Charts for the minimum-weight design of 24S-T aluminum-alloy flat compression panels with longitudinal Z-section stiffeners

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Material Information

Title:
Charts for the minimum-weight design of 24S-T aluminum-alloy flat compression panels with longitudinal Z-section stiffeners
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
41, 23 p. : ill. ; 28 cm.
Language:
English
Creator:
Schuette, Evan H
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Plates (Engineering)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Design charts are developed for 24S-T aluminum-alloy flat compression panels with longitudinal Z-section stiffeners. These charts make possible the design of the lightest panels of this type for a wide range of design requirements. Examples of the use of the charts are given and it is pointed out on the basis of these examples that, over a wide range of design conditions, the maintenance of buckle-free surfaces does not conflict with the achievement of high structural efficiency. The achievement of the maximum possible structural efficiency with 24S-T aluminum-alloy panels, however, requires closer stiffener spacings than those now in common use.
Bibliography:
Includes bibliographic references (p. 23).
Statement of Responsibility:
by Evan H. Schuette.
General Note:
"Originally issued August 1945 as Advance Restricted Report L5F15."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003804721
oclc - 123895558
System ID:
AA00009384:00001


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Full Text

hc(A L- 191


ARR No. L5F15


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WARTIME REPORT
ORIGINALLY ISSUED
August 1945 as
Advance Restricted Report L5F15

CHARTS FOR THE MINIMUM-WEIGHT DESIGN OF 24S-T ALUMINUM-ALLOY
FLAT COMPRESSION PANELS WITH LONGITUDINAL
Z-SECTION STIFFENERS
By Evan H. Schuette


Langley Memorial Aeronautical
Langley Field, Va.


Laboratory


WASHINGTON


SNACA WARTIME REPORTS are reprints of papers originally 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 Ihe Inllernel Archive
in 2011 wllh funding Irom
University of Florida, Ge':rge A. Smalihers Libraries with support Irom LYRASIS and Ihe Sloan Foundalion


hllp: WvW.archi.e.org delaiI3 charlslorminimumOOlang







NACA AR2 No. L5F15


IJATIONAL ADVISORY C OT17ITTES FOR AFRCIU'TCS


AD'.-iCE -?STICTED RTFOr:?


CHA TS :'' T'IE II U-LIiH' DEISIH F 2",.3-T ALIU..-; ,"' P1- .LO:,.

FLA' CC~:.I ? ESSI OIK' P:-aELS .-ITH LO GI:'GT I' 1 .-i.;- ,

Z-SECTIOil SPIJFLI' S-

By Even I.T Sc'.uette





Des3cgn charts are e'evel,-,r e- f .r 2'.,.-? il rni-1uri-
alloy flnt cci~ a.rsic ;:an1r3' n' ; ,itdin;l --section
stiffeners. '.ese cl.ac. .::n :..' ,. rle the 'es:jn of
the ligh-test nariels of -is :r a .ide? r-.>r.e of
design 'equi'em. .nts. r:a: l'3Es 1'.e o0 .::-.i harts
are gi- n n anrd It is ,oixr.t ;d..,,t 4 ,rA L'.c basis cf cU .s
e:,an;pl? s th-,at, ov e i, uwi'e r.2'ge i'f .'Lt.j.n 2conit ti'Ons,
the irair.tenrance of tuccle-fr s-.r ces dcs :ct conflict
with thi? L-i.. v? .1,-t of ti. r "utru : ...r fficienc. flz
achieve::lent 01 tr? a-_irr.:': .'o: .- s cr',.tu'- l eC fici-ency
with.L 213-T .11v-:in.;m-i. 1o:0 .a'ncl].s, tl.wJvve', roCuli.'en, c 1oser
stiffener sra"ings t'; l n c:ho3Ws r.o,, in i.'u.1.n 'IS:.


-T- Tr- i- r 1"


in -. lorrit 'd-inall- zti in whi 3h all th.e materiL is -. r : i'. in c -ryir.j lo ,
the requiremeint of n:ini:.:V:. ~. it is c -ta: '.! t to '- at
of carr.rin L.e 1 a. t :' :st .i-o3.i averia..e
stress. nle r'.-era.e stess e i- n-.-i
unldei th:e loadir n. co: dit c.n L 3 3d. ii :. i.:.-ct
measure c3 the str.c ..r 1 S y .'. If
longitAldinall-- tiffendi :',.-,: : .-s L .. l'.ls are to -.,
designii. for 'i,.-h jtr'.:ic ?.r 1. .. ..iti L Lt a ^r.-
nLmber of cut-c.nd-ryi'-' o- rta- -.i "a L .ait
design charts 'e pr rv.ale t'; _:..-,_ ... -.eT'- stress
att ainable -undLd.er va-ri: c icAr :- -- -cr. Ti3 .- re-
paration of such ci:-rts iecoi' s i. t a- it ',ale Jesi.ni
parameter in '."i-ich .. i. crt. condi tions are
incorporated be foL~d.







2 NACA ARR No. L5F15


It has been found that a suitable parameter for
longit-Ydinnally stiffened compression panels in the design
of which the transverse stiffness can be neglected
P.
is ---, where Pi is the compressive load per inch
L/I/c
of paiel width, L is the panel length, or distance
between su-pporting ribs, and c is the coefficient of
end fi.:ity ac tn ribs. The quantity Pi, which is
essentially independent of the distribution of material
in the compression panel, can be estimated for a wing
panel froc- the bendinS mcment on the winr and the thick-
ness .anC chod of the v;ing. The length L may be fixed
by. the presence of sucl installations as fusl tanks or
armament or may be arbitrarily assigned for the purpose
of arriving at a trial desigIi.

In reference 2 buckling stresses were plotted
F.
against the paramleter with slightly different

notation, to form- th; bc-sis of a theoretical study of the
efficiencies of vai':J.s tyres ao stiffening elements. In
the present papei' t5 .r. me paramieter has been used as a
basis cfr th-e repar.l._ l n of desi-n charts ficnc extensive
test data on 24.-S-T a' ." ."mn-lloy Z flat co-npression panels
..;Ith lorn.it.dinal Z.--rtion ctiffeners; the data were
obtain'eo from refer .e 1 and from additional tests com-
pleted since publica- ':r of reference 1. These charts
maLke nossible t'he c. .-- of Lhe igh!.- st panels of this
tyre to conform to _e range of dei:-. conditions.
An apper'li:i is press. I .f in which th r--7 zeu're followed
in preparin, g the ci.-.:". front. taot data is described and
Pi
the method for obtaiin .g as a natural parameter

against which the average stress may be plotted to obtain
a direct ,-easure of structural efficiency is developed.


