.
,: .;-.
m
TECHNICAL NOTE 3782
HANDBOOK
OF STRUCTURALSTABILITY
PART II - BUCKLINGOF COMPOSITE
ELEMENTS
By HerbertBecker
NewYork University
I
I
1
v
1
,
Washington
July1957
.
H
‘1
:,
#1,
. .
. . .
____
. .
TECHLIBRARY
KAFB,NM
Illllllllllllunln
OUbLbqA
NATIONAL
ADVISORY
COMWITEEFORAERONAUTICS
—
TECHNICAL
NOTE3782
HMJDBOOK
OFSTRUCTURAL
STABILITY
PARTII - BWKH3VG
OFCOMPOS~
EHMINB3
ByHerbert
Becker
SWMARY
The
localbuckling
ofstiffener
sections
andthebuckling
ofplates
witheturdy
stiffeners
exereviewed,
andtheresults
aresummar
izedin
charts
andtables.Numerical
values
ofbuckl~ coefficients
arepresented
forlongitudinally
compressed
stiffener
sections
ofvarious
shapes,
for
Stiff
mea plates
loaded
inlongitudinal
compression
andin shear,
andfor
stM?f
enedcylhders
loaded
intorsion.
Although
thedatapresented
consist
primarily
ofelastic-buckling
coefficients,
theeffectsofplastici@
are
fora fewspecial
cases.
discussed
RWRODUCTION
Thebuckling
behavior
ofsimple
plateelements
isdescribed
in
partsI andIIIofthis“Handbook
ofStructural
Stability”
(refs.
1 and
components
oftenconsist
oftwoormoresimple
plate
2). Structural
elements
soarranged
thatthebuckling
stress
ofeachisincreased
asa
result
ofthesupport
provided
by contiguous
neighbors.
Suchcomposite
elements
aretermed
stiffeners
because
theyarefrequently
usedto stiffen
a plateinorderto increase
thebuc~ingstress.A compact
stiffener
iS
described
as “sturdy”
whenitisnotsubject
tolocalbuckltng
andthereforeonlytheaxial,
bending,
andtorsional
rigidities
ofthestiffener
influence
thebehavior
oftheplate-stiffener
comb@ation
undera specified
Thedatapresented
inthisreport
onthebuckling
of stiffened
loading.
plates
pertain
to sturdy
stiffeners.
Thereport
begins
witha discussion
ofcalculation
oflocalbuckling
stress
of stiffening
elements.
Stiffener
structural
shapes
incommon
use,
suchasZ-,channel,
andhatsections,
havebeenanalyzed
forbucKMng
andcharts
arepresented
tofacilitate
buckling-stress
computations.
For
sections
whichbuckle
elastically,
failure
mayoccuratloadsconsiderably
Failure,
orcrippling,
of stiffening
elements
is
inexcess
ofbuckling.
treated
inreference
3.
Whentheproportions
ofa stiffener
aresuchthatitissturdy
with
respect
totheplatewhichitissttifening,
itactsessentially
asan
.
. — —.—
—..
.-
—-- —- --
.
.
2
NACATN3782
elastic
restraint
totheplate.Itmayassist
intheresistance
toload,
as dothespanwise
stiffeners
ina wingcover,
or itmaybehave
primarily
asa support,
suchasa transverse
rib.“lheither
case,itisnecessary
to consider
onlyitsaxial,
bending,
androtational
spring
properties
in
calculating
thebuckling
stress
ofa“stiffened
plate.Buckling
ofthe
composite
willthenoccureither
locally
intheplateorgenerally,
involving
boththeplatesndstiffener.
Theinformation
onbuckling
of
stiffened
plates
appears
inthesection
entitled
“Buckling
ofStiffened
Compression”
foruniaxial
loadandinthe
Plates
UnderImgitudinal
section
entitled
“Buckling
ofStiffened
Plates
UnderShearIoad”for
shearload.
Thebuckling
ofstiffened
curved
plates
involves
thecomplication
ofplatecurvature
inaddition
toaXLthepsmmeters
affecting
buckling
of stiffened
flatplates.Thebuckling
ofUnsttifened
curved
plates
has
beendescribed
h reference
2,inwhichitwasshownthattheory
isin
goodagreement
withtestdataforshearloading
andinpooragreement
withdataforaxialcompression
loading.
Forcertain
proportions,
the
curved
plates
approach
cylinder
behavior,
whichpermits
evaluation
of
theunstiff
ened-plate
results
inthelimiting
case.Analyses
of stiffened
curved
plates
arereported
inthesection
entitled
“Buckling
ofStiffened
Plates
UnderLongitudinal
Compression”
foraxialloadsandinthesection
entitled
“BucMing
ofStiffened
Plates
Her ShearLoad”forshearloads.
Znaddition,
thelimiting
caseoftorsional
buckling
ofa stiffened
cylinder
isdescribed
inthelatter
section.
Theresults
ofthetheory
andtestdataarecompared
withtheinformation
on stiffened
curved
plates
undershear.
Thebuckling
stress
ofa stiffener
ora stiffened
platemaybe found
fromthegeneral
relationship
(1)
in Whichb pertains
toa general.
dimension.
Itmaybe thewidthofa
flange
onanangle,
thedepthofthewebona channel,
orthewidthof
oneofthesidesofa rectsmgulsr
tube.Thebucuingcoefficient
kb
isthecoefficient
tobeusedtogether
withthisdtiension
b equation
(1).
TIM?
parameters
uponwhichkb depends
are a/b or A/b ofthe
plate,
theamount
ofelastic
rotational
restratit
alongtheunloaded
edgese,theratiooftheareaofthestiffener
tothatoftheplate
A/bt,theratioofthebending
rigidity
ofthestiffener
tothatofthe
plateEI/bD,
andthecurvature
psxameter
forcurved
plates~. The
.
—
. .
NACAm 3782
3
figures
discussed
in thefollowing
sections
show kb asa function
of
theseparameters.
Theeffects
ofmaterial
properties
onthebuckling
of simple
elements
werecovered
h ref=ence1,inwhichstress-strain
curves,
Poisson’s
ratio,
andcladding
andplasticity-reduction
factors
arepresented
and
discussed.
Plasticity-reduction
factors
forcurved
plates
andshells
are
described
inreference
2. Forconvenience,
a summary
ofpertinent
information
appears
inthe“Application
Section”
andtables
1 to3.
Thissurvey
wasconducted
s%NewYorkWversityunderthesponsorshipandwiththefinancial
assistance
oftheNational
Advisory
. Committee
for-Aeronautics.
,
SYMlms
A
areaof st~enercrosssection,
Sqim
a
len~ ofunloaded
edgeonlongitudinally
compressed
plates
ands~le elements
orlonger
sideofplates
loaded
in
shear,in.
b
length
ofloaded
edgeonlongitudinally
compressed
plates
and
simple
elements
or shorter
sideofplates
loaded
in shea”r,l
in.
.
flexural
rigidity
ofplateperinchofwidth,E+2(. - ,3],
in-lb
D
d
widthofbulbofbulbflange
E,Es,~
Young’s
modulus,
secant
modulus,
andtangent
modulus,
respectively,
psi
G
shear
modlihls,
pSi
h
widthofrec
tsmgubrtubestiffener
(seefig.5(c))
%ymbolsa and b pertain
todimensions
between
stiffeners
on
stiffened
plates
ortodistances
between
parallel
edgesohunstiffened
stress
isfoundfora single
element
ofa stiffaed
plates.Thus,buckling
plateandnotb termsofovemlldimensions
oftheplate,except
for
curved
stiffened
plates
undershear.Inthislatter
caseitismoreconvenient
toutilizea and b as overall
platedimensions
foreaseof
comparison
withcylinder
data.
.. ...
. .. . ...
. . _
--— —
.. ——. —-——
.- .
..
.
NACATN3782
4
I
4
bentlng
moment
ofinertia
ofstiffener
crosssection,
in.
