JKC/V L'I91 ARR No. L5FI5 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED August 19^5 as Advance Restricted Report L5FI5 CHARTS FOR THE MINIMUM- WEIGHT DESIGN OF 2US-T ALUMINUM- ALLOY FLAT COMPRESSION PANELS WITH LONGITUDINAL Z -SECTION STIFFENERS By Evan H. Schuette Langley Memorial Aeronautical Laboratory Langley Field, Va. . C rt" NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originaUy issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 197 \ Digitized by tine Internet Arclnive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/chartsforminimumOOIang NACA ARR No. L5P15 NATIONAL ADVISORY ADVAFCE RESTRICTED REPORT charts eof the ^animw-.veig-ht desic^n of 2i;.s-t alujir^^^-allgy plat compression Panels jitk longit^ioinal Z-SEGTION STIEFENERS Bj Evan PI. Schuetts SL^vUvIARY Desj.gn charts are r'eveloped /"or 2',lo-T al"i.rain."ai'.i- allcy flat coL:;nr3 3slc:i panels v.ltli longitudinal Z-section stlffenei^s. These charts .nahe ro.i;:-;ihle the design of the lightest panels of this type for a wide raj:.S9 of design requirements. Examples of" ;;he ixse of the charts are given and it is pointed out on the basis of chese eicamples that, over a wide range of design conditions, the maintenance of buckle-frae surfaces does not conflict with the achieve.-ri3-nt of high structural efficiency. Ths achie vor.ient of the rr^axirnun: y^ossihle structural efficiency with 2l(.S-T aluminvm-alloy panels, however, requires closer stiffener snacings than those now in coLTrnon use. INTRODTjCTION In a longitudinally stiffened co:.r}pa^ssion panel, in which all the material is active in carrying load, the requireraent of minir-uirri weight is tantamount to that of carrying the load at bhe hignest possible average stress. The average sbress developed by such a panel under the loading conditions i:...';0SGd is thus a direct measure of the structural efficiency of the panel. If longitudinally stiffened compression p;anels are to be designed for high structural effioienc;,'- v;ithoi;t a large number of cut-and-try conp^itatlons , it Is desiraole that design charts I'-e prepai'ed to indicate i:"::e average stress attainable under various loadir.grconditicns . The pre- paration of such charts requires that a suitable design parameter in v/hich the important Ic:;. cing conditions are incorporated be foLUid. 2 NACA ARR No. L5P15 \ It has been foirod that a suitahle paraneter for lonciti7dinall7 stiffened compression panels in the dsslgn of v;hich the transverse stiffness can be neglected is , where P-j_ is the compressive load per inch of pa:iel width, L is the panel length, or distance betv/een supporting ribs, and c is the coefficient of end fi-"ity at the ribs. The quantity Pj_, which is essentially independent of the distribution of material in the compression panel, can be estimated for a wing panel from the bending m.cment on the wing and the thick- ness and chord of the v/ing. The length L iriay be fixed \ij the presence of such installations as fuel tanks or armament or may be arbitrarily assigned for the pur-pose of arriving at a trial design. In reference 2 buckling stresses were -C'lotted Pi against the parameter -^, with slii-^htly different L/Vc notation, to form the basis of a theoretical study of the efficiencies of various types of stiffening elements. In the present paper the same parafneter has been used as a basis fcr the preparation of design charts ficm extensive test data on 2)^.S-T a''.'r.iinum-alloy flat compression panels with longitudinal Z-.?cction stiffeners; the data y/ere obtained from reference 1 and from additional tests com- pleted since publica' 1cn of reference 1. These charts make -Dossible the ch.:'ije of the lightest panels of this type to conform to a "vide range of desi>_ai conoitions. An appendix is pre so:-' tod in which the procedure followed in pre •oaring the charts from test data is described and D • •^ 1 the method for obtaining as a natural parameter against which the average stress may be plotted to obtain a direct measure of structural efficip.ncy is developed. SillBOLS AIJD DEPINITIOKS The swibols used for the pi'lnclpal panel cross- sectional dimensions ara indicated in figure 1. Iii addition, the following symbols are used: NAGA AHR No. LSFl^ Aj_ cross-sectional area per Inch of panel v.'idth, or equ5-valent thicl-Tiess of panel, inches L length cf nanel, inches Pj^ compressive load per inch of panel width, kips per inch E modulus of elasticity in compression, ksi . c coefficient of end fixity as used in Suler column formula k coefficient in formula for local-huckling sti'ess p radius of gyration of panel cross section, inches T nondimensional coefficient that takes into account red^iction in effective modulus of elasticity when paiiel fails as a column beyond the elastic range o^-p critical stress, or stress for local cuckling, ksi Oq average stress at coltmn failure, ksi ^max average stress at local failure, ksi af average stress at failure for any panel, ksi The average stress at which any particular panel fails, Of, may be a local-failure stress, a col-'jmn- failure stress, or the stress for a type of failure intermediate to these tv/o. r'ailure by twisting of the stiffeners is included as a form of local failure. Because the design charts are based on actual test data, it is not necessary to make anj distinction between local and twisting failure. Such a distinction, moreover, would be at best an arbitrary one, as the tv/o types of failure are interrelated in the case of stiffened panels. It should be noted that the local-failure stress ^r,-^Qy^, which represents the maximum value of average stress that can be acliieved in a given cross section as the panel length is reduced, is an average stress at failure and is not to be confused with the stress for local buckling o^p, which does not necessarily imply failuj^'e. i|. NACA AIIR IMo. L5.FI5 ^\ The term "Iccal buckling" as used lieroin incliides both buc'-:l?'.ng o.f th3 s^^ia and buckling of the stl.ffeners, bec'.iuse neither of these elements can buckle without e:certing moments en, and thiis causing defoiT'ation of, the other element. DESIGN CHARTS Design charts for 2lj.o-T aluji'iin-.am-allo;/ flat com- pression panels with longitudinal Z-section stiffeners are presented in figures 2 to 5 • '^^'^ procedure used in the preparation of t;hese charts from test data is desci'ibed In the appendix. Values ol" Ai/ts, necessary for arriving at a final design, are given in babies 1 to 5 for a v;ide range of dimension ratios. In order to show the maxir.um stress'^s attainable by the use of vscaels of the type to which the charts apply, envelopes are indicated by the dashed lines for each value of the ratio b^/ts in figures 2 to 5* These envelopes have been combined (fig. 6) to give the over-all envelopes for che .four values of the ratio t-^/tg. The values of ^3/'ts and 'o-.-j/t-fj nee dad in order that a panel will develop bhe stress indicated by an envelope are also given in figure 6. The design parameter — ;— :, against v;hich stress L/vc is plotted in figures 2 to 6, comprises the principal design conditions; the compressive load per inch of panel width; the length of panel, or distance between suriporting ribs; and the coefficient qT end fixity. The most efficient (lightest) p.anel for a given combination of these conditions is that panel v/hich will develop the highest average stress for the particular value I"" 01 -7-1. Disc us s 1 on p f _, ch a rts .