Z'TBOLS A.JD lEFPTINTIONS


The sTb, .bols use- for -he principal panel cross-
sectional dimei-.sicns .r- ine'ica ced in figure 1. In
addition, the following syrmfol3 are used:







NACA ARR No. L5F15


Ai cross-sectional area rer inch of panel width, or
equivalent thic:mess of panel, inches

L length of .anel, inches

Pi cor:pressive load per inch of psnel width, kips per
inch

Ec modulus of elasticity in compression, ksi.

c coefficient of end fixity as used in Euler column
formula

k coefficient in formula for local-buckling stress

p radius of gyration of panel cross section, inches

T nondir.ensional coefficient that tales into account
reduction in effective modulus of elasticity
when panel fails as a column beyond the elastic
range

acr critical stress, or stress for local buckling, ksl

Ca average stress at column failure, ksi

Omax average stress at local failure, ksi

Of average stress at fail-.re for any panel, ksi

The average stress at which any particular
panel fails, Ff, may be a local-failure stress, a
column-failure stress, or the stress for a type of
failure intermediate to these two. Failure by twisting
of the stifferers is included as a form of local failure.
Because the design charts are based on actual test data,
it is not necessary to make any distinction between local
and twisting failure. Such a distinction, moreover,
would be at best an arbitrary one, as the two types of
failure are interrelated in the case of stiffened panels.

It should be noted that che local-failure stress oiax
which represents the maxnimu-. value of average stress
that can be achieved in a Liven cross section as the
panel length is reduced, is an average stress at failure
and is not to be confused with uhe stress for local
buckling acr, which does not necessarily imply failure.







NAACA ALR 1o. L5F15


The term "iccal buckling" as use-d herein includes both
bue'-l1'.n o" th; s-in iand baJckl1 ii..i of t-he stiffe-.ers,
bec-.Lie neith. r of these elements; can bucicle without
exert-ng n-.menints cn, ard thus c--L.sing defor'r-ati.on of,
the o;her element.


F _ST'Th CHImTS


E.esin charts for 2,3-' all'/.:i-.n-allc fl!-it com-
pression 'arels with lorlr.it.udinal '-sectiln stiffeners
are pre.,entef in fi..j.u:es 2 to 5. The., rrocedLur" used in
the preparation of h.icse c'irT-s fro'i t3est d'at'a is
descr.itei n t'; a: -r.-d. V2.us 1of A l.'ts, necessary
for arrivir.* at a l e.l desPln, are driven in sables 1 to 5
for a wide ran-e of dQI'.sion ritiac.

In o-der to show t~"l jl .xuhm J-t..ess.-.s att'.nrable by
the uI?. of Da:vils of tl'F ty;: e to wn-vnch che charts an-ly,
envelopes a re ind late by t:he r.3..-ed 1 ies fo" each
value of the ratio LL/t in fiC-.urea 2 co 5.- 'iess
enveloc s have be( cc.mcrcd (fig. 6) to :-ive the ov;er-all
envelopes for ;he four values o: tl ratio t.i/t-. The
values of b3/tS andc b--/t nesd j in crie e '.at a
panrl will develop che stress "rndi zted b: an enr..loCe
are also i'iven in figure 6.
ri
ihe design r-ar:;neter -- agai t which stress

is plotted in figures 2 to 6, cc: .rises thle Q ir i pal
design zc,,it'.n.rs: the ccm'cressive Ica1- r er inch of
panel with;, the le.?th of prnel, or dst.ance between
sup- rti:n ribss; and th'- coefficient -f end fixity. Iie
most efficient (l.ightest) pa-iel .for: a gIlen combinaticn
of these con iticL:s is J-L:t ranrel .:hic.i will develop
the highest averf:.e stress for t'-? r r-tic..lar val.*-
i-
of



rn.-c ci' i-.c.al proportlr s. '11 .I-h. ch-:ts have buen
1--1
drawn for a value of -_ 0.4; 1L is s'-.own 1.n the

a.-r ndix (fi:-. 17 to 20), '-i~'v'.'e r, t-h.at curves
bF
for b- = 0.5 a".d 0.5 .wold be .'. close agreement
't, -;= 0 3 n








?TAC rj p:P No. L'P15


by
with h'e .c. urves for O-- = O.1. The c. .ares .f fi-ures 2
l
to 5 .lay, therefore b~, -r'lit.r .vith re na'bl)e a 3.'acy,
for -iy 'ile od ta ,, .j ..wes n I .3 end. 'D.R. The
available LCot data seere .o indicE.te, ..ore,'6er, tLht t.e
most ef'Iii.ct ue of mater:-.ial .;j11 be realized if a
ri'op-rLicon in thls .:ace sel ccaed. (.3e c-?endi i.)

'-Te short hior:zo'Lt.al liins cu.:at ir:ter-a' Ct t'he curves
uf fi ir:res to n. cate-, r f.r I-CI *.:-,no cross section
having aorocia .e local oic::-lin:, t't st-'es. at which
this buci:lling 3c.-' ra. In hi rt hi3ej 7r' is :trass is
taken as c'-nt .a-, hih-, t-i ccinO'2C S3i. ve st-1inr on one side
of' tlhe skin c r -..c- stfr:,1 : wj3u 'L:-_ 's to be reC' ce.
with incresin q c.ad. Thi- ae".:.itio:I f bucl.ing is
convenient for str,.s'c1.l 1 ..estin f"ou!. the SLJi,'IpOint
of aercaryn-ic sr.octirness, a.'-iprcisO c le uci lin ; probably
takes place st scrsssis son-ev.hat lowvr than t.h.se i:di-
rated on che cht'ts. Tt ''111 be niotd that for some of
the lower value cf tg/t and ';;/t'; no bucrir.ng stress
is slhov.n. I.Tr L-.ee c b.ses, Jhere v-ill un.3ibted.ly be some
brcx;ling ,but pres~uio- i- \:ill co.-?r a 't s strs coin-
cides:,; wit or .l;:, v.,- sl '.-.'.c b.etl': t!.e failure stress,

.I is -uint-" c';: that for -- = .79 and I.CO
;', tcS
(figs. 4 :C 5), the cr.'v,? fi-r "alu-.s cf 4- = 25 3iG 50

hve v.een oht~t.iec entirely by:. e::traooiati'mn.. These
curve-s should therefore be user-l ijth a ce-ur.in degree of
caution. .f fe.' ci]heCi iests pad:.- sine th: ':re-arL'ation of
t...e chart, 1-o.'ever, r Indicate tc-t L L:-. cur'v s ill1 in no
c ,se be m ore than 6 ," rce.lL .:n.or:serv.tive. L. all the
cteh3r curv.s, it is belisv:'. that Eany r:,o- ;-servatism
t-at a.;ay,- t:'. recent is cf :.uch m..ll:i rnj.kgitude.
n.iscusJ'..n o-' t-ests a.nd test ri-nels.- In order that
Ithe ..sign char cs ;, e .: r .. .., it .s necessary
tc. n-': sm.ti oi 'hs i; st r inels ca nd the tmst results
nJ w.:.ch the "ecrn charts *re h ed. ThD etalls of
-thel se tes,;: :re U-scr lI:ed ji r-efrc nc- 1; some of the.
...rtt:ienrt in f.r.- ti on :e-? c :.c~. -1 r- th a sts f I11 '.i :
rhe test panels ccrnsisso.d o si.: stiffe. ers .rd fi.ve
bUe3. The ounels r=re te3ted fl t-ended and without edge
su.pp,'t. .rixit:y coefficiert o.' 5.'75 ~sa3 u.sei in
rcduc.i'q.: tn.:. tas" d.it-.: for arplic-. rion to .ma effective
pin-e~n-ed '1nrgt. The average coi..pr'sJiv3 yield strength
for :h.:. material of "i'ich L-c ta~ct pa,'els :'cure crstr-cted
Jra .about .Ji ksi: th?. minriiL;- .vi'.'ld stren. .th, abo'Lut
41. ksl; and ths .ia::i..u'7m :, Id sti'-n th, a':Ji'.t .3.5 ksi.
T' e ri-.-et s -3l: r -... t--r'zul.-: :rnd ..cr,? d ivi1 b" h- t







