• 

, , 

LIP., 

CHAfJCE a 

STRt1rt-) [J ulr. 

NATIONAL ADVISORY COMMITTEE 

FOR AERONAUTICS 

TECHNICAL NOTE 

No, 1198 

SOME INVESTIGATIONS OF THE GENERAL INSTABILITY 

OF STIFFENED METAL CYLINDERS 

IX - CRITERIONS FOR THE DESIGN OF STIFFENED 

METAL CY LINDERS SUBJECT TO GENERAL 

INSTABILITY FAILURES 

By Louis G. Dunn 

California Institute of Technology 

Washington 

November 1947 

https://ntrs.nasa.gov/search.jsp?R=19930082178 2019-08-29T13:42:06+00:00Z
• 

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 

TECHNICAL NOTE NO. 1198 

SOME IlITVESTIGATIONS OF THE GENER4.!" INSTABILITY OF STIFFENED METAL CYLINDERS 

IX - CRXTEBIONS FOR TEE DES:I:GN OF STIFFENED METAL CYLTh1)ERS SUBJECT 

TO GENERAL INSTABILITY FAILURES 

By Louis G. Dunn 

SUMMARY 

An experimental invest'igation of the general instab ility of roinforced thin-walled metal cylinders ,-Tas made at the Cal if'orr..ia Institute 

of Technology, and a sUIllIJJ.ary of the pertinent desisn i nf ormation that 

was gathered during the course of the investiGation is gi ven in the 

present report. As a result of this investiga tion, parameters were 

evol ved which Inake it posstble to obtain an estimate of the stress at 

which general instability will occur for any given stiffened metal structure of circular cross section . It is considered that 'both the geometrical 

quantities and sectional properties of the structural 'members were varied 

over a sufficient range to establish, in general, the val idity of th~ 

parameters. Because of th~ catastrophic nature of ,a general instability 

failure it is. recommended that ample margins of safety be allowed in an 

airplane structure in which this type of failure might occur. 

A theoretical treatInent of the general-instability problem ,was not 

given because of the nonlinearity of the buckling problem of stiffened 

cylinders. The parameters presented for predicting the ultimate strength 

of stiffened metal cylinders subjected to pure bending and pure torsion 

were based on an analysis of the experimental results and on the existing theory of unstiffened metal cylinders. This method ,'la s preferred to 

that of a linearized theory which cannot correctly descri be the behavior 

of the structure. The results qf a linear theory would have to be mcdified and corrected to bring it into agreement with the' experimental observations, and thus the theory WOQld immediately be rendered an empirical 

method • 
2 NACA TN No . 1198 

INTRODUCTION 

With the extensi"ve use of thin metal sheet in aircraft fabrication 

a number of new design problems were introduced. Of these problems, a 

large number have either been solved' or sufficient Imowledge regarding 

them exists to enable the engineer to design satiefactory airplane 

structures . Howeyer, with the r apidly increasing' size of modern airplanes, a number of new structural problems arise, one of these being 

the problem of determining the allowable leads that can be carried by 

stiffened cylinders of large r adius . It i s known t hat certain combina tions of longitudinal stiffeners, fremes, and shee t .. rill give a 

cylinder that will fail in such -a marh~er as to involve all three structural elements simultane0usly. This t ype of failt~e is referred to as 

the general instability failure of a stiffened cylinder . The parameters 

affecting the failing loe,d of such a. structure 'are of primary importance 

in the design of large airplanes. 

In view of the fact that acceptable me thods were not available for 

the design of large stiffened cylinders, the' Civil Aeron~utic8 Authority 

started the s:ponsorship of a research prcgram at the California lnsti tute 

of Technol ogy. The inveetigation covering the failure of stiffened cylinders subjected to pure bending .ras carried out under this sponsorship. 

The inveAtigation of stif'fened cylinders subjected to combined loadings 

and to pure torsion was carr.:J-ed out uncler the s:ponsorshlp and with the" 

financial assistar.ce of the Nati{:mal Advisory Coromi ttee for Aeronautics. 

In' general, the purpose of the investigation was to determine two 

things: 

(a) A method of calculating the strength of cylindrical structures 

falling into the general-instability classification 

(b) The liinits of the general-instability regime 

The results of the investigation have 'been presented in detail in references 1 to 8, and ,the present, report summarize.s' the pertinent design 'i1+--

formation gathered ~uring the qourse of the investigation. 

ANALYSIS OF PROBLEM AJlID BASIS OF THEORY 

In order to clarify the meaning of general instability and why it 

may be considered as being a problem peculiar t o large airplanes , the 

functions YThich the elements of a stiffened metal cylinder must perform 

and the types of failure which may occur should be considered briefly. 
• 

NACA TN No. 1198 3 

Stiffened shells as used in metr:tl aircre.ft construction ccnsist primarily of the following elements: 

(a) The sheet-metal covering 

(b) The longitudinal stiffening elements 

(c) The t r ansverse stiffening elements, generally referred to as 

ribs, bulkhead.s, or f:cames 

The functions of the sheet-metal covering are to provide an aerodynamical 

surface upon which the air forces act Cf,"in~ 8 and. . c ontrol surfaces) ar..d 

to furnish a covering for the contents of the airplane . In addition to 

these functions., the sheet coverl~g is 80 6.esigned that it is a lead-~ 

resistins element and as such can be considered as pert of th& primary 

structure. In general, part of the lead acting on an a:l.rplane structure 

will be compressive in nature. S:i.nce thin sheet is wea.k in compression, . 

1 t is necessary to provide stiffening elem'3nts which .,ill fulfill one' or ' . 

both of two requirements; namely: 

(a) Add additional strength in resisting ccmyressive 1(;8.ds. 

(b) Maintain the aerodynamic -shape of the airplane . 

In e fuselage, for example, the first is a ccoplished by attaching stiffening members to the sheet parallel to the axis of the cylinder; and the 

second, by placine memb rs 'of the proper .shape perpendicul r to the cylinder axis. These perpendicular members also act as supports for th~ 

longi tudinal members. In the fel.loving discussion the terms "longi tudinal" 

and II frame 'I will be us~u. to d.enote these two clasoes of members, respec-' 

t1vely. 

If a cylindrtcal structure of this type is subjected to ccmpressi ve 

loads parallel to its axis) it may fail in one of fotrr distinct ways. 

The types of failure may be conveniently claSSified as material failure, 

loca.l instability, panel instability, a.'1d general inst<'.bility. 

In general, the bending:-:stress distribution is, forpurposes of' analy--

Sis, assumed to be in accord with the elementary beam theory. When buckling of the sheet occurs, appropriate modifications are made in cal culating 

section properties to allow for the reduc tion in the l cad-carrylng abili~ 

of the buckled sheet. The first type of failure ther efore offers no d.ifficulty tc) the deSigner, since it is necessary that only the ultimate strer.gth 

of the material be known in order to determine the strength of the structtrre 

as a whole. 

Local instability generally occ:urs in sect'ions haYing wide and thin 

flanges and is characterized by an instability failure of scme small 
4 NACA TN No . H98 

portion of either a frame or longitudinal. This c ollapse of part of the 

stiffening member .rill precipitate its failure as 'a column and may also 

cause premature failure of the whole surrounding structure . The length 

of the portion of the member involved in lecal buckling is of the same 

order of magnitude as its cross-sectional dimensions, and the local 

buckling stress is not, in general , 8. function of the total' length of 

the member . The buckling stress of suc·h sections can be either calcu'-

lated er determined. experimentally . 

A panel instability failure is defined as one vhich will occur over 

a length of structure equal to one fr&~e spacing and which is not caused. 

by local instability spreading to adjacent members. This type of failure 

will occur in a structure he-ving relatively heavY frames and .l·ight l 'ongi'-

tudinals, the structure tending .. to act as a ntunb er Df isolated, axially 

stiffened cylinders, each of which is one . frame spacing in :l ength . 

Failure vIill occur by some form of instabi.li ty of the long itud inals , the 

magni tude of the failure l ead be:;'ng dependent upon the' column· 'or torsional 

strength of the l ongitudinals, modified by the effect 'of. the attached 

buckled sheet . The only fun.ction of the f rames in this case .will be .. to 

determine the end fixity coefficient of the longitudinals. In the past, 

the design of stiffened shell structure~ has been based almo3t entirely: 

on failures of the panel ty,pe . .lU thou~h an accurate the oretical treatment cf t he strength properties of curved stHfeneo. panel$ is not yet 

available , it has been possible by experimental methods to design struc'--

tures in which f ailures tended to fall in the panel--'instabili ty 'classifi--

cation . 

The general-'instabili ty type of failure .Till occur in a structure 

which has frames and longit udine.ls of such a size that both will fail 

simultaneo"\.l.sly under the critical l oad, tha.t is, collapse takes place 

in such a manner as to destroy t.he lead-carrying properties of all 

three structural elements - sheet, frames, and longitudinals. The first 

three types of failure may occur r eearriless of the size of the airplane. 

In smaller a irplanes (gross weight of 25, 000 Ib or 1.ess ) tte frame sizes 

are determined by considerations of local loading conditions and practi-' 

cal manl.lfact~ing demands, rather than by reqUirements for stability . 

These considerations lead to frames which are sufficiently rigid t o 

preclude the possibility of general instability failures . s airplane 

sizes incre~se, these considerations do not r e quire a rop ~tionate in- ' 

crease in frame sizes; consequently, the relative dimensions- of the 

three structural elements may be very small compAr ed with the external 

dimer~ions of the structure. Since general instability i s a f~nction 

of the stiffness of the structure as a whole, its occurrence in large 

airplane s is quite possible and. should be investigated . 

