1、%-,.TECHNICAL MI!MORAI?DUMS ,J)k,.L, , ;NATIONAL ADVISORY CCMJITTEE FOR AERONAUTICS -”if .bBy E. El)nerLuftfahrtforschungVO1. 14, NO. 3, March 20, 1937Jerlag von R. Oldenhourg, M#nchen und Berlin, ,.f. , ,. ;, -.,- ! !Provided by IHSNot for ResaleNo reproduction or networking permitted without licen
2、se from IHS-,-,-.-Illlllllllli31176014374319_- .-.NATIONAL ADVISORY COMMITTEE_.-TECHNICAL MEMORANDUM. ,., . ,-FOR AERONAUTICSNO, 838.THE STRENGTH OF SHELL BODIXS . THIIORY AND PRACTICE*By H. ElmerThe monocoque form of construction characterized bythe fact that the skin is made as much as possible as
3、tress-bearing member, has become increasingly popular,especially in the fuselages of the latest metal airplanes.It has introduced a number of new prollems to the stresscalculator aild the designer.* The problems for the stresscalculator fall into two grouns: The determination of thestress condition
4、(shell s.t.tis)and the determination ofthe failing strength (shell strength). A large part ofthese, problems may, as a result of the research work ofthe last few years, be looked upon as being solved. Th”epresent report summarizes the most important theoreticald experimental results on this subject,
5、 special atten-tion being C;iven to the work done at the German ResearchLaboratory for Aeronautics (DVL).I. INTRODUCTIONDesigns of SIhell BodiesIn order to g,ain a comprehensive concept of the SYS-tems discussed in tho following, a survey is made of thevarious forms of construction of shell bodies a
6、s developedin Germany. The departures in the individual designs areless the result of differences of opinion as to what con-stitutes the best design from the point of view of strengthand stiffness than the considerations of simple manufac-ture , upkeep, and repair possibilities; aside from thatthe d
7、esign is governed by aerodynamic requirements, thenecessity of cutaway sections, installations, etc.Most shell bodies consist of a structure of stiffen-ers and lulkhead to which the metal skin is riveted- Thecharacteristic-of the shell body is that the skin actually-._ _ _ ._._-II*tlTheorie und Ve”r
8、suche zur fiestigkeit von Schalenrumpfen,ll ,Luftfahrtforschung , vol. 14, no. 3, Match 20, 1937.* For a survey of tb.ese problems, see Luftwissen, December1935.-._ .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 N.A. C.A. Technical Memorandum No.
9、 838participates as much as possible in the stress bearing.This may be accomplished either with a skin thick enoughby itself for all stresses or with a correspondingly thinskin in conjunction with a s;?stem of stiffeners. Shellbodies without stiffeners of any kind or such with bulk-heads only, are r
10、are; such bodies would have to be so de-signed that the skin does not buckle up to the failingload. Contrariwise, body shells with stiffeners and bulk-heads may be designed with buckling-resistant skin or with.?.sk-in ;rhichbuckles before the failing load is reached.The suital)ility of either arrang
11、ement depends upon thecircumferential loading defined 3jT the structural height,the loading of the body, and upon the curvature of theskin.A special case of shell body is that where only lon-gitudinal flanges at a few - four at the most - pointsprovide for the lolgitudinal stresses, while the stiffe
12、n-ers in between serve only to reinforce the skin but not totake up stress. In that case the skin primarily servesto carry shear stresses.The folloving contains a brief outline of variousGerman shell-design practices. Heinkel and Henschel em-ploy stiffeners and bulkheads of open Z-sections or .LJ-ch
13、annels (figs. 1 and 2). The continuous stiffeners arefairly evenly distributed over the circumference in,thecentral and rear portion of the body, but spaced somewhatcloser in the zones of greater compression stresses. Thebulkher.ds are joined to the inside edge of the stiffenerswithout touching the
14、skin. In the forel)ody, where thebulkheads are necessary for the load introduction and theinside nace must be utilized to the fulleSt ad-tagethe bulkieads rest on the skin a71(fig. 3). In view of thegener2.lly existing cutaway sections, the axial loads hereare carried in four concentrated flanges; t
15、he intermediatestiffeners merely serve as reinforcement and are interrupt-ed at the bulkheads (fig. 4).Junkers follows the practice of stiffeners of closdD channels, set fairly close together (fig. 5). The bulk-heads of high Z-sections are routed for the continuousstiffeners to which they are, attac
16、hed by half-round flangefittings. An example of a shell body with four reinforcedstiffeners which extend forward into the four strongflanges of the center piece is represented in the Junkersbody shovn in figure 6. Here the Z-section bulkheads areinterrupted to pass the four heavier stiffeners and at