J
4
moment
ofinertia
of stiffener
crosssection,
in.
torsional
k
buclsUng
coefficient
kb
general
buckling
coefficient
ofstiffener
pertaining
to
buckling
stress
ofelement
ofwidthb
%J%
bucklhgcoefficients
forcompression
andshear,
respectively
length
ofcylinder,
in.
moment
applied
to edgesofrotationally
restrained
element,
in-lb
number
oflongitudinal
stiffeners
onplateoftotalwidthnb~
ornumber
ofcircumferential
rtigsoncylinder
oflengthL
number
oftransverse
buckles
inlongitudinally
stiffened
plate
lycompressed
longitudinal
.
radius
ofcurvature
ofcurved
plate,
in.
correction
forpresence
of stiffener
on onesideofplate
platestiffness
(seefig.2 forcliff
erenttypes
)
thickness,
in.
platecurvature
parameter,
(b21+
- ‘e2)1’2
cylinder
curvature
parameter,
(L’ld
(1 - ,e2)l/2
factor
h
r dependent
upon n and q (seefig.12)
distance
ofstiffener
centroid
frommidsurface
ofplate,
in.
ratioofrigidity
ofelastic
restraint
torotational
rigidity
ofplate;
alsostrain
plasticity-reduction
factor
rotation
ofedgeof simple
element,
radians
wavelength
ofbuc=einshnple
element
orplate
~ in.
.—
. __— ——
NACATN3782
5
Ve
Poisson’s
ratioinelastic
range
‘cr
general
buckling
stress;
also,buckling
stress
ofcompressed
element,
psi
‘cr
buckling
stress
ofelement
loaded
inshear,
psi
Subscripts:
cr
buckling
e
effective
f
flange
L
lip
T
topwebofhat-section
stiffmers
v
web
IOCAL13UCKLINGOF
SKOWEMIMGELEMENTS
Behaviorof
Stiffeners
Whena plateunderlongitudinal
loadissupported
bya stiffener
in
thedtiection
oftheload,thestiffener
participates
tiresist~this
thepossible
buckling
modesofthiscomposite
are
load.As a result,
localinstability
oftheplatealone,
localbuckling
ofoneormoresimple
elements
ofthestiffener,
general
Wtabili& oftheplateinvolving
column
action
ofthestiffener,
or somecombination
ofthesemodes.The
_ses perta~to stfifen~pl.ates
a~lyto stm stiffeners
only,
and,consequently,
thesecond
modeisprecluded
by theanalysis
inthose
casesdescribed
h thelastsections
ofthepresent
paper.Howev=,in
orderto insure
thesturdiness
ofthestiffener,
itisfirstnecessary
todetermine
itslocalbuckling
stress.Thisisthesubject
tobediscussed
inthepresent
section,
whichpresents
thebackground
foranalysis
oflocalbuckling
instiffeners
andincludes
charts
forrapidcalculation
ofbuckl~ stress
forseveral
comonshapes.
Thelocalbucklhgstress
ofa stiffener
isthessmeasthatof its
weakest
element.
Consequently,
eachsimple
element
mustbeanalyzed
for
buckling
under101@tUdb31 load. Oftentheweakest
element
isreadily
evident
by inspection.
Theanalysis
oftheelement
involves
detemdning
thenature
ofthesupports
androtational
restraints
alongtheedgesand
.
.— ——.—._
-—
.
-—-.. —. ———__——
——.
____
._ _
_ ___
._
6
NACATN3782
thencomputing
thebucKling
stress
oftheelement
considered
asa simple
plateunderlongitudinal
loadwiththeappropriate
boundary
conditions.
Iugeneral,
however,
thereismutual
restraint
ata longitudinal
jointamongallthemembers
meeting
alongsucha line.Ifthisrestraint
couldbe converted
directly
intoa valueofrotational
restraint
e for
thesimple
element
beinganalyzed,
thenthebuckling-coefficient
charts
ofreferences
1 and2 couldbeusedtofindthebucliMng
stress
ofthe
simple
element,
and,conse@ntl.y,
the”
buclding
stress
ofthestiffener.
Because
oftherotational
interaction
amongthesimple
elements
at each
jotitline,whicharises
fromthepreservation
ofthecorner
angles
between
element
pairs (el= t12= . . . = en), howev=,therestraint
imposed
by eachupontheothers
cannot
befoundimmediately.
Itisnecessary
toanalyze
theproblem
asoneinthedistribution
ofmoment
among
themembers
ofa statically
indeterminate
Syst=. Whenthishasbeen
d~e, e canbe foundand Ucr canbe calculated.
libr
themostpart,thestiffness
ofoneelement
h itsownplaneis
sufficient
toimpart
support
toitsadjacent
elements
perpendicular
to
theirplanes,
although
thecorner
angles
mqycliff
erfromX“. Mostsimple
elements
ofa stiffener
behave
inthismanner.Ups andbulbsmaybetoo
weaktoprovide
complete
transverse
support
toan element
(invariably
a
flange).
Theyactas columns
thattendtoresist
elastically
thetransversedeflections
oftheotherwise
freeedgesoffI.anges
and,consequently, .
cannot
be ticluded
intheusualmethods
ofanalysts
oftheinteraction
buckling
problem.
However,
a flange
witha lipor bulbalongitsfree
edgemsytie
analyzed
asa stiffened
platetodetermine
therigidity
of
thiscomposite,
whichthencanbeusedh theinteraction
analysis.
Calculation
ofBuckling
Stress
!l!he
buckling
stress
ofeachsimple
element
ofa stiffener
meybe
foundfromegyation
(1).Cherts
of ~ forseveral
stiffener
sections
ticommon
usearepresented
h thisreport
endarediscussed
belowh
thesection
on “Numerical
Values
ofBuckling
Stress.
” Thegeneral
methods
ofconstructing
thesecharts
andforftiMngthebuckling
stress
ofa new
stfff
enersection
tivolve
a successive
approximation
procedure
suchasthe
moment-distribution
method
ofLundquist,
Stowell,
andSchuette
(ref.
4)or
thestep-by-step
procedure
ofI@oK1.,
Fisher,
andHetierl
(ref.
5).
methodisthejoint-stiffness
Thebasisforthemcnnent-distribution
criterion,
whichrequires
thatatbuctiing
thesumofthestiffnesses
of
thesimple
elements
meeting
ata jotntlinemustbe zero.Thisispredicted
upona distribution
of stiffnesses
emongthejoint
members
such
thatallhavethesamelongitudinal
wavelength.Thevanishing
ofthe
jointstiffness
atbuckling
folhwsfromthefact-that
stiffness
iseqpal
NACA
m 3782
7
to M/e.
Ehce
e isthesameforallsimpleelements
atthejoint
line,stiffhess
isproportional
tothemoment
carried
by eachelement.
However,
sincethesemoments
mustvanish
atbucld.ing
forsmalldeflectionsoftheelements,
thejoint-stiffness
criterion
follows.
Themoment-distribution
analysis
issimplified
~ theuseofchsz%s
ofelement
stiffness
andcarry-over
factor
prepazed
byKrollfordifferent
typesofboundary
conditions
alongtheunloaded
edges(ref.
6). Theseare
described
inthefollowi.ng
section
oqnumerical
values
ofbuckling
stress.
lhessence,
thestep-~-step
procedure
forcalculating
thebuclCling
stress
ofa simple
element
involves
thearbitrary
selection
ofa buckling
stress
together
withseveral
arbitrary
values
ofbuckle
wavela@h. llbr
eachofthesevalues,Ucr iscalculated
fromequation
(1)untilits
minimum
valueisfound.Ifthisisdifferent
fromtheinitially
assumed
buckling
stress,
theprocess
isrepeated
untiltheassumed
andcalculated
values
a~ee. Thisisthebuckling
stress
ofthecomposite
element.
Charts
of ~ (X/b,
~) areused(aspresented
inref.1)together
withtherigidity
tables
of~ol.1(ref.
6).
,,
Thebuckling
stress
ofa flange
witha liporbulbwasinvestigated
byHuandMcCulloch
(ref.
7),Gbodman
and130yd
(ref.
8),andGoodman
(ref.
9)whoconsidered
a largerangeoflip,bulb,andflsnge
proporsimplified
theanalysis
by selecting
thegeometries
usually
tions
. Gerard
encountered
indesign
anddefined
therangeofsection
proportions
in
whichtheelement
undergoes
thetransition
froma flange
toa webasthe
rigidity
oftheedgestiffener
increases
(ref.
10).
RoyandSchuette
havedemonstrated
experimentally
thatthelocal
buckling
stress
ofthesection
isunaffected
although
thesingle
between
adjacent
elements
isas smallas30°oraslargeas 120°(ref.
11). The
principal
effect
ofchanging
thecorner
anglefrcmW“ istodecrasethe
section
moment
ofinertia,
tiichdiminishes
itscolumn
strength.
Numerical
Values
ofBuckling
Stress
Thebuckling
stress
ofa stiffener
isdetermined
usingthebreakdownscheme
offigure
1. Eqpation
(1)isutilized
to compute
thenun@ricalvalueofthisstress
fortheweakest
element
afterthebuckUng
coefficient
hasbeenfoundaccording
toa method
suchasthatdescribed
inthepreceding
section.