Although a ccmplete and exact t heoretical treat.ment of the general 

instability of stiffened cylinders is probably unattainable, the validity 

of the results obtained from a theoretical treatment of the· problem will 
NACA TN No. 1198 5 

depend upon how closely the basic assumptions resemble the actual physical 

conditions. ·It is therefore' desirable to c onsider the basic assumptions 

underlying these treatments. 

Of the two possible types of failure which fall into the class of 

general instability, one occurs under bending loads and is characterized 

by a general flattening of the cylinder . This type of failure was discussed by lJ . G. Braiier, for the case of the unstiffened shell under 

pure bending) and his result3 have been applied. to the stiffened shell 

problem by N. J. Hoff (reference 9) . Both theory and experiment indicate 

that for general flattening to occur, the length-,-d::!.ameter ratio of the 

cylinder must be so large that it is ccmpletely out of the range of aircraft structures. 

The second class of fa.ilure ) for which two theoretical treatments 

are available, iel that in which the i,ave form of the buckle 1.s multilobed in nature and has, in general, a wave length less than the total 

length of the cylinder. This bucklina fo!m corresponds to the usual 

. I>diamond--shaped" wave pattern which is obseyved in the failure of unstiffened cylinders under compr essive loads. One method of investigation distributes the stiffnesses of the longitudinals and frames over 

the entire cylinder, forming an unstiffened orthotropic cylinder, which 

is treated as a simple unstiffened cylindrical shell . The ·thickness 

and stiffness of this Shell in the longitudinal direction differs from 

that in the circumferenti 1 d.irection by amounts depending upon the 

area Q and stiffne sses of the longitudinals and the 'fram0s, respectively_ 

This rearranging of the original stiffened cylinder into an equivalent, 

unstiffened orthotropic cylinder will be called the equivalent-shell 

method. 

A second method that can be used is to consider the sheet, the 

longitudinals, and frames as co~ponents of a statically indeterminate 

truss system. The longitudinals and f rames, each with its proper 

effective width of sheet acting, form the normal load-resisting members, 

while a suitable amount of sheet in each panel acts as a tension diaGonal 

to transmit the shear forces. This method will be called the equiv81enttruss method. 

Theoretical treatments of this problem have been given in references 

9 to 12 . . In references 10 and. 11, the eqn i valent-shell method has been 

used, while in reference 9 only the longitudinals and not the stiffness 

of the frames are distributed, the frames being used -as local elastic 

supports for the longitudinal el ements of the shell. The results. of 

the pure'-bending tests of reference 5 were later utilized by Hoff in 

reference 12 to modify his original ·theorY given ir. reference 9. 

With the exception of one test (see reference 9) no experimental 

dat~ were available on the general instability failure. A systematic 
6 NACA TN No . 1198 

experimental investigation appeared to be 'necessary to c.heck the validity 

of the theoretical results and, if no agreement could be obtained with 

these results, ·to determine a method of estimating the general-instability 

stress. 

Inasmuch as~ending . is one ' 9f the cri ti.cal loading conditions for 

airplan~ structures and. also . one" of · the eimplest loadir.g conditions to 

deal with both experimentally and theoretically it was Qecided to investigate first "the failure of sti'ffened m8tal cylinders when subjected 

to a pure be:Qding moment. It was realized that no airplane structure 

is subjected to beI;.dir.g moments without a certain amou11t of attendant 

direct shear. However, it was felt that a study of the pure-bending 

phenomenon would form a desirable background for the more complicated 

problem of bendir~ plus shear and for the more general combined loading 

conditions . . 

Upon completion of the pure-bending invest~gation (reference 5), 

the experimental work was extend~d to. cover the loading conditions of 

combined bending and transverse ·shear (reference 6), combined bending 

and torsion (reference 7), and pure torsion (reference 8)-. 

Since a condition of a , pure torsional load seldom arises in the 

design of fuselage or wing structures, ·tho problem of pure ' torsion as 

such might not warrant an inve stigationj ,hovTever, under a combined loading of bending plus torsion (reference 7), the ultimate load of th~Btiffened cylinder is dependent upon the ratio of the shearing stress at failure for combined loading to the shearing stress at failure for pure tor-

" sion. Hence, in order to predict the ultimate strength of a stiffened 

metal c~linder subjected to combined bending and torSion, a knowledge of 

the ultimate strength of the cylinder when subjected to a pure torsion 

loading is necessary . -

M Tmax 

SYMBOLS 

applied bending moment~ inch-~our.ds 

applied torsional moment at failure, inc~- pounds 

(jst ccmpress'ive stress in longitudinals) ' pounds per square inch 

T 

compressive stress in longitudinals at failu~e (when used in 

conjuction with the sheet covering or an unstiffened cylinder 

it c orresponds to a buckling stress), pounds per square inch 

~hearing stress in the sheet covering, po~ds per ;square inch 
,-- --...-~ - .. ----~------ --.~----~--~. -~---

• 

/ 

NACA IN No. 1198. 

Tmax 

Tcr 

E 

E' 

t 

· A 

R 

L 

b 

d 

Px 

shearing stress in the sheet c0veringat failure, pounds per 

square inch 

buckling shear stress of the sheet covering, pounds per square 

inch 

Young's modulUS, pounds per squaro inch 

~ffective modulus, pounds per square inch 

effective shear modulus, pounds per square inch 

thickness of sheet cover ing, inches 

area enclosed by sheet covering, square inches 

radius of cylinder, inches 

length of cylinder, inches 

spacing of longitudinals, inches 

spacing .of frames, inches 

radius of gyration of a longitudinal and effective sheet, inches 

radius of gyration of a frame and effective sheet, inches 

TEST PROCEDURE 

A description of the test articles and test methods has been given 

in detail in references 1 to 8, and no further discussion will be given 

here. For convenience, data pertaining to the various teste are given 

in tables I to IV. Croos-sectional dimensior.s, areas, and moments of 

inertia are g iven for all the stiffening elements in figure 1. Typical 

curves of the l ongitudinal strains for the various loading conditions 

have been included as follows : 

(a) pure bending, figures 2 to 4 

(b) · combined bending and transverse shear, figures 5 to 7 

(c) combined bend.ing and torSion,. figures 8 to 11 

(d) pure torSion, figure 12 

A number of photographs (figs . 13 to 16) showing the various types of 

failure are also included. 

7 
8 NACA TN No . 1198 

RESULTS A1W DISCUSSION 

Pure Bending 

The results of. ~ 8~mplifi~d theoretical treatment of the problem 

(references 9 to 11) were checked exPerimentallY ~ (;efe~enGe 5) ar:d it was 

found that they do not give ~~sults suffi~ie~tly acc~at~ for design pur~ 

poses. 

For a systematic experimental investigation it is necessary first 

to c onsider the variables involved in the problem ,of general instability. 

These variables may be divided into two classes - those dealing Ivi th the 

geometry of the structure and those which involve the sectional properties 

of the stiffening elements as well as the sheet covering . The geometrical 

variables are as follows: the longitudinal spacing b, the frame spacing 

d, the diameter, and length of the cylinder. The second group of variables includes the section properties of the longitudinals and frames, 

and the thiclrness of the sheet covering . 

By a systematic variation of these variables it is possible t o 

determine experimentally a sui table pax'ameter for predj.cting the leads 

at which a stiffened cylindrical shell will fa~l by general instability. 

Investigating first the geometrical variables, band d, it was found 

that the reciprocal of the maximum compressive strain at failure varied 

as ;jbd. The next question was in what manner do the radius R and 

the section parameters Px and Py influence the design parameter. 

By analogy with the buckling of unstiffened cylinders it was expected 

that for id,entical values of b, d; Px' and PJr the reciprocal of the 

cri tical value of the strain ,vould vary 11nearly with R . This assumption was checked exper,imentally and found to be correctj hence , it was 

concluded that the design parameter has the form 

41" .-, 

I\j bd R ------

f(px, Py) 

From dimensional reasoning, it follows that the'function ' f(PXJ Py) must 

have the dimensions of the 3/2 power of a length . The simplest assumption 

for the function which ' determines the influence of the section parameters, 

Px and Py ' is that it depends only on the geometrical mean yal~e 

r'p P Thus the 'design parameter appears in the form '" x y . 
~L CA TN No. 1198 

or 

R 

He'nce, the maximum strain at failure is (Si ven by an equation of the 

form 

r---

E f • R 

4 .' 

I Px Py 

j-~ 

Concerning the width of sheet to be used with the l ongitudinals 

and fr~e , it has been pointed out (reference 13) that the effective 

width associated with,buckling phencmena is Eot necessarily that basod 

on the load-carrying abil1ty of the sheet, but is proportional to the 

rate of increase of the a:pparent stre, s ,.,i th the actual stress. If 

it is assumed that for the present purpose the effective width as 

given by K and Marguerre fe equati on is sufficiently accurate, thenthe apparent stress aa is 

The effective width w* e for stability is then, 

9 

b 

(2 ) 

This equation gives an effective width which is two-thirds of that 

based on the load-carTying ab ility of the sheet. However, the influence 

on tbe numerical value of Px is quite srr~ll . For the specimens tested 

it was found that the Qifference was of the order of3 percent. Although 

an effective width as given by equation (2) vras used ln the experimental 

work, it is felt that either value is sufficiently accurate for all practical purposes. 
I 

l 

10 NACA TN No . 1198 

The amount of sheet acting with the frames is difficult to evaluate 

by analytical methods . Trial calculations indicated that the best results 

were obtained if the total width of sheet between frames was used . For 

this r eason it is recommended that the entire width of sheet be used in 

calculating Py . 

