvers, Massachusetts.
3.6 9 a l i t y and Accuracy Achieved i n t h e Large Scale S h e l l - Program.
Every e f f o r t was made t o a t t a i n t h e h ighes t q u a l i t y and
accuracy throughout a l l phases of t h e work. The fol lowing
s e c t i o n s summarize t h e r e s u l t s achieved.
3.6.1. S h e l l C i r c u l a r i t y .
The checks on c i r c u l a r i t y showed t h a t t h e s h e l l s d i d no t
d e v i a t e apprec iab ly from c i r c u l a r . The maximum amplitudes of
t h e excurs ions were of t h e o rder 0 .1 inch, s e e Figure 19 which
p r e s e n t s t y p i c a l da ta .
De ta i l ed a n a l y s i s ind ica ted t h a t :
(1) There was a tendency cowards o v a l i t y .
( 2 ) The l z p j o i n t s kept t h e genera to rs , i n t h e i r imme-
d i a t e v i c i n i t y , ve ry s t r a i g h t .
( 3 ) The l a p j o i ~ t s had a s i g n i f i c a n t in f luence on t h e
c i r c u m f e r e n t i a l dev ia t ions .
(4) The r i n g s had l i t t l e in f luence on t h e long icud ina l
dev ia t ions .
These l a t e r p o i n t s a r e made clear by t h e d a t a which is
given i n Tables VII & VIII,
3 . 6 . 2 . S h e l l End Qual i ty .
The s h e l l ends were p a r a l l e l t o wi th in 2 O . l O , and l o c a l
v a r i a t i o n s i n f l a t n e s s were c o n t r o l l e d t o wi th in 2 0.0005 incli.
3 . 6 . 3 . Load and Reaction Bearing Surface Qual i ty . -- The load and r e a c t i o n bear ing s u r f a c e s were ground f l e t
t o wi th in + 0.(3005 inch.
3 . 6 . 4 . F i t of S h e l l Ends on t h e Load and Reaction Bearing
Surfaces.
Checks wi th p l a s t i g a g e s showed t h a t the maximum gap
between the two s u r f a c e s - s h e l l and bear ing - was no more
than 0.001 inch. Such v a r i a t i o n s were few i n number and
were l o c a l .
3.6.5. Load Steadiness .
The servo c o n t r o l held t h e appl ied l o ~ d so s teady t h a t
no movement of t h e Heise p ressure gauge needle war d i s c c r n i t l e .
3.6.6. Repeatability.
The total system, load and instrumentation, gave excellent
repeatability. The strain readings obtained for nominally
identical loadings showed no significant variations.
3.7. Results Obtained. -- The results which were obtained in the tests made on four
large shells whose characteristics are given in Table IX,are
surrmarized jn che sections which follow.
3.7.1. Non-Destructive Evaluation. - The non-destructive evaluation methods which were devised
on the model shells were not successfully applied to all
large scale shells. The prime reason for this lay in the
incompatibility of the tesc system for the large shells and
the probing systems. It is clear from the earlier section
(3.3.1J that the test arrangements for the large shells were
such that there were, of necessity, considerable encmberances
around the outside of the shell. Their presence made the
application of the dynamic mass method unworkable. There was
insufficient room to use :he exiter system in an adequate
fashion. These enccmberances likewise restricted the full
operation of the wall static stiffness method. For the static
stiffness technique the probe was much smaller than the exiter,
but the transducer ring was too flexible. Thus, the dis-
placements which were caused by the applied normal force could
not be measured, it was thought, with instruments mounted
outside the shell. Wall motions therefore had to be
determined using transducers which were internally mounted
and this led, naturally, to such a time consuming process
as to be impractical.
It was not until the end of last test was reached that
methods of overcoming the difficulties were devised. At
this late stage it was recognized that the tie rods, being
under substantial tension, could well be used as the dis-
placement transducer supports. A very simple device based
on this concept was constructed and used at station 220°,
Bay 5, shell A. The relative stiffnesses of the shell wall
were ascertained for a side push of the order of 25 lb., for
axial loads corresponding to jack pressures of 800, 1000,
1200 and 1400 psi. It was found that these stiffnesses de-
creased linearly with applied 1oad.When the stiffners versus
applied pressure curve was extrapolated the indicated
critical pressure was 2170 psi. This was in excess of the
actual value of 2000 psi but was in excellent accord with
the 2195 psi value computed from the local strains.
