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.1EECKJICALXO-TES

K!+J?IOITALADVISORY COMkiI~TE13FOR AERONAUTICS

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~0. 542

!THE!INIYIALTORSIONALSTIFl?HESSOF SEELL$

WITH IiJTERIORWEBS

By Paul KuhnLangleyldemorialAeronauticalLaboratory

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AERONAUTICS

TECHNICALHOT3 170.542—

TEE IHITIALTORSIO:~-4LSTIYFl~SSOY S~LL’S

WITH INTERIORWEBS

By Paul Kuhn .

A method of calculatingthe stressesand torsionalsti$f-aessesof t’hins-hellswith interiorwebs is summa-rized.. Comparisonsbetween experimentaland calculatedresultsare given for 3 d.uralun5.nbeams, 5 stainlesssteelbeams, and 2 duralum.iawin~s. It i.sconcludedthat if thetheoreticalstiffnessis multipliedby a correctionfactorof 0.9, experimentalvaluesmay be expectedto check cal-culate~values within abo-at10 percent.

INTRONCTION

St is well.knowilthat the applicationof ordinary en-gineeringfornulasto tkin sheet-metalstructuresmay leadto seriouserrors in sotiecases. For certaintyyes of cal-culations,Lomever, standardformulaswill give a reasona-ble degree of accuracy if experi,nentallydeterminedcorrec-tion factors are ap~lied. Itithe present paper U.S. ArmyAir Corps data on the tests”of wings of the centralboxtype are analyzedand the correctionfactor for initialtorsionalstiffnessIs derived. Since the methods of cal-culatingtorsiontubes with interiorwalls are not verywidely known, th~ first part of the paper gives a s~i~ary

of a convenientu~thod elucidatedby a nunoricalexa=ple.The secoudTart of the paper discnssostie nest inportantfeaturesof.the test objectsand results.

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.H.A;6.A. ~echntcalEote No. 542’

. LIST OF SYX30LS

torque, in.-lb.

sheariagstress,1%. per sq.in.

thickness,in. .

differentialelementof perimeter,in..area boundedby median line,,sq.zn.

torsionconstant,analogousto moment 62 iner-tia in bending,in,~

modulusof shear,lb. per sq.in~

torsionalstiffness,1%.-in.2

angle of “twist-,radians (per unit length)..

factor of effectivenessin torsionalstiffness.

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1. KHEORZTICALFORMULAS

General rem.a~ks.-~he fundamentaltorsionformulasforthin shells such as shown in figure 1 are

f - -J-S- = 2At (1)

(2)

the integralbeing taken around the perimeterof the pro-file. The derivationand the assumptionsunderlyingtheseformulasi3ay be found in any good textbookon strengthofr.laterials,such as reference1.

The correspondingformulasfor shellswith longitudi-nal interiorwebs (fig, 2) are not so well knotinas thefundamentalformulas. Their derivationby differentu6th-ods Y:lay3e found in references2 to 5, of which 2 and 5

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X.A,C.A. TechnicalNote Ho. 542 3

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are nest readilyavailable. The yresentpaper will con-fine itself to showinghow the torsionalstressesandstiffnessesof such shellsriaybe calcula-ted.!!hemethodpresentedhere i.sthat given in reference4 and was chosen%ecause it pernits the shortestpossible eqosition of themzbjcct. The method given in references2 and 5 is verysimilar;reference3 gives,a method based on the men_brane- .—-_analo~y (reference1). The qost elaboratediscussionofthe physical foundationsof the theory is Given in refer+--eace 5. .. .