17、-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Memorandum No. 8-38 - 3tached to the others hy small angle fittings joined at the- webs-A shell- body built hy Dornie-r-is-very -:similar. Itha,s four continuous, hea longitudinal fl
18、anges of thickvwalled T-section, while the remaining tubular stiffenersare interrupted at the. bulkheads touching the skin (fig.7). This body islcontrary to orthodox practice, wider thanit is high. “The 3a,yerische Flugzeugwerke have developed a partic-ularly” interesting type. The metal skin “consi
19、sts of sepa-rate pnels bent on one end into a Z-section. These” lbulk-headsl are routed to permit passage of the U-c”hannel stiff-eners (fig. 8). These panels are first riveted togetherlengthwise and joined to the inserted stiffeners. Thenthe thus-obtained reinforced panels are joined together inthe
20、 uppermost and lowermost part of the circumference to awider stiffener which serves as butt covering.In one Arado shell body the skin consists of longitu-dinal ,panels, every second one of which is bent at bothends into fclrm-stiffener sections, in contradistinctionto the Northrop method (reference
21、1), vhere each panel isangle-shaped. at one end.II. DETERMINATION OF STRESS CONDITION1. System and LoadingIn ordel* to grasp tho most essential characteristicsof the stress condition of shell bodies - whether theo-retically or experimentally - it first is necessary to sim-plify their system and load
22、ing.The designed shell bodies have, in general, a lengthwhich is a multiple of the sectional dimensions (%/h = 6to 9; in cross section-they are usw.lly of oval shape,widening out downward or upward, with.a height slightlygreater than the width., In many cases the section is el-liptic, or evei round,
23、 as in “some J.S. shell bodies. Thebody shell may be largely considered as being cylindricalor conical, because the usual %otiJform tapers from an al-most cylindrical centerpiece very gradually ”toward thetip. For many fundamental siudies the assumption of cir-cular cylinder is sufficient.On the bas
24、is of this outer form of the shell bodies,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 N.A. C.A. Technical Memorandum No. 838, ,.it may be assumed that their stress condition on the wholeis in agreement with the elementary Ilbeamlltheory, which
25、postulates a great length compared to cross-sectional di-mensions and a gradual change in cross-sectional form overthe length. Another assumption of the elementary beamtheory is that the sections under load undergo no substan-tial form change - that is, possess the necessary trans-verse. stiffness,
26、a condition likewise met by the shellbody ith sufficiently rigid and properly spaced bulk-heads. After all, it should he borne in mind as regardsshell bodies, even vith still unbuckled skin, that by vir-tue of its greater circumferential extent and lower trans-verse stiffness than on the usual beam,
27、 the actual stresscondition dcpart,s to a greater extent from that of anideal beam computed according to ifavier IS flexure theoryor St. Venant-Bredts torsion theory. The disturbances.aro primarily due to the introduction of stresses not inaccord with the beam theory and their directional changesat
28、cutaway sections. Further disturbances are set up bythe restrained warping of sections under transverse loadflexure and twisting.Other stress deflections are encountered on reinforcedshell bodies with skin which is ilot buckling-resistant upto the failing load. once the panels between the stiffeners
29、have “uckled under compression and shear,The stress in the shell body is the result of the airloads on the wings and tail applied at the points of at=tachment; further, of the propeller loads transmitted bythe engine mount and the ground forces due to landing gearor float system and tail skid. These
30、 are supplemented inthe attachment points by the mass forces necessary forequilibrium of the structural parts attached to the body.Lastly, there are active mass forces distributed over thebody length but whose effect, compared to the other forces,is small and which may be allowed for a% forces combi
31、nedin several points. It is thus primariiy a case of con-centrated loads mhich stress the shell body visualized asbeam in bending and torsion. Bending of the end shell ofthe body is usually contingent upon a down load, and thetorsion and lateral deflection on an eccentrically ap-plied side load.Prov
32、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-p “- “ “-7N.A.C.A. Technical Memorandum No. 838 5a712. Stress Condition of Unstiffencd Thin-Walled Shellsa) Elementary theory .- As basis of the subsequent ar-guments, we shall first investigate the stress