The second method which was devised, at this time, was
the use of self adhesive strain gauges of the Hickson variety
These gauges were installed back to back on the skin and the
stringer lip. These devices likewise led to linearly
varying stiffness parameter versus applied pressure lines.
Several stations on the shell. were checked in this manner and
t h e lowes t c r i t i c a l p r e s s u r e de termined by t h i s means w a s
1995 p s i . T h i s v a l u e i s a lmos t i d e n t i c a l w i t h t l ie a c t u a l
v a l u e of 2000 p s i . There are two r e a s o n s why t h i s r e s u l t
may be somewhat f o r t u i t o u s . F i r s t , t h e Hickson gauges have
a tendency t o d r i f t . Second, i n o r d e r t o i n s t a l l t h e i n n e r
gauges i t was n e c e s s a r y t o c o n s t r u c t "mounting bases" by
b r i d g i n g t h r e e a d j a c e n t s t r i n g e r s w i t h a t i g h t l y s t r e t c h e d
L h i n s h e e t of aluminum f o i l . T h i s f o i l was bonded t o each
s t r i n g e r l i p .
3 .7 .2 . Maximum Load L e v e l s A t t a ined .
The maximum l o a d s which t h e s h e l l s c a r r i e d a r e d e l i n e a t e d
i n Tab le X .
3 . 7 . 3 . Buckling Behavior and Pos t Buckled Cond i t ion .
The s h e l l s a l l buckled i n a c h a r a c t e r i s t i c diamond
p a t t e r n and i n t h e normal snap f a s h i o n . There was, however,
a d i f f e r e n c e between t h e b e h a v i ~ r of :he s h e l l s w i t h ex-
t e r n a l r i n g s and t h o s e w i t h i n t e r n a l r i n g s . . For t h e s h e l l s
which had e x t e r n a l r i n g s t h e buck le p a t t e r n covered t h e
complete s u r f a c e . For t h e s h e l l s w i t h i n t e r n a l r i n g s t h i s
was n o t t h e case .
A f t e r removal of l o a d t h e wide sp read p a t t e r n on tile
e x t e r n a l l y r i n g s t i f f e n e d s h e l l s was s t i l l e v i d e n t tlzrougliout
t h e s t r u c t u r e . Rings were d i s t o r t e d from c i r c l e s i n t o some-
what f l a t s i d e d i i g u r e s . The e x t e n t of tile f l a t n e s s depending
m CJ G J U .
c u m
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u . Q) . u s
r l a u ,-I CQ 0 a1 clJ .G 6 r: a a -7.4
TI Q C L i d - 1 3 a 0 I) G d c ' s ri
a 3 U S c UJ UJ rd > 0 i\* L? v o u
ln (13
4-l a o m 0 C r 3 u
o L) -3 -! .d L L TI% u
GJ crl
a E L i a o o
&I c: a d ~4 ci
3 U S U U , 3 w &l
S<L4
g 6 E;:
---
A
c-4
rd c h .d r; a a J a c U U U GI u :g ri o rs e, cr o c: a &I 0 .:-I U a a
4-l rd a E G a a~ ;I;
u U
r i m . rLt 2% 0 r; s .ri 0 c 4 cd d
< di 3
LG
4 . r: c u : f i .d 'd LT? -. 0 3 .
A .n
L) 5: - r: V3 0 a
m ri
h 0 Q\
m m C\t
U
0 L 1 c-4 .. 02 rl
cn In
cn 'On
0 m
C
a
~2
a) a) Ln
m
I-
m
,-I I
IJ-l r3 C' v r- .n' n .. u a m
a n ' a I, C? b 0 r-l N u c i -
d 4
3 ... 4 Ln
L-
ri 03 N
n * CL) N
rn
I G C? - a ri
0 r n
n
cn ri
somewhat upon t h e a x i a l l o c a t i o n . There were , however,
no element f a i l u r e s of o t h e r t han a n i n s t a b i l i t y type . No
ev idence t h a t t h e s h e l l s o r any p a r t t h e r e o f had come i n t o
c o n t a c t w i t h t h e t i e r o d s d u r i n g t h e b u c k l i n g p r o c e s s
e x i s t e d .
