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)

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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

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llip

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ell

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ith

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la

r C

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,I.

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mp

aris

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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

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ark

Bu

ck

lin

g L

oad

( l

b)

Ac

tua

l b

uc

kli

ng

lo

ad

was

d

ete

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ed

by

S

ou

thw

ell

Met

ho

d.

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was

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ed

by

S

ou

thw

ell

Met

ho

d.

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l b

uc

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is

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e l

oa

d a

t w

hic

h

sna

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cc

ure

d.

(~

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ally

)

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to

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ins

tab

ilit

y

away

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om

the

cu

taw

ay

reg

ion

. A

ctu

al

bu

ck

lin

g l

oa

d i

s t

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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

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ou

thw

ell

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as

use

d f

or

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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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E

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0 0 0 0 0 0 C c c o L 7 0 o m 8 C . L n O 9 h N N N . - . . - . - -

0 O O C O O ~ 8 $ 2 s $ 8 8 8 8 8 4 1 o 0 0 0 - r?

Z I 1 I I , I I I ~ I I l I I

CC

r r r - c r i n m r - h n n u u u a c r 3 t n q u a z m e u u * l - I - I H r l d 3 i 4 ri

m - r : D a! i' tn V N - T ~ N O O E ~ ~ N 0 ~ h ~ t n ( ? r l 0 1 0 o " N N

$ 5 u a m d a m o n m 4 i o m n c h - t o c n l o W C Q ~ + O *O - LO

'=. ". _ ,"- C". m- u, u 9". =.O. ".").".". ". "." . . E e d L w a * m m ~ o r * m a i d N N N N , m m a , t n ~ ~ C Q C C u r . 3 ~

? tLL 3 3 4 r r H 3 r l N H rl - 3 3

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CC - $ 5 ; c F -

n 5, d - N

r c 7. 4 = Z U L L O ~ E l c h C

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0 - rl C

rr' L.

* LC " L L :. C C * C h

5 .r - - - - y y 1 = z r = ' = ' = : g k k : & F cuj; - - - G C W U \ i z ,,,,,,,, 2

Z 13 i 4

!&

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Ir C p

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- . . . - - - - . , u - I: C.

8 .-I 4

X X 2 0 : " . " ?

n e m

m a n

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-<ad v , x m ; d r o Z w m r i o ~ z u = u : r o - z + = - o Y z r : r ? v -

0 I 4

0 r l r n w i C I C - r ' r

L r C a' t- - ,. ;: .i

t C

2 s 2 . . , y, - 3 2

f , - * 2 3 * , - ; t

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0 r,

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2

- 1 r C i;

.* .- +. .- 0 i) .- - .- A

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 .

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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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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

(1) Arbocz, J. , "The Effect of General Imperfections on the

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."

N.A.S.A. TM X 53315, 1965.

(4) Weller, T., and Singer, J., "Experimental Studies on Buckling

of 7075-T6 Aluminum Alloy Integrally Stringer-Stiffened Shells."

TAE report No. 135. Israel Institute of Technology, Haifa, 1971.

(5) Babcock, D. C., "Experiments in Shell Buckling." Section 14,

Thin Shell Structures. Fung, Y. i., Ed., and Sechier, E.6. Ed.,

Prentice Hall, Inc., Englewood Cliffs, N. J., 1974.

(6) Horton, W. H., Singhal, M.K., and Haack, T. A,, h he Use of Models

in Structural Test!ng." Instrumentation in the Aerospace Indus-

try, AS1 72231, pp. 159-164. Instrument Society of America,

Pit tsburg , Pennsylvania, 1972.

(7) Haack, T. A., "TI-it Developmenr of New Techniques for t h e

Planuf acture and Testing of Cylindrical Shells. " >taster's Thesis

Georgia Ins-itute of Technology, Atlanta, Georgia. Elarch, 1073.

(8) Ford, J. S. i II , "Parametr ic S t u d i e s on t h e S t a b i l i t y of

S t r i n g e r and Ping Re i s Iu rced s h e l l s . " Ph. D. T h e s i s , Georgia

I n s t i t u t e cf Technology, November, 1970.

(9 ) Donnell , L. H . , "On t he App~ica t i - . ? . of Sou thwe l l ' s Method f o r

t h e Ana lys i s of Buckling Tes ts . " , Stephen Timoshenko 60 th

Anniversary Volumn, McGraw-Hill Book Co., 1938, pp. 2730.