- The charts include a wide range of nana 1 ■proportions. aH che charts have been drawn for a Vj.lue of --- - O.li; it is shown in the apnendix (figs. I7 to 20), iiowover, that curves bir for ^ = C.:5 and 0.5 would be in close agreement NACA MiR No. L31 bv with the curves for •^; = 0.1;.. The curves of figures 2 to 5 '-is-y therefore be applied ;vith reascnahle accuracy for aiiy value oT hp/l^^nr iD^tv/een (3.5 and O.S. The available ue&t data seem to indicate, roreover, that the most efficxert nee of material './ill he realized if a proporLion in this ra'age ici selected. ( Sde appendi:c. ) 'TJie short horizontal lines chat intersect the curves of figi.ires 2 to ^ indicate, for each panel cross section having appreclaole local Duckling, the stress at v;hich this tauc'cling occurs. In ;:his report this stress is taken as ch.at at v.-hioii. the compressive strain on one side of the shin cr tiie stiffener web begins to be reduced with increasing load. This definition of bucl-cling is convenient for structural testing; f^om the standpoint of aercdynsimic snoothness, appx'ociable buckling probably takes place at stresses somev/hat lovvfcr than those indi- cated on the chax'ts. It 'vill be noted that for some of the lower values of b3/t3 and bv//ty no buckling stress is shown. Ir. these oases, there will undoubtedly be some buckling but presumably it v;ill occur at a stress coin- ■ cident with or only very slightly belciv the faiiui-e stress. 4- It is r^ointed cut that for -- = 0.79 and l.CO ■^S be; (figs. Ij. and 5) J the curves for values of ~ = 25 and 50 have been obtained entirely by extrapolation. These ci-'.rves shoiild therefore be used \;jth a certain degree of caution. A few check tests mado since the preparation of tlj.e charts, however, Indicate that the curves -vill in no case be more than 6 ■percent unconservative . In all the other curves, it is believed that any miconservatism thab i;iay be present is of riuch snaller magnitude. D iscussion of tests and test panels .- In order that the design char'cs may be properly used, it is necessary to knov; something of the test panels and the test results on which the design charts are based. The details of these tests are described in reference 1; some of the pertinent information regarding the tests follov/s: ■ The test panels consi3T:ed ox" six stiffeners ti.nd five bays. The oanels were tested flat-ended and without edge support. A fixity coefficient oi" 5.75 '^'''^■^ ixsed in reducing the test data for application to an effective pin-ended length. The average coiapressive yield strength for b>ie material of which the test panels v/ere constructed v;as about Ijij. ksi; the mlnimiom. yield strength, about 14.1. ksi; and the maxi:n\irri ^leld strength, about ;j.6.5 ksi. The ri^-ets were coi'.ntersunk and were driven by the 6 NACA ARR No. L5F15 ^\ NACA riethod of inserting a flat-head rivet from the stif- fener side of the h.le, -"apsetting the rivet Fhanh into the Ticii':ers\vri?.c csvlty, and i::ill3i">;c off the prot .T'-dlng portion of the iipi'^c flbank. The rivei^r- wy-.-; A17~-'r (Aili.[.!4.2AD) and \;ere of the sis.^.'^ and spacinrs indicated by the following table ; tw Rivet spacinp; 0.51 .79 1.00 t 10 12 .5 12 ^ y 11 7 R i v et d 1 aiaet e r tcl' 1.50 1.8i| 1.93 1.95 Because ^he conpressive strength of stiffened panels may be affected hy the size and spacing of the rivets used to attach stiffeners to skin (reference 3), the rivet attachment must be equival.ent to that indicated by the foi'egcing table in order to oe sure cf realising the strengths indicated by the design charts. USE OF DESIGxT CHAPxTS AlIP EXAMPLES If sheet material could be obtained in any desired thickness and if no special limitations \i,ere put on the design, it '.vould be sufficient mai'ely to find those pro- portions that would give the highest stress for the ^v'en value of L.^^' Because certain limitations are usually imposed, nowevcr, the structure that represents the best compromise of fll the requirements must be chosen. The usual gages in which al'uminu;.:- alloy sheet is manufactured are such that if the I'cur ratios of t-j|ir/t3 in figui-es 2 to 6 are applied consecutively to a par- ticular skin gage, the four stlffcner gff;:;e3 that result will generally be consecutive standard gages. Interpo- lation between the cur\'-es of two consecutive charts (figs. 2 and 5» 5 and ii., etc.) is therefore unnecessary for most practical purposes. The particular procedu.re to be used in obtaining a design from the charts will depend on the nature of the results desired. Three possible methods are discussed, and examples are giv<=^n of designs obtained for a given load intensity and three different lengths by each ox" the methods. NACA ARR No. L5FI5 7 The dis tiiigu.islilng feat^ir-es of each rriethod ai'e : Ide al ds 3 i gn The method for obtainine; the Ideal design gives the lightest panel that could he obtained if the designer were not restricted, to the use of standard sheet gages. The design is obtained "by use of the over-all envelopes of figure 6 only. Short method The short design method provides, without lengthy computation, a near approach to the lightest panel that can be obtained by use of staridard sheet gages. The design is obtained by use of the enveloioes for given values of bs/tg that appear as dashed lines in figu.res 2 to 5« Maximu:LL efficiency The method of designing for maximujn structural efficiency gives the IL'-^litest panel that can be obtained by use of standard sheet gages. Th.e design is obtained through a complete stud;/ of the individual solid ciurves in figures 2 to 5« T^^^e riethod is somev/hat lengthy; ex-araples have been worked out by its use, however, to serve as a check on the shore m.ethod, so that that method can be used with confidence. Each of tlie three methods is given as a series of steps for reaching ttie final designs. In the method for obtaining the ideal design, tLie detailed computations for the four valines of t^y/t.^ included in figure 6 are given for L - 10, 20, and ^0 inches with P^;_ = 5.0 kips per inch and c = 1. In the other two methods, the detailed computations are given only for L = 20 inches and IT" = 0.79, again with P-; = ^,Q kins -oer inch and c = 1; final results are given, hov/ever, for the complete set of examples considered in the discussion of the first method. It is assumed in all cases that a skin thickness of O.CSij. inch is necessary in order to comply with other design re quire m.ent s . A value of bp/bv/ of O.Lj. is used throughout. In arriving at the final designs, no values of the dimension ratios outside of the ranges covered by the charts are given consideration. 