The s h e l l s w i t h i n t e r n a l r i n g s d i d n o t buck le i n t h e
saue manner. For t h e s e s h e l l s t h e buck le p a t t e r n d i d n o t
comple te ly f i l l t h e s h e l l s u r f a c e . Moreover, i n t h e s e
c a s e s , when t h e l o a d was removed t h e r e was no v i s i b l e s i g n s
of damage on a t l e a s t one h a l f of t h e s u r f a c e . I n t h o s e
r e g i o n s which were damaged t h e r e was s t r o n g ev idence t h a t
t h e s t r u c t u r e had v i o l e n t l y come i n t o c o n t a c t w i t h t h e
t i e b a r s d u r i n g t h e i n s t a b i l i t y . Frames were t o r n a p a r t
a t t h e i r j o i n t s ; t h e r e were v e r y s h a r p c r e a s e s i n t h e
s k i n and some l o c a l t e a r i n g .
3 . 7 . 4 . Load-Strain R e l a t i o n s h i p .
S t r a i n s were measured a t 180 p o i n t s . B ine ty of t h e
measuring s t a t i o n s were on t h e o u t e r s k i n and 90 on t h e
s t r i n g e r l i p s . The l o n g i t u d i n a l gauge s t a t i o c s were a t
t h e meets of 5 p l a n e s , normal t o t h e s h e l l g e n e r a t o r s ,
w i t h t h e o u t e r s k i n and t h e s t r i n g e r l i p s . C i r c u m f e r c n t i a l l y
gauge s t a t i o n s were 20" a p a r t and back t o back. The
v e r t i c a l l o c a t i o n s a r e g iven i n Tab le X I .
The s t r a i n gages used were of tlle Micro-Pleasurement
t y p e , CEA-15-250 UW 1.20. They were i n s t a l l . c d i n accordance
*
In
'2 0 -4 u Id u V3
e
d 0 .A U (d U V3
ol
eb -4 u (d U m
c\1
c 0 -4 U m U V)
4
G .d u (d U m
4 cl W z m
*
lrl
m 0 rl
0 al
* lrl
CC d
In
3
4
In
m 0 d
0 al
u m
cO rl
m u
9:
In
m 0 4
0 cn
m N
b 6
00 rl
In
u
U
m m 0 d
0 m
m L-4
b e
CO rl
In
e
C1
2 (d rl a a, cn (d e a,
e C
Lo a,
U s C
.A
a, $4 (d
a, rl e (d U
a,
P (d
c .,-I
V) U .ri c 7
a, s w
with t h e makers recommended procedures and t h e i r output
was processed by t h e ins t rumenta t ion system previously re-
f erenced.
Tables XI1 through XV a r e t y p i c a l d a t a p r i n t ou t s .
Each t a b l e con ta ins t h e f u l l 180 channels of informat ion
f o r a s p e c i f i c app l ied load. I n o rder t o cover t h e whole
family of s h e l l s t e s t e d one t a b l e is given f o r each of t h e
four s h e l l s . The broad spectrum of loading is represen ted
s i n c e each s e t of d a t a corresponds t o a d i f f e r e n t percent-
age of t h e a p p r o p r i a t e c r i t i c a l load.
The s t r a i n d a t a which was recorded shows t h a t a l l
s h e l l s behaved i n a s i m i l a r f ash ion i n so f a r t h a t -
(1) I n a l l cases t h e l o a d - s t r a i n r e l a t i o n s h i p s were l i n e a r
u n t i l t h e h ighes t load l e v e l s were reached.
(2 ) A t t h e h ighes t load l eve l s , reg ions i n which t h e load-
s t r a i n r e l a t i o n s h i p s became non-lir.ear e x i s t e d f o r
a l l s h e l l s ,
(3 ) When t h e load-s t ra in r e l a t i o n s h i p s became non-linear
t h e s t r a i n - d i f f e r e n c e s were r e l a t e d t o t h e load l e v e l s
by hyperbol ic equa t ions i n over 95% of the cases .
( 4 ) The s k i n s t r a i n s were g r e a t e r than t h e s t r i n g e r l i p
s t r a i n s a t t h e e x t r e m i t i e s of a l l s h e l l s , i n d i c a t i n g
t h e presence of moments a t t h e s h e l l ends.