Thecliff
erentstiffnesses
evaluated
byRYoll
intabular
form(ref.
6)aredepicted
infigure
2.
Theeffects
oflipsorbulbsareobtainable
fromfigures
3(a)and
3(b)whichpresent
thecharts
developed
by Gerard(ref.
10). Thebuckling
—.. — .. ——------ —-— ---
—..—.—.
——
-— ——
——.
.———
—- —-—----
8
N/MA
TN3782
strati
isshownasa function
oftheflangeb/t andtheedge-stiffener
proportions,
whichpermit
deterndnation
oftherigidity
of sucha composite
foruseintheindetermhacy
analysis.
Inthismanner,
these
charts
serveasanadjunct
toKroll’s
tables.
Buckling
coefficients
arepresented
forccmnnon
stiffener
shapes
suchas showninfigure
4, inwhichthedimensions
ofwebsandflanges
areshownforbothformed
andextruded
shapes.Thebuckliug-coefficient
charts
forchannel,
Z-,W, andrectanguhr
-tubestiffeners
appear
in
figure
5. Theyweretakenfromthereport
ofI&oll,
Fisher,
andHeimerl
(ref.
5). Thedashed
linesonthesecharts
deftiethesection
proportionsatwhichbothwebandfknge buckle
simultaneously.
Dataforhatsection
stiffeners
appear
infigure
6. Thecurves,
adapted
fromthose
ofVanDerMaas(ref.
12),covera rangeofflsnge”
sizesforcliff
erent
widths
ofcenter
andlateral
websofthehatsection.
Itshould
benoted
thathatandlipped
Z-andchaunel
sections
arestructurally
equivalent.
Effects
ofPlasticity
Theinelastic-buckling
stress
ofa stiffener
maybe computed
bya
method
suchasthemoment-distribution
procedure
ofLundqyist,
Stowell,
andSchuette
forelastic-buclWng
problems
(ref.
4). Thiswasdoneby
Stowell
andPride(ref.
u), whoobtained
goalagreement
withexperimental
data(fig.
7),forH-section
stiff
eners.Theplasticity-reduction
factor
foreachsimple
element
ofthesection
wasemployed
incomputing
thebuckling
stress
foruseinthemoment-distribution
procedure,
in
whichthejoint-stiffness
criterion
controls
thetheoretical
buckling
stress
ofthesection.
Itshould
benotedthatthetestdataatthelarger
strains
lie
about5 percent
belowthestress-strain
curve,
whilethetheory
band
se- to tidicate
that
is3 percent
belowatthemost.Thisanalysis
theuseoftheplasticity-reduction
factor
fora clamped
flange
would
be conservative.
Useofthesecant
modulus
fora simply
supported
flange
wouldbe slightly
optimistic.
BWKLCNGOF S~
l?IATllS
UNDERLONGITUDINAL
COMPRESSION
General
Background
As discussed
inthepreceding
section,
thegeneral
caseofbuckling
of stiffened
panels
involves
localtestability
ofthestiffeners
aswell
asthespring
properties
incompression,
bending,
sndtorsion.h this
section
thespecial
caseofsturdy
stiffeners
isdiscussed,
anda brief
description
oftheinfluence
oftorsional
rigidity
ofthestiffener
is
-——..
●
Y
NACATN3782
9
included.
Thisisofsignificance
sincethedesign
datapresented
in
thecharts
pertain
to stiffeners
withno torsional
rigidi~.
A description
ofthebuckling
behavior
ofa supported
andrestrained
rectangular
platemaybefoundinreference
1 forflatplates
andinreference
2 forcurved
plates.Thestiff
eningelements,
@ose localbuclCling
behavior
wasdepicted
inthepreced~ section
ofthisr@port,
provide
thesesupports
andrestraints
totheplates
at intermediate
positions
in
theplatespans.Theeffectiveness
ofthesesupports
depends
uponthe
axial,
bending,
andtorsional
rigidities
oftheplateandstiffeners.
Representative
arrangements
ofplate-stiffener
combhations
areshownti
figure
8.
Eehavior
ofStiffened
Plates
Her IOngitudhal
Compression
Thetwotestability
modestobe considered
inthissection
arelocal
buckling
oftheplatebetween
stiffeners
andgeneral
instabi~ty
ofthe
composite
element.
timostcasesthetorsional
rigidi~ofthestiff
=er
isassumed
tobenegligibly
small.,
thusexcluding
rotational
restraint
of
theplatealongthestiff
enerline.
Thebehavior
ofa platebuckling
underlongitudinal
loadandsupported
by deflectional
androtational
springs
isshownschematically
infigure
9.
Waveformsforthethreelimiting
casesofperfectly
flexible
andperfectly
rigidsprings
areshown.b general,
thewaveformsforfinite
spring
rigidities
donotchange
shapesignificantly,
although
theamplitudes
of
thewavesmayvary.Whenthestiff
enerrigidity
is sufficient
to enforce
a node,theplatewillreceive
noadditional
f1exural
support
fromthe
stiff
ener.Thisdescription
parallels
thatforcolumns
whichwaspresented
.
by Budiansky,
Seide,
andWeinberger
(ref.
14).
Calculation
ofBuckling
Stress
stress
ofa stiffened
plateunderlongitudinal
loadis
Thebuckling
usually
expressed
intheformofequation
(1)whereb isthewidthof
stiffeners.
theplatebetween
Thebubkling
coefficient
~ isa function
ofthepsxameters
ofthecomposite
element:
kC= kC(a/b,A/W,EI/bD,
Zb)
(2)
Eoththeenergy-integral
approach
andthedtiferential-eqpation
method
ofsolution
havebeenusedto solvetheproblem
ofbuclCling
ofa stiffened
ofboththeseprocedures
havebeendescribed
in
plate.Theessentials
reference
1.
-.. - -----
.-—. —____
.. . ____
. -_
. -.—-—
—
—..—-
.-
10
NACATN3782
Numerical
Values
ofBuckling
Stress
Thenumerical
values
ofbuckling
stress
forstiffened
flatplates
andcurved
plates
underlongitudinal
compression
areasfollows:
thebuckling
coefStiffened
flatplates
.-SeideandSteincalculated
ficients
forlongitudinally
loaded
simply
supported
flatplates
withone,
two,three,
andan infinite
nmberoflongitudinal
sttifeners
(ref.
15).
Theresults
appear
h figure
10inwhich~ isshownasa function
of
of coefficients
for
a/b fora rangeofvalues
of EI/bD.A summary
infinitely
longplates
ispresented
infigure
11forconvenience
indetermining
buc~ingstresses
forlongstiffened
plates.
Thecalculations
ofSeideandSteinwerebasedupontheassumption
thatthestiffener-section
centroid
waslocated
atthemidsurfaee
ofthe
thecaseinactual
practice,
inwhichthe
plate.Thisisnotusually
sttifmeriscommonly
located
ononesideoftheplate.Thisproblem
wasinvestigated
ingeneral
terms~ ~wallaandNovak(ref.
16). Seide
alsoevaluated
thiseffect(ref.
17)andevolved
a correction
forthe
charts
offigure
10applicable
toplates
witione,two,orinfinitely
q
stiffeners
@J-/~)e
. ~~
r = (EI/bD)
I
A~2I
(3)
1 + (Zm#’bq
fromwhichtheeffective
bending
rigidi~ratio (EI/bD)e
maybeobtained.
n, q) tifigure
12,inwhichA/b (Mb = a/qb,
Thefunction&q = f(X/b,
10. A
whereq = 1,2,and3) mustmatchthevalueusedto enterfigure
trial-and-error
a~roachmightberequired
since (EI/bD)e
~ occurat
a different
valueof q infigure
10thandoesEI/bDatthe a/b originallyusedtogether
with n (n= 1,2,and ~)to enterthesecharts.
Whentherearethreestiffeners
ontheplate,
itisnecessary
to satisfy
an equation,
otherthanequation
(3),appearing
inSeide’s
report.
compressive
buckling
Budians@ andSeide
investigated
longi~
oftransverse~
stiffened
simqily
supported
plates(ref.
18). me data
whichper&into a/b= 0.20,0.35,and0.50 appear
infigure
13. The
curves
covera rangeofstiffener
torsional
rigidity,
incontrast
with
thecurves
foraxially
stiffened
plates
forwhichGJ = O inallcases.
Thepreceding
datapertain
to general
instability
of stiffened
plates.