8 ■ NAG A ARR No. L5F15 \ IjQthod ji 'cr ob tainirg the lie el d esign,- This method consists of picKlng 'fron f If^ure 6' the "opt'imuir! proportions aiid the stress and co:nputins fron these the actual panel dimensions, ?he values and computed qu^uitities for the oondi- cions previously nentioned are given In table 1|. ^nd ai'e referenced to the steps in the x''ollo;ving procedui'-e : Pi (1) 3orapute . (2) Prom f±ie curves of figiire 6 pick off for each value of tv;/t3 ths values of h^/t^, ^/t,,^, and c^ ccrresronding to the value of ~~-:z. L/\'c (3) Pick fror/x table 2 the values cf ^±/t^ for the ratios c'eterniined in ster* 2, (If :; — = 0.3 or O.S o-,-. is used, table 1 or tiible y , respectively, should be used instead of table 2, ) (ii) Corrpute •D ^ _ "1 °fT- This formula is based on 'che eqiaality J^-? — 'J f .i-? a. J. J, (5) CoTipute t;v ~ ts v. = ^3 bv ^3 b". — tlv' t^ This procedure results in four desi^s for each length, corresponding to the four values of tv//ts, for KAGA ART Fo. the given conflitlons. (See tal'le li. ) The values narked with footnote a in tcble I+. ronr-esent tho^e chosen as apToroachlng nost closely the c'.esired conaition of t3 = O.O0I4. inch; these values theroi'cre give an indica- tion of '.he "oroporticns needed in a practical design to Tneet the desijjn reqi-'-irei.ients most f-ff icien tly. The resulting designs arc shown as the ideal designs at the tops of figures 7 to 9, along v/i uh har graphs of the average stress at failure and t;he huckling stress. The buckling stress for each design vi'as obtained by InterTolatlon from the short horizontal lines for buckling in figures 2 to 5- I^ seme cases in v/hich failure Is by col^jmn action, tno buckling stress shown by figures 2 to 5 'Will be greater than the failure stress for che designs obtained. vVnenever tb.is difierence occurred in the present examples, the buckling stress is sho'.vn equal to the failure stress. Short method for obtaining a practical design . - The sho:.'t ;nethod consists of ;::lcking the optir-ium value of b\f//t.7 and the corresponding stress for each value of bs/tc; from the individual envelopes of figures 2 to 5 and compjiiting from these values the actual panel dimensions. Panel designs that employ standard sheet gages are then selected from the various desi-gns obtained. The values and computed quantities for L = 20 Inches tv/ and — = 0.79 are given in table ^ and are referenced ^S to the steps in tbo following procedure; (1) Com-ute V\/^ (2) From the curves for a parclcular value tw of tijiz/tojin this example, fig. ii for -g-- =0.79 is used) pick off for each value of bs/t3 the val'ues of b^f/ty,/ (by interpolation along the dashed envelope) and a.^ (from the envelope) corresponding to the value of LA (3) Pick frova table 2 the values of A^/tg for the ratios determined in step 2. 10 NAG A ARR No. L5PI5., ■x ( .'1 ) C orapute t. = ^i Of T~ (5) Plot '^\\'/^\j> t^, and Or. against bg/to for the particular value of tij/tg. (The plot for the example being ccnsldered is shov;n in_fig. 10. ) Tabulate the Vf-dues of bg/to, ^j^/t-^t a.^-^ Of corresponding to Vn.'i point wherS tg equals the specil'ied value. (6) Check computations bj picking frorr. table 2 the valiie of A^/t-, corresoordins" to bhe ratios tabulated in .itep '3« li" all cori-.putations and plots are correct. I'i - o. X- t. f tg (7) Compute ^3 ^ 0'*r (3) Repeat steps 2 to 7 fcr other values of ty^/tg. Like that for the ideal design, this procedure results, for each length considered, in one design for each value of t-'/tg. It may not always be possible to find satisfactory designs undei' the conditions imposed for all values of t-^^/ts. (llote that no designs are given in figs. 3 and 9 ^or —^ = O.5I. ) All the designs resulting from the use of the short method utilize standard sheet gages and meet the requirement that tg = 0. 06I|. inch. The choice of desigi: now depends on arriving at a suitable compromise betv/een high stress axid wide stiffener spacing. IIACA ARR No. L5FI5 11 If the prsvcntion ci buckllnj^ vnder load is considered important, chen the buckling stress must also he taken into account In making a choice. The designs obtained hj carrying out the foregoing procedure foi- the several valives of L and tw/to are shown as the short-method designs in figures 7 to 9 along with bar graphs of the average stress at failure and the buckling stress. Met hod of designin g for maximu m structural efficiency , The maxim-jm-ef f iclency method consists of computing the thickness required as b3/t3 is varied for each value of b.y/tyr and selecting the designs for v;hich the skin gage is equal to that desired. The proced\u''e results In a series of possible designs for each value cT ty^/ts, from which those designs that provide the higliest ax^erage stress at failure can be selected. The val"u8S and computed auai-itities for L - 20 inches t- and -r— = 0.79 are gi\-en in taole b and are referenced to the step3 in t]:e follcv/ing procedure: (1) Oompute L/yc (2) From the curves for a ^articular value of t.-r/tq tj ■■" ^ (in this example, fig. k for — ^ = C.79 is used) pick off for each value of hv'/tv.y and b-^/to the value of Or corresponding to the value of . L,/ y> (?) Pick from table 2 the values of A.^/tg corre- sponding to the I'atlos used in step 2. (Il) Compute T " A " i (5) Plot t^ and a .0 against b3/t3 for each Ci value of bv.;/t.^- and tv.-/t at L = 20 inches witn 7~" = O.b'j, and at L = ^u inches with -— = 0.79* I^T- ^L^igure 6, however, the highest envelojje, which gives the lightest design, is that 4- for -— = 1.00. This apparent contradiction results from the fact that in working out the examples a skin thickness of O.Ooli. inch was specified. In order to CJ"."." reach the curve for rp— = 1.00 (fig. o ) , a study of table h. shows that the skin thickness 'would have to be O.03I;- inch at L = 10 Inches, O.Oiil inch at 2U inches, and 0.0l;.6 inch at 50 Inches. Moreover, the stiffener spaclngs for designs having such small skin thicknesses are very small. (See table h..) Because of iim.l tat ions Ik NAG A ARR No. L5P15 \ en skin gages and stifiener sspaclngs, therefore, it is frequently not possible to reach the envelope values of stress and hence tl;3 lowest possible weight. Pirures 7 '^o 9 show that the best panel (that with highest Of) obtained at each length ''oj the maxlnurc- efficiency iiiethod does not buckle until failure or very close to failure. The best paiiel designed by the short method, although it may not have quite so high an average stress at failure as the maximum-efficiency panel, also does not buckle ^antil very close to failure. This condi- tion has been found to hold true over a v/ide range of design requirements. It is therefore evident that over a v;lde range of conditions the maintenance of buckle- free siirfaces does not conflict with the achievement of The simultaneous achievement 2i4.3-T alumin-am-alloy panels, closer stiffener s-nacings For exariiple, the maximum- 3.0 kips per inch and high structural efficiency, of both these ends by use of however, apparently requires than those now in ccmLion use efficiency designs for ?i ~ t^ = 0.06l\. inch have the three lengths: following spacings for the i T i (in.) be tc (in. ) 1 10 i 20 i 50 26.0 1^.2.1 l+o.o 1.79 2.69 2.56 CONCLUDING REMARKS Charts are presented for the minimum-v;eight design of 2i^.3-T aluminum-alloy flat com.presslon parcels v;ith Icngiti^dincil Z-section stiffeners. From exe;mples based e use of these charts, it is concluded that, over a on -l-Vi vi/ide range of design conditions, the m.aintenance of buckle-free surfaces on longitudinally stiffened compres- sion panels does not conflict v;ith the achievement of higii structural efficiency. The achievement of the msxlmum pos.