(5) A t t h e lower load l e v e l s , t h e s k i n s t r a i n s and the
s t r i n g e r l i p s t r a i n s were s u b s t a n t i a l l y t h e same over
t h e region from 18.0 inches above base t o 90 inches
b
t
tn
5 .rl U (d 4J rn
* C 0
U a U rA
m
!3 rl U a U ~1
N
do .rl U t'J U rA
rl
c 0 4 U
U V)
h al
H
Li al u 5 0
,
u
0
Li a 5 +I
U 3 0
h g) c E:
W - Li
U 3 0
Li
g c H
&
U 7 0
3
\ ~ ~ m ~ a m w u m m m m m u ~ ~ ~ w U N m N b m U m m Q a m N U m m q e m m ~ m u m m m m m m m m m m m m m I I I I I I I I I I I I I I I I I I
m c C r l u m r l m b O m C O u m 4 r l m d \ o o ~ m m w ~ h w c o \ o r n c o ~ n ~ w o m ~ u u m m m m m m m m m m m m m u m u 1 I I I I I I I I I I I I I I I I I
b \ c r ) N N E O r l ~ N v l ~ h l U 0 \ Q Q I Q Q ) I n h m c o r - . o h . o Q ~ - a r r a a m b h b w m m m m m m m m m m m m m m m m m m
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
N d ~ O m r l c O m m O m w m 4 m m b r l b a m r - m m I n I A u ; m u u u m V ) m m \ o m m m m m m o m m m m m m m m m m m I I I I I I I I I I I I I I I I I I
~ a ~ ~ ~ i r l o m ~ ~ ~ o m ~ m m m m m m c o b Q f i w b a b a m a m \ O a Q Q = ' - m m m m m m m m m m m m m m m m m m I I I I I I I I I I I I I I I I I I
r - w m c o r \ l r 9 u r l \ O + m * * r ( m h * m W b Q r - w h h c o r - h w \ O h m m b b m m m m m m m m m m m m m m m m m m m I I I I I I I I I I I I I I I I I I
r i C O C O * C O \ O b N h Q O \ O W N m b b 1 c o a \ o r ~ r t \ ~ m \ ~ a ~ b h a 3 m m m m ~ m m m m m m m m m m m m m m
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
r r l \ O \ o h l W N U ~ d G \ O r l O V t A b r \ O L n U l v ) U I A \ O m \ O h \ r ) O I m b \ b m \ o \ o m m m m m m m m m ~ m ~ m m m m m m I I I I I I I I I I I I I I I I I I
d b b \ d N h U U b N m r l m m m I cn 1 d o m r l N m m a m o m N m r l b ~ w ~ m m ~ m m m m m m m m m m m ~
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
m m m m ' , r ! m m u c n u m \ o ~ o m v l m d o m m m o r l r l m ~ c i o o r l r l h l m u e m m m m u ~ u m m m u u u u u m I I I I I I I I I I I I I I I I I I
Ta
ble
XI\
J ---
Shell A
. S
tra
ins
(m
icro
-in
ch
pe
r in
ch
) a
t 7
5% o
f C
riti
ca
l Load.
Sta
tio
n 1
Ou
ter
I -1247
- 1334
-1228
-1296
-1,724
-11
66
-1
22
9
-
-
-1296
-135'8
- 1358
-1134
-1312
-1334
-12!6
-1333
-1373
-1
19
5
<
Str
ltio
n 2
1
Inn
er
-If216
-971
-1E26
-1E3.3
-1017
-1134
-1015J
-1GlE5
-1111
-99
6
-1221
-11343
-915
-985
- I103
-1E79
-1E17
-18
32
Ou
ter
-1189
-1164
-1163
-1125
-1144
-1150
-1166
-1132
-1 237
-
-11-28
-1072
-1132
-11
59
-1194
-116a
-1161
-1229
Inn
er
-977
-1226
-1266
-1219
-1248
-1156
-1189
-12
94
-1
2A
2
-1279
-1169
-1115
-1255
-13
94
.-I239
-1234
-1256
-12i3
Sta
tio
n 3
Ou
ter
-1235
-1178
-1211
-12
63
-1176
-125'5:
-1154
-1239
-1295
-1224
-1161
-.I315
-1i76
-1223
-1251
-12
21
-1
18
0
-1292
Inn
er
-1214
-1234
-1273
-1281
-1275
-1177
-1229.