6 KACA ARR ITo. L5F15


1A'12A retho-1, of inse-r:.r-,, a flat-, cr d r1i" t from the stif-

t" U "D .. .' '' 1 ? :d L ;L tue ...' r
pc:' -... o. 1 .. .4:. T iL .1 .- -'- ...', .. .. C L..J.42.7AD )
andr ..c. o": -i., 'e z -.-j apCl] i s tnC icat. d b.y .he? following



t- i t

t. I 1C.0 1. O

.71 I 12.7 I 1.95
i .,j 1 r;
1.7o 11.7 1.95

Bc.:.use J7 c- '-.rssiv ;-.zc strnr'tlh of sti 'fener panels may
be aIffe J : tth c-ize -rnd jpacing cf ;he rivets used
to -..ttazi s tit'en:r t- skin rifrenc, ), the rivet
at '.:.chm.. t *i' t 't. : ui"'Il ?en.t to CL.t in,-oicatcd 'by the
fo.ri.-e rinL t .fe in c r.r.e: to .:e surle cf reaiizing the
str eng i3 in;.:.cat i-Ly .he ,-It: ign charcs.

-'"-.,' 0. ._.i, : C. H... :: EX..-9 L .ES


i shecL mTater.i,-. coul,..i be o':t.in'?d in any desired
t'-.ickn'.:sc ai if no :Secial li-.italonjs were put on the
d.ssign, it .joul-1 .t silificic-t i:-iely to find. those pro-
portions that woula ive the hi,-hnst stress for -he
--^
gri;n v_.luc oif -. Fecause ce:'t-:in limitations are
usi.all-.' inrpo.:ed, '.ovV r, t-he stt xct.uie that represents
the b.-st' coi,..ic..iie of .11 -c re 'Z irere.nts m-ust be chosen.
The uu:.ul. .l.aes in which alurinnL.-alloy sheet is
manoufan ctur--d. are s,.' i ,-,t if t i- I cur ratios of t" /tS
in fi 't ?3 3 to "6 re a- liC. c ,.nsonti vei-r to a p-r-
ticula- : .- E.a:g tr.'-2 ":-1' Ltif' r ,; -- that r silt
will g;crcnril; b coneicutz.-e 3 C:n. r:. ages. Interpo-
latiorn l-etrl.-cn the cur'.-es of t.jo consecutive charts
(iigs. : and 5, 5 and I, etc. is therefore unnecessary
for most oirctical pu :.-.oses.

Th-e particular prccedri.e to be used in obtaining a
desi-n from the charts will cer-ondu on: the nature of the
results desire. Three possible methods are discussed,
and examples are given of designs obtained for a given
lc3s intensity and thirce differ-ent lengths by each of
the methods.







NACA ARR Ho. L5F15


The dist:inguishing features of each method are:

Ideal design

The method ftr ottainina the ideal design gives the
lightest panel that could be obtained if Lhe designerr
were not restricted to the use of standard sheet gages.
The design is obt.taned by use of the over-all envelopes
of figure 6 only.

Short mithcd

The short design method provides, without lengthy
computation, a near approach to the lihttest panel that
can be obtained by ,se of standard sheet gages. The
design Is obtained by u1se o.f ;he envelo.pes for given
values of b3/t3 that a;-ear as dashed lines in
figures 2 to 5.

Kcaximum e ficienc r

The method of desi.r inng for maximiti structural
efficiency gives the li.test r-.nel that can be obtained
by 'se of standard sheet ga:es. Tli- de sign is obtained
through a complete stufl- cf thle indiidual solid curves
in figures 2 to The riethod is somewvhiat lengthy;
examples have been worked our by its use, hov:ever, to
serve as a check on he s-,crG method, so that that method
can be used .v ith confidence.

Each of the three methods is --iven as a series of
steps for reaching the final designs. In the method
for obt-aining the ideal desi-:, ti-h detailed computations
for the four values of t.,/t included in figure c are
given for L = 10, 20, and 30 inches with P, = 5.0 kips
per inch tjnd c = 1. In che o-ther two '*etho-is, the
detailed computations a.s- given onl .- for L = 20 inches
t.,o
and = 0.79, aa3sin with Pi = 5.0 kirps rcr inch and
c = 1; final results are civen, hocvrever, for the comple-te
set of examples considered in the .isc.ission of the first
met-od. It is assumed .n all cases that a skin thickness
of C'.C14 inch is necessary in crde., to comcrl with other
design requirements. value of by/bn.; of 0.4 is used
throuh31ut. In arriving at rL-e final desi:ns, no values
of :he dir.c.rnsion ratios outside ci .... ran-g s cov:rE; d by
the charts ro grive.n conliderAtioL.







8 NACA ACR No. L5F15


:.nt'rod ..cr obltal-nIr thje il- design.- This method
consists of r.ic.in^ fr7o,-. fi, ure b t-he optimur. proportions
v d Jthe stress a:Cn co:.-utinS from these the &ctual panel
&ir:ensions.

The values 2nd cor. iuted qu'ltities for the condi-
tions -areviously mentioned are given in table A!nd are
referenced to the steps in the 7ollo.ving procedure:
Pi
(1) Mor.pute --.

(2) Fr'',: ie curves :of fi, r'e 6 pick off for each
value of i/t t '.--alues cf bs*/t b.'/t.-, -nd Cf
corresron-lr.g to the value of ,

(3) Pick f'or. table 2 the va&l.-s f Ai/t for
b.
the ratios Ceternined in step 2. (If = 0.3 or 0.5
L .... "
is used, tab.le 1 cr table 5, re'oLecti '.ely, should be
used instead of table 2.)