^ible structural efficiency with NACA ARR Ko. 1,5 Pl^ 15 2ij.S-T alruninfm-alloy ppjiela , ho'A'ever, requires closer stiff ener spacinge thai", those now in coir.T.on. v.se. Langley Kernorial Aeronai'tical Laboratory National Advisory Co.'iir.iittee for Aeronautics Langley Field, Va. _ l6 NACA ARB IIo. L3PI5 -, --S APPENDIX ME:[K0D 0? PHEPAPATTOF OF DE3IGF CHARTS Pi Development cf de3ic:n -narameter ■ -.- As stated . : lM in the Introduction, the average stress developed "by a longiti-idinally stiffened corapresslon panel is a direct measure of the struct^oral efficiency of the panel. It is further "orought out that a suitable design parameter against which this average stress iiiay be plotted is '—, \;here F. is the co'npi'essi ve load 'oer inch of peaiel width, L is the panel length or distance between supporting ribs, and c is the coefficient of end fixity at the ribs. The following derivation shows how the paraiueter ^ L/Vc evolves fron the usual coliKin fo±Triula: The column formula ■■■nay be wi'ittsn (Al) IIu.ltiplicaticn and division of the right-h.ond side of equation (Al) b'y Pj_- gives ^c = '^ Ti-AM (7-7-^/ IA2) If the stiffened panel is go have a strength just equal to that required by ■bhe design conditions, T-^ = ^-i'-^c and equation (A2) rr.ay therefore be written a „ = IT T E c c Vi/WvV\"c/ NaGa akr No. l5.^'15 17 or cj . ... 2 / which may be written l7 ^^V Wvc/ (a5) 3'~o — The quantity x/tt-Eq In equation ( A5 ) is flx£d for a given ructer^ol, as is the relstlonshin he i: we en Cq and t, Pi excerit for neglhaible shaoe effects. The quantit" h/yS is the design parameter; o/:i± is diniensionless -ind is determined h^- the relative rather than the absolute dinen- ^i sions of a -nanel. A nlot of a^, against - ■ ^ ■ _ is thert3fore ■W v'"^ dependent on the ratios of the various panel al::iensions and not on the absolute values of the dimensions. Determination of average stress at local failure 0-.,^„ Prom equation (A3), •^'•le best -oanel of a given material P-; for any value of '^^~ on the basis of column strength lA'c" apparently is that panel vi/hich has the highest value of p/Ai. Changes in proportions that result in an increase in c/kj_ 'vvill, nov/ever, generally cause a decrease in the local -failure strength of the panel. (Local failure as used herein Includes the phenomenon of tv/isting, which is in reality only a form of local failure that occurs when the lateral bending stiffness of the out- standing stiffener flange is relatively small.) The optimuia panel for a particular ar)pllcation is given by the compromise of co'luj-^n and local-failure strengths that gives the highest stress at the given value °^^ ~^-* Ju/ A/c l8 NACA A?.R No. L5Fa5 The value of ^lie average stress at local failure o'^(^q^ is difficult to determine theoretically. Certain test data are available, however, from reference 1 and fi'ora additional tests completed since the publication of rei'er- ence 1. Those data that were obtained from the shortest panels of e_ach cross section arei sun. narized in figure 12, in whi:;h o~j _ is plotted against ty^/by,, for various values of ti^/t^ j..nd bcj/t^. The ratio b,^f;/t-,j"; has been Inverted in this plot in order that the additional point cfpjj^-j^- = when ~ = o ! — = <^ I might be used to 0'j,Y \^t';^r J aid in fairing curves through the test points. The plots of figure 12 make possible an interpolation of Oj^^^j^ bjtween test points for intSx^Kediate values of the ratio bv.;/t\,i/. By plotting values of o'^..^„^ picked from the curv-es of figure 12 against t^/bg, values of ^{^f^^ v\rere al^o determinei? for intermediate values of bc;/tg. All the data eliOA-n in Tip-ure 12 jre for a value of —LzzC.li.. Tsst data for -— ~ C.5 and 0.5, how- ever, were also employed as a guide in fairing the curves, and the curves will be shown to be reasonably accurate for any value of t-p/oyj between O.p ai^d 0.5 . Determination of stress for local buckling cj^v..- If the'~r:ianel did no't buckTe locally before failui'e, the theoretical results thus far presented, used in conjunc- tion ".vith values of CJ^r^ax' ^'^'^''^Id. be sufficient to construct a design curve of o^ against — -j-— for any L/y'o panel. A typical curve for ^\anel3 that do not buckle before failure is shown in figure 15. Unless the width- thickne'ti's ratios of the various plate elements of the panel are small or the panel is relatively long, however, there, wall generally be soiae local buckling before failure. vFnen this buckling takes place, the cross- sectional moment of inertia of the panel is reduced by the presence of ineffective areas; the original curve of colunn strength therefore no longer applies and the point at which b-..cklirig takes place must be connected with the line foi ].ocal failixre by rreans of a reduced curve. /' tj-oical curve, adjusted for the effects of local buckling, is rjhcwn in fi^'uie l[|.. NACA ARR No. LSFl^ 19 The foregoing dlsciission shov/s that it is necessary to Imow the stress at which buckling takes place. Data> on buckling stresses i'rom reference 1 plus additional data now available are therefore plotted in figure I5 bi? for ~ = O.I^.. Because the measured value of b/t for the element (skin or stiffener web) that first showed bTickling in a test panel was never in exact agreement with the specified nominal value, the observed buckling stresses from reference 1 were corrected for use in figure IS according to the following formula: (fi ' *^^ corrected ^^'observed , .p 2 measured ^. '' nominal v^fhere tl-ie value of b/t is that for the web of the stiffener or for the skin between stiffeners, depending on which of these elements first gave evidence of buckling. This correction formula is based on the fact that, other factors being equal, the critical stress is inversely proportional to the square of the v.'idth- thickness ratio. No account is taken herein. of the fact that this relationship is not entirely true for stresses beyond the elastic r,ange ; it is assijuned that neglecting this fact will have no significant effect because the total correction is relatively small. The method used in fairing curves through the test points in figure I5 is as follows: For the horizontal portions of the curves on the right -hsind side of figure I5 , the skin I's primarily responsible for the buckling; the ordinate s lor the curves in this region are determined by drawing average lines through the test points. as the value of ti/v/by/ is reduced, however, the responsibility for the buckling shifts to bhe stlffenei's and there is a reduction in ^cv Tn the absence of adequate test data for low values Oi t;:;/b^Y^ certain theoretical considerations are used of 0^^ 20 NACA ARR No. L5FI5, ^ It is possible to describe certain limiting condi- tions that determine curves between which the correct curves must lie. As the value of t-^y/b.