-1213
- 1258
-iT
-53
-1221
-la77
-1168
-1177
-1243
-1215
-1191
-1182
Sta
tio
n 4
Ou
ter
Inn
er
-1181
-12
25
-11lir4
-1275
-1162
-11
82
-1
114 -1292
-1191 -1223
-11
09
-1241
-1184 -1196
-1163 -1234
11
5 2
-1149 -1254
-1181 -1264
-1158 -1195
-11
82
-1
25
3
-1171 -1252
-1153 -1180
-f)8@
-1164
-1148
f
Sta
tio
n 5
-12
26
-1217
-1227
Ou
ter
-12A9
-1232
-1149
-1276
-1247
-1159
-1233
-1255
-i1
46
-1211
-1241
-1287
-12
56
-1303
-1152
-1236
-1272
-
Inn
er
-1136
-1269
-lugs
-944
-1220
-1103
-1156
-1173
-1178
-1145
-!I46
-1124
-1131
-1162
-1204
-1234
-1~30
-1191
b
above base. Thus the end moments died out within 18
inches and the central region was under almost pure
axial conpression.
(6) As the load levels grew to their highest values there
were alternately regions in which the skin strain
exceeded the str'7ger lip strain and regions in which
the reverse occurred.
(7 ) The strain differences along the panel verti-1 a 1 joint
liaes were always small.
(8) There was one region at the mid-heig!.t of c $ch shell
for which the strain-difference exceeded all others
at the highest load levels. At this locality the
skin-strain always exceeded the stringer lip strain.
In view of these similarities it might well be conjec-
tured that the buckling behavior of the four shells 1:ould
be identical. It must be remembered, however, that ti~ese
are merely qualitative similarities.
rZ clearer understanding of the instability behavior of
the individual shells must come from a more detailed
quantitative treatment of the data obtained at the highest
load levels. As noted earlier, under these conditions tlicre
were a c+mher of strains which were such tllar t h e strail1
differences were rrlcited to the load in 9 hyperbolic
fashion. In these cases the Southwell rnc~tllod can be used
to estimate the load levels which would corrcspon~i to an
i n f i n i t e s t r a i n difference. This has been done f o r a l l
s h e l l s and the r e s u l t s of these computations a r e presented
i n Tables XVI t lrough XIX. It is c l e a r from these t a b l e s
t h a t t h e lowest values of c r i t i c a l load computed i n t h i s
manner a r e always i n c lose agreement with those ac tua l ly
at ta ined. It is equal ly c l ea r t h a t a l l the load values
which a r e derived from t h i s non-linear da ta do not cor-
respond t o inward motions. Moreover, t he values which
a r e per t inent t o an outward motion a r e most f requent ly
a s c lose o r c loser i n value t o the achieved c r i t i c i l load
than a r e those which correspond co an inward motion.
It Is well known t h a t s h e l l s u d e r a x i a l compression
col lapse inwards when they become ur:stable. It is con-
cluded therefore t h a t those elements which a r e tending
t o i n s t a b i l i t y outwards can and do a c t t o t r i g g e r i n s t a b i l i t y
inwards. It would seem l i k e l y t h a t when they reach t h e i r
c r i t i c a l condition and move outwarls they a r e res t ra ined
from excessive d i s t o r t i o n by t h e remainder of t he s h e l l .
Nevertheless, t h e i r sudden "yielding" must be accompanied
by a sudden r ed i s t r i bu t ion of load over those regions which
have not yet reached c r i t i c a l conditions. This red is t r ibu-
t i on , a l l i e d with the st:;ses induced by the &=s t r a in ing
ac t ion , then p rec ip i tn re s i a i l u r e of those elements which
a r e na tura l ly unstable inwards. It seems reasonable t o
TABLE XVI. LOCAL STRAIN CONDITIOP!S
AN
D CRITICAL LOADS DERIVED FROM HIGHEST LOAD LEVEL DATA I
1 SHELL A
Station 3
6 constant
& constant
1.243
[o]
! .I63 [i]
1.608
[o]
1.355
[i]
1.154 [o]
1.140
[i]
6 constant
&' constant
1.081 [o]
1.098
[i:
1.021
[o]
1.521 [i]
0.991
[o]
f constant
8 constant
1.448
[i]
---
Angle
I
kcees
Station 4
8 constant
1.875
[o]
* A
[il
1.381
[o]
1.000
[i]
1.275
[o]
0.999
[i]
1.402
[o]
1.010
[i]
1.177
[o]
$' constant
4 constant
$ constant
1.124
[o]
8 constant
/ constant
J constant
-- 1.400
[ol
40
6 0
80
100
120
140
160
180 I 2
00
220
240
260
280
300
320
340
--
-
Remarks
COMPLETE
I SHELL
BUC
KLE
D
AND
DANAGED
-
1
Station 2
S constant
1.190
[o]
1.516
[o]
8 constant
0.972 [o]
6 consts lt
1.245
[o]
1.719 [o]
0.995
[o]
---
1.095
[o]
*A
[ol
1.147
[o]
1.217
[o]
6 constant
1.271 [o]
4 constant
1.069
[o]
-
, 1 6
Strain difference
[! tering ; inst
ability outwards
1 $r
6 reverses in sign
unstable inwards
6 c
hanging very zapidly
has a step change
be innin to decrease
General
TJocal critical load values normalized to actual critical
1 Note
of 233,705 11
.