(ix) '-cr.:.te




This'3 Tr'r,.ila is based on :he equality
Pi
Pe = --.1i

(5) Cc.irie

t tV



b,-
bs = t/
ts





T' "_ proced'r. results in foun" ce.si.rs for each
length, corrosrr-n. .nC to t1h-.e'c '.a :l:-3 cf t,/tjs, for









I..AC. T, ,' o. L.TF15' 9


the i :-i ,i co:;'it-ions: ('-e ,.e "le i] .) rThe- values marked
v.it: f:o '.rncte a in t: lb -, r..!,i- rt '-'-e c'i.s n as
ap'io3h-.rg '"io-'t clr.el1;v the "siri:; condition of
tS = 0. '. ...IC :.; vt.e:e v:.1.-s tL- rcl'ore give an indica-
tion o- .he r,'-crort.;.cns need>-,1 in a practical ,design to
mu'tn t:he e"'.e sigr r-qiren.prts .:Cst efficiently .

Th.:- resulin ces:i ns a.; s'..'i .n the ide-al designs
at t-h cI:r's of fi;-'3es 7 t7'o ', SC with bar graphs of
the ave;-',e stress at fa-.iur-e :nd T::e buckllin stress.
The bu'!-.:inr stress for each -;sS.n was cbt-rined by
int.errolttion fro.-r the short '*L..riz. tal lines for 'uckllng
in fi=L'r 2 :.o .. IIn srme c,3es .'n ::l'ic. failure is ':,
colujmn ,action, t-LI? ;:u .:ling s-'reJz shown "y ..'iCurs 2
to 5 jill be ,iac- tha tsl -: fri "Ire stress for Lhe
designs rbtai.r.ec. ..i':- never i ls -erence O.Cc'r.1 in
te p.resen..t e:...- i, the Lbu1:'. in. stress is shown equal
to tlhe failltj r st'c s-

Short r;ltho'r. -r o:'bt tn:,:i- 3. .raitic al a'esi:: .-
The sh, ..t Ce. c..- co si sts ,. 2 ,.i.., ;:L-.; c.: .Ch 1 .'alue
of b.r,',, :ui the cc'.:'--sron ".. ess for ee.ch value
of b i3/tS ": -r t'Le i r-:i '.i. e:i '?e o':,-s of figures 2
to r a:.d co':-*tin. r:, ',- ; e-e allies the actual panel
dime.ns i:r:s. ranel czi j.ns t:-at e.::'loy st jn.li-T'd sheet
gages are thinL selected 'fr-' t" .. various designs obtained.

The- values and computed quantities for L = 20 inches
t:j
and = 0.7 are given in table r and are referenced
ts
to the steps in the following procedure:

(1 Co-ute -- .
LAV

(2) Frc;i the curves for a p-.-: cular value
of t;,/t3 (in this e::-.i-le, fig. Ij for -y = 0.79 is
us-E.j r;i.ck.: off fo: each value of :/t the vc-lues
of b-y/tU; (:,- interpol-ation aloni the dashed envelope)
and 1- (fL'or. the envelope) corres.ondiinrg to the value
0i
L/.' 'o

') Pic': fro i table 2 t.-: values of Ai/tS for
the ratios -t-..r.,:.'mined in ste: 2.







10 NACA ARR No. LSF15,


(t) Cmripuce

ts

tS

(5) Plot by/tb;, t3, and -of against bs/t
for the particular r value of t./tS. (The plot for the
exLmple being considered is shown in fig. 10. ) Tabulate
the values of bs/t, .t ,/tv, and of corresponding to
the point wherA tS equals the specified value.

(6) Check computations by picking from table 2 the
value of Ai/t3 corres-ojrdin' to the ratios tabulated
in step 5. If all computations and plots ars correct,
Ai
Pi = of t- ts
i f t g S

(7) Compute
t-V


bs = tS
bS
bW
b = tW

(3) Repeat steps 2 to 7 for other values of t\r/tS.

Like that for the i-eal design, this procedure
results, for each length considered, in one design for each
value of 't/tS. It !,;a,. not always be possible to find
satisfactory designs under the conditions imposed for
all values of tw/tS. (ITote lh-t no de3igns are given in
figs. 8 rnd 9 for 11 = 0.51.) All the designs resulting
ts
from th' use of thir short method utilize standard sheet
gages and meet the require.:lent that tS = 0.064 inch.
Th: choice of desi~ now der pnds on arriving at a suitable
cor 'roc-nse between 1.1 t stress a~ l1 wide stiffener spacing.








'!ACA AR?. No. L5Fl5


If th-e irevpntion cf bucklin ,:. i;:r lci:'.. is considered
ir.iportant, ,chen te ba'2.:lin,- st.-e s -u t lso be tal.:en
into a uccucLf in :,.kin? a choice.
The designs obtained b- car--linr out the foregoing
procedure fr-i the se ve'l v.ljueI3 cf L ain, tw'/tS are
shown .s che short-method .desig s.- in figures 7 to 9
alcng v.lth b;.r g-rphs3 1 tin: a er' stress at .falure
an b .t intJ .. str:-s..

i.,lthod of drjsigning.- f r .-ma-:ir'urm str'i:'i:.ral eff .iciency.-
The tn,-;;; m r n-ef iciency :- t- cun;i.: .s cmL- i-! t e
tilc':;i:esC3 requir.edr, as b;3.,.- i.3 rij. for each value
orf b..'/ti -;d selec'-i.cl th.: &;s'lr..: for which the skin
gace is equal -l th. t -.esir ';i. '"'.e cro.?cedure results in
a series of nosit'-le .sign. for C-,,n value of tw/tg,
f;roTm 'vwich t-cse : esi Inst t. pr .v'.'le the hi .iest average
sires.s ot faillur cs2n Ie se '?cted.

The values iand computed quantities for L = 20 inches
tw
and = 0.7'9 are given in tale 6 and are referenced
to the steps in the foll.cv.n c proceilu:'.:
Pi
(1) Compute / .
L/Vc

(2) Pro,: the curves for a 'Articular value 6r tw/tS
t;r
(in this 3xr.L.ple, fig. l. for 0.'" is used) pick
ts
off for each value of by/t and t.3/t the value
Pi
of r o correspondrMI to the value of --
L/A

(5) Pick from table 2 the values of Ai/tS corre-
sior.~in to the ratios used in step 2.

(4) Comrpute

tS Ai


(5) Plot tg and f a~ai."t b3/ts f'or each
value of b ,/tWy and t -/t:. Plot the Particular value






12 NAtHA ARR No. L3F15
Nt
of b'-/t at the value of bt./t- for which tS equals
the s -,-cified value uand m' l: e value of stress at that
value of b-!/t The plots of this s.;cn for the e;.:n.nle
lun:r cons eration A'e giver in figure 11 &.s trie short
lines for the several values of ./ty lIacted. In
order to avoid unnecessar-" cor.f'usicn, only slcrt rorticns
of the curves, except the curve .Cr --= 2., are s-own.

(6) A.f'r step 5 has been completed fr ll the
values of b./t ., draw curves of stress a. J of b/tv-
agai nt bS/tS through the points d~tei;rn!.-Ued in1 stel 5
(heavy curves in fig. 11).