^ approaches zero, with all other dimension ratios held constant, the skin tends to become Infinitely stiff by comparison with the stiffener and ti-.e stiffener approaches a condition of complete fixity at the edge where it is attached to the skin. This condition of complete fi:clty represents the upper limit of buckling stress. The value of k, the coefficient in the formula for local-buckling stress (reference I].), when applied to the stiffener web may be taken for this condition as the geometric mean of the value of k for the web of a Z-section column bp with — = O.J4. (about 5.77, soe reference h.) and the value of k for a flat relate fixed at both edges (about 6.98, see reference ^). This value of k is v^"^? ^ 6.98, or 5«13. The upper dashed curve in figure 15 gives a^p for k = '■j .15 • The use of the geometric mean of values of k to obtain the critical stress for a plate with different restraints along the two imloaded edges is discussed and justified for prac- tical use in reference 5' hi ^3 l^.Tnen — = -— , it is a reasonable and probably conservative assumption to consider the stiffener hinged at the edge where it is attached to the skin. This hinged cone! it ion represents the lower limit of buckling stress. The value of k for the web of the stiffener may be taken for this condition as the geometric mean of 5.77 ^^^ the slraiole Z-section and the value for a fla'c plat e hinged at both edges ([|..00, see reference 5) or k = \h'Tl ^ Ij-.OO = J.SS. The lower dashed curve in figure 15 gives a^ for k = 3.38. In the preparation of the two dashed curves, the effect of reduction in the modulus of elasticity for stresses beyond the elastic range v;a5 determined from figure 3 of reference 6. The solid curve on t?ie loft-hand side of figure I5 is dravm in to give a gradual transition from the lowei'' bv, b^ dashed curve in the region where — ^ = — ^ boward the t'jr t c unper dashed curve as t'v-r/bi;/ approaches zero. In the NAOA AflH No. L5FI5 21 ['J S regiOii vvhSi^e -r— = -rr- the curves are I'alred into the horizontal lines drawn through the test points. A sin^^ls curve was considered sufficient for all values of t-.^/to for the left-hand portion of figure 1^ , because the few test Doints that were available in this region indicated that the individual cur\;es vifould be so close together as to be almost indistinguishable. The curves of figure 1^, like those of figure 12, were cross-plotted to give bi:ckling stresses for the intermediate values of bs/t3 that anpear in figures 2 to 5. ' PJ^eparat ion o f fin a l curve s.- The procedure used in the prep^aration o~f the final curves of figures 2 to 5 ^s Illustrated in figure i6 . An outline of this procedure is as follovvs: (1) Drav/ curve for coluiun strength corresponding to the value of p/A^ for the panel cross section. For the curves cf this report, the column curve for 2li.S-T ^alumi nuin alloy v/as obtained from equations (5) and (b) and table I, all of reference 7« (2) Plot the values of stress for local buckling and for local failure of panel obtained from the cross plots of the curves in flg'ares 12 and 15 . (5) Plot available test data and fair curves between buckling stress and local-failure stress. This fairing 'was done first for those curves for which test data v;er3 available; the remaining curx^es were then faired In a manner consistent v^fith the curves already established . In a -few cases (low b3/t3 with high hiY/ty^) the test data Indicated that the curves dld^ not follov; the smooth transition between column and local failure indi- cated by x'igure 16. Instead the curves tended to bend over sharply, in sorne cases even belo"w the buckling stress given by figure 15, and to follow very nearly a straight line up to the average stress for local failure. No exnlanation is offered for this phenom.enon; the available test data were used as the sole guide for fairing the curves in -^-hese cases. 22 NACA ARR No. L5P1^, Correlation between c'esign curves and test data . - The test data of rei'erance 1 as well as the additional data made available since the Dublicatlon of reference 1 Pi are plotted against tne parameter in figures I7 to 20. Appropriate curves taken fron: figures 2 to 5 are also drawn in these figures and good agreement betv/een the Dp final design curves and the test data for — = O.J4.. exists throughout the range of the data. In order to make it possible, if desired, to check the correlation on a larger-scale 'olct, the test data for r— = O.J, 0.[|., and 0.5 are given in table 7 ^^ a form suitable for plotting directly en the design charts (figs. 2 to 5)« Table 7 a^'^ figures I7 to 20 also make it possible to determine in which regions the design charts are sub- stantiated by test data and in which regions they were obtained by interpolation or extrapolation. Figures I7 to 20 indicate tliat there would be little hp difference in the curves for ■:; — = 0.5, O.li, and 0.5 hut 0;/ Op that the cui'ves for — = 0.2 and probably 0.7 v/ould be lower than those for - — = O.ii. The most efficient use of material will therefore be realized if a value of bp/b^; betv/een 0.3 and O.5 is used. It is for this range that the design charts are intended to be used, although thev are based on bhe specific data for 7— = 0.^. hw V NACA ARR No. L5F15 23 REFER.^KCE3 1. Rossman, Carl A., B^rtone, Leonard IvI., and Dobrowski, Cbarles V. : Compressive Strength of Flat Panels with Z-Section Stiffeners. ITACA ARR No. Ij-BOJ, 2. Zahorski, Adam: Effects of I.Iaterlal Distribution on Strength of Panels. Joiir. Aero. Sci., vol. 11, no. 3, July I9JA, FP. 2I4.7-253. 3. Dov;, Norris F., and HiclQnan, V/illiam A.: Preliminary Investigation of the Relation of the -Compressive Strength of .Sheet-Stifiener P.anels to the Diameter of Rivet Used for Attaching. S'taffeners- to ^heet. NACA KB No. ll\.113 , l^kk- [j.. Kroll, ,.'. D., Fisher, Gordon P., and Hainerl, George J.: Charts for Calculation of ' bhe'Critical Stre-ss for Local Instability of Columns with I-, Z-,. -Channel., and RectangLilar-Tube Section. NjiGA-AltR-N-o.. 3KOi4-, 19^3. '3 . Lundquist, Eugene E., and S.toTifell., Elbr±ifge Z. : Critical Compressive Stress for Plat Rectajigular- Plates Supported along- All Edges and Ulastically Fiestrsdned ..aga5-nst Rocation alcrg.,thc Unlaad.ed Edges. NACA Rep. No. 733, I9I.2.'' 6. Keimerl," George =1., and Roy, J. Al^.'rrt: Praliminary Report o;i Tests of 2.ijS-T .Al--Lainuni-Al-]-oj Colufrins of Z--, Ghfniiiel, , and K-Section That De velop -Laoal Instability. :!ACA RB No. 3J27, 19a3 • 7. Tenrli.n, R. L". , Sturm, R. G., Plartmsna/E". G .,,. -and Holt, ?,i.: Ccl^lr:ln Strength- of Various - Aluminum AII07/S. Tech. Paper No. 1, Alumin-'a!Ti"rLes.. Lab.. 