The results of the experiments a;re shO'lm in figure 17 in ,·,hich acr 

E' 

is plotted as a function of ~.j p~- P;: ;;~~-~;/bd. In the majority of 

tests the frames had a solid r ectangular cross section (fig. 1) and were 

therefore not subject to local instab ility. Hhen frames, such as the 

channel section, are subject to local instability, the failing l oad may 

be as much as 60 percent lower than that giv9n by the curve of figure 17 

since the channel does not devel o:!? the strength corresponding to the calculated value of Py . This can be illustra.ted by considering the behavior 

of an open-section colmnn subjected. to an axial load . Since the initial 

failure of the frame occurs over a relatively short leng~h, the discussion 

will be confined to short columns. For col umns having stable cross sections, t hat is, columns "Thich I:u'e not,.' subject to l ocal instability, the 

cri tical buckling str ess is given "ri th reasonable accu:::-ac3r by the Johnson 

parabola, namely, 

r' 

af3 = ay II 

2 2 

cry 7. l 

4rr2CEp2 J 

It has been shown that f or columns w'hich fail by local instability 

(reference 14) the buckling stress ac G~ be calculated by the e~ua

tion 

r 

i 1 I 

'-

(4) 

If the crushing stress acc i s lower than the yield-point stress 

the column wilJ. not develop the stress given by e~uation (3), but will 

fail at some l ower stress given by equation (4) . For columns which fail 

by local instability a reduced effective radius of gyration Peff can 

be cal~ulated in such a manner that if Peff is substituted in equation 

(4) the resulting stresses will correspond t o t he values given by equation (3). This requires that for any column length the value of Peff 

be such that 
NACA TN No. 1198 

from which it follows that 

Peff = 

l 

2" 

11 

.It is reasonable ,to assume that the frame behaves in a si;milar man--

ner and that a reduced effective re.dius of gyration can be calculated . 

In applying this method to three specimens, in which general ~nstability 

fail~e was precipitated by local :i,nstabili ty of t he frames, the resul t- -

ing val ues of Peff were such as to bring the experimental value s in 

good agreement with the curye of figure 17. The length L' was taken 

as the distance between loneitud~nals . 

The experimentally derived parameter R / fo;- Py /bd/P -Py i s t he 

ratio between the radius and a quantity having the dimensions of a l~ngth 

defined by j;~ Py ~ Py/bd. . By analogy with the buckling of unst1ffened 

cylinder s, it appear s that this l ength is pr oportional to some extent to an 

equivalent thickness of the reinforced' cylindrical structure . 

The failing stress of an unstiffened cylindrical shell of r e.dius R 

is given by 

kt 

(6) 

E' R 

Replacing the t hickness t by the r adius of gyration p , of a strip of 

the shell of unit width, equation (6) can be written in" the form 

O'er 

E t , , R 

For c omparisdn, ,the failing streBS of the stiffened. cylinders can be 

written in the form 

where k' is a numerical cQnsta.nt. , 

(8) 
12 Nfl, C II. TN No. 119EBy introduclng the geometrical mean value J-px Py it can be assu.med 

that the irrfluence of tho anisotropy of ·the structure is approximately 

taken into account. Then by comparis,on ·of equations (7) and (8) ap. ef,-

fecti ve r adius of' gyration can be defined as . . 

k' 4 /px · py . _ 

Pe ::: k ./ bd jPx Py - cPjPx Py 

... 

where k' . 4 ipx P; 

cP ::: T · J bd can be -c·onsidered as a correction f actor to the 

ratio i PxRPx.., · .Now b/Px ie. t he. l~pderne s rati o of the longitud i nal 

considered as a column b!'itween· :t wo frame s) and simil a rly d/ Px i s the 

slenderness ratio of the frame considered a s ·a collUnn between t wo l ongitudi nals. If the geometrical mean value of thes e two slenderne ss r atios 

is defined by ~, that is, 

r- --

A, ::: j bd . ,Px Py 

(10) 

then the correction factor can be expY8ss ed as 

k' 1 

cP ::: 'k .,fI 

It is eVident that if the stiffened shell vTere to be considered as 

an eCiui valent shell, in 'tlhich all t he mater ials a re uniformly dist ributed, 

then the appropriate pa rameter t o be u8A, d i s j Px RPY . The appr oprio. te 

parameters which enter into the problem of ucl~ing of a t russ are t he 

slenderness ratics which appear in the Ciuanti ty A::: / bd__ The f act J Px Py 

tha t the experimentally deri ved relat~Qn i nvolves both paramet ers, 

Jpxpy R and A} indicates that a stiffened cyl i nder cannot be troated 

either as an eCiuivalent cylinder of uniform t hicID1ess or as a cyl i ndrical 

truss. 

If i t is assumed tha t k::: 0. 3, whi ch is a reas onable average value 

for unstiffened cylinders in the r anBe of inyol ved, and i f the values obtained from the experiments are used for kT; then t he numer ical 
NACA TN No. 1198 13 

values of cp can be calculaterl. . The average slenderness ratio ).. varies 

from 280 to 26 and the values of cp o~re3ponding to these limit~ng cases 

are cp = 0.259 and cp = 0.865. The lower limit is for a specimen with 

10.12- inch longitudjnal and 16-tnch frame spacing , whereas the upper limit corresponds to a specimen with 2.53-inch longitudinal and 2.0-inch 

frame ftpacing. These resul t 'e indicate that for structures in which the 

stiffening elementf-' are \videly spaced it is necessary that a mnl tiplyine 

factor much ['maller than unity be applied to the quantity J Px p;, 

whereas in close spacings the factor is of the or der of 1 . 

If a reinforced cyllnder, fails by panel instability, the buckling 

stress should always be lower than the stress necessary to cause a 

gener9.l instability failure . This is o!Jvious because, in order for panel 

ins tab il i ty to occur, it is necessE'.ry that the frame be sufficiently 

rigid to maintain closely the shape of the etructure at the frame. If 

the frame is not sufficiently rigid, the frame .Till fail before the panel 

instability stress is reached, resulting in a general-instability type 

of failure. The test results shown in figure 18 confirm this statement. 

Length Effect 

Inasmuch as all the pure bendir~ specimens had a length to diameter 

ratio of 2.0, it was necessary to determine whether tee failing leads of 

these sp"3cimens ",'ere influenced by length . The main purpose of this investigation, therefore was to determine the length to diameter ratio 

LID at "Thieh the failing load beccines i ndependent of length. 

Eight specimens having LID ratios of 1 . 2, 1 .6, 2 .0, and 2.6 were 

tested, four in which the frame spacing was 2. 0 inchee and four in which 

the spacing ,vas 4 .0 inche e . The spacing of the longitud.inals and the 

diameter were the same for all specimens, 2.56 inches and 20 inchee, 

respectively. 

The failing strain as a function of t he LID ratio ie shown in 

figure 19. It is seen that the specimens having LID ratios of 2 and 

2.5 failed at approxima.tely the same strain . As the LID ratio decreaSes the failing strain incr eases somewhat and at an LID ratio of 

1.2 the increase i s 12 and 23 percent for the 4- and 2-'inch frame spac--

ings, respectively, From t1+ese test results it can be concluded that 

the failing loads of the pure-bending specimens used in the previous experiments were not influenced by length . 
14 NACA TN No . 1198 

Ccmb1ned Bending and 'Transv8rsp, Shear 

In the pure-bendiI1..g tests, the problem of detertninir.g th8 maximum 

strain-associated .nth the failing load was relatlv91y simple because 

of th9 uniform leading' over the length of the crpec imen . However, when 

the test 8pe cim~m 1E sub ,jected to combined bending and tranfwer se shear, 

the bending moment and the corresponding strains vary over the ler.gth 

of t he' specimen . Hence, the method of measuring, ever tte specimen 

length, a maximum mean strain at failure and aesi _ning this measured 

Etrain to the faHir.g l oad can no longer bc applied . The variation 

of strain and the end conditions of the Epecimr.·n maim it particularly 

difficult to a380ciate a particular strain witt ttA fai1in J load . The 

maximum mcment 'occurs at' the fixed end; however, this maxim\Jm moment 

and the 'correspond:ng strain crumot be cOI).8id~red as being a measure 

of the ultimate strength of tho cylinder bec ause of the fixed-end 

c ondi tions . ' 

There are two possible method.s of 'Present:l~,g the t<0st data . One 

method would. be to measure the strain at a nurnbCir of points along the 

length of the specimen, and then pre2ent these meaeuremeLts as the existing strain cendi tien along the le:1gth of the specimen when failure 

occured . .A..nother method vlould 1::e to n:eap.ure the failind strain A..t the 

point at which the first buckle ap:r;:ears d.uring the loading proc('!ss and 

to consider this to be indicative of the -maximum strain to which the 

specimen C8.J."1. be' subjected before failure occurs . 

Both methods tave certain disadvantageE' . The first d oes not l end 

itself r eadily to application in practical o.esign . ' It is custamary , for 

maximum struct-~al efficiency, to de s_gn a reinforced cylindrical stru~ 

ture in such a manner as to keep the stress nearly ' c onstant Aven though 

the bending moment is variable, This is usually accomplished by taper 

of the section and alGo of t he effective bending material . From this 

point of view the second method. is preferable. However, th~ main objection to the second is that thB v~idity cf associating the etrain condition at a point with the failure of the cylind.er may be questionable . 

The seccnd method has also one other advantage, namely, f or the 

pure bending failure a parameter has beon derived 'Thich appf'ars to be 

satisfactory . In determ.ining t he lnfluenc e of the transverse shoar en 

the maxim.um t3train at failurE', it is con'IJenient to have a single value 

of the strain for ccmbined bending and shear ' to compare with the strain 

value for pure bend.ing . 