(7) E-Lch of the curves drawn in step r.ep1enents
a series of designs, 1 of whil have the- .-quird
value of tS (in this case, 0.064. in,). The :.1ix:ir..u
point on the curve of 1 Inlicates I- d"in icr
maximum structural ef'-ciency for ith par-ic:..la: ':'lue
of tw/ts ;. Lot this r..:'::1.n- value of the value
of bs/tS at which it is rEca-'., and the v-.lu'
of b./tN, which can be p'.c~'-, from the cu.r'e of b.v,/tj
r.i p. st bs/to.

(8) Check computations by picking i r:! tole 2
the value of Ai/tS corresci- ,!. to the ratic: sZel3cted
for maximum structural efficien-;,- in step 7. T' all
computations and plots are correct,

Ai
Pi = f -S tS

(9) C- r': ute

to

S tS
b, --1 tS
b"i


(10) ReTat steps 2 to 9 for ct.-itr values of t ;/tS.








HACA A.rA ;i0. L[515


2his p'-s cedu.'ee resl.,its, for each 1-.rn.-Lh considered,
in cne oes'in for cvEach 'value of t;,/ts. The choice of a
design C.eTrends on ari-ri.-in- at a Jult'ale coam-,rcnise
between high stress and -Aide .ti.rfe.ner spaac 'l., 'with
possible con.s:der:-ation for 'the ':ucklin' stress.

The designs obtained bi- car-;-viinI oIt t';i- foregoinZ
prcced-.2re for the several valu.Js of L and t,,,/t.- are
shown as the ms'iximum-.- fcienc- ,.esik ns in figures 7
to 'C along .1 th Z, r 3 o7L jhs of- the -. ver..-.e stres33 at
failure an7d the b,-ckl. i st"-.es3.


T-S?US'.Il..


?Fiures 7 to 9 '-ror'-ie a .isual .comparison of the
desist s th t re'Ctr frr,:m .is-e c'" t he thre-2 methods pre-
ser.ted. The short :.e-th.od cf des i-: -.i'-es in everI case
an ave .'a. z. L-' s :.t f.:i_1u. .' v-. close to i-at obt ined
. s;- d.sinini, c Ln Lh- b.si-s '" n ...:r.:....,; s u-rLctural erficierr..cv;
tlhe .-'jl lin :, tr T..... r 3 -i..e c es s i'ia l t
,C,'et'" I-. an .-1 ,'t- r th:- ira Lr'.:r;,i -c f' l c- : c: pan'l.

he th. tr he es i cot .-r.'.]. "- ; -' shor-' ri: thrd or
the de.lign "OE r miaxi:..,L ef Ifl i. n?. is sole jd., the es
design rcr 'i = 3.' h:-.ys ._r i-nch, :,n th' _.:-sis of

stress, is obtained at L = 0 inches .ith -- = U.51,
t.. ts
at L = 20 inches with = :., ai-d at L = j' i.incI]es
't-. L Q

tS
envel ope, which _A,i "'.es The lightest .les'm, is that

for -- 1.00. Thic .p:.,ent .,ntr-iction results
t
f'rr. .the fact tih r: ir -:Cr;-:.ln o't, the exa'-nles a skin
thickness of o.j.,: inch wa3s zpecfied. in order tc

reach Lhe curve for -- 1.'1. (f-. ,), a tud7 of
-' S
tale shoas tit t in -1L ic' iness ..'ould have to
"e .-. -... inch at L = 11.. in h:s, 0.C041 inch t 2u inches,
and A.., in h : C i:-.cl-es. .or c ve--, the stifji" -ner
snacin s o,", d&3es r ns h...''-i suzh :':.all skin thic.ne sses
are ver;. sim il. (.e .* .) Because of imita tons







NACA ARR No. L5F15


on s!cin gagcs and Ftiffener spacings, therefore, it is
frequently not possible to reach the envelope values of
stress and hence the lov.est possible weight.

FiCures 7 to 9 show that the best panel (that with
highest af) obtained at each length by the maximum-
eLficiency method does not -,uckle until failure or very
close to failure. The best pa-nel designed by the short
:-.ethod, although it m-a, not have quite so high an average
stress at failure as tle pmxi.um-efficiency panel, also
does not buckle until very close to failure. This condi-
tion has been found to hold true over I.; wide range of
design re uirements. Tt is therefore e'.ident that over
a wide ranje of conditions the :q.irntenance of buckle-
free s'3rfaces does not conflict ;wth the achievement of
high structural efficiency. The simultaneous achievement
of boi- these senrs bt- use of 243-T alur:inum-alloy panels,
however, apparently req'Liros closer stiffener snacings
than tl ose now in comurnn use. For example, the maximun-
elficiency desi-ns for Fi J .0 kips per inch anc
t~ = 0.06. inch have the following spacings for the
three lengths:


(in.) (in.)

S 13 2:,0 1.79
20 42.1 2.69
30 40.0 2.56

C0011CLUTID IG REP AR KS


'Charts are presented for the r inlmurn-weight design
of 23S-T aluminuRm-alloy flat colnreass:-n p?'rels with
lcngitvd.linl Z-section stiffeniers. Frcm exr-:ples based
on the use of these clha.ts, it is concluded that, over a
wide range of design ccndi tions, the maintenp.nc, of
buckle-freR surfaces or longitudinally stiffened compres-
sion p-nasls does not conflict with th-e achievement of
L.i~ structural efficiency. The achievement of the
n2xlimum possible structural efficiency with











2LS-T a'l.i':niTrn- lor 3 r pn-els, -ow':e'er, requires closer
st iff ,e r 3" inC-c e:-:'. tIhose r'" i'i ,2 C on u1 se,.


La.ngle" i"'qnri "l e-.e-.:'ti-,. t ? l L.nLtcr-atory
iltior.al Ad.-:is. r. Co L ';itte f'or Aeronautics
Lzngl ey F '1, 'a.







.IACA AFr ;no. L5F15


APP.F'DIX

ME2K.T O'' 0? rTPAEATT''I 'P r'ESTI, C^.'T.S

PFi
D'evel :e'ent cf design nar?.ie ter -.- As stated
___ _L/', C
in the Introduction, the average stress darelope,~ by a
lonit, l .i'.nill.y sti.ff,.edc. compression :.rnel I as direct
nmesur.e of the structural e. icienc-' of the Ianel. It
is further L.roct.l.t out that a suitable ces.in iarm.-reter
g.inr t which -.:.. aver- 3- stress .-Ir be pcotte.-
is --- where t is the coM:pressive 1oai 1 er inch

of 1.r nel :dth, L is the panel length or .-ist.-r.e
between su:,--orting ri.-, and c is tho corefici nt of
er.nd fin-it at the ribs.
Pi
The folo.i,: de. ovation shows hc t-e ? araj.eter --
L/v'
evolves from the usual column foiulula:

The column fo-rrmi. may be writt-'i

iTE27
oc2 (Al)


pv 2

Tlltiplication and division of the rifht-h.nd slie of
equation (Al) by Pi2 gives

p2_i \2
Co= 72TE c I.A2)


If the stif'-ene,-j panel is to have a str:t?;,gtl just equal
to tha t requir.'.i '.y the .si -c conditions, i --
arad eq'ilution (A2) r.:- r.l-.refore be writtene n

p =
c cc c t








'IN CA A~r' i: L5 '15 17


or





which may 2; v.ritcen








Pi
_-e vintity Cn in E iui3ri-cn (..5) io fixed for a
:-i\. *r- --1 I, :.is i *3 e t-lj :-n-i 1 be ..e-en OC -adj-if T,

exc3 ,' : fxc.r .'1g..- 1-e :-ane effect The quantity --
L/A
is t.':e e..,-n a-ra.!et'. r '. .." 1- sionless and is
deter:.ined I:'- the reelative r t'he: ch-'; the absolute i:jien-

.3c n f.3 a -rel,1 A nllot of %C against -- is tiierefore
deri-nient on the ratios of the various '1- Jicrsions
*and not cn t!e absolute values X- the -ci.ne.'sions.