Method of calc~latio~.-The interiorwebs will divide _<the cross ~;ion. of the shell Into a nWmbOr of separatecells. Humhers from one to n are.assigned to t“li-ese

--

cells; the ntunberzero is assigned to the space-outsideof -“the shell. T>e wall and anything-pertainingto it bf2~W0~21th-otwo CC1lS” i aad j are designated%y the subscript .-

ij. For each ctill i is now computedthe area Ai andfor each wall ij

.-t&.f3line integral —... -:-...-.:.&.. ........

ds “aij=j~ .(3): ““—...._ —--.An auxiliaryfunction 1? is now introducedfor each celli except cell zero, and the-equation .-.-

— -----...-..._=..-:.=.’--------,.—_ -_T= 2 ;;: Yi Ai ‘ ‘- ‘ iaj“- “--~

.

and n- .e.quationsof tileform ‘. ~ ..

(5)...

.-:‘:

D-ay‘Dewritten down- The summationii equ~~~oh“(5)ex-tends over-all walls boundingthe cell t, i.e., for jare substitutedin turn all numbers betweefi’-”%~roand nthat designatethe cells surroundingcell it --

.- -.—y .%e system of equations(4) and (“5)is solvedfor—the””:“=”..-:

unknowns GQ and Ti. The.sheai?ingstress in the wallij is then given by

.

-.l’.- Fi

..:(6) “ .._,.‘Sij = ‘–”-tij .-.— --—

.

4 -H.A.C.A. TechnicalKote No. 542.‘%

The direction ij is positive if a point travelingalongthe wall keeps cell i on its leftt In figme 3 the pos-itive directionsare indicatedby arrows. It is evidentthat

fsij = -f~ji

The torsion constantfollowsfrom

(7)

(8)

The equations(4)and (5) applied to the three-cell~ysten of figure2 are

1K;[ 1? + a12(3’2 --alo 1. 1Fz) +2~e=o

1[ 1-a20F, + a,l(~z - F=) i-a2=(F3 - F.) + 2Ge = ~

}

(5a)1;

& rA3 L-a30T3 + a32(F’ 1-l?=)I+2we=o

For a shellwith only one interiorweb (fig. 3), thevalues of

??i

J

where A

Fi and J can be obtainaddirectlyfrom

a20% -#--a=2A————.———2 ~T’”

a20~l -1-~2A2 -i-aolA22

1~01A2+.a12A ~. .T ~

——— I (9)A.a + a12A2 + aolA22a20 1.

a2 o% 2 + a12 -42+ aol~?~ .,.—-—.——.— Iao1a12 + a12a20 + a20a01

)

=A1+Aa

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N.A.C.A.TechnicalNote No. 542 5

For more than one interiorweb the formulasbecome toocumbersoine,and it is more convenientto write d“ow~-”~=–equations(4) and (5) after the coefficientshave %ben ob-tained and to solve these numericalequations.

The method discussedcan be used for analyzingashell such as shown in figure 4 where the cover sheet isprovidedwith closed longitudinalstiffeners. Considerfirstithe”case in which tho top and bottom sheetsare of

-— ._

tke same thicknessand all stifi’oner~-a-z=eo“Tthe sa-ti8size(fig. 4(a)). As indicatedon “thefigure by dottingallbut one of the n stiffeners,only one stiffenerneed beconsideredbecauseall functionswill be the same for allstiffeners. Insteadof o%taininga systemof (n+ 1)equatioasof the type (5), only the followingt’hreeequa-tions appear:

——_ ._:. .. .

.-

.=

-.

. ..,

where Al = A ~ nAa, A denotingthe area boundedby theouter shell and Az the area under one stiffener;the—line integrals a2 o and ala are taken for o- stiffener..- -.— —- .

In the nore usual case where the top and bottom covershave ciifferentthicknessesand stiffeners,the equationsbecone ..

.-

T= 1.-

2EF=4 i-nF..&+ ~3AJ

[-alOF=

[-~oF2

m3’.3@3

2Ge = O

-’1)1

+- 2G0=0

‘--1

(11)

.—

1ii;[

-a30T?3‘=Jl(F1 -s&) 1+ 2G9 = OJ

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6 Y,A.C,.4.TechnicalKote ITo.542

In these equations,the cell number.1 refers to the main “part of the shell,number,2to the area under a top stiff-ener (as in fig. 4(a)), and 3 to the area under”a bottomstiffener;there are n top stiffenersand m -bOttorlstiffen-ersc

When computingthe line integral ai for a itiffent3r,it is conservativeto use the full developedlengthand un-conservativeto use the developedlength betweenrivets.If the aworago of the t.yolengths is used, the error i.n Jshouldbe very small becausestiffenerscontributenormal-ly only little to tho total torsionalstiffcess.