I G
ener
al I
Lo
cal
cri
tic
al
load
va
lue
s n
orm
aliz
ed
to a
ctu
al
cri
tic
al
No
te
of
25
5,9
07
lb
,
m
Cn
TA
BL
E
XV
III
LOCA
L ST
RA
IN C
ON
DIT
ION
S AN
D
CR
ITIC
AL
LO
AD
S D
ERIV
ED FROM H
IGH
EST
LOA
D
LE
VE
L DA
TA
--
- ---
-
SHE
LL
C
--- b
Ang
le
Deg
rees
0
2
0
40
6 0
8 0
1
00
1
20
1
40
1
60
1
80
20
0 2
20
240
260
280
300
320
340
Sym
bols
C
Sta
tio
n 2
1
.06
8
[i]
1
.11
2
[o]
1.8
83
[
i]
*A
[il
1
.17
2
[o]
1.4
43
[o
] *A
[ iI
1.0
29
[o
] 1
.00
6
[i]
--
- 1
.14
2
[o]
6 m
O*
1.2
20
[o
] $
co
nst
an
t --
- 6
co
nst
an
t $
co
nst
an
t 1
.14
2
[o]
6 S
tra
in
Eer
ence
[o
] te
nd
ing
to
in
sta
bil
ity
ou
twar
ds
+ s
rev
ers
as
sig
n
[i]
u
nst
ab
le i
nw
ard
s A $
ch
ang
ing
ver
y r
ap
idly
I
Sta
tio
n 3
1.0
31
[i]
1.0
34
[o
] 0
.96
1
[o]
1.0
28
[
i]
1.0
15
[o
] 1
.03
8
[i]
1
.13
0
[i]
* 4
dev
elo
pin
g
$ l
ine
ar
0.9
92
[o
] 1
.06
1 [i]
I
Sta
tio
n 4
f
err
ati
c
$
co
nst
an
t 1
.16
7
[o]
f li
ne
ar
0.98
2 [o
] 1
.09
6
[o]
0.9
97
[
i]
1.0
45
[o
] 6 c
on
sta
nt
8 c
on
sta
nt
8 c
on
sta
nt
1.1
33
[
i]
Rem
arks
CO
MPL
ETE
SHE
LL
BUC
KLE
D
0.98
4 [o
] &'
c
on
sta
nt
1.0
63
[
i]
1.1
33
[o
] 8 c
on
sta
nt
1.0
47
[iJ
4 c
on
sta
nt
0.9
79
[o
] 8
co
nst
an
t .4
..
lin
ea
r
AN
D
DAM
AGED
VABL
E X
IX
LOCA
L ST
RA
IN C
ON
DIT
ION
S AN
D C
RIT
ICA
L L
OA
DS
DER
IVED
FR
OM
HIG
HES
T LOAD LEVEL D
ATA
C- ',L D
. A
-
T
Ang
le
Deg
rees
0
20
4
0
60
80
10
0
12
0
14
0
16
0
18
0
200
220
240
260
2 80
300
320
340
Sym
bols
Gen
eral
N2te
C
Sta
tio
n 2
$
c
on
sta
nt
I I
I1
6-0
6
err
ati
c
6~
0
t-0
1.1
32
[
i]
8 e
rra
tic
--
- 8
co
nst
an
t --
- 1
.14
6
[i]
1.
117
[o]
0.9
75
[
i]
6 l
inear
f
co
nst
an
t *A
[ i
I
Str
ain
dif
fere
nc
e
[o]
ten
din
g t
o i
ns
tab
ilit
y o
utw
ard
s *
$
rev
ers
es
in s
ign
[i]
un
sta
ble
in
war
ds
4
f ch
ang
ing
ver
y r
ap
idly
Lo
csl
cri
tic
al
load
va
lue
s n
orm
aliz
ed
to
ov
era
ll c
riti
ca
l, 3
09
,65
9
lb.
Sta
tio
n 3
1
.11
2
[i]
*A
[o]
* LO
1 6
de
cre
asi
ng
1.