Determination of aver.i stress at local failure 0 '. .-
Frorn ec:u L t ( ; .:' .-? .: -" .' nit,-er .uit rrJ l
Pi
cfr rin value of on the basis of column strength

ar.parently is that panel which has the highest value
cf p/A I Charges in rropcrt l.,rz that result in an
increase in p/Ai will, however, generally cause a
r'ecre-..se in '-he local-failure s'renith of the rFinel.
(Lcc-!l failure as .used herein includes the phenomenon of
tvisting[, rhiclh is ii realitY: only a fcr.n of local failure
that oc"cu_- .".hn the lateral b.?nr.'nI stiffnPss o'- the out-
staniirnr stiffener fliiia- is relatively: small.) 'he
,optii.i' iriel foni a particular anrplication is iven by
the ',;r.pror-.lse of column .s, local-failLrre strengths
that ,-. l.es the hi-hest stir.ss at the given value
of








MACA ArR No. L5F45


Ther value of 'e a'.era]- str.j.ss t local failure oma
is diff'ic-vit -on d-te mine theoretically. Certain test
data are aval)...ble, boaever, fro.n re.fercnce 1 and from
additional tests c mFletec? since the publication of refer-
ence 1. Those data that wer-- cbtaineJ. from the shortest
panels of each cro3s section .are s.m: larized in figure 12,
in .hI ;h o.ma is plotted a3gLnst taj/b,; for various
values of t.v,/tg 'rnd bs/tS. The ratio bw./t.- has been
inverted in this pict in order that the additional
tA, b,"
point Ucrxv = 0 /when 0 = might be used to
ht t
aid in fairing curves chrouL th~-. test points. The plots
of fi-"u..'e 12 r:.l.ke D-O.s_'ile .n :-.te'nclticn of may
botw'eeoi .:est :.-int.s f r' nr .. :--i .te values of the
ratio b- t Ev. E., ol.i. s -- ; I y :picked from
theb cur..-,s of ri1 .-_Fj 11 Ag ._njt ts, b, values of Omax
were :i c determiri--:' for int ~?ime_.iate values of bs/tS.

All th3 data cl,. i n i 'ur', e 12 :.'e for value
b-. tF
of C.. Tezt d:iar for -- 0.5 and 0.5, how-
b ,'. .
ever, -.Vere al7o nmpl.yd as a i..'i.e in fairing the curves,
and the ir es 'will be st c.ni c. o- res :.nab bly accurate for
any Vaiie I ,:.`, e ee. '. d O.eA .:

;er-n.uiition uf stress -'c' 1'-ccal~ buckling ac.--
If th "-znel did not o'1 e: e oc e :mi:.lu>r the
theoretical results thus far presented, usd in conjunc-
tion ith values of Omax, wculd be -.ufficient to
Pi
construct a design curve of Of a -inst for any
L ''\,'c
rael. -. t:i-ocal curve for -'nels that do not buckle
before ra~il ,: is shown in figure 15. TiTrles.- the width-
thickness r. ios of the various plate elemr-nts of the
p..-el are small or the panel is relatively Ic.ng, however,
there, will enrerally be some local buckling befo,,re
failure, 'ihn -hi3 buc-:lirng ta'.s place, the cr:,ss-
sectional i-,ncnt of inertia of those "anl is rccduced by
:e;- rir-sence of ineffective areas; the original curve
of column st-er.,th therefore no 1-nger api:].ies and the
po'nt at which bh-.tkl?. -takes pla.:n;, must b, connected
w'th the line foi- I.ocal failure .-- reans of a i. daced
curve. A typical curve, :.->justd for the effects cf
local tbu-klirn, is shown in f 'u...L 14.









NACk AL.. I1o. L5F15


The foregoing discuss ion show's that it is necessar-y
to know' the stress at which Lucking takes lacce. Data.
on buckling stresses 'rom reference 1 plus additional
data now available are therefore plotted in figure 15
be
for = 0.L,. Because the measured value of b/t for

the element (skin or stiffener wob) that first showed
buckling in a test ranel was never in exact agreement
with che specified nominal value, the observed buckling
stresses from reference 1 ,iere corrected for use in
figure 15 according to the follc.ving forrrimula:


( -t t :I (' as ured
corrected or'cbs r' ed 2

Nominal

where -1.e v.:1-3 f b 'c is lthat f'or the wi' of the
stiffener or for the st:ln 1:etwe'.en stiffeners, deperning
on which of these ele;menrts first ave evidence of
buckling. This correction fo.r'ula is based on the fact
that, other factors 'be:tin equal, the cr-itical stress is
inver.-Iely proportional to the s'iqure of the width-
thickincss r1tio. Io *ccount is taken herein.of the fact
that this rclatioshi, is not enti'.rely true for stresses
beyond the elastic r.-uige; it is azsu'ed that neglecting
this fact 'will ha"e no significamint effect because the
total correction is relatively small.

'The method used in fairing curves through the test
points in figure 15 is as follows:

For the horizontal portions of the cures on the
right-hland side of figure 15, -the skin is pri'm-arlily
responsible for the buckling; the ord-,rtes for the
curves in this region are deter! ined by. draw-ini average
lines through the test points. i.s the value cf tA I/b'
is reduced, however, the responsibility for the b-uckling
shifts to the stiffsners and there is a reduction in 0cr*
Tn the absence of adequate test data for l"i: values
01o t-\;.;;, certain theoretical cons i-erations are used
for .1?termninlnn t:he val'.es of ir in this region.








