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Ark1

Side 1

INPUT DATA - GENERALr1 = 2690 mm outer radius of conical shell

r2 = 1815 mm inner radius of conical shell

alpha = 19.1 deg angle of outer cone deg

L = 250 mm length of conical shelll = 985 mm !ertical length "et#een ring stiffeners

s = 12$5 mm length "et#een !ertical stiffeners

t# = 15 mm thickness of longitudinal stiffners

h = 250 mm height of !ertical stiffeners

t = 20 mm shell thickness

n% = 0. &oissons ratio

' = 210000 ()mm*2 'lastic modulus

sigma+= 55 ()mm*2 %ield stress

p0 = ,1.5 ()mm*2 factored design pressures#itch = 0 s#itch- 0= lateral pressure .... 1= h%drostatic pressure

& = ,800000 ( !ertical load

hr = 200 mm #e" height ring stiffener

t# r = 9 mm #e" thickness ring stiffener

"r = 90 mm flange #idth ring stiffener

tf r = 12 mm flange thickness ring stiffener

Ar = 2880 mm*2 area of rin,stiffeners

rf = 218.2 mm radius to top of stiffener

"r

definis/on a! sti!er

hr

re = 28.2 mm eui!alent radius

le = 10$2.8$ mm eui!alent length

stresses in unstiffened cylinderssigmaa = ,2.269$ ()mm*2 aial stress

sigma" = 0 ()mm*2 "ending stress

tau = 0 n)mm*2 shear stresssigmap = ,18.95 ()mm*2 lateral pressure

sigmaph= 0 ()mm*2 h%drostatic pressuer note either sigmap or sigmah eual to

3ero

sigma/ = 1.625 ()mm*2 eui!alent stress

4 = 21.$152 "atdorff parameter for unstiffened c%l.

4s = 1.01508 atdorff parameter for stiffened panel

stresses in ring-stiffened cylinders

"eta = .06022 factor = le))1567rotret::

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Ark1

Side 2

le0 = 9.859 mm effecti!e flange = le)"eta;osh2"eta:,cos2"ets:)

.................................... Sinh2"eta:

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Ark1

Side

unstiffened s(ell %uc"ling

lamn"da*2 = 1.0$559 eui!alent reduced slenderness suared

sigmacr = 2$5.958 ()mm*2 critical stress

utili3ation 0.28$1

Buc"ling #f cur&ed +$nels

N#te/ N#t &ery *ell c(ec"check aspect ratio ?he calculations for cur!ed panels onl% !alid for leffB s other#ise u

leff = 10$2.8$ 10$2.8$ her ligger korrekt !erdi

s = 12$5 Cn the present case the calcuations are ...... not !alid

stresses/

sigmaa = ,2.269$ ()mm*2 aial stress

tau = 0 n)mm*2 shear stress

sigmap = ,18.95 ()mm*2 lateral pressure

sigma/ = 1.625 ()mm*2 eui!alent stress

Buc"ling c#efficients f#r cur&ed +$nel +l$ne +$nel

psi ksi ro psi

Aial $ 21.259 0.2$1 2.8995?ors)shear 11.0$615 12.29$88 0.6 8.1$99$

circimfer 5.888081 5.9188$ 0.6 $

k = pi*2')121,!*2:t)s:*2

El$stic %uc"ling stresses leffBs leff s

; sigma' $8.999 69.81$8 knekksp. uten hens%n til krumnin

sigma'a= 9.05521 $$.655 aial 202.1658

sigma't= 1.2829$ 650.5955 shear 569.029sigma'p= 6.810 $.8801 circumferential pressure 29.$859

rel$ti&e c#ntri%uti#ns

sigmaa)sigma'a = ,0.0052$5 ,0.01151

sigmat)sigma't = 0 0

sigmap)sigma'p = ,0.5861 ,0.696

epont in s

sum = 0.59106 0.6$$81 1.162$$

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Ark1

Side $

REULT

cur&ed +$nel %uc"ling

lamn"da*2 = 1.0$9 1.28809

sigmacr = 2$1.$98 ()mm*2 21.6utiliation 0.552$ 0.81619

PANEL 1LONGITUDINAL2 TIFFENER BUCKLIN

Doment of inertia of stiffener including plate flange

C eff 228126 mm*$ 2$91$9

A 50 mm*2

gammas 25.0121$

effecti!e flange calculated from panel or unstiffened shell "uckling

sigmacr 1 2$5.958 n)mm*2 +rom unstiffened c%lidrical shell

sigmacr 2 2$1.$98 ()mm*2 +rom cur!ed panel "ucklinmg

sigmacr 2$5.958 ()mm*2 used 162.5229 dette kalle

see = 11.2$11 9.$919 effecti!e flange- sigmaa)sigma+sigmacr)sigma/

11.2$11 her ligger korrekt uttr%k

stresses

sigmaa = 16.69$5 ()mm*2 aial stresstau = 0 n)mm*2 shear stress

sigmap = 18.95 ()mm*2 lateral pressure

sigma/ = 11.0125 ()mm*2 eui!alent stress

4 = 21.$152 "atdorff parameter for unstiffened c%l.