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KNfH ONCOf^ ^rO»-t OOn l/M/NCO 0_d-0>«v0 LTNlTN OnvO tC\i-t ON.C — ^-o^K^^- K^ iTNK-vrvj o o^ trNU^l/M/Vd" CrN-^_;JT\J rH f-* oj iTnOm/n rH aNC^ir\_:t ry OOOC-CO fO\f\J O ONCO K^K^K^f\i rg iTNtO O sO_3-KN Aj Tgrg nO rH r— irv^l/N NO-ltrH O^r-iTN nOnO^^ i/nlT^i/n irMTM/N-d'-d' rrxOCO C-^x> sO irM<\f\| rH ONf— »0-d"«^ fC\rC\»CiKNrr\ ocor-r-co ry OONCOC^ nOGDOJ ir\KM-vj oj CO irN_d'-:t iTN -li-rH ONr-if\rr\ nO^ iTNlfM/MTN GO fVp-ry On rH OCT) t^lTN irNu~wtJ'-:t NO-^K^nJ fM _d-rrvrvj rH O f\J iTNONlfNrH cONO_d''<^f^J ONt^t^p^cO o ONoo r-NO t^ONj- (VCMOJ CNi/N»C\fg knno rH ONtwiTNrOirH NO IfMrMrMTM/N OnCOnO WV^ ooor^r-h- tC\r^ O 0*-20 CO fNJvO AJ ON NO iTNi^CVi O »r\ »r\ KN K> KN t^^NO f-co OnCO C— *0 ITN r\j rg r\j r\j f^ CO rHvO K^rvJ o rgoj nj IfNOJ f-i rH KNvO o^^--l^«K^r^ on o u~\rH r-iTN CDso irNN~\r\j »r\f\l rH rH f\J rH OONCO C^ iTNKNrxj rH CJn KNK\hr\»r\tM sO U">sO^-OCO oo p— ^ u■^-d• f\j f\j nj r\j (NJ rH r\J KvJ' ITN NO f*-CO OnO f\l_H-vO00O r\J_:tNOCOO ifSO iT* \ OSC « O HHO: t-ttd NACA ARR No. L5F15 34 -*|. M^* % ^ » K\0O KNCTmTS _4-KMOvK\CM r\) ri fH O O CTnOnQ^oS KN<\i ry (M ry f\J rgnjr\j ooJcc ry osoi ry oj f>j oj PJ cy t\) r^ lt* CO r^^O^ i/MTN r-rH ONCOO u^ojco trsf\j OJ f\| •-( fHrH t^(VCO_:tO &S'-0 ^ CTM<^ rococo r-t^ fMf\ifMrvjr\JC\J OJtMt\JOjry OJf\Jf\J<\Jo fy COCO c^t*-t*- ^ococ^ vo iH r— OJ »j-crvco^ moNK^c^ryo) r<^O^l/^^^co io\ry ry ry rH rH aNOf\jtr* rH rH O OO vO rH O KNOO CO_:tOvX>f\i OnCTnOsgOCO h-ry nj vO UfMP* ryryryryryry ryfyajryoj ruojajryoj ^O^OCO rr\0 f\J ry rH rH rH ONONrH-Z+Os ONvO-4''-*CO O O O OCTn fyOsO-drH _j-ONvo ry ON O^ODCOCO t^ o ry-j3 ry ON vO KNOCO l/N CO iTNt^ O\0f\J ^O lTNl/n fyr\jry(^(\jry ryf\jfyryry fyryrycyrH h»<7sirvo ONvo o j-ONJ'Oirs iTN^-fycoso rHf^J-O^- ry pHTHrHO p-corH^ory O O OnC\ON t— -O CTNinKN ONLfNrHCO iTi COCO CO ^-^— _40»^\0^^ ocofy 00 K^o U^l/Nl/N f^Jfy^^i<^Jf^Jf^i ryryojryry ojojr ry r^o ONtrvKN KM^ry r-*r\crs _4- KN KNfy ry i-h l/NONir\KNK\ i/NrHco ifNry •H rH O O O _d-00 f\J CO lTi 0>^0-3"'-*C7N CTsCSOSO^CO CO ^cxcTxr-r- COvO BfNrH ON rH rH f- t/N rH t^ (Mryryryryrvj ryryryryry t^lTvf-OJ OrH iTNO U"VjH f^pr\ if\»r\ry ry i-* rH ir\ococr) as ooo ON f^Q\ Ol*-KNOCw ooc^r-p-^o ry iTNry ryco ir\ f\j cy f\l fv v4> l/M/NiAl/N M>cor- OMTnOJ ryr\jryojry(>i ryryr l/Nh-KN,H KNp^ .Zt-OsinrH C^KN ry rH rHrH O O _:j-KNK\irs(7s Or-^rHCO o a\osa"co _^rH OsCOCO so jrH osr- oocooo ^-^- rH^-^-co^y 00-vOsD r*-ON ^t — i/SKSrH OsU^lPi OJfMfMCy'MrNJ OJf t*-rHCOC0 rH^O OsOrHr-_d-0 rg rH rH O O O .zf^Mi^oory P-^d-rHCO',© OCTNONCOro oov© J-_:tu-s '-r-r- rHCO tr\C\J O O OnCTsOKS GO iTvKNry o l/N lPm/su^lTn ^O KNO (M ry 'M ry f\i c\J o lrNN^lr^ONlr^ r^rMCO-d-O t^ rH rH O O O ON f\J oo OrH r^ ON^-tf^»<^ cor-r-r-t^ \0 IT^^O ONlPi OVO KNOCO vD-d-OJOCO l/Ni/MfSirYJ^ r>j (>j OJ ry r>j rH rHOOOt^ffs KNUSCOWNON rHCO iXNKXO o>cocococ6 .^KNirsOvO »c\ o ^ CTsiTviH t»-_3-rH OOO CsOnOn pc\--o O ir*ni CO l/N KNOCO coco coco r— ooory_^ NX>-=trg oco fyry ir«oco i/sry osr*--d- vOsO l/NtTNi/N v^ r^ONfMso ry ocof-t/N rH rH ir. ry o>ko cor-ov^tf^'^ iTNrH r-_JrHCO o o onctnosco KN-»0 rHCO ur\ l/NOJ O P—I/N oocooo f-P^- j-ir^ocOrH fOrH 0\^-^ t — t — nOsOsO O rH LPirH ON KNO p-uNry vOsO l/Nij-MiN GO o ryvO'-* o osr-irvd- O-CO KN O t^lTN _^KNKN O t~t l/NrH OsO ryoo j-rHt^i/N O OnOnOSCOCO KNC^MNO ON ry ONr-irsry CO ONrH_ctCO OCO r-3-fMO ITCO jry rH OOi/NKNrH Os irM/NlTMTN-^ ry LfNCTsJ-CTs r-UNKNtUO 00 rHCO t^i/sry uso\tf>^tr>co (\icovo i/sm soovryvorH KNt^j-ry tr, -d«> ry t-t^i- -:^coi/n _^0 t^3^rHCO V* HNrH Ot^ l/N»f\fy O O^ O KN«H ON*^ l/N^fNry O o OJ u oryj-r-o _^C0 KNOOH^ _^K\KNK\«NK\ fr\KNK\K>»r\ KMf\»r\KNK\ OJfMOJfMCVi (NJfMOJCMfy fUtMCVJ ON»~*CO O Ifs GO iHKNt^O kOHNP-ftJ 1 O O Q\0^ CO f*^o^o ir> ^, OJ t^rr\QO 00 O N «H fH O _:tKMO»K\K\N~\ »r\K\KMr\K\ »fsK%»r,f\j cv <\jftjrvjf\j<\i rMfMojcyrg cvjCNir^ t^«\C^croo OJ O'co r-s3 u'vd' ojG0aq»-4< ONCO vOOO H,:^00 »H o a\ H O CT\ rr\KNK\pr\M%»r\ K\K>KNK\»rv rcvKNojojoj (Mojojoioj rgrvioiojnj c\jr\i<-( C^t— ^Of\J_^(M vO_d-t^KNK> J r-vo 1AJ■K^ f\J t\J r^ O C On»-«_^co ru O>£0 H t*-NO VO r-t t^-OJOO iTvr-ON K^N^K^N^K^K^ »r\fr\K\K\»rs ojoioinjcxj (\jrur\jojt\j ojojnjfxjrvj rNjrvjrH ^i JOJ OJrH»H t-NO_:±C-r-rvj OOHOJ j-S- C\JvO LTNt^fNJ H O ONONCO O rH ITNf* ON iHnO i-( C-CM CO C^C^-NONO (\l r-t r*-cOir» l/^CO iH l/NO mo OJOd »f\r-ION 0»r\NO o ar\KMN>nj rg ojojojrgoj ojojojojoj ojojojojoj ojojojrHrH ^-t/N O 1-4 LTNiH O C^Oj C^KNON OJlTM-tCO t^ irNrHCO_:t*-l *-t H O O ON ^O i-t ONONrH ono^cococo OnlTNOn r-sONO CVJ OJ OJ nj OJ OJ Oj Ol tM OJ OJ ojojojojoj oj oj oj oj (H iH rH fH rH rH fH iH r-i C^ H-t*-U>^ OJ coT^^:f OJ C^ coco t"-^ONO tr\ OJ_H-CTNt-<0 CMT^OJCO_d' K^OJ OJ OJ rH OJ N-OjCO_rl- iH O O ONON o r-J-r-ioo OnOOCOCO C^ NO J-ON OJ r=-(\j t— sONO OJ OJ OJ OJ OJ OJ f\J fVJ OJ OJ OJ OJ(MOJC\JOJ OJOJOJiHrH iH tH rH tH rH C-^O fH iH iTNOJ OJ lr^cr^K^^-oJ CO c— sONO iTvirN r^ojOT_d-o NOKSor-_H- nj OJftJ rHH r-CO K\t-t rc\ CO K\ONLrN»H O O OnonOn 00 NO irst--t-i t^-d-'HOONO CO COCO r— t^ (MOJOjnjOJOJ OJCXJOJOjrvJ ojojojojoj OJOJrHrHrH r-lrHiHrHr-l lHr^r^ C^ONnO t~-K\OJ NO ctnnM^oj C^ U~nOC0 OnOJ OJCO KNOnnO ^tC\t<\C\S OJ f-J-OJKV=J- OJ ONND KNO OJ r-t r^H r-t OJ^O O K\ ITNONO OJCO O O OnOnCO OnCO ONrHNO _H-rHaON£) f<^ COCO r-r^c^ ?^z OJ OJ OJ OJ OJ OJ OJ f\J OJ OJ OJ OJ OJ eg OJ OJ OJ OJ r-l rH rH r~i r-t i-^ r-i r-< r-i r-t f~i r^rH 0_^rH OJ 0_dCO OJ t^OJ r*-fOONL?^rH tAK\OJ OJ OJ UNKNHXjJ-C-- CO tTNOJ ONNO ri r-l rH O O NO OCO 6nK\ r-i C^OJOO tfN O ONC^COCD r-i O OJNO r-i OJ OnnO t<-\r-i CO f-^-t^r- nO O On irSrH^ vOnO l/N OJ (\J OJ OJ OJ OJ OJOJOJOJOJ OJOJOJOJOJ OJ fH fH rH rH r-i r-i r^ f~i r-i r-i r-i r^ P^KMTNO O OJ _^OJ ON OJ rH rH rH O NO tC- _J-»r\KNOJ CM r-i f\J (M CM CM CM rvJ .d" OnnO _zt iTN knonno rc\o rHOOO O CM OJ CM CM OJ r^O IT^CM ON C^ ir CM o (^ OnonCT'CJnCO ^-0^-::t^'^^'^ ksonno k\C> CO F-t^t^t^ NO rHCONONO t^t/NOJ OOD nOnOnOnO i^ rH fU ON _±OnO i~i r-i ri f-i fi U-NNO t* NO C^-CO OnO NACA ARR No. L5F15 36 Eh o H CO g I-) << is g " M O m •« o • c g CO o M Eh < o CO > n •ri X O . II a> CO ^ :?* CVJ KNfO\C\J OnO t^-uTN ^O ONCT\rr\ COCOCOCO rHOJrHrH irv_d-^_:d- O i-t f-i r-t r-i 1-1 rH iH rH at 4 at CO a t— t~-co O _:J-cM f'Vrt" OvocvjiXN vO_:tC\l O tc\0 t>-_3- cON>i-IC^ .... .•». .... r-ir-tf-irH CM CVJ iH r-» CVI CVJ CVJ iH Gt ct cd ^ 5 iTNrHCOrCi KNvO tO\rH rH ifN CVJ rH rH KVcf-:^- C"~.vO K^K^K^K^ KNKVzh^ _d--:T-^-^ oooo oooo oooo .... .... .... O (0(0 at 0) ■p CO 00 a •P "rl COvOOhTN CVJCVjOrH _d-ir\CVJrH rHCVJ^-d" ^<^^H^H^H Oj F-C-'vO MD tr\I3-i-MD LTV-d- co^oirvrj- oooo oooo oooo • *•« •.*. .... o at at at Oi ■p CO •Hi CO < l-P c^cvj o r- ONcvjcgco t--ovoco c\j c3md K^ CVJ iH •p to OvO C--::t C>-.j:t"sO CVJ O rH 00 VO .... *•«. .... _:d-Lr\vO C— OOOrHCVJ ir%C— C— OD K^K^K^^^\ cvj K^^f^^^^ cvj cvi cvj cvj at cd at ^|4? CVJ cvj CVJ cv] ^<^K^cvJc\J hfVKMo>hr\ col CO P l-P t-co CTxCTN CVJ K-v_:d-Lf> _d-trNt"-co CVJ CVI oj rvi ^c^K^K^K^ ^f^K^K^K^ J'U" rHrC>ONO rHKNCJsO rHKVCTNO irVsO C^O ITN^O >-0 LfNvO f-o .... .... .... O rH r-i rH 0) CO PL, ^1 fj ft O LTN O K\ f-i t-i ... O o o o rH CVJ rrv o • o II CO ■p o ■p c s ID •H g. (D h xi o at o o. at ■p at Xi •p 0) a n c o «H Tt C B 3 H at > 0) CO o M o ^ CO o M CC < i-l O O w ^g << Eh SE M O \ 37 NACA ARR No. L5F15 \ TABLE 5 VALTTES AND COMPUTATIONS FOR OBTAINIKO PRACTICAL DESIGN BT SHOW METHOD IPj = 5.0 klps/ln.; L = 20 In.; o - ■• ' *• - " "'^' *- • - i; tg = 0.064 In.; ~ = 0.79] step 1 Step 2 Step 5 step h Step 5 Step 6 Step 7 Pi L/v/c /klps/ln. \ V In. J fs Of (kal) Al ts 's (In.) ^S (ksl) Al ts Pi klps/ln. (In.) fs (In.) bw (In.) (kal) For tg = 0.06^ In. 0.15 50 n 50 50 28 26 30.9 31.7 29.7 27.1 2.006 1.862 1.71,1 1.53U o.ouaii. .0508 .0590 .0722 1+5.5 26.1 28.8 1.619 2.98 0.051 2.77 1.35 23.5 TABLE 6 VALUES AirO COMPUTATIONS FOR OBTAINING DESIGN FOR MAXIMUM STRUCTURAL EFFICIENCY til (r>i = 5.0 klps/ln.; L = 20 In.; c = 1; tg = 0.06U In.; ^ = 0.79^ step 1 Step 2 Step 5 Step 1; step 7 Step 8 Step 9 Pi '"f L/\/0 /klps/ln. N bw Of (ksl) Al ts ts (In.) bs ts *C\ -t tf> ■4 -* i'L? o o o in o o p-l^* s tr\r-tH O K>Nor-o (M P"*-* trv CCOCSiH fy r-)0 s§^s i-t(n(T4D ^Slf o r>j ry rvj iH • • • • • • • • CM N W ^ a • • • ni oinirH K\f\joj r- KNcy o \t\ rHcrCOlA -d-^tfNOJ t a a • O 9\vOM OlHrHrH OJ rH HiH «^l;? ir\ KN -^ ITN J^ -:* iri -it • UN >flJ o o o O O eol « o P II CO r-NO T°-^-^ rt »r»4r\»rN U>nO^ACO (TCOGO O OlO OnO r^t-iojvo K\t^rHO OJ t-oocsj prs»r\f\j'^ KMTVOJ rH OJ(VC«rt CJCMCy rH OJOJOIH C\J m o o o O OJ OJ p"|.