176
[i]
6
lin
ea
r 1
.22
5
[i]
1
.01
2
[o]
0.9
93
[o
] 1
.09
1
[i]
0.
975
[o]
0.9
15
[0
] 6
co
nst
an
t 1
.41
1
[i]
6
co
nst
an
t 8
co
nst
an
t 1
.20
0
[i]
0
.98
0
[0]
Sta
tio
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Rem
arks
No
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11
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I I II
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suggest, i n l i g h t of the l o c a l c r i t i c a l load values and
d i s t r i b u t i o n s shown i n the tab les , t h a t t h i s mechanism
explains the d i f f e r e n t behavior pa t t e rns exhibi ted by the
she l l s .
3.7.5 Line-Load Distr ibut ion.
The d i s t r i b u t i o n of a x i a l compressive force around
the circumference of the s h e l l is d i r e c t l y assoc ia tab le
with the circumferent ial d i s t r i b u t i o n of cent ro ida l s t r a i n .
Calculat ions of t he cent ro ida l s t r a i n s over t he e n t i r e
spectrum of loading show t h a t remarkably uniform dis t r ibu-
t i o n s were achieved i n a l l cases. This i s i l l u s t r a t e d
c l e a r l y i n Tables XIX through X X I I I . I n these t a b l e s t he
values of the cent ro ida l s t r a i n a r e given a t t he 18 s t a t i o n s
around the circumference f o r each of t he 5 longi tudinal
measurement posi t ions. For added c l a r i t y these s t r a i n
values have been normalized t o the mean value f o r the s h e l l
a s a whole. Each t ab l e is per t inent t o a d i f f e r e n t s h e l l ,
but i n each case the load l e v e l q ~ o t e d i s of t he order of
75% c r i t i c a l .
It J s i n t e r e s t ing t o note that,when the f u l l s e t of
values f o r each s h e l l a r e considered a s a family, the
cumulative t o t a l s versus s p e c i f i c s t r a i n l e v e l plot as a
s t r a i g h t l i n e on probabi l i ty paper. This implies t h a t the
Tb3LE XX. SHELL A . CENTRO iDAL STRAINS.
Local Centroidal Strains Normalized to Mean
Angle (" 0
2 0
40
6 0
80
100
120
140
160
180
200
220
240
260
- 280
300
320
340
Station 1
0,983 - 1.022
0.970
1.016
1.028
0.955
0.977
1.080
1.035
1.065
1.048
0.924
0.995
1.060
0.986
1.049
1.056
0.957
Station 2 0.944
0.983
0.998
0.964
0.980
0.962
0.980
0.987
1.034
---
0.953
0.906
0.977
1.005
1.009
0.988
0.996
1.012 L
. Station 3
1.026
0.998
1.027
1.039
1.002
1.030
0.983
1.028
1.061
1.029
,985
1.037
0.985
1.009
1.043
1.007
0.986
1.049 .lo:
Station 5 1.014
1.022
0.943
0.981
1.030
0.954
1.011
1.027
0.963
0.995
1.012
' 0.990--
1.017
1.052
0.946
1.032
1.052 - -
----- I
Station 4
0.998
0.966
0.976
0.976
1.004
0.960
0.992
0.993
0.989
0.986
1.307
0.977
1.005
0.998
0.970
0.997
0.986 - .-
9791.
-
TABLE =I.
SHELL B. CENTROID& STMINS
Local Centroidal Strains Normalized to Mear
-
Angle ("1
0
2 0
4 0
60
8 0
100
120
140
160
180
200
220
240
260
280
300
320
3 40
Station 2
0.997
0.974
0.980
0.992
' 0.967
0.966
0.993
0.977
0.996
---
0.967
0.959
0.989
0.991
0.996
1.019
0,981
0.970
Station 1
1.007
0.990
1.019
I 1.028
0.998
0.990
1.016
1.002
1.022
1.057
0.980
0.966
1.002
0.993
1.023
1.027
0.991
0.994
Station 3
1.010
1.002
1.035
1.021
1.010
1.004
1.013
1.053
1.042
1.065
1.009
1.015
1.004
1.026
1.023
1.033
0.988
0.996
Station 4
0.971
0.984
0.980
0.984
0.976
0.964
0.984
1.001
1.025
1.002
0.981
0.964
0.975
0.971
0.989
0.984
0.994
0.968
Station 5
1,001
1.007
1.000
0.976
1.025
1.036
1.039
1.045 -
1.046
1.017
----
1.021
0.993
1.024
1.003
0.976
0.989
0.984
TABLE XXII .