Gallaher
andBoughan
(ref.
19)andBoughan
andI?aab
(ref.
20)determined
localbuckling
coefficients
foridealized
web-,Z-,andT-stfff
enedplates.
Thest~ener-web
composites
wereidealized
as showninfigure
14,h which
thebuckling
coefficients
szepresented
asfunctions
oftheproportions
of
theccunposite.
—.
.-. —
.- —- .--. —
NACA
m 3782
.
11
.
Stiffened
curved
plates
.-Theinformation
forstiff
enedcurved
plates
relates
to thatobtained
fromsections
ofcircular
cyltiers.%tdorfand
Schildcrout
investigated
thecompressive
buckling
ofa simply
supported
curved
platewitha central
cticumferential
stiffener
haxdng
notorsional
rigidity
oraxialstiffness
(ref.
21). b addition
todetermining
thetheoretical
buckling
stress,
whichwasdoneusingltiear
theory,
thepercentageincrease
inbuclil.ing
stress
overthetheoretical
valuewasobtained
ofthelowqerimentalvalues
of
andisshowninfigure
15. Because
buckling
stress
compared
withtheresults
ofthelinear
theory,
I!atdorf
andSchildcrout
recommended
a@@ng thetheoretical
percentage
increase
totheqerimentalbuckling
stress,
values
ofwhichmaybe foundinreference
2. Themaximum
possible
increase
fora curved
platewitha given
valueof a/b and Zb isshowninfigure
15(a),
whilean increase
less
thanthemaximum
isobtainable
fromfigure
15(b).Furthermore,
thevalue
of EI/bDrequired
tocausea buckle
nodeatthestiffener
lineisobtainablefromthesefigures
~ cross-plotting.
Notethatno gainisindicatel
when a/b>0.7 orwhen ~
greater
thanthevalues
showninthetablebelow.
is
9
a/b 0.600 0.500 0.417 0.333 0.250 0.167
%
28.o
14.0
7.8
4.1
0.7
1.9
4
!Ihe
charts
offigure
15weredesigned
topermit
an estimate
ofthe
increase
inbuckling
stress
tobe expected
inanaxially
compressed
curved
platewhenthecentral
circumferential
stiffener
haslessbendhgrigidity
thanthatreq~ed to enforce
a nodealongthestiffener
line.Whenthe
stiffener
hasthisminimum
rigidity,
thelength
oftheoriginal
platemay
be considered
tobehalved,
andthedatainreference
2 should
beusedto
obtain
thebuckling
stress.
Thisapproach
alsoapplies
toplates
withaxialstiffeners,
which
wereanalyzed
by Schildcrout
andStein(ref.
22). Thecurves
forthis
typeofpanelappear
infigure
16,inwhich~ appears
asa function
of EI/bDfora rangeofvalues
of a/b and ~. Tnordertoaccount
forthedisparity
oftestdatawiththeory
forcurved
plates,
Schildcrout
andSteinrecommend
thefollowing
procedure:
(1)Determine
thecliff
erence
between
thebuckling
stress
ofthe
stiffened
panel(fig.
16)andthatoftheunstiffened.
panel(ref.
2).
(2)Tothisdifference,
sddthelarger
ofthetwofollowing
stresses:
(a)Thebuckling
stress
oftheunstiff
enedpanel
(b)Thebuckling
stress
ofthecorresponding
flatplate
.. ..
. . . ..— —..
- . ..— ----- —
—
-—-
.—-c
-..
—
—-—
. .
-.
-.
12
NACATN3782
for
Whenthecurved
platewidthexceeds
thelength,
usethecurves
cylinders.
Usethecurved-plate
buckling
dataonlywhenthelength
exceeds
thewidth.
Effects
ofPlasticity
Plastici@-reduction
factors
for stiffened
panels
depend
uponthe
factors
pertinent
to eachelement
ofthecomposite.
Forexmqle,the
factor
forsupported
plates
wouldbe ~ected toapplytotheplateelementsbetween
stiffeners,
whereas
sturdy
stiff
enersbehaving
ascolumns
should
follow
thetsngent
modulus.Iftheseconditions
holdinthecomposite,
theelastic-qepsrameter
EI/bDkuld becomelZ#/qbDinthe
inelastic
range.
Gallaher
andl?Qu@an
compared
testdataon Z-stiffened
panels
subject
to localbuckling
withbuckling
stresses
computed
usingthesecant
modulus
astheplastic
i~-reduction
factor
andobtained
theagreement
showniu
figure
17 (ref.
19). Someofthedatapertain
toplates
withsturdy
stiffeners.
However,
a largeportion
applies
to composites
inwhichthe
stiffeners
buckled
locally.
Effect
ofTorsional
Rigidity
ofStiffen=”
Thebuckl~-coefficient
charts
discussed
inthepreceding
paragraphs
wereprepared
forstiffeners
withnotorsional
rigidi~.Actually
all
stiffeners
havesometorsional
rigidity,
andclosed
stiffeners,
ofwhich
thehatsection
istypical,
mayfuuction
asfullyrigidstiffeners
in
torsion
forscmeapplicatims.
Inreference
1 a chartbasedupontest
datawaspresented
depicting
theeffect
onbuckling
stress
asthetorsional
rigidity
changes
relative
totherigidity
oftheplate
‘being
stiff
enea
. Thishasbeenreproduced
hereb figure
18,inwhichmaybe
seenthecomparative
effects
of stiffeners
withlargeandsmalltorsional
rigidi~.
Thegaininplatebuckling
stress
realizable
withstiffeners
offinite
torsional
rigidity
depends
upontherotational
restraint
e provided
by
thestiffener.
~is isrelated
to thecliff
erence
inbuckling
stress
between
stiffmer
andplate,
wherethestiffener
isnowconsidered
tobe
a simple
element
of specified
elastic
properties,
inorderto satisfy
thejotit-stiffness
criterion
iUEcuss&i
= thesection
entitled
“Loc&l.
Bucuingofstiffening
Elements.
“ Thus
,
‘Crplate
)
(4)
d
-———.
—-——.
.
NACATIV
3782
u
Thisissubstantiated
by figure
18,whichshowslittle
gainover
simple
support
whentheplaterigidity
ishigh(lowvalues
of b/t).
BUCKLING
OF STIFFENED
PIATES
mm smm LOAD
Behavior
ofStiffened
Plates
UnderShear
.
.
Whentransverse
stiff
enersareattached
toa plateloaded
inshear,
theymayberigidenough
to enforce
nodesattheattachment
linesorthey
maybe soweakasto exertvirtually
no influence
ontheplatebuckle
pattern.Theextreme
caseofweakstiffeners
wasexamined
by Schmieden
(ref.
23),Seydel(ref.
24),andWang(ref.
25)whilerigidstiffeners
wereexsmined
by Thoshenko
(ref.
26).
.
Theintermediate
rigidi@rangewasanalyzed
byCrateandIawho
demonstrated
themmnerinwhichtheshearbuckling
stress
ofan infinitelylongflatplateisincreased
longitudinally
as stiffener
rigidi~
risesuntilitissufficient
toenforce
nodesalongtheattachment
lines
thebuckle
pattern
ofthepl-.te
changes
(ref.
27). Duringthisprocess
fromthewaveformforanunstiffened
plateofinfinite
length
andof
width (n+ l)b tothatofa platewidthb. Testdataobtained
by
.
CrateandLofollow
thetheoretical
trendof ~ asa function
of E1/bD
Thescatter
islargewithmostofthedatalyingbetween
thecurves
for
simple
support
andclamped
edges,
as showninfigure
19(a).
SteinandFYalich
analyzed
buckling
oflongflatplates
withtransversestiff
enerssubjected
to shearload.
(ref..
28). Thebehavior
is
analogous
tothatofa longitudinally
compressed
platewithtransverse
stiff
en=s. tifigure
19(b)testdataareshowntoagreewiththethqq
ofSteinandl?ralich.
SteinandJaeger
analyzed
buckling
ofa curved
platewitha central
stiff
enerplaced
either
axially
orcirctierentially
(ref.
29). Although
thegeneral
behavior
pattern
corresponds
tothatforflatplates,
the
additional
factor
ofcurvature
modifies
thebuckle
pattezm,
whichtends
toward
thatof a cylinder
inwidecurved
plates.