« o ^§1 .^tNOC0(5 0| r^r^O^ f\J rH O O 3u^rHCO COOJ O I^ ir\fc\(\j o iTNCy HO -d^OJ HO o lb 5 o c^ryco rciCO O^O C0»rvO_:t KNOMTOJ a\inc^_:t iTNOsO OS OJ OJCZ>Oi _d-»fx^-=»- mC'^^co ONOJ O^-:* rr\tf\f\| iH 0^'<^C^J^O (U ry OJ rH ry Ol "HrH iHOirv4 irv»r\oj »H rHOvOlTN »r,K\OJ «H OJ rHsOsO O HSOtTN KNKN OJ H .s-|j= O -^ -^ -t -:t *r\ -:t iTs »C\ J- ^|J= O o K^ o o ITS o CM ml CO CM u^ ►c 39 NACA ARR No. L.5F15 I 4* a o u ^U CO KSO-_=f nj r-IO O B^^ CM HO o S^S^ no O - - - - t^OJsOr^ r^CO^ffS t^CTMHOO so so NO (S rMOCOrH O CM O nj ^CM iTN-:* r-ir>o •Bm »f\r-*r-fO ffsCMf^ON fM (HO O NOC^iTCO vOvO CTy^ (M^OO ^Slf ro irs OOOfHNO KNH .-40 o 4^ «4 oo-4^ir^ OcMOCM O ^r-l oi^^^ trM>(7^CM »n ^\e\tr^o\ fMmOJrH covoifxr- cgtyry f-i ^0_±fMVO rM tM (M<-( iT^o »r»>o fM(MCMif\ CM CM •-•H ^\^ o UN K\ -^ u% • -^ K\ ^ • ^U o ITS % O o CM i'l-" o • 5 crmooco KNCOCM ITN tr^rHHO O^K^lH C*- CM ONfM tr* tO*rH i-t O HOO 1 t^OOiTN o^o r-CN _;J-CMrHO O 1 I 1 ^r^O^CM_^ C^OONON r-^(Hif\ .d-rHVOO 00 CTnCO o O CTvOJ 1 CM oa>»-i NMX) CM ir- ^\r^astf\ _d-o^^ir\ ry ooo t^ O r^COCO Oost-TO (VfM CM "H CM CM fH 1 CO If^fH l/^ njoj eg rH CO O^rvj^:^ CM rg CM H r^mnjNO CM CM CM H t^lTNOKN CMCMCMH ;o^lxf 6 • ^ lf\ ^ • KN -:d- IT. • .PlJ- ni o ^ O O (M CM ^u« O ■s, a • • • « o O OnHMTN CM rHOO • • * • 1 1 1 r^a^ 1 CM r-t O 1 • • • 1 I • • • • (TMfso m _=tCMrHO .6-1 O^J■O^K^ ON-dtDCy COfU_^_d- HMTvfVJ H »r\»r\fM r-i j-tM ir*o CM CM CM H (MrH r- I iTsrgco 1 rM CM f-l 1 ■ oco_zt^o mO fcs_:t irNO,:^'^ L" CM NACA ARR No. L5F15 40 •< < I-) a KVOvO rj CO f-.zt^ KNiH HO rg H O O 1 iTVt^O K\Hi-l O <\J HOO co_d-cr>K\ -d-oj-d-o »fNKNP-j- M>OJCO_d' ryHOO cy H O O O ^-<^^-* KN -:t l/N KS -H "C >F|J o ni o i'U" o 1-4 O c O OGO K^ J-OJrHO 3(\|HO _J-fVNOvO OnC3 (W l/N KNCg HO K\rMHO 1 1 IfMH 1 ITS KNftJ 1 O O rH iH O KNtTNt-CD OJ (M rH^O Ht^o_d- c3no o_d- KNiHrHO »OrHrHO O I ^ •^ '" 5 K^K^(M f-i (M K\K\H • « • • 1 COO UNNO HM\JCOCO IO.KNOJ 1-4 mt^tM UN (\| OJ ITNH <\J HCO t^ H O 'vO t^ KNKNOJ t-l rOKNCyrH ^1^ • O • • KN ■H ITS KN ■^ ": ^\^ O i? o «"U" . coo o o 41 NACA ARR No. L5F15 J'U a O Ovo K^ CM >H O O CTN^OinKN OsOnO k\ •Hr-t OO J4HOO Noco ir\cM HOO<3 o OfMKNvO • • • ■ OMDrHKS rHt-(MCO CM cy cy H fMJ^C^C^ ^CMO_4 CM CM CM H CO H H K\ CM CM CM "^ iTNOMTNtH • • • • fMCMCM rH KNr-tO>-:± CM CM HH njcococo 0_^CM *H • ■•• •••• '^cmcm'h^ 'cmcmcm'h^ M^ O -^ \r\ K\ J- tTN KN • • ^u O CM . O •a m\ m tc M C rvivo OMfN M^r^ o o M t-saco CM rHO O fVJCO KNSO CM H O O vD CM CM CM H CMCMCM*-! CMCMCMr^ ^li= • -It • • -=f lA HN -t "C i'lJ' o ITS CM O IT* ml m o iJ a c •H -drvj HO -Zj-OJHO H C\J KMTN _:J-CMHO KAOCOCM KV»0 O^ K>sr-lrH O KNrH i-H O coorocn mcrso J- KN»-« I-40 r-l KMOCO O O ITN^O CM i-lOO ir»r+0 O o ' ' KNGDCOV^ t^C^rr\ir\ iH iH OOJ l^t^KNtH ^* ^- - ■ i7i Q ^ ' ;^^'-i>^^-. '^^ /^ ^ S > Sto T^ ^ g ^^"^^-^-^^ j^^'^ V s ? ^^-^=^^^^^2^ i-i^ kS ~ ^=-=— c X 2X^-^4 4- s ^ Ik*^ ^ ^v, \;rr ^ S « n ^^ V- \ ^ -^ G- 4- ^-^^^^ ^^ \ I "^ "-^■-A^-- "^. .0 3 V \ § . ^^^^^^-^"-^ lE \^ ^ ^^ 1|- ^"^^^^Z^S^S^ ^ CL* c ~ "^i^ ^^^^ ""== — l^ ^N^v^s A^ i^^^S S^ ± it X ^^^ ^^^^^^^^ ^ ^4S ^^^^^^^^ \ ^ \ ? -:^^.-N^ ^^ \y \ j ~^C^ii.^--^ ^^. , r^ \^ "V """^^-n^^-^^^--^ V^ \^ ^^S^^*^ ^^:^ \\s; -■=^=-— ^v^^\^^ ^^^i^S^ ^^v^v^ ^s^^i^^v ^ ^^^,^^^5^"^^^ "O N ^■"5;^^^"^^ " "^5^~~ ^^~^~~~ «o tn '^== = ^^~~ -^ ""^ 1^°°" ill LP !S>| ' ^O NACA ARR No. L5F15 Fig. 2 Cone. T3 Q> T3 _3 o 5 u CO Q> L. 3 s OQ -s-i '^IJ' ~ ?i 1 5 !^ _ 3 i"? o J " g z ^ ^ J \^ u \ \ o 1 ^ 1 \\ * S k i \ \ ' '}? M A '■ \ 1- ■^ '^ I s \ .in ^ T -- s^\ \ N > \ t \ ^-. V s ^ \ T ^■^ ^ ^A li *; == :~ :::; $^ . c > - Q. - j^ vv° ^^3 s »_ ip . o K o _| S^ 1^ \ ~_ Ql* V^ \ \\ 5 ^ kJ M \ ^ ti A ^A\ \ c :> -- o v\ ^ ^v Sj s a \ ^ s \\\ ^ V V, N \ ^V \ ^v c ? _ to ■»-> - 1 \ ' *JQ Fig. 3 NACA ARR No. L5F15 I- E 1= "> o 5 » t_ U § ,o c «= § 1 5r Of ^ ^ . - o' ^ ^ ^ CO ifc-f^ CD •- O \ O Tf Cr •♦- .2 I 9 CO ■o M ♦? i5 s _>.3 S- - a, ii I ? 3^ s '' ± "ii ^5 t o 1^ E ^1 1 -^ 1 O 4rS - -a S K"^ S -14- J^-- o- --2 ^ ._ I . ° .V^^ fe ^\ ., .o .«2 ^ _. 3s,Si - -9 S ■" v^"^- 1 S JL «>« A ^D^4 - S 1^ \ ^^^^^ ^- t _^. o^^^^^"^^ y.^- o- -i, ^ § ^^^-^f'r-r--^ /'^ 5^ \ ^oV^-'^^--^--^^y ^ ^ O .r. i-^ <^ "'^^i:;i'~-^i^S:-- J^^ S s :\ ^^ L II ^^^Sa-s^^ i ^-. "^^v -[ s { V \ \ «T ^_Av° "^^^^ C^l •§" .^_ A 4^^^^ N--. - ^ \ ^ ^^^^-.V --- ^ i\ \ '^ ^ t^^^"^^""-- ^ i^r "I^K "^^i k~ '^-^^z^^^^-^ cT ^ V o^t^ ^, . •" ^■^== = ^S=; = _ f\L;^ ^;^ ^^5 L =--- = - — N^_ N^^v.\ 5 ^ ^ \^^ ^y. V ^ • 4^^^^^^^, \^^^ ,, ^s. ^^^^ sis ^ ->:^^t:^^^ O " \\ ^ ^"^^^s::-:^ 8 ^^^. \ o -^r-5-^^-. \\ v,^ \ \ '^^^SsrS^: V\ s,^ A ^ = = \^^'^^\- '- ^^^^^x ^^%^\ ^^L^^^^^ O ' «S ^>^:-~.^~^^ c\i o- ^^*!;^-~-^^^ II "^^S^" ^"^^■-~- *" "^ "^Sr^^S: -^ *^ ^"-■==— 1 , 1 r- ? o !S>| ' ^o NACA ARR No. L5F15 Fig. 3 Cone. ■a Q) o U I 21 J_ Mk. ^ 3 ?" |r "2 t^ O =ife S E^ « i - >»* :^: O ^ O ji 4r § ■ e «g ol Ji 8 ~- 1v ^^ if^^ ^ 9 o V\ ^. t -2 ^A \ ^ «/) ^ * ^o K4^ !i£. JJ° i^A o" - ^ ^s ■": ' \'^ ^j Q A^C^ Q. it ^h- v^v^ t ^A^C "^v, O - t ^^^ v^^^ O - t ^^ l« ■^^~~-^^--'~^-~- 1^ *^== = ^::; ^ = -^^ 4^4- "" — = = ■=_ 4* o Ai °- i\ iV S *A « as:x ^vV t V4^V ^ ^^A^5^ t ^v^^^^ ON H ^S^S^ -+, o o ^:;\ ^ ■~~- ±- ~~~ ~-- " ^ J^"*~^ i"--^^ r? *" ~^-fs-S~-~=: *^ r= = MM " o o s \S>\ ' *jQ I^ig. 4 NACA ARR No. L5F15 -2 i » fe Q ^ - ^ -;»- ^ '*- g O) ® 'O — f ttf'? \ ~ ^ ^•^ ■^ ^ \ lO — to '^ '^ \ ;r S-^ \ Ul^ ' ^x o - -'^ K ^ " dC \ vx \ 5 ^ :::^ ~-- 1 " 1 "^^^^ \ - \ \:- ■^c v--- \ ^- ^ V \ ^ - ^s k !j ^^v- T \ D - \"-- ^ J ^^ ^ ^^^ - \, --J ^ ::::; ^\^>^ \ s. — . Ss - \iv^^ \ 1?! =" : ^^^- '\ \, \ , ^: ■^. "^s ^ k ^ ^ N \ V s " ^. \ <:^ ^~ \ in __ <\j " -.^ -^ c> -- ^ :;:^ ~^ ■^ ^ ^ ~~ S;: ■' = ^ ^ ,, .. 1 r ^ o 1^ o !S>| NACA ARR No. L5F15 Fig. 4 Cone. -a Q> I J - . C S- I • cj -- i ' < i i_ e m 9 u O 1 E " 3 1 ^ ' I c s > I " 8 \\ n\ N \N \ - \ ■< ^ \ 1 e- o V \ ^- 1 -=4 ^^ ^ ^T'^-i- Ml '■ ■^^^^^S: .__^1 > a. ^'^ ^ pSk - \ S \ tn \ -? \ \ ° J^« t \!\ >^ cT \.N^ , I ^^. *^ \ ^, - \> s\ s \ S w ' 8- o V^S. ■•> "^ ^^^^V./^^ . 9 S^StS^ -___ 1 —4-^= ^^^=,,, '. 'V ?T \ > , ^ ^ ''. \ 1 . s\\ , \ L \, \, y i S i ^\ ^ — ^^^ V ^\ O CJ N:>i^v- i O ^ ^o~*-~~-. 1 ' ^^:^:r~C; -^-^ to P CO ■•-> - - ''~"~'*==l: ^~=5 =:t- ~ - =•=-— , _J J " s? s !S>| ' ^O X Fig. 5 NACA ARR No. L5F15 ^ g J fc "9 ^c> ? 5^ :5 i 8 o- 1 .onO "a tsl ♦? iT JD 9 <^ m ^1 £= -r 2 5 f s ^ ^i 1 s \ s i4^ r^Q 4_ -2 "" 3 ^ ^ ._ V4-^ t r O ■ - ^ 3 3t «2 ^s V" \ ^« - ^o . S^ 9 X m N tf) \\\^ ^ \^ 3 . . IS \\^^^^ S ^ t V ^.