;ACA ARR No. L5Fl5.,


It is possible to describe certain limiting condi-
tions that determine curves between vwh.ch the correct
curves nmst lie. As the value of t;i/bW approaches zero,
with all other dimension ratios held constant, the skin
ten-s to become infinitely stiff by comparison with the
stiffener and the stiffener approaches a condition of
co:r.plete fixity at the =,dge whsre it is attached to the
skin. This condition of complete fi:-ity represents the
uiper limit of buckling stress. The value of k1, the
coefficient in the formula for local-buckling stress
(reference 4), when aprli7 d to tle stiffener web may be
taken fcr this condition as the geo-mitric mean of the
value of k for the web of a Z-section column
bp
with -= 0.4 (about 5.77, see reference 1.) and the

value of k for a flat late fixed at both edges
(about 6.98, see reference 5). This valup cf k
is -,.77 x 6.98, or 5.15. The u ..er da:bed curve in
figure 15 gives (cr. for k = 5.15. The use of the
geometric mean of values of k to obtain the critical
stress for a plate with differentt restraints along the
two unloaded e ces is discussed and justified 'or prac-
tical use in reference 5.
b rb
V.ihen = it is a reasonable anda probably
t; ts'
conservative assumption to consider the *stiffener hinged
at the edge here it is attached to the skin. This
hinged condition represents the l>.aer limit of buckling
stress. The value of k for the web of the stiffener
mnay be taken for this condition as the geometric :mean
of 5.77 for the sLlinle Z-section and the value for a
flat plate .!in ed i'. both edges (4.00, see reference 5)
or k = x 4.00 = 3.88. The lower dashed curve in
fi.re 15 givcs Tr for k = 3.3. In the preparation
of the two dashed curved, the effect of reduction in the
modulus of elasticity for stresses beyond the elastic
range was deterin.lnd from figure 3 of reference 6.

T'-i- solid curve on the left-hand side of figure 15
is drawn in to give a gradual transition from the lower
b
d3:h-d curve in the re:ion -.'1.,'re = toward the
tw t s
u-.( r da'.hed curve as t''/br.: ap.roachss zero. In the









i-'?.A AL.- :'IcO. L5Fi 21

b ,, bS
3
rego h e 2e the C.:ri a re '. aired in to the
.. t .. t 3
horizontal lines drawn c:hroujh the tIst rdints. A single
curve u.s cons id red suifi int for a.ll values of t- /t
for tlie lfIt-hand pFort1on of fi iure 15, because t.,e few
test rrjCints that were availatbe in this region indicated
that -the in.iiidual cures would be so close to-;ther as
to be al:nost inristinguishable.

Th.e ciurv s of figure 15, liie those of figiare 12,
were cr,:ss-rictted to Live bvckillig stresses for the
intermediate values of b/.'tS that anealr in figturs 2
to 5.

-Preparatih n cf insl c.iurves.- The rroi-edure used in
the M'e.ratin of tie final curv-es of fi.ires 2 to 5 is
illustrated in fijt're 16. an outline of this procedure
is a3 follo,.:s:

(1) iDrawV' c,'rv. for colrrmn strength correspo-nding
to the value of' p/Ai for .he panel cross section. For
the curves of this report, the column curve for
24S-T alurini.rm all':; wras obtained from equations (5)
and (. ) and table I, all of reference 7.

(2) Plot L-he values of stress for local .buckling
and for ioc.I failure ..f panel obtained from the cros-
plots ci the curves in fivu-res 12 and 15.

() Plot available test data and fair curves
between bucl:lin stress and local-failure stress. This
fai'in:; v'ia- dona first for those curves for whichh test
data 'eri-a available; tLe .eriaining curves were then
fired in a ma-inr consistent with the curves alread:r
estab is hd.

In a few cases (low bS/tS with high bw/ty) the
test dC..ta indicated t`hat the curves did not follow the
s:.octh. tran-ition bet.;raen column and local failure indi-
cated by ft:.1 e 16. Instead the curves tended to bend
over shrpply, in some c:ses even below the tuc.:lirg
stress given by fli'u-_ 15, and to follow very nearly a
strai,jt line up to the ave_-.:-r- stress for local failure.
No e:.-:xl.:nation is of'tred for this lince:c-nonen; the
avaiil -1le test data were -I.a- 3 as the sole guide for
fairin- thl- curves in these cases.








NACA ARR No. L5F11.


Torrelacion between cesi.gn curves and test data.-
The test data of reier:nce 1 as well as the additional
data made available since the publication of reference 1
are plotted against the parameter -- in figures 17
L/Lf
to 20. Appropriate curves taken frc1. figures 2 to 5 are
also drawn in these figures and good agreement between the
"F
final design curves and the test data for 0...
by.
exists throughout the range of the data. In order to
make it possible, if desired, to check the correlation on
bF
a larger-scale plot, the test data fo -- = 0.3, 0.4,
rnd 0.5 are eiven in table 7 in a form suitable for
plotting directly on the design "harts (figs. 2 to 5).
Tsble 7 :and figures 17 to 20 also make it possible to
determine in which regions the dJsign charts are sub-
stantiated by test data and in which regions they were
obtained by interpolation-or extra'clation.

Figures 17 to 20 indicate tlt there would be little
bF
difference in the curves for -- = 0.5, 0.4, and 0.5 but

that the curves for = 0.2 and probably 0.7
bW bF
would be lower than those for 0.4. The most
efficient use of material will therefore be realized if
a value of bF/byj between 0.5 -.nd 0.5 is used. It is
for this rcr.ge that the design charts are intended to
be used, although they are based on the specific data
bp
for = 0.4.
orbw .









NACA ARR No. L5F15


REFER ENCES


1. Rossman, Carl A., Birtone, Leonard hI., and Dobrowski,
Charles V.: Compressive Strength of Flat Panels
with Z-Section Stiffeners. ITACA ARR No. 4305,


2. Zahorski, Adam: Effects of materiall Distribution on
Strength of Fe.nels. Jour. nero. Sci., vol. 11,
no. 5, July 1913, pp. 47-255.

3. Dow, Norris F., and Hic!kana, iillisam A.: Preliminary
Investigation of the rAlation of the Compressive
Strength of S'2-c-t-Stif:'enr P -,niels to the Diameter
of Rivet Used for Attacl-irc- :-.ciff'eners. to TSheet.
1.ACA AD No. L l.oL, 190.

4. Kroll, ... D., Fisher, Gordon F., and Beinerl, George J.:
Charts for Calc.ilation of tl..e-Critica St-rass for
Local Instability- of Coli.:-.s Aith I-, Z-, -Lhannel,
and R.ectaragulas-Tube Sect._on. "Ti-A-A o..5 D4,


5. Lunidquist, E-uiere E., andi Sto.t'ell, Elbri~rge 2.
Cr.-t r.:al Com.r e essive Str.es for l' -It r;.ctau ulLiar
Pl1rez SIpor .-Jr aJlTCi: -ll Ead-s Lazd Il astically
rLestr aJind against .ocatiorL aclc"' .thbc Unloaded
E.se,. CA, n. No. 7, 1 ..

6. Hei r-l, Ge~rc;e J., a&d Rcy, J.. A' rt: Preliminary
.c ort o1 TEsts of CJ!-'r .Zl-. L.10r C I-, C.jel., and -'ection Thi -L develop -Lacal
ir.st-ility. '.,CA 2B Lo. 3J27, 0195.

7. Ter-nlin, R. L., St-ir., r. G., Hartminu,-L. C.,. and
1.Tolt, *.: Col'. m 3tre-nr-th- of variousou s Aluminum-
i/.IL. -'. Tech. I j.,r io. I, Alu ini. 'r res.. Lab..
Aluxinus Cc, of t-:. $.. _1 '.

