A stiffened
cylinder
represents
a limiting
caseofstiffened
curved
pertaining
tothiscasecovers
‘test
results,
plates.Mostoftheliterature
themajorportion
Ofwhichapplies
towedcstiffeners’
thatbuckle
locally
or
to stiffeners
rigidenough
to mforcenodesandthereby
causethecylinder
2,
tobehave
asa groupofplates.Thesecasesareaiscusseain reference
whichdealsspecifically
withthisproblem.
Stein,
Sanders,
andCrateinvestigated
thebucklj.ng
ofcylinders
loaded
intorsion
andstiffened
byringswithfinite
rigidi@(ref.
30).
.— . . . ———
.. .
. . . . . —.—
—
.——
—
.-—
—
- -- ———
---
—-—
.-
--
—.
NACATN3782
14
A largerangeofvalues
of % wascovered
fora corresponding
large
wascompsxed
withtestdatawith
-e ofvalues
of EI/bD.Thetheory
20, in whichthe&eoryisseentobe sliglrbly “
theresults
showninfigure
optimistic
.
Calculation
ofBucklhgStress
(1)inwhich
Thebuckl@ stress
isexpressed
intheformof equation
thebuckling
coefficient
ks isa function
ofgeometry
andloading.
As
h thecaseoflongitudinal
load,thebasicparameters
forflatplates
are a/b, A/bt,and EI/bD,
whileZb isanadditimal
parameter
for
CUPRd pkteS d
ZL 13~lieStO CyliIlderS
. h the theoretical
investigations
thestiffeners
wereassumed
topossess
notorsional
rigidity,
and
thecentroids
tiere
assumed
tolieh themidsurface
oftheplate.
Nmerical
Values
ofBuckling
Stress
Thenumerical
values
ofbuckling
stress
forstfif
enedflatand
curved
plates
andcylinders
intorsion
undershearloadssxeasfollows:
Stiffened
flatplates.
- Thetheory
ofCrateandb forlongflat
plates
loaded
h shearandstiffened
longitudinally
(ref.
27)ispresented
infigure
19(a),
inwhichks isplotted
asa function
of EI/bDfor
bothclamped
andsimply
supported
plates
withcmeortwostiffeners.
The
results
ofStetiandIYalich
(ref.
28) fortransversely
stiffened
flat
plates
appear
h figure
21. Fromthislatter
figure
itmaybe seenthat
theminimum
valueof EI/bDremind to aforcea nodeatthestiffenerattachment
lineincreases
rapi~ @th a/b. Approxtite
values
areshown
inthetablebelow.
Ill
a/b. . . . . . . . . . . . . . . . ...1
Minimum
valueofEI/bD
fornode . . . . . . . . . . . . . ..lOl~
2
5
700
ofthetheoretical
investigaStiffened
curved
plates.
- Theresults
oncurved
plates
loaded
in shearandsupported
tionofStetiandYaeger
by a central
stiff
ener(ref.
29)appear
inthecharts
offigure
22. EOth
axialsmdcircumferential
stiffeners
areconsidered
together
withwide
plates
andlongplates.me results
areplotted
intheformof ks as
a function
of EI/bD,
inwhichb istheshortside.Thispermits
comparison
withthecurves
f
orunstiff
ened
plates
p
resented
inreference
2.
0
-——.
—
—
..
.—
—
—
-
NACATN3782
15
Thecurves
areplotted
forseveral
values
of Zb .- a/b= 1,1.5,
plateaimlenand2 (where,
forthiscase,a and b aretheoverall
Sions
). Inaddition,
thelimiting
curves
ofinfinite
a/b forlong
plates
andthecyl~er curvefor-wide
plates
areinclud-ed.
Thela~ter
maybe checked
against
thecurves
forcylinders
to bediscussed
inthe
following
paragmph
andpresented
infigure
23.
Stiffened
cylinders
intorsion
.-Stiffened
cylinders
h torsion
represent
a limiting
case.
ofstiffened
wideplates
inshear.Stein,
Sanders,
andCratecalculated
thebuckling
stress
asa function
ofthe
cylinder
andstiff
enerparameters
(r&.30). l?he
curves
appear
infigure23,inwhichks isshownasa fuuction
of EI/bDfora largerange
ofvalues
of ~ andforone,two,three,
andfourhxtemmxliate
rings.
Thecurves
pertaining
toonerhg msybe seentoagreewiththe“cylinder
curves
offigure
22(d)forwideplates
witha central
cticumferential
stiff
ener
,
Theseresults
wereobtained
forstiffeners
withno torsional
rigidity,
withthesection
centroid
inthemidsurface
ofthecylinder
,Q1.
Effects
ofPlasticity
.
Theplasticity-reduction
factors
forstiffened
plates
undershear
may
befoundinreferences
1 and2 forflatandcurved
plates
withspecific
boundary
conditions
. Thisinformation
should
applytoplates
withstiffenersrigidenough
to enforce
nodesalongtheirattachment
lines.Nodata
exist,
however,
forplasticity-reduction
-factors
forplates
stiffened
by
elem&tsofrigidi~lessthanthatrequired
fora node.
AEPIJCATION
SEZ!KIDN
plates
has
Theuseofbuckling
chsrts
forstiffeners
andstiffened
section
beendescribed
inthepreceding
sections.
Inthisapplication
areexplained.
andthetables
theresults
aresmmarizedforrapidreference
loaded
incompression.
Table1 contains
dataforstiffening
elements
Homation on stiffened
plates
loaded
inlongitudinal
compression
appears
intable2,anddatarelating
to stiffened
plates
loaded
inshearare
fouudh table3. Inallcasesthebuckling
stress
canbefouudfrom
equation
(1):
. .. . .... .. . . -.—
.—— ——
—-
.—
-. -.——--————.———
--
—
.
NACATN3782
16
Plasticity-reduction
factors
appear
inthetables
wheretheyareapplicable.Forfurther
information
onplasticity-reduction
factors
and
information
cladding
reduction
factors
also,seereferences
1 and2. l?br
onfailure
ofstiffeners
seerefer=ce
3.
.
I?&ring-stiffened
cylinders
intorsion,
acr= &~~
Forthiscase,~
depends
upon ~
tisteadof~,
Itshould
benotedthat a and b aretheoverall
platedimensions
comparison
withthedata
plates
undershear.Thispermits
forstiffened
forring-stiff
enedcylinders
intorsion.
Research
Division,
College
ofEngineer-,
NewYorkUniversi@,
NewYork,N.Y.,April15,1955.
—-----
.-—.
Y
mm m 3782
17
1.Gerard,
George,
andBecker,
Hqrbert:Handbook
Of Structural
Stability.
PartI - Buckling
ofFlatPlates.NACA~ 3781,1957.
2.Gerard,
George,
andBecker,
Herbert:Handbook
ofStructural
Stability.
~
III- Buckling
ofCurved
Plates
andShells.NACATM3783,195?.
Stability.
Partn - l?ailwe
3. Gerard,George:Hbook ofstructural
ofPlates
andComposite
Elements.
NACATN3784,1937.
4.Lundquist,
Eugene
E.,Stowell,
Elbridge
Z.,andSchuette,
EvanH.:
Principles
ofMoment
Distribution
Applied
to Stability
of Structures
Composed
ofBarsw plates.NACAWl?
L-326,
1943. (Former~
NACA~ 3K06.
)
5.Kkoll,
W.D.,Fisher,
Gordon
P.,&d Hetierl,
George
J.: Charts
for
Calculation
oftheCritical
Stress
forIota.1
hstabil.i@
ofColmns
withI-,Z-,Channel,
andRectangular-Tube
Section.
NACAWRL-429,
1943.(Formerly
NACAARR3KD4.
)
6. fiO~, W.D.: Tables
ofStiffness
aadCarry-Over
Factor
forFlat
Rectangular
Plates
WnderCompression.
NACAWR L-3g8,
1943. (Formerly
NACAARR3H27.
)
7. Hu,PaiC.,andMcCulloch,
JamesC.: TheLocalBuckling
Strength
of
Lipped
Z-Columns
With9nallLipWidth.NACATN 1335,15#+7.
8. Goodman,
Stanley,
andR@, Evelyn:Instability
ofOutstanding
Flanges
Simply
Supported
atOne~ge andReinforced
by BulbsatOtherEdge.
NACATN1433,1947.
9. Goodman,
Stanley: Elastic
Buckling
ofOutstanding
Flanges
Clamped
at
OneEdgeandReinforced
by Bulbsat OtherFdge.NACATN1985,1949.
Instability
ofHinged
Flanges
Stiffened
by
10.Gerard,
George: Torsional
Li.pSand Bulbs.NACATN3757,136.
ofAngleoflknd
11.Roy,J.Albert,
andSchuette,
Eva H.: TheEffect
Between
PlateElements
ontheIocalInstaBili~
ofFormed
Z-Sections.