In view of these conSiderations, t he f ollowing methed of presentat10n 

YTas adopted. It was found that the initial buckll3 or buckles appeared over 

a relatively short renge , being on the average ahout 14 inches from the 

fixed end f or the 32--ir:ch-diameter cylinc.ers and 10 inches for the 20-

inch-diameter cylinders. For this reason the strain at failure was considered to be the average of the strain meas~ements over a dietance 

extending from about 4 to 24 inches from the fixed end. 
NACA TN No. 1198 15 

The typ!'l of failure in compined bending and shear differs particularly in one .respect from that of the pure bending failure. For' the 

combined loading -the failure is, in manY . cas6B, gradual; that is, ' 

the buckles, although extending over several frames' and longit~din~s, 

slowly ,:l.ncrease in depth a:p.d size with increasing load until a sildden 

collapse occurs with a marked. increase in d.epth and size of the buckle 

or buckles. L~ the case of the pure-bending specimens, the or1ginru_ 

cross-section shape is closely maintained until failure occurs. The 

failure is particularly violent and accompani~d by large and deep buckl4'! 6 

with as much ·as a two-thirds drop in the a?plied load . 

During the early part of the investigation, it appeared fr om a 

visual observation that fail~re of a specimen was either of the bending 

or the shear type, that is, the begir~ing of a fai11rre was confined to 

either a region of maximum ccmpression or 'a region of maximum shear. 

The rather definite separation of the r egions of failure indicated that 

when a failure occurred in the comprees:on region the failure was nearly 

independent of the ap~lied shear and de~ended primarily on the state of 

compression strainj whereas, .when failure occurred in the r "gion of 

maximum shea+ the failure was independent of the state of comprezsion 

stre.in and depended , only on the applj,ed shear. 

The ne observations ~ere b orne out by the experimental resuJ.. ts. In 

figure 20 are plotted the ratics of the compressive strain E: /E: 0 as e. 

function of VR/M for a number of specimens of both 16-1nch and l~-inch 

l:adiue, where (is the maximum compressi VEl strain value (at the position 

previously described) for the c ombined-loading condition, (0 is the 

same strain ·value for pure bending, V is th~ applied shear, R is the 

radius of the s}:ecimen, and M the bending moment . Since M:: VL, 

where L is the distance from the applied shear load to the point whore 

the strain is measured , it is seen that the ratio VR/M is eqUivalent 

to R/L. This presentatton i s merely to indicate that when the failure 

occurs in the compression region the maximum ccmpressive strain is independent of the applied shear. For these spe;.cimens the applied shear 

load varied from 503 to 1450 pounds for the 16--inch-radius specimens, 

and for the 10--inch specimens from 710 to 2310 pounds. The minimum 

moment arm L was limited by the iength of the specimen. 

In figure 21 are plotted ratios of E: It 0 as a function of V Iv 0 

for one series of tests, where Va is the shear load which causes a 

pure shear failure and V is the shear load corresponding to E:. It is 

eeen from this figure that specimens 116 and 117 failed at the same shear 

load but widely different values of ( (i.'e ~, bending moment). The 

photographs (fiBS.l!~ and 15) indicate that specimen 116 failed simultaneously by combined bending and shear, whereas specimen l17 failed in sheer. 

It appears from these results that the ' interaction curve for this type 

of loading consists essentially of two perpen4icular straight lines. 
16 NACA TN No . 11:3 ' 

The .str ains at f~ilure, for tbe specimens which failed by bending, 

have been compared with the 'par ameter obtair-ed for the pure-bending 

failures and are shown in figure 22 . The test values follow the same 

trer.d as . the curve for the }lhl"e-bepding failures; hm.,rever, the experl-' 

mental scatter is somewhat gre(tter ~han for the purs-bending S1!0c:l.mens . 

It is 'felt that this scatter ~c p~imar~~y due to the following: (a) the 

accuracy of the strain measurements depends on· the reliability of the 

e18ct~ic strain gages and an accuracy greater tha~ 5 .0 per cent is not 

to be expected, and (b ) adopting a strain 'v&lue at a constant dista"lce 

fr om the fixed end as being indicative of the strain at failure also 

leads to some inaccuracies. 

Pure Torsicn 

In determining a parameter for ' 3)redicting the general instabHity 

failure in torsion, the same general procedure was followed as was us ed 

in r ef erence 5 . Tl:e var:;"ables t o be considered are the same as those of 

the pure-bending problem land qan ~gain be divided into two groups, namely, 

those deal ing with the gecmet+y of the structur e and those involving the 

sectional properties of the etiffenip~ elements ae 'well a a the shaet 

covering . The georr.etrical vaTiables' are the lcngi tud:inal . = "'-'c ~g b, 

the frame .spacing d, the diameter, and the length of tce cyli~d. . 

The second group of variables includes the section properties of the 

longi tudinals Br.d frames and the t hickness of the sheet cover1ng . 

A number of specimens were teeted in wl:ich the geometrical variables 

b and d were systematically varied while R was kept c cnstant and. 

equal to 16 inche~ . The r esults of these tests L"ldicated t ha.t T ID.aJC 

var ied as ~bd . For the buck~ing of Q~ tiffened cylinders ~ucjected t p 

pure torSion, the experim~ntal results of ~efc:) renc e 15 h'ld icate that, for 

vall;.es . of LIB equal t o and greater than 3.2, T crlE . vari es approxirr.ate -

'(;t)3/4. . ,Ir-t/L . ly as .1.\ 'V It was therefor.3 assumed. that, for identical 

and the critical shearing 8tres~ for the 

general instability of a. stiffened cylinder would vary as the r eciprocal 

of ,/ 'cd Jf /4 . 

were cond.ucted 

d . A plot of 

In :.order to verify this as c~pt n, 8. number of tests 

on 10-inch-radius specimens and e~ious values of band - 3/d. Tmax as a function of ,/bd R . 'f or the 10- ar..d 16-

inche. spec.imen~ is shown in figure 23 . Theso r esults indicated that 

the a~ 8umptio ioI-as justifiei and it Has the:refcre concluded that the 

parame ter f or pr edicting gener.c3.l ins ta'b il i ty in torsion is of the form 
NACA TN No. '1198 17 

J"bci R:>/4 

f . (px ' Py) 

From dimensional r easoning, it fol101vS that the function f'(p 0) must - x' y 

have the dimensions of the 7/4 po.,er of a length. The simpl est a.ssumpticn 

f or the function which determi nes the influence of the section-?..!'a111etmB, 

Px and Py, is that it depends on only the geometr~cal mean value 

../ Px Py . The parameter therefor e appears in the form 

In checking the validity of this parameter .• it is' necessary .t o evaluate 

the amOUi"1t of sheet ac ting .wi t..~ the fra...'J.es and l cngi tudinais in order 

to calculate Px and Py ' It is quite diffi cult to evaluate by analytic 

means the amount of sheet acting with the reinforcing rebmbers; trial 

calculations indicated t bat the b e st re sults were, oo'tained. if the total 

width of sheet was used. For t his r eason Px and Py were caloulated 

witb. the entire width of sheet assu''D.ed t o be effective . 

Specimens wer e also tested in which both the sheet thich-ness and 

sectional properties of the l ongitudinals were varied . The resu1ts of 

all tests are eh01ID p_ot"ted in figure 24 . It is seen that up t o values 

of 1 0,000 pouncts per sq!l8.re inch all t est values s catter closely about 

a straight line . For hie her values of T max the r8 is a sudden shift 

in the experimental value s . However, the maJority of tests aoain follcw 

a straight line ha ving the same clopA as t he line corresponding to the 

lowe-r values of T max ' Since the observed diagonal-tensi on field varied 

betwe~~ about 300 to 500 , it caIl be shmm that for a shear str ess of 

10,000 pounds per square inch the c orrecponding tensile stress 'would be 

betvleen 20,000 and 23,000 pounds per square inch . I t was thousht that 

this tensilA stress might be sufficiently close to the proportio~~l 

limit of the sheet c overing to explain the s~dden shift in the experimental values . Howe ver, ~~ examination of the stres8 tr ~~ curves 

indicated that thtl t ensile stress at a shear str ess of 10, 000 pounds 

per square inch is well below the proportional l::mit . 

A more de~irable presentat i on of t he test dat a would be to pl ot 

/, j '"PX Py (J Px ~y )

3 

/

4 

TmaxtGE against bd R / since T ma.."{/~ cO!Tl3 8ponds 
l 

18 NACA TN No, ll9"3 

to the she aring strain r . Such a presentation would be more general and 

would allOW for mater ials of different pbysica:" propert:es or for cbanges 

in the physical properties above the pr oportional llmi t . It had not been 

realized at the beginning of the test IJrogram that it wou.ld be d.esireble 

to ab cain a measure of T ~ at failure . For' this r eason angular de--

formations were measured on only a number of specimens . Not enough 

measurements are aV.flilable to make such a plot. A plot of T rriax/E as a 

functi on of /Px !!x 

,Jbd C

· J£!~RPY )3 /4 . is' given in figure 25 . The vaJ,.ue 

of E in this figure corresponds to that of the sheet coveri~g and WEB 

taken as 10 7 pounds per s quare inch, Bince this corr esponded closely to 

the actual test values obtained f or the sheet. 