Zhe e~uati’onsfor the case of figure 4(a) may be ob-tained in a slightlydifferentmanner that is~ perhaps,alittle more physicallyobvious. Since the stresscondit-ions are equaland uni.fernalong t~e top and bottom sur-faces, the stiffnessof thtishell is obviouslynot changedi.fall the stiffenersara transferredto one side and com-bined into a continuouscorrugated~hcet (fig. 4(3)). Allrivet rows except the out6r two may :nowbe removedand the Jshell is reducedto a shellwith a singletntcriorweb for .U-”tho ~urpose of computingthe initial st-iffncss.

.Naturally,

such a relocationof stiffenerswould change the stiffnessunder largo torquesas well as the skrength. ●

.-Approximater~eth.odfor stt$fene’d,c.Qveu.-.The calculat-

ion of th~–torsion~lstiffne~ %y tho method.describedreq,uiros~ in some cases, more “fimethan Is warrafited.cor.-sideringthe probablemagnitud~of the discrepancies“oo-twcen calculationsand tests and consideringt-he-purposeof tho calculation. In all cases where only an osti.nateof t-hetorsionalstiffnessis required,and possibly inother cases, it will be sufficientlyaccurate to use thefollowingapproximatemethod for shellswith stiffenedcover,

Find the cantroidof a single st-iffener(withoutskinattachedto it) and join the cent-roidsof all stiffenerson one cover sfie~tby ,aline.

Along the line thus established:distributethe l~of-fectiveiima.torialof–all stiffoncrs. The effect:vemate-rial of one stiffener“is the actual materialmultipliedby

the ratio ~ (fig. 5).

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There are now two separate”sheets:the actual cover

N.A.C.A. TechnicalNote No. 542 7

sheet and the 11substitutestiffenersheet.”——

Replace the ‘“=two hy a single sheet locatedat the centroidof the twoand with a thicknessequal to the sum of the two thick-nesses.

The fundamentalformula (1) can now be used to calcu-late the stiffness.

The re~ul.tso%tainedby this approximateme~hod willapproach those obtainedwith the more exact method as theamount of material in the stiffenersbecomes smallerinrelationto the amount of material in the cover sheet andalso as the ratio SA decreases. For the simplebeams

=2discussed in part 11, tileapproximateresultsfor thostiffnesswere from 2 to 8 percent higher than thoso front’acexact method.

Numericalexamnle.-As a numerical exampleof the gen-eral case, the.sti.ff~=sscalculationfor-the schematicyrofile of figure,6will be given. 17ith “ —

a { Al = 89.31 Aa = 250 A= = 125.-

● alo = 514.4 aao= 18?’5 a30 = 5190

a12= 166a7 aza = 333*3

the equationsbecome.- —

T = 2 (89.3 FI i-250 Fa + 125 F3)

1———89.3[

-514.4 231+ 166.? (I?a- 3?1)1+2Ge=0.

1z’!im-[-1875 F2 + 166.7(FZ- Fa) + 333.3(FS- Fa)] + 2GG = O

.-

1——-125 [ 1-5190 Fa + 333.3 (Fa - Ta) + 2GQ = O

The resultsare” ..._ .-

FL = 0.001667 T

3’2. = 0,001254 T —..

l?,.4.c.A. TechnicalNote Ho. 542

Pa = 0eOO0310T

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:Ge= 0.01036E?Substitutionof these values in equations(6) and (8)gives the shear stressesindicatedia figure 7, whero thedirectionof the stressesis also indicated,and the tor-sion constant J = 193~2 in.4. The torsionconstantofthe outer shellalone is Jo = 113.6 in.~.