)
NACAWRL-268,
1944. (FormerlyNACARB L4126.
1.2.
vanDerMEU3S,Christian
J.: Charts
fortheCalculations
oftheCritical
Compressive
Stress
forLocalIhstabili@
ofColumns
WithHatSections.
Jour.Aero.Sci.,vol.21,no.6,June1954,pp.399-403.
13.Stowell.,
E1.bridge
Z.,and~ide,Richard
A.: Plastic
Buckling
of
Extruded
Composite
Sections
inCompression.
NACATNlg71.,
1949.
.
-. .-
-.-—- _______...
—.—.
—
- ..— _ —~----
—
-.—
-.——
._ ___
.. _ _
NACATN3782
18
14.BuaisJls@,
Bernard,
Seide,
Paul,andWeinberger,
Robert
A.: The
ofa Column
onEqually
Spaced
Reflectional
andRotational
Buckling
Springs.
NACATN1519,lW.
Buckling
ofSimply
15. Seide,
Paul,andStein,
Manuel:Compressive
Supported
Plates
withlongitudinal
Stiff
eners.NACATN1825,1%9.
16. Chwalla,E., andNovak,
A.: TheTheory
ofOne-Sided
WebStiffeners.
R.T.P.
Translation
No.2501,I&itish
Ministry
ofAircraft
Production.
(FYom
Bautechnic
- SuQP1.
dermbEUl, vol. 10,no.10,MSy7, 1557,
pp. 73-76.
)
ofIOngitudinal
Stiffeners
Located
onOne
17. Seide,
Paul:TheEffect
Sideofa PlateontheCompressive
Buckling
Stress
ofthePlateStiffener
Combination.
NACATN2873,1953.
18.hdiEUISky,Bermurd,and Seide,
Buckl@ of Simply
Paul:Compressive
Supported
Plates
WithTransverse
Stiffeners.
NACATN1557,1948.
19. Gallaher,George
L.,andI@u@an,RollsB.: A Method
ofCalculating
theCompressive
Strength
ofZ-stiffened
Panels
ThatDevelop
Iocal
NACATN1482,1947.
Instability.
20.Boughan,
RollsB.,andBaab,George
W.: Charts
forCalculaticm
ofthe
Critical
Compressive
Stress
forIocalInstability
ofIdealized
Web-and
)
1944. (FmmrlyNACAACRL4H29.
T-Stiffened
Psnels.NACAWRL-204,
Murry:Critical
Axial-Compressive
21.Batdorf,
S.B.,andSchildcrout,
Stress
ofa Curved
Rectangular
F%nelWitha Central
Chordwise
Stiff
ener.NACATN1661,1948.
.
Axial-Compressive
22.Schildcrout,
Murry,
and%ein,Manuel:Critical
Stress
ofa Curved
Rectangular
PanelWitha Central
Longitudinal
stiff
ener
. NACATN1879,1949.
23. Schmieden,
c.: TheBucklingofStiffened
Plates
inShear.TranslaWkshingtxm
NavyYard,
tion No; 31,U. S.lhsper~ental
ModelBasin,
June1936.
Subjetted
to Shear
Plates
24.Seydel,
Edgar:WMnklingofReinforced
NACATM 602,1931.
Stresses.
Stiffened
Plates
UnderShear.
25 Wang,TsunKuei:BucklhgofTransverse
Jour.Appl.Mech.,
vol.14,no.4,Dec.1947,p.A-269- A-274.
●
ofElastic
Stability.
Firsted.,McGraw-Hill
26.Timoshenlm,
S.: Theory
EookCo.,MC., 1936.
-—.
—
-— ..
..
“
19
NACATN3782
27.Crate,
Harold,
andIo,Hsu: Effect
oflongitudinal
Stiffeners
onthe
Buckling
LoadofIongFlatPlates
UnderShear.NACATN 1589,19$8.
28.Stein,
Manuel,
andFYalich,
Robert
W.: Critical
ShesrStress
of
Infinitely
Long,ShplySupported
PlateWithTransverse
Stiffeners.
NACATN1851,1949.
DavidJ.: Critical
29. Stein,Manuel,
ShearStress
ofa Curved
andYaeger,
SW?fener.MACATN1972,1949.
Rectangular
PanelWitha Central
Harold:Critical
30.Stein,
Manuel,
Sanders,
J.well,Jr.,andCrate,
Cylinders
inTorsion.
NACARep.989,1950.
Stress
ofRing-Stiffened
-----
____
________
.__,
- ...—
—..
—--
-- --—
NACATN 3782
20
TABLE 1
STIFFENER ELEMENTS IN COMPRESSION
[See fig. I for breakdownof typicalsectionsintotheir component
elements]
Buckling
coefficient
Section
Fig.
Plasticity-reducfion
factor
5(a)
12c
‘w
‘E;:;:J~]
bw
j(b)
kw
Nonereported
kh
Nonereported
k+
Nonereported
t-i
j(c)
bh
‘
D
bt
6
JY
—
..-
-— .. .
—.—
NACATN 3782
TABLE 2
STIFFENED
PLATESUNDERLONGITUDINAL
COMPRESSION
GJ=O]
[ Seefig.8 for sketchesof plate-stiffener arrangements;
Section
Pfg.
- Plasticity-mductIonfactor
(a)
Endview
10
A
w
x
v
A
A
w
n=l,2,3,a)
End view
4(a)
WhenMfenersenforcenodes,
~
Infinitelywide
Endview
4(b)
~=(i)(a
~+,[++’
=
Infinitelywide
Endview
4(c)
T T T T
4(d)
Infinitelywide
Side Wew
Endview
15 -
:=:
.
Whenstiffenersenforcenodes,
Endview
usedata in ref. 2
16
4
an, numberof stiffenerson plate;
~,
..
—..-.
—.
●,
sturdy ~ffen%
transversesupportwithno restraintof lateralmovement.
-- —-—————-————
--——
__._-
—- ..—
.—
-.. ...— .-—.-. . -
NACA
TN3782
TABLE 3
STIFFENED PLATES UNDER SHEAR
1
See fig.8 for sketches of plate-stiffener arrangements. GJ=O
Fig.
Section
(a)
1
Plastlclty7eductIon
factor
Endview
9(a)
n=l,2, co
Lomplates
only
Side
view
Endview
21
iv ~
1A ~6
:;
v
Lowplates
only
Endview
:2(0)
❑nd
2(b)
When
stiffeners
enforcenales,
7 = (%/E) (l~e2)/(i
4
Endview
:2(C)
and4
2(d)
=
- V2~
Sideview
.
w
u
A
23
m
n=l,2,3,4
Simply
SUpprted
ends
%, numberof stiffenersan plate;
~,
●, sturdy stiffener;
transverse
support
withnorestraint
of lateralmovement.
—-.—.
..
23
Figure l.- Breakdownofsngle
andZ-stiffeners
intocomponentplate
as,simply
supported.
elements.
— —. .. .——.——
.-
—.
.
—.—.
.——
—-
- -—- -—.
NACATN 3782
24
s
‘c+
.
s’
s“
s’”
.
S’v
JW3-
M
M
M
M
stiffnesses
offlatplates
withdifferent
boundary
20- Rotational
conditions
. Momenti
varysinusoidally
alongplatelangth.
.
.—.
. ——._
Y
NACATN 3782
./c
T
s
4@ff
.
\
\
\
,
/m
.
(a)Lipflanges.
Figure
3.- Buckl@ stratiofhhgedflanges.
Lfi = 3.5;
.
%@2 t 2.Ve = 0.3 (dataofref.10).
E
cr=12(l
-.—. —.—..... . _
__
-
_
)()
z=’
Ve
.._
___
__
_
—.
—-.
—
————
. .—
26
NACATN 3782
./0
~
“
a
Ce
Do/
. .
Y\
.
\\
uNs77wEMm
FLANGE
~\\
.000< “/0
\
1
I
“
/00
(b)Bulb”
flanges.
=e
3*- Concluded.
——
NACATN 3782
27
r
b
‘1--J
L
b
.+
r
r
&f “
-m
.-
bw
LJ
bf
.
(a)Extruded
sections.
(b)Formed
sections.
Figure 4.- Typical formed
andexlamded
stiffeners.
. . .. . .. . . .
____________
___
—-—- —.
——-
.——
—:.
—— --
.
28
71
I
WEB BUCKLESFIRST
1
(
/
.