Combined Bending and Torsion 

For a ccmbin~d:-loadil1g condition it would. be a dHfi-:::1.J~t a.."ld lep-8thy 

task to obtain ex:per1men-:;ally a para'J.e t er des:::rib.ing the failure of a 

stiffened cylinder . For this reason tbe ultimate streo 68 at failure 

were presented in t he form of int er9.cti on curves; that is, 0/00 was 

plotted. as. a function of T /T 0 , where (J is the nor;rJ8.l c c::npression 

stress at failure for c ombined loading and (J o is the same stress at 

failure fer pure bending, and similarly, T and. T 0 are the shearing stresses at failure for combined oadir~ and pure rsio~, r espectively. The shearing stresses were computed. by the equati on 

1>1 

2 AT (11) 

~.yo sets of data are shown . The first set (fig. 26) c orresponds to 

stresses 8S measured by the r esistance strain gaGes and. the second set 

(fig . 27), t o the stresses as obtained from the d.ial--ga.ge measuremen ts. 

In either case a" considerable amount of scatter is evident . The interaction equations of the form 

)8 + ~ \ 2 = 1 (l2) T J. 0'0 o · 

and 

(J 

-+ (T~ )2 = 1 (13) (J ' 

0 0 
NACA TN No. 1198 19 

are compared with the experimental results. Figure 26 indicates that for 

the reslst.ance-strain-gage measurements ab-out two-thirds of the test values lie fairly close to the curve of equat~on (13); whereas the majority 

'·of the dlal-gage measurements scatter about the curve of equatlon (12). 

SUMMARY OF DESIGN CURVES .cum EQUATIONS 

A summary of the. design curves and 'equations for the· cond.:i,tions 

studied is as follows: 

(1) Pure bending 

For the ultimate longitudinal strain at failure it is recommended 

that the lower curve of figure 18 be used, or be calculated frem the 

equation of this curve, which is 

kl .;-p;p;- ---,---" 

E ' R 

/Px-Py 4 ----

/ bd 

where kl = 4.13. The strain values t~U8 obtained corre~pcnd to the 

lower limit of the experimental strain values at failure. 

(2) Combined bending and transverse shear 

For th:Ls load.ing bro types of failure are pos'sible - a bending 

failure in the zone of maxDnum compressioa or a shear failUre in the 

zone of maximum shear. It is recommended that these failures be checked 

in the fo11o~~ng manner: 

(a) Bend.ing failure.- The lower curve of figure 18 or the equation 

of this curve as given above . 

(b) ~hear failure. - The possibility of a shear fa:i,lur~ can be checked. 

by calculating the m~imurn shear stress anQ comparing this shear stress 

with the ultimata shear stress of figure 24 . The four shear failures 

listed in table II have been cempared 1.n th the curve of figure 24; three 

are in fair agreement and one (specimen 117) failed at .a shear strees of 

approximately 25 percent less than that given by the cUrve of figure 24. 

(3) Combined bel1ding a..'YJ.d torsion 

For thls.1oading the equation 

is reccmmended.. 

(J _ .(T.\2 1 '. -+ -) ::; . . ao To' . 
, 

20 NACA TN No. 1198 , 

CONCLUSIONS 

As the result of an investigation of the general instability of stiffened metal cylinders, parameters were evolved which make it possnle to 

obtain an estimate of the stress at which general instability will occur 

for aD0T given stiffened metal structure of circular cross section. It is 

felt that both the geometrical quantitieo and sectional properties of the 

structural members were varied over a suffi~ient range to establish, in 

general, the validity. of the parameters. Because of the catastrophic 

nature of a general instability failure it is re'commended that ample 

margins of safety be allowed in an airplane structure in which this type 

of failure might occur. 

,No attempt was made to give a theoretical treatment of the generalinstability problem because of the nonlinearity of the buckling problem 

of stiffened cylinders. The parameters preoented for predicting the 

ult imate strength of stiffened metal cylinders subjected to pure bending and pure torsion ,.,ere based on an analysis of the e}..-perimental results and on the existing theory of unstiffened metal cylinders. This 

method was preferred over that of a linearized theory which cannot 

correctly describe the behavior of the structure . The results of a 

linear theory would have to be modified and corrected to bring it into 

agreement with the experj~ental observations, and thus the theory would 

immediat'ely be remd,er ed an 'empirical method. 

Guggeru1eim Aeronautics Laboratory, 

California Institute of Technology, 

Pasadena, Calif., August 1, 191~4. 

REFERENCES 

1. Guggenheim Aeronautical Laboratory, California Institute of' Technology: 

Some Investigations of the Gen~ral Instability of stiffened Metal 

Cylinders. , I Review of' Theory and Bibliography. NACA TN No . 

905" 1943. ' 

2. Guggenheim Aeronautical laboratory, California Institute of Technology: 

Some Investigations of the General Instability of Stiffened Metal 

.Cylinders. 11 ·- Preliminary Tests of 'Wire-Braced Specimens and 

Theoretical Studies. NACA TN No . 906, 1943. 

3. Guggenheim Aeronautical Laboratory, California Institute of Technology: 

Some Investigations of the General Instability of Stiffened Metal 

Cylinders. III - Continuation <?f Tests of Wlre- Braced Specimens and 

Preliminary Tests of Sheet-Covered Specimens. NACA TN No . 907, 1943. 
HACA TN No. 1198 21 

4. Guggenhei:n Aeronautical Laooratory .. Calif .:>rnia Institute of Tevhnology: S0me InYestigati ons of th3 General Instability of 

S~iffened Metal Cylinders. IV - Continuation of Teets of SheetCov~red Spe cimens and Studies of the Buckling Phenomena of ULstiffened Circular Cylinders . NACA TI~ .No . 908, 1943 . 

5. Gug3Elnhpim Aeronautlcal Laboratory, California Institute of Technology: Seme Investigations of thg Gen~ral ILstability of 

Stiffened Metal Cylindors . V - Stiffened Metal Cjlinders Subjected to Pure Bending . NACA 'TIl]" Nj . 909, 1943. 

6. GuggenheL~ Aeronautical Lator~tory, Calif rn~a Institute of Tevhno oe~: Soma Investigations of the General Instability of 

Stiffened Metal Cylinders . VI - Stiffened Metal Cylinders Sllb-

,jected to Comb ined Bending fu"Ld Transve rse S~ee.r. NJ'...CA TN No. 

910, 1943 . 

7. GU8genhe~11 Aeronautical Labor atOl'Y ) Ca:..ifornia Institute of Technol0p.y : .some Investigations of t he Ger.eral Instability of 

Stiffened Metal Cylj.ndars. VII - Stiffened Metal Cylinders 

Subje cted to Combined Bending and Toraion. NACA TN No . 911, 

1943 . 

8. Dunn, ~o is G.: Some Investigations of the General Inst~bility 

of Stiffened Iv'etal Cylinders . VIII - Stiffened Metal Cylinders 

Subjected to Pure Torsion . NACA TN No~ ll97, ~947 . 

9. Hoff, N. J.: Instability of Moncco~ue Stru0tures in Pure Bending. 

Jo~. Roy . Aero . Soc . , vol . )+2 , April 1938, pp. 291- 346 . 

10. Taylor, J . L.: Stability of a Mon co~ue in Compression . R. & M. 

No . 1679, British A .R .C. , 1935 . 

11. Dschou, Dji, Djllan . : Di~ Druckfestigkeit versteifer zylindrischer 

Schalen. Luftfahrtforschuns, vol . 11, no . 8, Feb. 1935, pp. 

223-234 . 

12 . Hoff, N. J .: .onerel Instab:.'.li ty of Mon Jcoque Cylir.ders . Jour. 

Aero. SeL , vol. 10, April 1943, pp . 105- 1l11-; 130 . 

13. Cox, H. L. : Stress Analysis of Thin Metal Construction. Jour. Roy. 

Aero. Soc . , vol . 7, March 1940, pp . 231-282 . 

14. Lundquist, Eugene , E . : Local Instability of Centrally Loaded Columns 

of Channel Section and Z-Section . NACA TN No . 722, 1939. 

15. Donne 1 , L. H.: Stab::!.lity of Thin-Walled Tubes under Torsion. NACA 

Rep. No~ 479, 1933. 
[All Lmgi tudimla 51] : 

Tes'\; FrQle Shen Lalg. 

No. Thiakc, Spaoinc.. 

b 

(in. ) (in. ) 

25 .010 2. 53 

26 · 2.63 

21 2. 53 28 2.53 

29 

30 6. 06 

31 6.06 

32 . 6.<M 

34 10.12 

36 10.-12 38 10.12 

81 10.12 

sa 6.08 

38 ,-010 2.53 

TABLE I 

Test. of Longitudinal - Frame Combina.t1Ct1a 

Frame Ba.d1ua )lax. 

Spuinc, Unit 

4 Stn.1n 0d Px 111)( ·r eJ 

(in. ) (in. ) 

8 16. 92 .00110 2.120 .1168 .02$36 .01U6 2822 . Geoaral 

• • .00208 1.18:5 .1165 .02611 .01320 2160 • 

2 .00288 1.600 .1165 .02836 .01380 1110 • 

16 .00130 2.520 .l1S9 .01816 .01010 39'70 Started 

Final F

1. .000$2 2.998 .1160 .018'75 .01023 t660 Panel I

8 .00140 2.520 .1161 .02335 .01190 3310 Gezieral 

• .00190 2.120 .1169 .02817 .01826 • 

2 .00256 .1161 .01836 .01380 2060 • 

16 .00088 3._ .1110 .01876 .00016 5820 Started 

Final F

8 • 00120 2.998 • 1120 .02336 .01180 .120 

• .001M 2.620 .1122 .02811 .01280 3136 • 

Z .00200 2.120 .1111 .02888 .01330 2&tO . • 

1 .00283 1 .. 500 • 11M .02801 .01380 1166 • 

1 .00826 1.281 .UTO .02801 .01360 -1.18 • 

-
Test Frame Sheet Long. Frame Hi.dius 1hx. 