11. COM??ARiSONSaETIYXENCALCULATIONKHD IWPERIU3MT

.Tests on box beams.-Figuro 13(a)gives tho dimensions . ......— ——

of three duraiuminhox beams tested by the U.S. Army AirCorps (reference6); figure 8(b) gives the di.mensioasoffive stainlesssteel beaus tested by the same agency (ref-erence7). The test points for any given test run alwaysfel’1very close to a straightline; individualtes$ curvesare thereforenot reproducedin the presentpaper. a

The experimentalvalues of the torsionalstiffnessesare Given ii table I, which gives also the torsionalstiff-nesses calculatedby formulas(2) or by equations(5) and . .’(8). The thickness t of-the verticalwalls of tho steelbeams was replacedin these calculationsby the offoctfvothickness te=$t

.because these walls formed di-agonal-

tonsionfields at low torques. (See reforonco8.)

The value of the shearmodulus was taken as G = 4 X 10Gpounds per square inch for duralurninand G = .1OX106 forstainlesssteal, The’shearmodulus for st~nless steelwastaken lower than for ordinary steel in accordancewith thofacts that the tensionmodulus of elasticity E for stain-10SS steel is c,onsiderabl?lower than that of ordinarysteel and that tho shearmodulus of other highly alloyedsteelshas been found to be as low &s 8 X 10s:

Table I gives next the ratio of experimentalstiffnessto calculatedstiffness. It will be seen that the averageoratio of all the leans is 0.90.

In the group of stainlesssteel beans, beam 4 showsthe smallestratio,which may be at+rilnztedto the conpli-catod sectionof the built-upstiffentirsrequiringmanyjoints.

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N.A.C.A, TechnicalNote Ko. 542 9

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8

Duraluninbeam 1 has a ratio considerablyin excessof unity. The test reports(references6 and 7) note thatthere must have been somo test irregularity,becausetheexperimentalstiffnessof beam 1 was higher than that ofbeams 2 and 3, which-doesnot seem reasonable.

Possib,levariationsof elastic constantsand of sheetthicknessesfrom the nominalvalues, however,may togetheraccount for perhaps 15 percent of the‘excessstiffness,which would reduce the experimentalstif~fnessconstantpracticallyto the theoreti”oalvalue. S“_inceno direct er-ror could he found that would make it necessaryto elimi-nato the test result on beam‘Isit was includedin the av-erage.

A number of tests describedin reference6 and dis-cussed in reference8 dealt with cases where the stiffnessdecreasesvery materiallywith increaseof load. Tor thepresent ~urpose only tho initial stiffnessosof those beamscomo in question,and-tlioyare not sufficientlywell de-fined experimentallyto give detailednumericalvalues;“-inspectionof the results indicatesthat the ratio of ex-perimentalto‘theor-0ti6alstiffnesslies ‘ingeneralb“etw”een0.9 and 1.

It is suggested,.t-herefore,that ~ = 0.90 be used.as a general factor of effectivenessfor “coxbeams in tor-sion.

..- . ..... .L.-

Effect”ivenessof stiffeners.~The outer cover of a-— ——shell is more effectivein re~ting twisti-ng”s—trO~””sesthan any material on the inside”of the shell. It seemedof some interest,therefore,to calculatefor the testbeams the torsionalst$ffnessoy’the outer cover alone,disregardingthe stiffiitiersentirely,and to compar”ethisstiffness GJO with ~he calculatedstiffness GJ, whichincludesthe influenceof tho stiffeners. The stiffnessGJO, as well as tho ratio of G3 to GJO iS given in ta-ble 1. Next in the table is”listed the reinforcement,expressedby the ratio of the area of t.hostiffeners tothe area of tho stiffenedsheet. Yigure 9 s_howsthe curveof increasein stiffnessagainst reinforcement;it shouldbe rememberedthat this curve is not genera”ilyapplicable.