/
y
.4
fZAME BUCKLESFIRST—
5
4
kw
[v
\\\\
\
\
\
\
\
\
\
I
,
.P’f
\
FUNGE, bf
2
~
t
“ WEB,bw
9
‘&l-l
s
EO)IIIIIJ
.2
I
4
20’.8
.6
●
(a.)
ChannelandZ-section
stiffeners.
acr=
8!0
I
12
I$#E t#
12(1- Vez)r
lllgure
5.-Buckling
coefficients
fcmstiffeners
(data
ofref.5).
-—-—-——
—— —-———-—
—
—-.
—
—. .
.—
-.. .
NACA
TN3782
●
7
7
6
5
4
kw
3
2
/
FLAh@&bf
o 1111111111
.2
o
#
.8
/2
10
;
&w
(b)H-section
stiff
eners.Ucr=
~2E
%2
.12
(1- ~e2) ~
Figure 5.- Continued.
0
.
..— ...-
___
___
. ——.
-.——
_
__
. ..—
“
NACATN 3782
kh
l-+--i
.
I
I
I
stiffeners. am =
(c)Rectangular-tube-section
*($
Figure
5.- Concltid.
0
-- —
.
1
i
6
I
5
I
u
4
I
1%
4
k,
3
2
1
0
Figure 6.-
I
1
Eucklingstcessfor hat-sectionstiffeners. t = %=%=%;
~21J
t2
—.
(E&a of ref. 12.)
% =
U!(1 - Veq bq?
NACATN 3782
32
85
.
STRESS- STRAIN
o
75
7G
C*,
ksi
65
6G
55
.005
.0/0
.0/5
of
buckling
ofthecmy
andtestdqtaforinelastic
Figure 7.- COmpsrison
H-section
stiffaers.ecr=
%+%2
Q= 1.();
+$ =0.5 ~
12(1- ve2)b#;~
0.8. (I%ta
ofref.13.)
.
—-
—.
.—..
..
..
5Y
NACATN 3782
LON61WWN44L
STIFFENER
AXIAL
STIFFENER
33
TRANSVERSE
ST/F~AfEk?
— —.
CA?CUMFEW6AL
STIF=NER
combinations
underionFigure
8.- IIIYPiCal
arrangements
ofplatestiffener
gitudinal
compression.
._
—..-. .——.
-.—
——-—
...—
—
— -
- -.
NACATN 3782
34
EDGE
STIFFENER
El=
EDGE
GPO
o
I
.
me
behavior
ofaxially
compressed
flatplatesuppofied
90- BucKling
bydeflectianal
androtation~
springs.
___ ..
5
4
\
3
k.
2
‘2
/
-0
/
2
3
4
56
7
8
o“b
(a) One stiffener. A/bt = O.
Figure 10.- Ccmqressive-buckling
coefficientsfar shply sqpportedflet
plateswith lcmgitudinelEtiffenem
●
of ref.
15. )
... .*Y.
(Data
.
4
‘%
\’+<:;—---J”
\_ 40
3
kc
2
/
/ -
~
~/b=a/b+
F
[
Lllllllld
‘o
A/b=oA2b +A/b=o/3b
/
2
3
~
4
db
(b) One stiffener.A/bt = ().2.
m
lo. - Continued.
,
6
7
I
8
.
5
4
3
kc
2
/
.
L,,l,l,ll
00
/
2
I
3
I
,
4
I
5
o/b
I
(c)
one
stiffener. A/bt = 0.4.
Figure10.- Chtin’ued.
I
I
I
6
7
8
I
w
5
0)
“4
3
kc
2
\
/
Axb=a/b-#--
IIlllllil
0
0
/
2
3
4
b+=wa’
5
6
.’
1“
7
8
(24)
M
!3
6tiffener6.A/m = o.
F’Uwe 10.- Continued.
,
,
s
.
T
5
)’
4
A
1
3
k=
\
2
20—
\G
‘/0
I
,’2”
\
/
I
\l
\
I
hl~
\ I
-
I
J
7
8
—.
ti
o
0
/
2
4
3
5
0/’
(e)
Two
stiffeners. A/bt =
Figure10.- Ccmtimed.
6
5
-T
4
3
k=
2
\
2
/
o
(
11111111
/
2
3
5
4
6
7
4
(7A5
(f) Twu Stiffeners.A/bt=
0.4.
Figure
10.-Continued.
,
w
-1
al
n)
*
,
,
5
4
I,.
3
kc
2
I
{
i
/
!
0(
i
“\
/
2
3
4
5
oh
k) Three stiffeners.A/bt = O.
Figure10.- Continued.
I
6
7
8
J
5’
4=
Iv
5
4
1
3
kc
2
/
q
11111111
/
z
3
4
5
6
7
8
u/b
(h) Three stiffeners.A/bt.0.2.
-10”-
-tfi~d”
>
,
5
El
4
3
4
2
/
o
o
/
2
3
4
5
6
7
8.
Cvf!b
(i)Three Stiffe?mra.A/bt .0.4.
II
. .
F@u.’e
lfl. -
Contintid.
5
I
I
l\
I
I
4
3
4
2
I
/
o
0
/
2
3
4
U/b
(J) Infinite nunberof
Fil!3m= 10. -
5
6
7
8
‘Mb
stiffeners.
A/bt = O.
Continti.
.
,
*
,
,
5
I
w
4
4
Is
3
&
2
/
\.1
o
111,,11~
\
75
I
0
/
2
4
3
OA
5
‘
6
7
Mb
(k) Ihflnitenumberof stiffeners.A/bt = 0.2.
Figure10.- continued.
I
I
I
g
5
4
3
2
I _
o
/
2
3
4
5
6
O!!b ‘M
(2) IMtnite numberof stiffeners.A/bt -0.4.
Figme 10.- Concluded.
7
8
.
,
5
4
3
k
2
/
o
./
/0=
/
/oa
.g
FigureIL- C!cmpresslve-buckJ.lng
coefficients
for infinitelylong
with lcmgltudiw
1 stM&ners.
.
shlp~ S~
flat
—
plates
k#E
‘m=
K!(1
-
ve2)
o.
.&~
b
(Date d ref. 15. )
a34
4
n=2,
UA!FAUZED
STURDYS77ffEWRS
3
/
\
z—w
+
2
/“-
n=l, q=f
I
n=2, q4
r
fpw
c
J/b
Ilgure 12.
-
l/~q
aa a functionof
(m/bD)e
pattern.
r=—=
(EI/bD)
stiffenedplate proportions
1+*
crosssection. (Dataof ref. 17.j
VI
-a
0)
N
stiffener
A
‘s”=’”
.
‘Y
49
NACA
.
m
.
#
75
4
50
e,
u
I I
I
[
---
100
(a)
.
Zm
a/b= 0.20.
Figure
13.- Longitudinal-compressive-b~
coefficients
forsimply
supported
withtransverse
T= =
stiffeners.
J21
( - ~e2b2”
)
(Data
ofref.18.)
. . . ..—
------
—.—- -.—.
..— —
&x2~2
._.
—
-—.
——
—.——
_—
NACATN 3782
50
5C
-4
30
~
2C
/c
a
La
w
E]
n
(b) a/b= 0.35.
Figure
13.- Conttiued.
.
.
.—
—.
—.
t
51
2(
k
/6
5
6
(c)
a/b= O.50.
Figure
13.- Concluded.
.—
——
.-..-—
.—.
.
.-—
NACATN 3782
52
.
?
.
6
5
4
k,
3
2
/
1
IJlllllllll
2
4
00
I
I
.6
.8
I
D
bp/b*
(a)Websttifeners.
0.5< ~/ts <2.0 (Data
ofref.20.)
wide
coefficients
forinfinitely
Figure
14. - Compressive-local-buckMng
idealized
stiffened
fkt p~teS. am =
*:7”
. .— —
-. .— ..- .—. --
.-. . .-—
—
.
.
53
“
7
.
6
5
4
k=
..
3
.
2
/
o
z
u
.4
s
.8
10
M
bw
~
Z-section
stiffeners.
ofref.19.)
%/% =0.50snd0.79. (Data
Figure
14.- Continued.
..
. ...— ..__ _
___
—
——.
——..
——
——
———. —.. .
.
7
.
6
5
4
k=
3
2
/
00
2
.8
.6
LO
b~
~
(c)
= 0.63 enaLO.
Stiffalers
. i#ts
Figme14.- Continued.
.
(l)ata
ofref.19.)
55
NACATN 3782
.
7
.