4s = 1.01508 atdorff parameter for stiffened panel

Buc"ling c#efficients f#r +$nel stiffener

psi ksi ro

Aial 1.$561 15.26255 0.5?ors)shear 9.591 8.61869 0.6

Lat press 12.200$2 $.8$9292 0.6

El$stic %uc"ling stresses k = pi*2')121,!*2:t)le:*2

; sigma' 69.81$8

sigma'a= .258 5$.0819 aial

sigma't= 10.85116 58.1865 shear

sigma'p= 12.5$256 86.6 lateral

rel$ti&e c#ntri%uti#nssigmaa)sigma'a = 0.0088

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Ark1

Side 5

sigmat)sigma't = 0

sigmap)sigma'p = 0.20$001

sum = 0.2$89

REULT

+$nel stiffener %uc"ling

lamn"da*2 = 0.$858

sigmacr = 19.091 ()mm*2 eui!alent reduced slenderness suared

utiliation 0.5596 critical stress

PANEL RING BUCKLING 1E3TERNAL PREU>'+. EnF ;lass. (ote $.5..

L = 250 mm length "et#een effecti!e supports = "5

le = 10$2.8$ mm eui!alent length "et#een ring stiffners = "19

Ar = 2880 mm*2 cross,sectional area of ring stiffener = h#t#= .18$29 stiffness ratio stiffener )plate 121,n%*2:Cef)let*:

128.082 atdorff parameter "et#een effecti!e supports L*2)rt: 1,n%*2:

;1 = 1$.911 uckling coefficient ring "uckling

sigma' = 1600.18 ()mm*2 elastic "uckling for ring stiffener pi*2')121,n%*2:t)L:*2

;2 = 11.92998delta = 11.9186 mm eui!alent imperfection = 0005re

4L =

21:)1

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Ark1

Side 6

rf = 218.2 mm effecti!e radius to ring flange = re , hr = "2

m% = 1.0$6$11 factor in &err% >o"ertson formula = 3tdelta)ief*2rf)rel)le01,;G);1

k = 0.01289 factor for calculating critical pressure = trf1

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Ark1

Side

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Ark1

Side 8

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Ark1

Side 9

d000 e unstiffened shells

plan plate:

ummation-c

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Ark1

Side 10

228126

general "uckling

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Ark1

Side 11

E2

i!e eff plate flange

::

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Ark1

Side 12

:)1,n%)2:

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Ark2 2:

Side 1

Design of stiened plane panels against Buckling

Exercise #7 - Solution

Eimensions are in ( mm Dpa and the likes:Input data

s = 600 800 1000 distance between longitudinal stifeners

h = 99 $01 5 web height longitudinal stifener

t# = 12.5 11.5 12.5 web thickness o longitudinal stifener

"f = 120 120 120 ange width longitudinal stifener

tf = 26 2$ 25 ange thickness o longitudinal stifener

"f

$25120 $25120 $00120

h

definition of stiffener dimensions

Pressure on plate side

H=06 0.99908 0.9921$9 0.991989 plate induced ailure -plate side in compression

H=06 ,0.$825 ,0.$02$$ ,0.1515 plate induced ailure - tensile yielding o stifener

H=10 0.826668 0.8$$$1 0.8611 plate induced ailure plate side in compression

H=10 ,0.602$ ,0.9062 ,0.81199 plate induced ailure - tensile yielding o stifener

H=10 0.81212 0.858188 0.9168$ stifener induced ailure -stifener in compression

H=10 ,0.18288 ,0.26669 ,0.221 stifener induced ailure -tensile yielding o plate

A total = 1662.6 216.89 2928$.99 The Total Area For Plate and Stifner

s#itch 1 1 1 switch or accurate calculation o moment o inertia = accur

l = $000 $000 $000 rame spacing

t = 1.58$9 1.699 21.59$9 plate thickness

0. 0. 0. Poissons ratio

' = 210000 210000 210000 !lastic modulus

250 250 250 yield stress

p0 = 0.2 0.2 0.2 actored design pressure plate side

p0 = 0 0 0 actored design pressure stifener side

15 15 15 "-stress

190.061 19.65$9 202.9$9 efecti#e a"ial stress during buckling -plate induced ailure