A nore logicalway to remresontthe effect of thestiffenerson i%e torsionalstiffnessis asagine the stiffenersremoved;then increaseof the sheet from which the stiffenershave

follows: Im-the thicknessbeen removod

until-thetorsional stiffnessis the same as it was withtfiestiff~z?ers-preseilt.Calculatetbc amount of.natmrialthat had to b? added to the cover ~ileets;the ratio ofthis material to the actual stiffenermaterialgives ameasure of the effectivenessof the stiffener and is list-ed ii]the last row of table I. The efficiencyof the hat-shape stiffi3nercalculated on this basis is only about 7percent,

Tests on.commletewinEs.-..——— ——. The experimentalwingde-scribedin reference9 was chosen.asthe first examplo ofa co~l~leteduralumin-wing. The importantcharacteristicsof tnzs wing are shown in figure 10. It consistsof acentral box with corrugatedcovor; but a smooth sheetferns a continuouscover over the nose, the centralbox,and the trailing-edgeportion.

!f!hewing was first tm-stedin t~e elastic range to de-termine the stiffness. Then it was subjectedto the usualstatict-ests,which were carriedto:destructionin the~ligh-angle-of-at,tackccnditi.on~The bmalzwas repaired,antithe elasticstiffnesseswere dqt-mrminedagain in thefollowingthree conditionsof the wing: (1) complete;(2)aft-erremovalof leading edge, leav.in~the central lox andtrailingedge; (3) after removal..af.leadingand trailingedges, leavingonly the centralbox.

Figure 11 shows the calculatedand experimental.re-sults for the box alone. The agreeti~ntis very good ex-cept at the last~t~3xrn.near the tip. Tigure 12 showsthe results for the combinationof box and trailingedGe;the cal.cnlatedcurve for the box alone is shown in dottedlines., It is apparent that the effectivenessof the trail-ing-ed~eportion .isvery low, a, fact that can be easily ex-plained. The trailing-edgeyortion,buckles into a diag-onal-tensionfield. In order to realize the-theoreticalstiffness of such a field, rigid flanges-mustbe providedto take up the transversecomp,onentofthe diagonal ten-sioa. The trailing-edgestrip,however, is so flexiblettlatit furnishespracticallyno resistancetu thesestressesand the cover sheet caiznot-developany stl,ffil~ss.Figure 1’2shows that .nolarge errori”scoi~~itt-edif t-hotrailing-edgeportion aft of the rear spar is entirelynsg-.lected;.this proced’ure.recommendsitselfalso because itreducesvery materiallythe labor o? computingthe st-lff-ness of thecomplete”tii,ng.,a two-celiMox requiringVorY.much less computationthan a three-dellbox. Th”otrailingedge was therefor”bneglectedin calculatingthe stiffness

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U.A.C.A. TechnicalNote No. 542 11+

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of the completewing and figure 13 shows excellentagree-ment between the calculatedand the experimentalt-wist.

A point that deserves some mention is the calculationof the effectivet~licknessof the Webs. T!hesewe%s hadtriangularlighteningholes, making the webs, in effect,trusseswith,double diagonals. The ef”fe=tivethickness6f ‘-these webs was calculatedby formula (11) of reference10.!I!his formula i.svalid for pin-jointedtrusses; the trussesin questionhere have rigid joints,and the effect ofthese jointswas taken into account by multiplyingthecalculatedeffectivethicknessby a factor 1.20 based oncalculationsand tests on similartrussedwe%s given inrcfcronco3* -—

Farther outboard,the webs had circularlighteningholes. The effect of these holes on the shear stiffnessof the we%s was estimatedfrom tests (reference11).