SHELL C , CENTROIDAL STRAINS
Local Cen t ro ida l S t r a i n s Normalized t o Mean
S t a t i o n 5
1.034
1.013
0.997
0.997
0.969
0.990
0.955
0.976
0.995
0.976
0.950
0.995
0.934
0.993
1.022
1.039
1.039
1.057 - 4
S t a t i o n 4
1.015
0.980
1.001
0.993
0.981
0.956
0.959
0.937
0.982
0.971
0.953
0.975
0.992
1.003
0.998
1.006
1.000
1.013
S t a t i o n 3
1.050
1.007
1.004
1.030
1.020
1.010
0.986
1.017
1.010
1.014
1.011
1.003
018
1.041
1.043
1.031
1.018
1.056
S t a t i o n 2
---
0.980
0.975
---
0.998
0.985
0.964
0.982
0.998
---
0.982
---
0.973
1.009
1.002
0.989
1.025
1.034
Angle (" > 0
2 0
40
60
8 0
100
120
140
160
180
200
220
240
260
280
300
320
340
S t a t i o n 1
---
0.982
---
0.996
0.986
0.959
1.019
---
1.044
1.049
0.993
---
1.015
1.038
1.030
1.056
1.021
0.992
TABLE XXIII.
SHELL D. CENTROIDAL STRAINS
Local Centroidal Strains Normalized to Mean
Station 1
1.03
0.984
0.976
0.979
0.995
0.952
0.965
---
0.981
1.016
1.017
0.990
1.018
1.025
0.991
1.009
1.027
1.054
Angle ("j
L
0 1
20
40
Station 5
1.089
1.038
1.033
1.045
1.017
0.974
0.991
0.985
0.988
0.974
1.007
1.030
1.057
1.067
-----
1.013
1.015
0.398
>
Station 2
1,009
0.971
0.953
0.969
0.974
0.998
0.988
0.953
0.982
---
0.955
0.959
0.977
0.992
0.999
1,008
0.987
1.004
J
160
180
200
220
240
260
280
300
320
340
.. Station 3
1.039
1.028
1.025
1.037
1.043
1.016
1.006
1.010
1.018
1.. 020
1.014
1.005
1.032
1.058
1.046
1.016
1.051
1.038
Station 4
1.011
1.003
0.990
1.004
0.993
0.966
0.962
0.947
0.962
0.977
0.951
0.980
1.002
1.005
0.996
0.986
0.981
1.000
variations which are ex~erienced are of a random character.
The smallness of the coefficients of variation lead to
the opinion that it would be extremely difficult indeed to
achieve closer correspondence.
3.7.6. Load-Displacement Histories. -5
.4 large amount of data on the motions of the shell
walls induced by loading was acquired. This data has nct
yet been completely analyzed. The analysis which has been
made does not, however, show any unexpected trends or
behavior patterns.
4 , Conclcsions
The studies which were made with small scale plastic
shells showed clearly that non-destructive methods of
evaluation of axially compressed cylindrical shells are
feasible. The experier:ce with the large scale vehicles
indicates, however, that if such techniques are to be
applied to large scale testing the loading and probing
system must be designed to work in unisoa from the onset.
The work on large scale cylindrical shells shows
that vehicles with excellent quality of geometric form
can be fabricated. It demonstrates, too, that provided
sufficient care is exercised in the fabrication of the
loading devices, and in the machining of the ends of
the specimens, excel lent control of load distribution can
be attained.
References
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Buckling of Cylindrical Shells. " Ph. D. Thesis, California
Institute of Technology, Pasadena, 1968.
(2) Babcock, D. D., "The Buckling of Cylindrical Shells With an
Initial Imperfection Under Compression Loading." Ph. D. Thesis
California Institute of Technology, Pasadena, 1962.
(3) Katz, L. "Compression Tests on Integrally Stiffened Cylinders."
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(4) Weller, T., and Singer, J., "Experimental Studies on Buckling
of 7075-T6 Aluminum Alloy Integrally Stringer-Stiffened Shells."
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Prentice Hall, Inc., Englewood Cliffs, N. J., 1974.
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7 5 - 4--~--- -----.-
( i 6 ) Duggan, PI. F. , "A Study of t h e E f f e c t s o f Geometric Imperfec-
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