No. Thick. Spacing, Spaoing, Unit 

b d strain 

(in. ) (in. ) (in. ) (in, ) 

40 F5 .015 2.53 16 15.92 .00104 

41 2.53 8 .00182 

42 2.53 4 .00215 

43 2.53 2 .00280 44 5.06 16 .00066 45 5, .06 8 .00146 46 5.06 4 .00167 

47 5.06 2 .00249 

48 10.12 16 .00048 

49 10.12 8 .00128 

50 10.12 4 .00150 

51 F5 .015 10.12 2 15.92 .00250 

52 Fl .010 2. 53 16 16.00 .00180 

53 2.53 8 .00216 

54 2.53 4 .003732 

TABLE I (CONTD) 

0d Py 

2.520 .1175 .01723 .00955 

2.120 .1180 .0217€ .01140 

1.783 .1184 • 0260E .01310 

1.500 .1184 .02819 .01410 

2.998 .1140 .0172:1 .00935 

2.520 .1150 .0217E .01120 

2.120 .1151 .0260E .01285 

1.183 .1151 • 02875 .01380 

3.560 • lOt .01723 .00870 

2.998 .1049 .0217e .01050 

2.520 .1060 .02608 .01195 

2.120 .1061 .0287£ .013OC 2.520 .1168 0.1281: . • 0430 2.120 .1165 0.0811 .0303 

1. 18:5 .1168 0.0982 .03500 

t f}J 

4210 

2960 2168 

1696 

5110 

3580 

2630 

2060 

6520 

4640 

3360 

2600 

938 

ll20 

81 2 

General 

.. 

.. 

r

General 

.. 

• 

Panel I

General 

• 

• 

Panel I

• 

aw.neral 
Test FraIlIS Sheet Long. Fr&me iadiua Ma.x. 

No. Thick. Spe.oing. Spaoing "(hit 

b d strain 

(in . ) (in . ) ( i ll . ) ( in . ) 

55 Fl .010 2.53 2 16 .004.775 

56 5.06 16 .00090 

57 8 .00228 58 4 .004350 

59 Fl 2 • 006154 

60 F6 8 .OOZ43 

61 4 .004927 62 5.06 2 

63 2. 53 4 .004045 

64 F6 2.53 2 16 .005100 65 F5 2. 61 4 10 .003150 

66 2. 61 2 .004200 

67 5.22 4 .002950 

68 5.22 2 .003750 

73 2.61 4 .003200 

74 F5 . 010 2.61 2 10 .004400 

-

L 

UBLB I (CCWCLU%lEl» 

VW fj 

1.500 .1168 .11000 .0:578 

2.998 .1150 .06330 .0250 

2.520 .USO .08110 .0300 

2.120 .1160 .09820 .0350 

1.783 .1165 .11000 .0378 

2.520 .1270 .06340 .0251 

2.120 .1270 .06400 .0254 

1.783 .06180 

1. 783 .1278 .06400 .0255 

1.500 .1278 .06180 .0247 

1.798 .1163 .02677 .0132 

1. 510 .1168 .02836 .0138 

2.175 .1165 .02677 .0132 

1. 798 .1166 .02836 .0138 

1. 798 .1162 .02677 .1032 

L510 .1164 .02836 .0138 

636 

1920 

1345 

965 

742 

In5 

1245 

1045 

905 

1362 

laJ6 

1650 

1300 1365 

1095 

a.oe

Pane

Pane

GeneM

" 

Pane

Gene

Tens

GeneM

" 

" " 

It 

n 

" 

II 
all sheet = .010 in. 

all longitudinals 1. 

Test Long Frame 

Spa 0- Spa 0- Radius 

ing. ing. 

b d 

(in. ) (in. ) (in. ) 

75 5.06 8 16 

76 II II II 77 II II II 

78 II It II 79 n 2" n 

80 n II \I 81 It n It 

82 It II .. 

83 10.12 4 " 

84 " 2 " 

85 It " " 

86 .. " ., 87 II It \I 88 5.06 4 It 

89 It It " 

90 It " " 

Ultinate Malnent strain 

Applied arm - at 

Shear to f'ind Failure 

end 

(lb) (in. ) 

1057 128 .00161 

1050 116 .00153 

1450 92 .001516 

995 116 .00151 

2000 128 .00270 

1850 107 .00211 

2175 86 .00242 

2070 64 .00189 

563 128 .00154 

825 128 .00212 

915 104 .00195 915 80 .00218 929 66.5 .00213 

2115 80 . 00216 

1910 66.5 .00187 

1212 128 .00209 

nBLEII 

t;;; It 1fr1frY 

2.52 10 1167 .02335 .0119 

n .1167 .02335 .0119 

a .1167 .02335 .0119 

II .1167 .02335 .0119 

1.785 .1172 .02836 ,Ol3l:l 

.. .1170 .02836 .0138 

" .1170 .02836 .0138 

It .1170 .02836 .0138 

2.52 .1117 .02677 .CUl8 

2.12 ,1129 .02836 .0135 

.. .1127 .02836 .0134 

" .1130 .02836 .0135 

II .'1130 .02836 .0135 

" .1170 .02677 .0132 

" .1169 .02677 .0132 

" .1170 .02677 .0132 

rt

33

3

333:

2020

20

20

3

25

25

2

2

2

2

2
aU sheet - .010 in. 

all' longitudinab 81 

Te..-t Long Frame 

8pao- Spao- RAdiuB 

ing, ing, 

b d 

( In.) (In. ) (iD.) 

91 5.06 4 16 

92 " 8 It 

93 It " " 

94 2.62 " 10" 

95 " " " 

96 It It " 

97 " " " 

98 It 4 " 

99 It " " 

100 " " It 

101 " " " 

102 2.53 2 16 

103 It " " 

104 " It " 

105 " " It 

106 2.62 " 10 

Ultimate 

Applied 

Shear 

(HI) 

1331 

503 

1353 

960 

1283 

1711 

2900 

1310 

1660 

2250 

3300 

2480 2860 

4200 

4500 

1490 

mm,g II (CCtlTtD) 

Moment Strain 

arm - at 1bd to fixed Failure ?x 

end 

(iD.) 

116 .OO19oi 2.12 .1169 

194 .00152 2.52 .1161 

74 .00135 11 .ll66 

1U .00174 - -

88.4 .00290 2.14 .1165 

65 .00265 .. .U66 

40.5 .00207 - -

113 .00340 1.80 .1163 

88.4 .00330 • .U64 

65 .00270 - -

40.5 .00280 - -

137 .00282 1.50 .1160 

U2.4 .00277 It .1160 

89 .00343 " .1157 

65.1 .00218 - -

113 .00396 1.51 .1161 

fJ-

.02671 .0132 

.02335 .0119 

.. .OU9 

- -

.02335 .0119 

.. .0119 

- -

.02611 .0132 

T .0132 

- -

- -

.02836 .OU7 

" .0137 

It .0137 

- -

.02836 .0138 

25

33

33

18

18

- 

13

- 

- 

1717

17

- 

10
all sheet - .010 in. 

all longitudi nals 31 

Test Lcng Frame 

Spa 0- Spao- Radius 

ing, ing, 

b( inJ d{iD) (In. ) 

107 2.62 2 10 

108 " " II 

109 5.24 8 .. 

110 " " II 

111 " 4 n 112 " II " 

113 " " 0 

114 2.53 " 16" 115 " " " 

116 " " • 

117 " " " 118 5.24 2 10 

119 w " w 

120 " II n 

121 " " • 

122 2.62 1 .. 

123 .. " n 

124 " " " 

Ult:1nate Moment 

Applied arm -

Shear to fixed 

(lb) end (iD) 

2760 65 

4270 40.5 

450 11:5 

1470 40.5 

660 113 

1780 40.5 

930 88.4 

1900 137 

2010 112.4 

2400 89 2450 65.3 

no 113 

990 88.4 

1460 65 

2310 40.5 

1665 113 

2140 88.4 

3220 65 

'lABLE II (COOT'D) 

Strain 

at 

Failure f} 

1.51 .U60 .02836 

.00398 " .1161 .. 

.00186 2.54 .1162 .02:5:55 

.00242 2.54 .U66 .02335 

.00251 2.14 .1110 .02677 

.00290 " .1169 " 

.00265 " .1169 .. 

.00216 1.785 .1162 " 

.00194 " .1163 " 

.00217 " .1162 .. 

.00136 - - -

.00360 1.80 .1170 .02836 

.00364 - .1170 

.00353 • .1169 " 

.00374 " .1170 " 

.005%5 1.21 .U59 .02801 

.00492 " .1160 " 

" .U60 • 

--

itf}i;I 

.0137 

.0138 

.0119 

.OU9 .0132 

.0132 .0132 

.0132 

.0132 

.0132 

- 

.0138 

• 01:58 

.0138 

.0138 

.0136 

.0136 

.0136 

-------
[spec. 125, long. 

spec'e 126 to 129 longitudinal Sz 

all sheet = .010 in.] 