As”the second exampleof a completeQUraluminwing,the wing shown in figure 14 was c-hosen.It has a“centraltwo-cellhox coveredwith smooth sheet stiffened%y closed.-section stiffeners. The leadingand trailingedges arefastenedto the centralbox by means of piano hinges lea@-iag t-nomvirtuallyopen sectionsineffectivein torsion,at least at low loads. The torsionallyeffectivepart ofthe wing is indicatedby the full lines in the plan and %ytho crosshatchingin the sections. -,

The interestingfeature of this wing with respect tocalculatingthe torsionalstiffnessis the large iiellforthe retractingwheel. Obviously,only the box %etween thecenter and rear webs is effective;%etweenribs 1 and 3.At rib 5, the full sectionfrom front web to rear web iseffective. Between ribs 3 and 5, the front part of tiebox is cut up to form the recessesfor the landing-gearstruts. No detail drawingson which an estimate of theefficiencycould be based were availablofor this portiofi;it was assumed,thereforo,that the torsionalstiffnessvaried linearlybetween ribs 3 and 5.

The cut-outbeing close to the root, tho loss in tor-sional stiffnessof t’heshell is partly balancedby ‘thobonding stiffnessof the spars. The twist at rib 4 wasthereforocalcula.tcdby fori~-~la(lOa) of roforence10, us-ing weighted avoragos of moucnts of inertiaand torsionalstiffnessbetween tho root fittingsand”ri% 4. It Is iib-.--—----........ -. .—.. — — -.,.-

12 Y,.4.C.A. Technicali?oteNo. 542

yiously not possi%leto calculatethe curve of twist bo-t~en the rootand rib 4, but this lack is of no practicalimportance,

The-test load was applied in four incremmts; t-hetest points plott-edin figure 25 are the averaws of thefour sets of readings. The outboardpart of the shell,buckledabout in the middle of the”teat range; calcula-tions were thereforemade for the nonbuckledstateas wellas for the buckled state. The agreementb~tweenexperi-ment and calculationis good in the out-ooardpart; inboardthere is”a ratherlar~e percentageerror,lmtithis erroris not large”in absolutemagnitude;it may be partly due ‘to jig deflection.

Stiffnessunderlarge tor~ues<-!l?.hetheoreticalfor-...———. -.+—mulas discussedgive the initialtorsionalstiffnessundervery low torques. i?ortorques in the practicalyorkingrange it will ve:y ofton be necessaryto ayply corrections.O,ne“typeof correctionhas been petitionedand used in thetext: If the smooth covor buckles to form a diagonal‘ten-sion field, the actual sheet thickness t nust be replaced

ant.by th~ ‘affectivet-hicknosste = ~ Thfs cffectivo

thicknessmay be decreasedmuch fuitherat high loads (ref-erence8). Corrugatedor well-stiffe~edsheet oan pro%-ably be assumed to lose not more t“h~,n5 or 10 percent ofits stiffnessuntil failureoccurs althoughthere is nodirect expe>-imentalevidenceavailableto substantiatethis claim.

It–is apparent,thenj that it is necessarybeforestartinga stiffnesscalculationto.define the load range.in which it is to apyly and to Vake,correspondingcorrec-tions if necessaryto the formulasfor initialstiffness.

LangleyMemorialAeronauticalLaboratory,NationalAdvisory Commibteefor Aeronautics,

LangleyField, Vs., July 16, 1935.

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N,A,C.A,Technicali~oteNo. 542 13

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1. Timoshenko,S.: Strengthof Haterials,Part IS.D. Van Nostrand Co., Inc., 1930.

2. Atkin, E. E.: Torsion in Thin Cylinders. Tlight -The AircraftEngineer,Sept. 25, 1931, pp. 70-72,”and Oct. 30, 1931, pp. 76-7’7.

3. Iiertel,Heinrich: Die Verdrehsteifigkeitund Verdreh-festiglceitvon Flugzeugbauteilen.D.V.L. Jahrbuch,1931, S. 165-220.

4. Van der Xeut, A.: Twistingand Bending by End Load ofKultiply ConnectedBox Spars. Verslagen en Yerhan-delingenvan den Rijks-Studiedienstvoor de Lucht-vaart, Amsterdam,Deel VI, 1931, p. 67. (Dutchtext, English summary.) ...