6
5
d
BUCKUN6
OFSKIN
‘EWRAWEO
BYSTIFFENER
4
k.
8UCKLIN6WWIFFEWW
RWRAINEOeY WW
3
bf bf b~
2
~
.
/
4
m’ TTr
o0
.2
.6
.8
L2
.
bf
%? 0.25.
t_& = 1.0;~> 10;~>
(d)T-section
stiffeners.
s
(Data
ofref.20.)
Figure14.- Continued.
.-—. .—._ ----- .
——. .
——
—..
. . . .——
—.
.-
———.——
—.—- -. . - ---
56
NACATN 3782
7
6
5
4
k,
3
2
I
1
.8
40
.6
m
I
o
o
mm
,t,
.2
4
.6
b/b
Ws
I
E
“
(e)T-section
stiffeners.
tw/tf= 0=7;bf/tf> 10;%/bs >0.25.
(Data
ofref.20.)
Figure
14.- Concluded.
.
,
1
I
I
0
(a)Maximumincrease.
I
I
I
I
.2
.3
.4
(~ti~)(~b)”
i
I
./
(b) IiuxeaseXor
given
stiffbms.
stressfor siqplysupportedcurvedplateswith a
Figure15.- Increasein compressive-buckldng
centercircumferential
stiffener. (Dataof ref. 21.)
58
NACATN 3782
.
6
5
I
A/bf=O
.
A/bt =C12 _
“
.
k. 3
.
oo~
4
/2
/6
.
12
048
16
6
I
t
A/bt-+.4 _
5
A/W
=0.6
4—
~= 3 2
/
00
{
4
8
/2
/2
A? 048
B
~gure 16.- Compressive-buckling
coefficients
forsimply
supported,
curved
plates
withcenter
longitudinal
stiffener.
am =
*Y”
(Data of
ref.22.)
-
NACATN 3782
59
.
I
A/bt=O.2
\
oo~
24 3? 08
6
I A/bf =0.6 I
●
1.
A/bt=O.4
.
5
+
\
3
2
f
‘O
.
8
/6 24 32 08
<
tf524 32
.
(b) a/b= 2.
Figure16.- Continued.
. . -. .——. -.--—-
—
—-—...
—.—
———
. ..—
—.
—
.——
. ..— —
NACATN3782
60
DxzIl”
6
5
4
kc 3
2
/
0
I
)
6‘
I
I
I
I
.
A/bt=O.4
5‘
4
i
/6 32 48 64
A/bt=0.6
\
zg250
1
k. 3’
/
2
I
324w&?
O
/6 324864
.
(c) a/b= 3.
~gure 16.-
continued.
.
61
6
5
_
ai
N.
4
Zpfjo
kc 3
1
I
>
o
2
///!//////zw/z/
/
=b
- /ww///wzu’
f
I I I I I I
Ot~163?486480$W[
6
I
/6 32 48 64 80 96
_
5
I
I#Mbt=Q6
\
4
3
2
A
/
‘O16324864&U96
O /6
324864
8096
El
m
(d) a/b= 4.
Figuqe
16.- Concluded.
.. —.-— — .—.—
—..
.—
.—-—
— .—.
—
..-—
.. . _.
_.
62
.
50
MAXIMUM
40 – STRESS- STRAIN
CURVE
.
.
30
STRESS-STRAIN-
G5
.
ksi
.
20
/0
q
.002
.004
.006
.Ot ?
oftestdatawithsecaut-modulus
theory
for
Figure
17.- Comparison
inelastic-locsl-buckMng
stress
ofZ-stiffened
flatplates
uuder
ofref.19.)
compressive
load.(Data
.
.
I
8
I
7
I
I
UWG,EDGES CLA@’A?5D
TORS1O)WL Y
– RIG/D S7iFi5ENEf?
6
5
—
LONG EWES SYMRY
w’PmrED&-4.oo)
4
—
3
I
-o
50
/50
ItLgure
18.-
Effdct of torsionalrigidityof stiffeneron bua
ficiemk fm flat plateB. (Dataof ref. 1.)
A?50
300
coef
-
m
—m
m
I
7MWY
o
nmj
--------
n
~.p
———
/
v
/
n am
40
❑
If*30
o
m,
O/w s77FFEm -
0
m
CLAMR5Z Em
NY
SU+0R7ED
EDsm
—
/0
o
EI/bD
(a)
C1.aqedand shply Slqpcrted
plates;longitudinal
m
.
stiffeners.
19.- Cmqparimn of theoryaud. test“datafor shearbucklingcoefficients
of long flat plates with stiffeners.
,
,
/0
on
0
‘1.4
u
.2.4
A“
.4.8
5
A
DATA
L4, 2.4,4.8
TEST
THEORY
0/. =
00A
0
E//bD
stiffeners.
(b)Wmplysupported
plates;
trsnmerse
-----
... . . . . ..—
——
——
-.—
----——-
-.
—————
__— —_. — ..-
————
q.~=o
—-
.— -
7
--T———~—
—=s
- ––––
~= “-–f
___
4*
●
137
N~OFUAWS
Ch!w#n
ON M
o
u
Sro?lw
ON ONEW
Mm-
me
Qkl
●
0
.1
I
10
SEcm
WOE
10=
. .
10”
10’
E.I_/iiD
FigureZO.- Comparisonof theoryend test data fm dmply sqpported
circuhr cyMnd.ersstHfened by rings and loadsdin torsion.
NACATN 3782
67
.
m
u
—
48
4
00
‘
S/m
r
bYJPmR
KAn%s
G!ED+4“ 8‘e :1
16
m
so
E1/bD
(a)
a/b= 1.
#
6
.
/
4
z
k,
. J_
m
b
#-
–-r
00
40
“
“
80
L?o#oma
,11
E1/bD
(b) a/b= 2.
.,
E7/bD
a/b= 59
Shear-buckkn
coefficients
forlongshplysupported
flat
.
(c)
@dH3
withtiEUM3VETSe
StiffeI,IerS.Tm=
lsf#r2E&2
)() “
I-2(1- Ve2b
(wta of ref. 28.)
..
- .—.—— .—— ———
—.
-.
— .. ..-—
—
—.
NACA?CN
3782
68
●
.
w
0
1
I
.-II I I 1111111
I I IlllllJ
1 I 1111111
/
./
/d
- /0
El.
-m
(a) Centersxial stiff~j
axial
,
/03
-.-
.‘.+.
.,-*,-“:
%.>>
.. , -.
length
greaky~hsncircbnferential
width.
-j
:...,,
Figure
22.- Shear-budding
coefficients
for”
si&# &zppdr$ed
curved
plates
ofZ&b 29,.)
.;
withC(?31ti Stiff tie)?● (Data
$
-..
..
--——
—----
.——
—-. —____
____
._ ._.
.
~
‘ -7
NACATN3782
/
CYUWER
/00
50
Woo
/
z M
20
100
CYLL4D
/0
I
[
/
30
20
tts
“z~
b
200
69
CYLJ!E
10
!
–
“
-
30
20
10
6
30
L5
/0
I
48
CYLINDER
!
: “-
“
0
J
/
‘
-
.
d
/03
(b)Center
axialstiffener;
circumferential
widthgreater
thau”sdsl
length.
..
—.-.
. . ..— .—— —. . . . .
.
—
-— ——.—.
— - —. ---
70
NACATN 5782
200
/m
60
30
20
/0
I
40
r
20
k,
m
/0
2
R ‘=
30
M
‘
.
30
/
20
45
2
/0
6
/0
“1
:zz‘II:
30
20
m
i:
I
“
“
44
“
1
10
6
4
‘5
m
/
0 .f
/
(c) Centercircumferential.
sti&ner;
t--al
———
{
/7-b
\UJ
——.
w
/0
fop
/03
axial length
greater
thancXrcum-
ferential
width.
Figure
22.- Conttiued.
—.
J
.
NACATN 3782
.
n.
I‘ ‘
Q
/ .~
200
100
60
40
20
/0
z~
b
300
CYLINDER
f(~~
CYLINDER
poo
100
(d)Center
circumferential
stiffener;
ci&muferentialwidthgreater
than
-al length.
Figure
22.- Concluded.
. . ... .
-- - .——.
--—.
--
—
----- .. ——
- ..—-
-1
N
I
.I
t
/v-
#v
{U”
I
EV20
Figure 23. - BuckMng coefficients
for t3imply
supportedcticulercylinders
stiffenedby r*6
and loadedin torsion.
Ta
=
&-#r”
(Ik&a
of ref. 30.)
,
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