(10) Tuckerman, L. B . , " H e t r o s t a t i c Loading 2nd C r i t i c a l A s t a t i c

Loads," Na t iona l B u r e a ~ of S t anda rds Research Paper RP 1163,

J o u r n a l of Research, ;;.B.S., 22, 1939, p ~ . 27-38.

(11) : ra ig , J. I., "An Exper imenta l Study of Waii Motions i n

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 Under Combined Loadings."

Ph. D. Thes i s , S t an fo rd ITnQersity, S t a n f o r d , C a l i f o r n i a , 1969.

(12) Bank, M. H. 11, "Some D i s c u s s i o n s on t h e S t a b i l i t y of S ~ r u c t u ~ a l

and Mechanical Systems. I ' Ph. D. T h e s i s , Georgia 1ns t i : c t e oL

Technology, A t l a n t a , Georgia , August, 1971.

(13) S ingha l , M. K . , "S tud ie s on t h e E l a s t i c S t a b i l i t y of Bodies."

Ph. 3. Thes i s , Georgia I n s t i t u t e of Technology, A t l a n t a , Georgia ,

1973.

( 1 4 ) Nassar , E. E . , "On t h e Dynamic C h a r a c t e r i s t i c s of Hcnms, I'l:lt es

and S h e l l s . " Ph. D. T h e s i s , Georgia 1ns t i :u te of TecIino;oy:y,

A t l a n t a , Georgia, 1973.

(15) Horton, C'. H . , S ingha l , !I. I(. , and S a s s a r , L . I: , "On t h c :;on-

D e s t r u c t i v e Determinat ion u i t h e C r i t i c a l 1,oacts f u r S h e l l I5odie s . "

To be pub l i shed by t h e S;<.-ii i n Experimental ~ l ec l i an i c s .

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-

t i o n Upon :he S t a b i l i t y Behavior of C y l i n d r i c a l S h e l l s Under

.Axial Compression." t i a s t e r ' s T h e s i s , Georgia I n s t i t u t e of

Technology, A t l a n t a , Georgia , December, 1971.

(17) Cra ig , J . I., and Duggan, M. F., "Non-Destructive S h e l l

S t a b i l i t y Es t ima t ion by a Combined Loading Techni-que."

Experimental Mechanics, Volume 3 , p. 331-387, Sep tenbe r , 1973.

(18) P e t e r s o n , J. P., "5uckl ing of S t i f f e n e d C y l i n d e r s i n A x i a l

Compression arid F~- J ing - A Review o f T e s t Data." KASA TN-

556;. ;970.

(19) ilrbocz, J . , and dabcock, C. D . , "Exper4mental I n v e s t i g a t i o n

of General I a p e r f c c t i o n s on ;he Buckling of C y l i n d r i c a l S h e l l s . "

C a l i f o r n i a I n s t i t u t e of T e c h n o i ~ g y . G a l c i t Repor t SN 48-7, -968.

( 3 0 ) Horto3, 1;. H . , anu Cra ig , J. I., "Experimental S t u d i e s or, t h e

- - z r f e c t of Genera l ImperLect ions on t h e E l a s t i c S t a b i l i t y of

Thin S h e l l s , " I s r e a l J m r n a l of Technology, 7, (1-2), 91-103, 1969.

(21: S ingz r , J . , Arbocz, J . , and Babcock, D. C. J r . , "Buckling of

imperfec t S t i f f e n d C y l i n d r i c a l S h e l l s Under A x i a l Compression."

Prc-sedings of t h e AIAA/AS>IE 1 1 t h S t r u c t u r e s , S t r u c t u r a l D,na-

r r ics , and ? f a t e r i a l s Conference, A p r i l , 1970.

( 2 2 ) Block, D. i ., Cord, X. F . , and Niku la s , ?.I. >I. J r . , "Buckling

cf E z c e n t r i c a , , ~ S t i f f e n e d O r t h o t r o p i c Cy l inde r s . " N . A . S . A .

T:q 3 . 296J, 1965.

(23) Craig, J. I., Bailey, S. C., and Horton, W. H., "Xon-Destructive

Stability Evaluatio~ of Large Shell Structures by Direct Computer

Tontrolled Testing." instr~nentation in t h e Aerospace Industry

AS1 72231. pp. 165-172. Instrument Society of Anerica,

Pit tsburg , lennsyibania, i 9 7 2 .

(24 j Arthur, \.i. F. "Initi 31 Imperfection Pleasurenent of Large Scale

Cyiindrical Shells." Graduate Special Problem. Georgia ifist.

of Tech. Unpublished.