19.521 181.662 18.06 efecti#e a"ial stress during buckling -stifener induced ailure

A = 810.5 $91.5 68.5 cross-sectional area o long$ stifener = hw%tw&b%t

tp = 281.261 282.1926 265.5$88 centroid o stifener e"clussi#e plate ange

e = 10.26$ 0$.862 282.9119 eccentricity o stifener re 'g ($)C = 1.5'

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Ark2 2:

Side 1$

plate induced failure

Cef 1 = 5.$'

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Ark2 2:

Side 15

20.606$ 2.906 25.910 critical buckling streess plate induced ailure 7= 415

229.91 2.2$ 25.121 critical buckling streess plate induced ailure 7= 14

stiffener induced failure

10968.$ 9$8$.008 1.55 buckling stress with k=415

9$8.6$8 $1$.2$ 2568.152 buckling stress with 7=14

0.15092 0.16258 0.18202 reduced slenderness ratio or 7=415

0.25162 0.2059 0.1200$ reduced slenderness ratio or 7=14

0.12$101 0.1696 0.21869 plate imperection actor =,1,8%41448%l%3tie+,

1.1$689$ 1.19612 1.26691$ stifener induced ailure 7=41

1.18$1$ 1.2$299 1.29215 stifener induced ailure 7=14

221.89$1 21.005 201.85 critical buckling streess stifener induced ailure 7= 415

220.95$ 211.681 199.19 critical buckling streess stifener induced ailure 7= 14

I J I

I IKI

IIJ III

IIKIII

IJ III

IIKJII

I IIII

1

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Ark2 2:

Side 16

te

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Ark2 2:

Side 1

*e else/

*e else/

/ %s

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Ark2 2:

Side 18

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Ark2

Side 19

Buc"ling #f stiffened +l$ne +$nels

input datas#itch 1 s#itch for accurate calculation of moment od inertia =1 accurate

s = 985 mm distance "et#een longitudinal stiffeners

l = 12$5 mm frame spacing

t = 20 mm plate thickness

n% = 0. &oissons ratio

' = 210000 ()mm*2 'lastic modulus

sigma+= 55 ()mm*2 %ield stress

p0 = 1.5 ()mm*2 factored design pressure plate side

p0 = 1.5 ()mm*2 factored design pressure stiffener side

& = 800000 ( !ertical load

stressessigma= 18.8 ()mm*2 ,stress

sigmaa 2$.9861 ()mm*2 effecti!e aialM stress during "uckling ,plate induced failure

sigmaa s 196.585 ()mm2 effecti!e aial stres during "uckling ,stiffener induced failure

sigma%= 2. n)mm*2 %,stress

tau = 0 ()mm*2 shear

h = 200 mm #e" height longitudinal stiffener

t# = 9 mm #e" thickness of longitudinal stiffener

"f = 90 mm flange #idth longitudinal stiffener

tf = 12 mm flange thickness of longitudinal stiffener "f

definition of stiffener

h

A = 2880 mm*2 cross,sectional area of long. stiffener = h#t#

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Ark2

Side 20

Cef 1 = 6915016 mm*$ effecti!e moment of inertia = C < e*2A)1< A)set::

Cef 2 = 692$9 mm*$ efecti!e moment of inertia , accurate calculation

Cef = 692$9 mm*$ effecti!e moment of inertia actuall% selected = Cef 2 if "$=1 = Cef

ie*2 = 91.118 mm*2

3p = 20.955 mm centroid of stiffener #ith plate flange

3t = 201.02$2 mm distance from outer edge of ring flange to centroid of stiffener inclus4ep = 2$0$6 mm* effecti!e section modulus #rt. plate falnge = Cef)3p

4et = $68$5.6 mm* effecti!e section modulus #rt. stiffener flange = Cef)3t

se p = 68.6$ plate induced failure

;alculation of effecti!e plate flange ,plate induced failure

"eta = 2.02$9 plate slenderness =s)trotsigmaf)':

; = 0.6981 18)"eta ,08)"eta*2

sigma%u= 206.$ n)mm*2 ultimate trans!. stress = sigmafs)l;

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Ark2

Side 21

sigma"s= 0 ()mm*2

plate induced failure

sigma'6= 15128.2 n)mm*2 "uckling stress #ith k=06

sigma'1 = 5$$6.15 ()mm*2 "uckling stress #ith H=10

lam"da 6 0.1518 reduced slenderness ratio for H=06lam"da 1 0.25511 reduced slenderness ratio for H=10

omega = 8.80928 plate imp factor = 00015l < 0653p1,A

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Ark2

Side 22

1 else:

i!e eff plate flange

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Ark2

Side 2

1 else:

i!e eff plate flange

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Ark2

n" factor

n" factor