33、conditionof an unstiffened thin-walled cylindrical shell underflexure aild twist. The wall thickiess s may vary overthe circumference, although it is assumed to be small withrespect to the transverse dimensions of the shell. Therearc no stiffeners for the present but bulkheads spacedsufficiently clo
34、se are assumed to preserve the cross-sec-tional fornoThe classical theory of beam ilexure established forthe bean of solid cross section results in linearly dis-tributed tension stresses a and derivated shear, stresses T:z Ev = Qy Sz = y.+ L z, Qz Zy+- .-z Y Jz I)z Y bYwhereby:Y, z are the respectiv
35、e distances of “the relevantfibers fron the principal axes of inertia.r;/iJz = y2 dI, 22-y./ Y =the nrincipal moment ofF“” inertia.3”s /z = y U?, y =./ rZ dF the stat:-cnonents of theisolated cross-sectional:piccc with respect to theprincipal axes of inertia.bY bz the section nidths.BTr9 2z the bend
36、ing nonents about axis yo and axis z.Qys Qz the transverse loads in axis y- and axis z-direction.In the application of the _bea,ntheory to thin-walledsections (fig. 9), it may be assurled that the tension and.shear stresses are evenly distributed over the wall thick-ness s. Tlen the llse,r flO?r t =
37、 s! according to ele-mentary theory of flexure is:,$l ._. _. . _ -.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Memoraildum No, 838 “The inertia moments are:Jz =$y sdu, Jy=$z2sduand the static moments:, ;U_z=/ysdu +S(0)ory=”uz d
38、u+ s(0)sJ z / Y!.o 0Hereby u denotes the circumferential length measuredfrom any zero point a.sfar as the particular point. Forclosed symmetrical sections the choice of the points ofsymmetry as zero points ic advisable, SO thatCJ (o)zand y(0) = ()otherwise, S (o) must be deter-s (0) a,ncl _ythe cons
39、tants _zmined from the condition of torsion free bending:To insure torsion-free bending, the individual trans-verse loads must he applied at the “shear centerf.whichfor symmetrical sections lies on the axis of symmetry; forunsymmetrical sections its nosition must be defined fromthe condition that th
40、e shea flows ty and tz must pos-se:;sno moment w-ith resect to the shear centerTransverse loads applied outcide of the shear centercm be represented by transverse loads in shear center andpure torsional moments Mx on the longitudinal axis; theystress tlcylinder in bending and torsion. In torsion,St.
41、 Venants theory for solid sections mfforcls, with unre-straiiled warping, a pure shear stress condition. For thin-wnlled closed sections r.”shear stress constant over the wallthickness may le assumed. Then , according to Bredt, the uni-form silear flow for .tnistint: momentmProvided by IHSNot for Re
42、saleNo reproduction or networking permitted without license from IHS-,-,-IT.A.CA. Technical lemorandum No. 838 7and the enclosed surface I. is:and the torsional stiffness is:The results obtained, for cylinders from the elementarytheory of bending and -torsion can be applied with the samedeEree of ap
43、proximation to tapered shells. Then it mustbe observed. th:lt in bending the maximum tension stresses oocc”llrin sections perpendicular to the surface elementsand have components in transverse load direction. Theshear stresses T in these sections then have to carrY.only a share of the transverse loa
44、d Q. Then (fig.10):By0= 5s- - t =TS=*J COS a JvithB= -PO(X-XO)-PI(X-XI) - =(Q-)xHere J and denote the respective inertial and stt”.ticmoment , computed mith the smallest wall thickness s (indirection of the normals of the shell surface), a is theangle of the surface elements to the longitudinal axis
45、,x, x, xl, a71 *O. the respective distances of the sectionor load points from the cone tip of the relevant sectionpoint.*3) Membrane shell theor.- Substitution of the mem- _ _brs.ne shell theory for the elementary beam theory affords. _ _-*Instead of distances” from cone tip the heights at thesectio
46、nal or loading point can be introduced. See Wagner:Luftfahrtforschung, vol. 13, no. 9, 1936, pp. 281-292.This also contains ,detailed study of the bulkheadstresses.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 N.A. C.A. Technical Memorandum No. 8
47、38a more accurate picture of the actual stress condition inthin-walled transversely reinforced cylinders (reference2). The membrane theory stipulates, as is known, vanish-ing flexural and torsional stiffness of shell surface,thus leaving only the lmembranc stressesll ax, au andT constant over the wa
48、ll thickness. The introduction ofthe external forces in cylindrical and tapered shells withtransverse stiffeners (bulkheads) is devoid of circumfer-ential strsses au according to the membrane theory. Inpure - i.e., shear-free bending - of transversely rein-forced cylinders, the linear distribv.tion of the tensilestresses with the condition of sections remaining undis-torted in its plane, is compatible with the memb