^^^-\ ^\ y :n ^ ?e > ^, o ^■*'::-::s;^. ^. y § ^«? ^ « ^>^^::^^^ y O i^ V \ ~'^'^~S = S=: '^: :«: ^:!' v v- ^-=.3 ^ ^j' Jn^ \ \ s^ r-L ^^ '^ ° V d" ^\ Q ^^. ^.1 \ N. •§- '^ t ^ ^S^>iv ^O _ ^ 1 » y "^^^ :^ "^ iTN L r "^^^1^-^ s, iR _ V ^T V Y ■- — — == v-r~-^ . ri \ ^ , H \ ^ 'NS^feSr- L 2:^^^ :^ ^ ^^ — — \\ ^ ^N ^^ ^ i - ^^"^^ § V ^ ^^^^^^ \ ^ S^^^^x 9 \^ \^^^r^ ^ ' \k V ^^^^^-- "^ ''^ S V ^^i-s5"---~. Pv "^ ^ \ ""^^^^^-^ 'X ^v V V ■■---.-__ ^5^^^ ^ V '" ^^v^^x °: ^^ =^:^o^^ is ^^^-^■^-,'^ 9 ^^J:^^^ X- " «s ^^5^-^^ \ CM ^?^^^-~,V « ^5==S^^ •oIm ^•=-S;^fe§^ -D !•»-» P ^ ~~ 1 1 1 1 " !^ S o !S>| ' *o NACA ARR No. L5F15 Fig. 5 Cone. T3 -o c o O <_ Z3 <3> . , f -> c § c < ^ iL o It 3 i_ = 5~ o u «M o . O o 1 " -o <2 ^ ° s T ^S ^^ - . 0» _ V^ L. rj ^^^i 3^ .*o ^ - 8 ^^^v1 p - ^^^s \ t : ^i; ^s . m = ^ S=:—- ^ f CJ ""~*'^= S lata ".^ c s " s 8. 1 ^ o V ^ 9 j^ I lO ^L At § V I dT N ^ \ ^ 2J ^^^\ ^ o - f° ^^S \ ^^^ ^ o . ^ ^^^^-\ O " • ^*«fc ^; JW) to ^» ^^ « : ^ s^ & — = = s==.^_ - 1 1 1 1 ' o 8 S !S>1 ' ^JQ Fig. 6 NACA ARR No. L5F15 11 Im 'n K jj M lin W ifl U 'Til X -I t fl ± ^L?p^So/ct ^ \\\ini \vttj \Wt^ 3^/2 ^^^^ ^^^ <£''^ 2'^ ^^^^^-^^^ Q O O « •♦ «o— !Z L s«jSSSo7$r ■ "^^-{^1^27 '^ icZ ^ ■V y ' y 1 B y y / PI -i ^-' / ' i ii5y it --J; '' ^■^ i P — ^ ==; ^^^ 1 1 \ c o JL^ o o CM *> m S^ ON O "O V \ L .1 „ . , . , _. . 4 t ^^c t ^\ A 5j ^ J u\^V- u XaX V > 1 ^^^^ ^^A ^ \vv-^ 5^ ^ AVV^ 5^ ^ ^XS \ ^vV^^ ^^^s ^§^^^ ^5^5^^ S^^^s, "^ §^ '^^ ^§*=2^^ ~-i^=5 i^-^ "~^^5S =: — ■"™s = a a. y *- o o CO o >s O T^ ? i^ C J3 E ^ -o o c o H 1 0) «- 3 3 — — O O > ci: JC 4- ♦- ° ^ •» s r i: 0) (0 CO C <*- CO Q) «.- O o 0> ^ <0 > C o .2 C * X Q.-0 1 Q) -o (D c QJ '*- c 1- 3 o> !S>| ' *jO NACA ARR No. L5F15 Fig. 7 0.51 Ideal dQsign -.0315 .0618 J^ L f r~Short •»'< phort Co3Z J method J L Maximum t.032 efficiency t L .63 fshort Co40 r J method J J C Maximum P^.040 f" efficiency I J /" .79 Short method -.051 I Maximum efficiency 1^.051 £ ^ Short method 1.00 1^.064 Maximum efficiency -.064 I.I.I i I I I 1 I L. 1,1,1. 2 3 4 Inches f 1* 1* ^t 1^ ::l ofcr YL 20 30 Stress, ksi NATIONAL ADVISORY COMMIIIEE FOR AERONAUTIC! Figure 7. - Designs of 245-T aluminum-olloy panels 10 inches long with Pi-3.0 kips/inch, c-1, and ts =0.064 inch. Fig. 8 NACA ARR No. L5F15 ^W 0.63 Ideal design *-.0386 ^■0612 L 'cr r • .63 <^ Short method -.040 Maximum efficiency -.040 t/* 1^ r Short method .79 Maximum efficiency -.051 .051 r 1.00 < Short method Maximum efficiency -.064 .064 _1 I I I L I I I . I I I I I _1_J I I I I L. 12 3 4 5 6 Inches 1 20 30 Stress, ksi NATIONAL ADVISORY COMMITTEE fOR AtRONAUTKS Figure 8. - Designs of 24S-T aluminum-alloy panels 20 inches long with Pc3.0 kip^lnch, c-1, and t5 = 0.064 inch. NACA ARR No. L5F15 Fig. 9 % 0.63 Ideal design -.0425 f .0675 ■'cr .63 < Short method -.040 Maximum efficiency ^.040 ■■ l^^l ^^Bl // ' va ^^^1 ^^^H \\ 1 L_,i_J 1 1 r .79 < Short method Maximum efficiency .051 .051 Mi ^^^1 ■ ]~ ■■ ^^H ■ // ' _,t_J 1_ 1 r 1.00 Short method Maximum efficiency L^ ± .064 -.064 I I I . I J I I I I I I I L. 3 4 Inches % % 20 30 Stress, ksi NATIONAL AOVISOflV COMMITTEE FOR »!RON»UTICS Figure 9.- Designs of 24S-T aluminum-alloy panels 30 inches long with Pi'3.0 kips/inch. c-l. and t5-0,064 inch. Fig. 10 NACA ARE No. L5F15 tc, in Qf, ksi 26 24 Design point, bs/t5-43.3; bwAw = ^6. 1 30 35 40 b. 45 50 NATIONAL ADVISORY COMMinEE FOR AERONAUTICS \ Figure 10.- Plot for obtaining practical design by short method. Pi=3.0 kips/inch; L=20 inches; c= I ;t3= 0.064 inch; tw/t5=0.79. NACA ARR No. L5F15 Fig. 11 50 40 30 20 .08 .07 ts, in. .06 .05 Of, ksi =0.064 NATIONAL ADVISORY COMMITTEE FOIt A£l!ONAUTICS FiguTG 1 1. -Plot for obtaining design for maximunn structural efficiGncy. Pi = 3.0 kips/inch; L=20 inchesj c=l; ts =0.064 inch; twAs'0.79. Fis. 12 NACA ARR No. L5F15 \ NACA ARR No. L5F15 Figs. 13,14 ? f c J- ■_c- _ c_ to 13 Q) CO HI to - CU- /^ ~ to n Q> ^1. UJ C3 ■< •: or -J o ^ Q) -^ T5 2: ^- o C - ! Lki • t— ; ^- h'" 1 1 \ _ o_ E o O 2 o Q_ to 8 1 1 ^ '^^ m N.N -i^ V jL .^ • to o c 2 -•— >- oc o =3 ■< Z o (0 Q)- c >• o ■< UJ ■< ^ ■< z o Ll. UJ UJ 1 o E .■:3 ■< z s s - o o 1 ■o o ^^ ^ L _ CL i^l i6^ Q) O) "> H ^ h- u> Q> c CO O Q) s_ {^ O =3 W- cn Ll- Fig. 15 NACA ARR No. L5F15 Figure l5.-5tre55 for local bucklinq of 24 ST aluminum - alloy flat panels with Z-section stiffeners. b^^bvv=0.4. NACA ARR No. L'BFlS Fig. 16 CO in V Q) . >- 1- O "a c / c Ci : •< I ac l< ^* Cl -« -: or . 1 c \ Sis < 3> V. = 1 s o \ ^ \, "^ 4- ►^ Jo ■f, tf> to 2? Q) ^^ ^ tn a o 13 V ^ 5 ^ - * 42 a o c -a c o s. Q> 1- Q. C Q> to 13 Q> 1_ Z3 "O Q> O o Q_ Q_ ~ { r* 5 -f t o E c 3^^^ S >v "^^ C ; ^ ^ — _ ^ c o '■*- a i_ +- if) 3 I a> .3^ lO Kig. 17 NACA ARR No. L5F15 \ ^2D 40 ao- 40 20 0^ 40 Of. ksi 20 3S SO 7!) ^^yr .' ■ ' ■ — cL-cfc y ^ X A^{ ■ / / U 1 ^''" : ^ ^ -^ : /' / /■ 2ZZZ- ^# : ^r- ' >^ : ^1^ : ; .41- ^ f? / r D / : ; ^ <^ 1 :^ b ; ; ; ; ^ / -» : : J ■1 ; ;/ ; ^ » ; — X Pi L/ve ' ^^^ =C£^; ■^ : : -/^an v^ - 7^ 25 : rO- : :^ : :/ ; 30 : x^^ : :40 : C 3MMnl tE F0( m6i AERON lUTICS ^/1 -X ■ r DO .2 .4 kips/in. in. Data from rgforence Previously unpublished data .£ 0.2 .3 .4 .S .4 Figure 17. - Comparison of test data with design curves for 24 5-T alunninum- alloy flat panels with Z-section 5tiffeners. tw/ts^O.SI. NACA ARR No. L5F15 Fig. 18 40 20 40 20 _40r ksi 20 40 20 40 20 bs 2D .... X ■ ■ / / ; :/ ; : . \ '■ / ^ ^^ \ / , ;/ \ A 3D DO ^ ■ ■ ■ ■ . . . ■ L' ■ ■ ' : "^ n^ ts^ - / / r f^ ^ ,t^ -i^ >_ ; :/ -f :/ / ^• ; y ; : ; ' 4 3 ; ■f ; : '-■■L : R L/V? 7D , , . , .... .... :^ ^ :')^ ' ' . I , . Xi \ ■ ■ ■ ', »o .... , . . . .... ' ' ' ' .... .... .... .... ' ' ' 'jl ■ / y /* S^— ^>^ iCl -^^ : / J \^ :r*^T ' i \ ;/ \ w 20 2D ^^^ ; 30 40 .' ' ■ ' 1 . F 1 .... ' ' ' '. , , , , .... .... ' ' ' ' . .... .... ' ' ' ' .... . . , , * ' ■ ' ' ' ■ ■ "": : -7 ^ ^- - [ : ^ / / y' F /^ . — ■ / 7 1 Y ; / / / NAIIC 1AL AD ISOflY . cm WTTFI FOR « :ron»u ■ict .... .... .... .... , , . :" .... .... .... .... . . . .' , . > . .... . , , . .... . : . ,■ . . J . ... ■DO Previously unpublished datar ^ Figure 18. -Comparison of test data with design curves for 24S-T aluminum- alloy flat panels with Z-section stiffeners. tw/ts = 0.63 . Fig. 19 NACA ARR No. L5F15 1-5 ksi 40 20 40 20 40 20 .<§- -tA / ; 4 / ; ; ; ^ 5>^ ^ ; : / S ' : 7 ; ; ; .■^ < sP ; '''A 46 ; :/ : i DO : "^=^1^" ' 7S : ; <^ / ^_ : » :^ : 7 : njo| bvv t-w 20 : /" «>- ^ ; 3 ; / i 25 ADVISOI V 30 3 .2 .4 .2 .4 Pi kips/in. br L/ve in. bw { ° 02 Data from reforQnce ij° .3 /] (<> .5 \ Figure 19. - Comparison of Test data with design curves for 24S-T alunninunn-alloy flat panels with Z-section stiffeners. %/L5-0.79. NACA ARR No. L5F15 Fig. 20 ^ = 35 DO 75 Of, ksi 40 20 40 20 40 20 ^^ l_ ; /^ \ ^^ ■ /^ r \ f : : 7^ O '■ W- Z -£_-^- — 1*. ; ^ ^ «- o : f ; ; ; : '- ^ *^< i^ : ■f : ; 20 2S ; ■ fp ^ ; f : / f NO DMMIT lONAL EE FOP IDVISOF AERON i lUTics: 30 £ .4 z A Pi kips/in. L/€ in. bw (° 02 Data from referonce I <° j. .5 Figure 20.- Comparison of test data witin design curves for 245-T aluminum-alloy flat panels with Z -section stiffeners. tv/t5 = l.00. \ UNIVERSITY OF FLORIDA 3 1262 08106 472 6 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. 60X117011 GAINESVILLE. FL 32611-7011 USA \