Test Long Frame Ul tilrll. te 

Spe.o- Spao- Radius Applied 

ing, ing, Shear 

b!lnl d( in.' (in. ) (n) 

125 2.62 1 10 5280 126 5.06 4 16 1600 

127 " n " 1940 

128 " " n 1445 

129 " " n 2340 

Moment 

arm -

to fbed 

end(iD) 

40.5 

109 

89 

137 

65 

I 

'1'!.BLE II (C<J1ItLUDED) 

Strain 

at n;;- ,P)( Failure 

.00479 1.27 .1160 .02801 .OlS0 .00207 2.12 .1150 .02677 • 0131 

.00192 " .1150 " .0131 

.00208 " .ll50 " .0131 

.00205 tI .1150 " .0131 

- - - - --
I SPEC. STIFF. FRAME 6 cI {bd Ig NO. NO. NO. Un.) in.) 

. 149 82 F5 5.12 4 4.52 16 8.0 

i 162 82 2.56 4 3.20 16 8.0 

171 81 2.56 4 3.20 16 8.0 

175 81 2.56 8 4.52 176 81 2.56 2 2.26 

177 81 5.12 16 8.98 

178 81 5.12 8 6.36 179 81 5.12 4 4.52 

180 81 5.12 2 3.20 

181 81 5.12 16 B.98 

182 81 5.12 8 6.36 183 81 5.12 4 4.52 

184 81 5.12 2 3.20 

185 81 5.24 8 6.48 10 5.62 

186 81 5.24 4 4.58 10 5.62 187 81 5.24 2 3.24 10 5.62 

189 81 24 32 1B.l 16 8.0 

190 81 16 12, 8 16 8.0 

TABLE III 

(pl1 I pr.p'1{II fiG. 1''1 

" 

36.1 .1061 .0269 .00594 

25.6 .1169 .0269 .00648 

25.6 .1145 .0269 .006!56 

36.1 .l145 .0234 .00563 

18.075 .1145 .0285 .00670 71.9 .0967 .01732 .00313 

50.9 .0967 .0218 .00456 

36.1 .0967 .0262 .00536 

25.6 .0967 .0289 .00584 

71.9 .0915 .01525 .00318 

50.9 .0915 .0202 .00406 

36.1 .0915 .0251 .00491 

25.6 .0915 .0289 .00556 

37.4 .0961 .0218 .00453 

25.8 .0961 .0262 .00533 

18.2 .0961 .0289 .00581 

144.9 .0895 .0143 .00296 

102.5 .OB99 .0188 .00376 

u

16.45 

25.3 24.82 

15.6 

S1.05 

5.19 

8.94 

14.8 

22.8 

4.42 

7.97 

13.6 

21.7 

12.1 

20.6 

31.9 

2.04 

3.67 
SPEC STIFF i'lWo!E Ibd' e1+ .0. NO. NO. (j/;3 I flu 

],91 Sl W5 0.24 8 8.98 16 8.0 

192 S1 0.24 4 6.:56 16 8.0 

193 81 2.06 8 4.52 16 8.0 

194 S3 5.24 8 6.48 10 5.62 

195 S3 5.24 4 4.58 

196 S 5.24 2 3.24 3 

197 32 2.62 8 4.58 

198 32 2.62 4 :5.24 

199 S2 2.62 2 2.29 

200 S2 2.62 2 2.29 

201 S2 2.62 1 1. 62 

202 S2 2.62 1 1.62 

203 31 F7 2.62 8 4.58 

204 Sl 2.62 4 3.24 205 Sl 2.62 2 2.29 

206 81 2.62 8 4.58 

207 31 2.62 4 3.24 208 81 2.62 2 2.29 

209 81 3 2.8 

-

'l'A.BLE III (CCELOIlZD) 

PI< JO'1 

n.9 .0699 .0234 

50.9 .0899 .0269 .00514 

18.075 .1145 .0285 .0067 

37.4 .0947 .0228 .00466 

25.8 .0947 .0266 .0063:5 

18.2 .0947 .0287 .00571 

25.8 .1166 .0228 .00558 

18.2 .1166 .0266 .00641 12.85 .1166 .0287 .00683 

12.85 .1152 .0285 .00673 

9.05 .1152 .0281 .00665 

9.05 .1152 .0281 .006836 

25.8 .11:56 .0385 .00866 

18.2 .1136 .0428 .00950 

12.85 .1136 .0436 .0966 

25.8 .1110 .0316 .00708 

18.2 .1110 .0415 .0092 12.85 .1110 .0453 .0097 

15.72 .1110 ,0435 .0965 

6.:53 

10.1 

37.05 

12.45 

20.65 

:n.ro 

21.60 

35.20 

63.20 

52.40 

13.50 

15.7 

33.6 

52.2 

T!.2 

27.5 

50.5 

15.5 

61.5 

--
TABLE IV 

COllBIlfED BENDING AND TORSION 

Sp ... Sh.et Stiff- Frame Long1tu- Torsion U1tinate 

1Jun thiok- ener .pac- dina 1 bendinr; bending 

ne •• I&diu. Frame ing llpa 0 inr; manent 

(in. ) (in. ) (in. ) (in. ) (in.-1b) 

149 .010 16 '5 Sz , 6.01 Torsion 0 

150 5/1 Zl6xl02 

151 287 

162 2/1 472 

15:5 1/1 770 

1M 1/1.5 900 

155 1/2 1000 166 1/2.5 1175 

167 1/3 1150 

158 1/3.5 1210 

159 B«lding 1400 160 1/1.5 8ft 

161 5.06 1/5 1200 

162 2.5:5 Torsion 0 

183 1/1 820 

lEK 2/l 575 r 

Ultimate Co

torsicna1 st

moment f'a

(in.-lb) (i

1070xl02 5'

1080 7.

860 7.

945 10.

770 13.

600 14.

500 18.

470 18.

365 16.

355 16.

0 16.

583 14.

Z.co 16.

2.

820 7.

1150 5.
r-----, -

TABLE IV (CCliCLUIlID) 

Spec- Sheet St:1,ft- Frame Longituimen thick- emer ape.o- dina1 bending 

ness Radius Frame ing sp&cing 

(in.) (in. ) (in. ) (in. ) 

165 .010 16 F5 Sl 4 2.5!5 1/2 

166 1/3 \ 

167 1/5 

168 1/2 169 

, 

1/1 

170 S2 2/1 171 Sl Torsion 

172 

1 

1/1 

173 II r 1/2 • 174 .010 16 F5 Sl 4 2.53 1/4 

Ultimate Ultimate 

bending mamenul0 toraio:oal momentx1d 

(in.-1b) (in.-1b) 

1390 695 

1900 633 

2540 508 

1600 800 

1050 1050 

550 1100 

0 ll85 

900 900 

1280 645 

1880 460 

Compre

strain 

failu r

(in./in

10.95 14.00 

17.6 

12.5 

9.4 

5.25 

1.85 

9.75 

14.10 

21.40 
NACA TN No. 1198 

.028 " 

, 

x x.320" 

I~ * 1.- ~20"-.J 

STIFFENER- 51 

Areo: 0.0324 'l,P-.000374 

FIG . 

x.320" • I~ t 

t.- ~2d·..l STIFFENER-52 

Areo·0.Q'368 'xp-·000407 

Note: All drawI19s ore tWice actual sIze 

--tr-.o24 • 

STIFFENE R - S 3 

Areo.0.02295 I =0.000326 xx---

t 

FRAME-FI 

Areo=O· 02355 I x=p-.OOO31194 

I , 

x+r---_ ±-;---_-:-I -x .125 II 

l3~ , 

FIGURE I. FRAME-F7 

Area=O.04688 I

xx6.I08XIO-5 

FRAME- F 5 

Areo=O.0291 'xx '.537XIO~ 

• x-F-+ -1--XJ875· 

L.50~ • 

FRAME-F6 

Area=0.09365 I

xxO.000274 
UNIT DEFORMATION 

90,00 I I VS. APPLIED 

80,000 ) 

BENDING MOMENT I 

I---

/ 

70,00 

I j I 

IJ)' 60,000 

CD 

...J 

I 

:I: 

C,) 

Z 

150,000 ) 

J 

IZ W 

o 40,000 

(!I 

Z 

o 

Z 110,000 

w 

CD 

II 

,/ j 

j / j 

I / ! I 

j f / 

! ! ! / 

II j 

)/ 

ij ,7/ 

'/ 

/ 

L 

! V 

L 

f1 

----1 f} 

l! 

/ V 

/ } 

j / 

JI 

If 

) j 

J II J 20,000 

) I j j ! -, j 10,000 

I II 1 

o 

./ / 

V 

/ 

/ 

/ 

/ 

-r-- - r-- -

/ 

V 

/ 

I 

[1 i-- - -- - r--- /1 A 

r-7 

V 

J 

/ 

I I I 

I 

TENSION 

tr-A COMPRESSION 

1-.0004-

FIGURE 2. UNIT DEFORMATION 

IJ)' 

CD 

...J 

:I: 

C,) 

r 

tZ 

W 

o 

(!I 

Z 

Ci 

Z 

w 

en 

UNI1 DEFOR

vs 

APPLIED BENDING 

260.00 

22a.OOO 

20a.000 

60.000 

I 

( 

/ / 

I / 

1/ / 

.J 

ff I / 

) J. 

V ' 

, lI; (

180000 

80.000 

140,000 

120,000 100.000 

I J j I 

V bf 

' / ! I 'V 1I II 

60.000 

40,000 

20,000 

o 

UNIT DEFORM

FIGURE 3. 
· . . . 

TENSION 

STRAIN 

FIGURE 4. 

SPECIMEN NO. 159 

BENDING 

//' ------ / 

V j 

I !/ 

VlJ 

A v 

\ / rJ! . 

1\ / vI ! 

V V v 

V .(' "---f 

r---... 