5. Duncan, 1?.J.: The torsionand Flexure of Cylindersand Tubes. R. & bl.~Oo 1444, BritishA.R.C., 1932, ‘

6. Greeae, C. R., and Younger,J. E.: IietalWing Con-struction. Part I - ExperimentalStudiesand Dis-cussion. A.C.T..R., Serial Ho. 3361, UatdrielDtvi-sion, Army Air Corps, 1929.

Carpenter,S. R.: Metal 17ingConstruction. Part 111 -Compilationof Test Data. A.C.T.R., Serial No. .“”3333, lfat~rielDivisioa,Army Air COrpS, 1930.

7. 3rowa, C. G., and Schwartz,E. H.: Metal Ring Construc-tion. Part IV - Spot-17eldedStainlessSteel Box3eams. A.C.~.R., Serial No. 3900, HatgrielDivision,Amy Air Corps, 1933.

8. Kuhn, Paul: The TorsionalStiffnessof Thin DuraluminShells Subjectedto Large Torques. T.Il.?i!Oa500,11.A.C.A., 1934.

9. Brown, C. G., and Greene, C. F.: Static-Testand Stress-DistributionStudies of the Hate’rielDivision 55-FootCantileverA1l-Eetalwing. A.C.I.C,No. 66S1 Yat&riel Division,Army Air Corps, 1932.

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K..-,A.A. TechnicalNote No. 542 14

10, Kuhn, Paul: Analysis of 2-Syar wings with SpecialReferenceto Torsion and Load Transference. T.R.NO. 508, Y.A.C.A., 1935. ..

11. Kathar, J.: Beitrag zur Schubsteifigkeitund. Knick-festigkeitvon gelochtendunnen Flatten. Abhand-lungen aus dem Aero. IDst. der TechnischenKoch-schule,Aachen, Heft 10, 1931.

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TABLEI

Experimentalad CalculatedTorsionalStiffnessae

Numberofbeam

I Expertien~alshiffnessGJ (1061~.-in.2)

Calculatedstiffm3r18”G3

Ratioof ~xpertieutdcalculatedstiffnees

to

Aver~erati~(rI)

stiffnessG-JO diehgar~ingstiffenare

Ratioof GJo to Cal-latedGJ

Ratioofstiffenercross-sectimmlareatoareaofcoversheet

llffectivenessfactorforstiffenerstseetext)

“

Duraluminbeams

T—

1 2

45.1 41.5

38.5 53.8

&.%7

1

23.2

2.32

4.10

0.41

3

43.2

55.5’

.778

Stainlesssteelbeams

4 5

X).2 23.9

25.6 25.4

18.49

1.38

2.5-J.

.27

~7,4

1.46

2.52

.37

6 7

29.8 30.6

30.2 32.7

.9CH’ .935I

.901

28,1

1.08

.52

.37

32.3

1.01

.52

.06

8

aJ.2

23.5

.8611

22.9

1.13

2.24

.09

Dwalumin: G = 4-X 10blb.pers~.in. &m.torque:T = 500ClIn.-lb.forbeams1 t.o3Stainlesssteel:G = 10x 1~~lb.pa! eq.in. !C= 40@lin..lb.forbeam A to6.

%Y approximatemethod.

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N.A.C.A.TechnicalNoteNo.542

~:~.

Figurel,-Simpletorsiontube.

Figure2.-Shellwithinteriorwebs.

om“

Figure3.-Diagramfornotation.

.-

-.— ---

.—

-..—

. .—.__. -

—

—

..—

. .. ..—

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s

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N.A.C.A.TechnicalNoteNo.542 Yigs.4,5,6,7

‘d ‘L_Iis-lI

1

a-— -—II II

-id L}-_lJ I_[_ > L(a) (b)

Figure4.-Boxbeamwithstiffeners.,-___ ___

eS2

Figure5.-Stiffenersection.

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