2i~Sgr0t N U4AN NO.
DI p
u".' A.4 'D "oDif n U.. '-m 1
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TABLE 5
VALUES AND COMPUTATIONS FOR OBTAINIIO PRACTICAL DESIGN BY SECRT MEbOD

P = 3.0 kIp/n.; L = 20 In.; a = 1; tg = 0.064 n.: = 0.79

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7

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TABLE 6
VALUES AND COMPUTATIONS FOR OBTAINING DESIGN FOR MAXIMUM STRUCTURAL EPPICIEHOT

[ = 3.0 kips/in. L = 20 In.; a = 1; t = 0.06k In.; a 0.79]


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NACA ARR No.


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-







NACA ARR No. L5F15


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Figure I. Symbols for panel


Fig. 1


dimensions.






NACA ARR No. L5F15


N


0..5 .- ;n- 0

a, .- ,


L. rj ,
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0
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NACA ARR No. L5F15


C
45 C
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NACA ARR No. L5F15


I It







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NACA ARR No. L5F15


2 f a
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NACA ARR No. L5F15


Fig. 4 Cone.


0 0
0

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NACA ARP, No. L5F15
NACA ARB No. L5F15


E iI >o 47

E 0
a 55 .9

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IsN '*Q







NACA ARR No. L5F15


Fig. 5 Cone.


IIO
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NACA ARR No. L5F15


tW
tS
0.51


idealn .0315
design f -.0618 J


SpFShort d .03Z
.51
M maximum .032
efficiency j .


Short .040
j method
.63 <
Maximum .e040
efficiency


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maximum -.051
efficiency


1.00 <


ocr


I 1 1 I 1, I 1 I 1, I 1 I L I I
0 I 2 3 4 5 6 20 30
Inches Stress, ksi
,:u*ri I OR i LR khlnr Cl

Figure 7.- Designs of 245-T aluminum-alloy panels 10 inches
long with Pi-3.0 kips/inch, c-I. and ts-0.064 inch.


I


Fig. 7


r


f


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Fig. 8


tw


0.63 Ideal
design


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Short
method

.63

Maximum
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Maximum
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Short
method

1.00 -

SMaximum
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0 2 3 4 5 6
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20 30
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NariTOWt lsoa~OT
COW MITTi IOR ALaWifUTI


Figure 8.- Designs of 245-T aluminum-alloy panels 20 inches
long with Pi-3.0 kips/inch, c-1, and ts-0.064 inch.


NACA ARR No. L5F15




NACA ARR No. L5F15


Short
method .040

.63

Maximum
efficiency .040





Short
method 51

.79


Maximum
efficiency .051






Short


1.00 <



efficiency .064

1I,1 i, I II I II I,
0 1 2 3 4 5 6 20 30
Inches Stress, ksi

COMIIITTE FOR NIROhaurTtl


Figure 9- Designs of 24S-T aluminum-alloy panels 30 inches
long with PI*3.0 kips/inch, c-1, and ts-0.064 inch.


Fig. 9






NACA ARR No. L5F15


35


bw



25

.08


.07 -ts-0.064 -
ts, in. _

.06


.05
32




Of, ks,

Design point,
bs/ts=43.3; bw/tw=Z6.1
26- -


24
30 35 40 45 50
bs NATIONAL ADVSl RY
t COMMIT FOR AERONAUTICS

Figure IO.-Plot for obtaining practical design
by short method. Pi=3.0 kips/inch; L=20 inches;
c-1; ts=0.064 inch; tw/t- 0.79Q.


Fig. 10







NACA ARR No. L5F15


40
bw
tw


t5, in.

.06


.05
35



30


ar, ksi
25


30 35 40

ts


45 50 55 60
NAHlONA ADVISORY
COMMITTEE FOR AERONAuTICS


Figure II.-Plot for obtaining design for maximum structural
ef ficiency. P i= 3.0 kips/inch; L=20 inches c=l; t =0.064 inch;
tw/t 0.79.


Fig. 11









Fig. 12


NACA ARR No. L5F15









0)o 0s



Q




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0
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0
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NACA ARR No. L5F15


$


- --C
4 -C

O -




Q) L


LL
L 4.-


C-

ma
-o

oO






Q) L
O 0
CL


Figs. 13, 14





NACA ARR No. L5F15


L- 20
.79
2- .51







ts
050

10 :T--: 7----- 5 ~\ -


o O.WQ-

NATIONAL ADVISORY .63
/0 COMMITTEE FO AERONAUTICS 0
o ,6 1 i *1.00
0 .OZ tw .04 .06
by

Figure 15.- Stre55 for local bucklinq of 245-T aluminum-
alloy flat panels with Z-section stiffeners. bF/bw=0.4.


Fig. 15








NACA ARR No. LIF15


4-
L


C






0

L







4-
C


0













L
Q.






co







O


bc
c









1-
L
b--
c'
.0











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-E-
c-







_E- ----- -..


Fig. 16






NACA ARR No. L5F15


bs=
ts


40- ...

20
I' o '


40






40 ....



0


---30





/ ---"-- 40
r r --/- -


0 p .4 0
Pi kips/in.
L/vE in.

Data f

Previous


Z .4 0 .2 A
bF
bw


rom reference 1 0 ..3
) .4
.0
ly unpbihd d.5
sly unpublished dotao .4


Figure 17.- Comparison of test data with design curves for 24S-T aluminum-
alloy flat panels with Z-section stiffeners. tw,/t4 0.51.


Fig. 17






NACA APP No. L5F15


40

'-ZA-


0
oQ-.---






20
0








20 .. .


- 30






--40


0 2. 4 0 2 4 0 2 .4 0 2 4
P, kips/ in b._
L/V in bw
( 02
S3
Data from reference 1 4



Previously unpublished data 4*


Figure 18 -Comparison of test data with design curves for 245-T oluminum-
alloy flat panels with Z-section stiffeners. tw/ts 0.63.


/,


I~


Fig. 18





NACA ARR No. L5F15


bs3
35
ts


0 2 .4 0 2 .4
PI kips,./in bF
L., -'r in.
(a 02
Data from reference 1 '0
4
e> --


Figure 19. Comparison of
aluminum-alloy flat


test dato v.;ith design cur.es for 24S-T
panels with Z-section stiffeners. tw/ts-0.79.


Fig. 19







NACA ARR No. L5F15











bs
t- 35
ts


Of.
ksi


0 2 .4
Pt kips/'in.
LVc in.


Data from referee


0 2 .4
bF
bw
a 0.2
S.3
.3


Figure 20.-Comparison of tesT doao with design curves for 245-T
oluminum-olloy flaT panels with Z-section stiffeners. tw/ts-.00.


Fig. 20
















UNIVERSITY OF FLORIDA

DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
R0. l BOX 1170116




GAINESVILLE, FL 32611-7011 USA











i.










.21




i




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