I 

/ 

V 

/

28 24 20 16 12 8 4 0 4 8 

-Tension 

UNIT STRAIN x 10

STRAIN DISTRIBUTION SPECIMEN 

FIGURE 5. 
o 600 Ibs shear 

'V 1200 

o 2010 (fallur,) 

---

:----..., I J 

,/ I I ,/ / 

1/ j / / \ 

I i/ / \ '// / 

V 

\ l11 1/ 

\ V VI / 

'" I I / V 

,./ 

----- ---

24 20 16 12 B 4 0 4 8 12 16 20 24 

Tension Compression ----.. 

UNIT STRAIN x 10 

STRAIN DISTRIBUTION - SPECIMEN NO. 115 

FIGURE 6. 

l.---- r

/V / 

/ j 

L 1/ V 

(YV 

f/ 

\ 4. 

\ //j 'j '" K /, /' 1,,-/ I 'i- / 

--

24 20 16 12 8 4 0 4 

-T,nlion 

UNIT STRAIN I 

STRAIN DISTRIBUTION SP

FIGURE 7. 
TENSION 

STRAIN 

IN LB.XI0-2 

FIGURE 8. 

SPECIMEN NO. 161 

TORSION _ I 

BENDING -5 

TENSION 

STRAIN 

/ 

/ 

I 

1.0004 r-

-

--

Vl\ 

\\ 

BENDING MOMENT IN LB. 10-2 

\ -

\ 

I'---.. 

--

\ \ 

,

--f00

FIGURE 9. 
TENSION 

STRAIN 

/ 

/ 

I 

----l.0 004 

v V-- ---------

1\ 

\BENDING MOMENT IN LB.XI0- 2 \ \\ \ 

\ 

I--- t-----'" 

FIGURE 10. 

SPECIMEN 152 

TORSION 

_

2 

BENDING -T 

'\ 

\ 

\ 

/ 

/ 

\\ / 

to-- STRAIN 

COMPRESSION 

1 1 

TENSION 

STRAIN 

/ 

/ 

/ 

-l .0002 t-

/ v---

t 

• \ BENDING MOMENT IN 

\ 

I---

-

\ 

\ 

0 

\ \ 

I .. 

\ 

t 

_.:.

FIGURE II. 
NACA TN No. 1198 

(1) 

v 

- z 

o ' 0 _ z CJ) 

a: 

zO 

Wf-

~ 

- W 

ua: 

w~ e; a.. 

-L 

C\J 

o 

o 

q 

T 

~ r-

>-------..... -r:----- 17-- .!... 

1/ 

:r--

\ 

\ 

~ ~ --

--~ 

FAILUR 

1070.....--~ 

800 

600 

400 

200 

~t 0 

x 

cD 

..J 

~ 

Z 

Q 

!Q 

0 

f-

-~ 

~ 

"'" I 

~ 

4 

.... I 

j 

/ 

/ 

z 

o 

iii 

CJ) 

W 

~ff 

:~ f-O 

CJ)U 

C\J 

o 

o 

Q 

FIG. 12 
NACA TN No. 1198 Fig. 13 

• 

t') 

r-4 
r 

I 

Figure 14.- Combined bending and transverse shear. Failure 

occurr ed in maximum compression zone. 
Figure 15.- Combined bending and transverse shear. Failure occurred in maximum shear zone. 
NACA TN No. 1198 Fig. 16 

I 

• 
.0064 

,0056 

,0048 

,0040 

,0032 

E' 

,0024 

,0016 

.0008 

o 

v 

" - .01 0 SHEET· FRAME FS - R • 16 j f--- @- " " . " " • R • 10 

• - .016 " - " U _ R • 16 V 

f-- 0 - .010 " . .. F. - II • " 

EJ - II " - " F - Ii , " " j I 

Go I 

V 

I"" / 

"" 

"" @j 

L 

iJ 

I 

Qf. 

V 

A 

ya 

GENERAL INSTABILITY FAILURE 

/ PURE BENDING 

/ 

V 

o 5 10 15 X 10· 

FIGURF 17. 

.0064 

.0056 

,0041:1 

.0040 

.0032 

fir. 

E' 

,0024 

.0008 

o 

® - ,010 SHEET - FRAME ,." - R 

r-- @- .. .. - .. " • R 

• - .016 " - .. " • R 

I--- G- - ,010 " - .. F. - It 

6 

f---

/ 

o 

[!) - II " - " F - ,,

, 

!i5l-PANEL INSTABILITY 

J 

t; 

r5 ( 

Voo 

@J 

ij 

%I/i 

1:1 

!l 

5' 

®/ 

V) 

If 

GENE

V flx

b

FIGURE 
FIGS. 19,20 

006 

. 005 

,004 

903 

-

1.0 

NACA TN No. 1198 

I I I I I I I I I I I I 

EFFECT OF LENGTH ON THE GENERAL INSTABILITY FAILURE OF A REINFORCED 

CYLINDER SUJECTED TO PURE BENDING 

~ ............... 

---......: 

---

- ~ r---

~ 

I 

1.0 

£ 

r. 

0,8 

0,6 

0.4 

0.2 

o 

j 

1.5 

'" 

f- ~ 

0.1 

I I I I 

I I I I 

LONGITUDINAL SPACING 

FRAME SPACING : 2.0" 

-

~ FRAME 

2D 

>0 

FIGURE 19. 

.. " e 

VR 

M 

0.2 

FIGURE 20. 

SPACING = 4.0" 

0 

t:I 

I 

I 

: 2.56-

2.5 

75 - 78 4: 92 

118 - 121 

rn 

0.3 
.00 

.004 

0 

1.0 

0 

.004 I 

0.8 

t • 003 . 

0.6 

.002 

0.4 

0,2 .0016 ) 

/ 

o 

0.2 0.4 0.6 

V 

0,8 1.0 / 

V .0008 

/ 

V 

FIGURE 21. o 

o 2 

0 

0 V 

0 

0 

) ° 0 G

f¢ T

46

* VAt<; 

bd 

FIG
FIG. 23 

<J) I/) c c Q) Q) 

.-

E E 0 .-

0 

~ Q.l 

if: ~ 

II) II) 

:::l :::l 

.- "0 "0 0 0 

0:: 0:: 

I I 

.s=- .s=- 0 u c c - - I I 

(,() 0 - -

I I 

0 ~ 

---~ 

~ ~ 

.-~ 

0 0 

0 0 0 

0 0 0 

0 O· as C\J' 

'U! 'bY'Sql U! 

V 

0 

0 

0 

CD' 

SSaJ~S 

NACA TN No. 1198 

I 

/ 

0/ 

f 

/ 

/ 

.. ; 

/ 

V 

cr6 I. 

/ 

/ 

VO~ 

0 0 

0 0 

0 0 

V' N' 

JOa4S a~OW!~ln 

It 

0 

o 

V 

o 

C\J 

o 

o 

rt) 

(.\J 

w 

a:: 

::> 

l!) 

~~ LL.. 

<l< 

o~ (Q 

o 

<T 

o 

C\J 

0 
t--

SHEET R 

1/ .010 16 <> 

t--- .015 16 "- I SI .020 16 .. 

r-- .010 10 .:- / LI 

.015 10 + I ) 

.010 16 Gl / V 

- .0115 10 

S2 .010 10 v / 

I - .020 10 + 

- 53 .0115 10 x / / 

51 .0115 10 fr / -

51 .020 10 / V 

20000 

18000 

16000 

14000 

/ I 

/ 

/ / 

/ 

r • 

;I 

/ 

./ 

12000 

z 

g 

III 10000 

ID 

....J 

8000 

1--. 

.. 

Q 

)C 

. Y 

/ 6000 

1 

I 4000 

" 

Li - 2000 

• -

I I I I I I 

o 10 20 30 40 50 60 70 80 

FIGURE 24.-

( )

3/4 V'X::y Yl'x;y X 10 5 

GENERAL INSTABILITY FAILURE; PURE TORSION . 

SHEET R 

2 0 

18 

16 

14 

f---- .010 16 Q f---- .015 16 

SI .0 20 16 C\ 

.010 10 

f----

.015 10 4- 

f----

.010 16 III 

t--- .0115 10 

S2 .010 10 v t--- .020 10 -t 

t--- 

S3 .0115 

10 x 

SI .0115 10 .... 

t---

SI .020 10 ..). / 

12 / 

1/ 

/ 

[7 

10 Ir • 

B .J! 

.J 

" yr 

6 1/ 

4 i V 

A 

2 :1Jr I 

Q 

o 10 

FIGURE 25.-

20 30 40 

-Yfd, ,P, \ 

bd R / 

GENERAL INSTABILITY FAILURE; P
%0 

-

La 

0..8 

STRAIN - GAGE READINGS 

GENERAL INSTABILITY FAILURE; COMBINED BENDING AND TORSION 

• 

-:::: -.. . 

...... -........... . 

..... 

..... 

• " I 2 ' 2 " =-1 

\d\ I I 

, \ 

0.2 

a 

a 

}x \ 

-STIFFENER SPACING 5.0.6 : S2':.,..----;-\+I----I 

I( "2.53 S 2 \ \ 

/::; "2.53" S I \ 

0..2 0..4 0.6 0..8 La 

FIGURE 26. 

:.. 

LO 

0.8 

0..6 

a: 

70'0 

0..4 

0..2 

DIAL- GAGE READIN

GENERAL INSTABILITY FAILURE; COMB

f"-,- ., 

"- "-

, 

..... 

..... 

". "-

)..'" 

" 

"-

(%Jf,.j!,- 1\ 

\ 

\ 

• STIFFENER SPACING 

t---

5.0

)C " " 2.

" . " 2.

I I I 

0.0. 0 .2 - 0.4 0.6 

VT'o 

FIGURE 27.