Determine Mode

8/3/2019 Determine Mode

1/20


2/20

X

YZ

a=L 2550mm

b 850mm

B 3400mm

tp 16mm

hw 235mm

tw 10mm

bf 90mm

tf 15mm

E 205800MPa

Y 313.6Mpa

p 0.1MPa

0.3

D

wopl 0.12t

3

212(1 )

Et

Y

E

b

t

Three longitudinal stiffeners

Only applied on longitudinal compressive loads

Lateral pressure loadNeglect(=0)


3/20

Overall Collapse (Mode I)

Collapse of plating together with stiffener as a unit


4/20



1 sx sxx

n AE E

Bt

1

sy sy

y

n A

E E Lt

(1 2 )

x y

xy

x x y y

E EG

E E

22 33

0 012 2 2 12 2 2

fx fx fxwx wx wxx wx wx x fx fx wx x

b t tt h h t tI t h z b t h z

0yI

0

( / 2 / 2) ( / 2 / 2)wx wx wx fx fx fx wx

x

wx wx fx fx

h t h t b t t h t z

bt h t b t

00 yz

0.53 2 3 3

0 0

2

( / )( / 12 / ) /12 /

( / )( / ) ( / )( / )

y x x x y y

x

x y x y y x

E E Et Etz EI b Et Etz EI ac

EI b E E EI a E E

y

y x

x

E

E

23

0

12(1 ) 1

x x

x

x y x y

Etz EIEtD

b

230

12(1 ) 1

y y

y

x y x y

Etz EIEtD

a

31

2 3y x x y xy

tH D D G

10

7

9

247792.2794

205800

2.6967 10

7.66886 10

3.64605 10

x

y

x

y

E Mpa

E Mpa

D Nmm

D Nmm

H Nmm


5/20


Determine value of Am in terms ofxav

3 21 2 3 1

22 4 4

1 23 3 3 3

2 2 4 2 2 4 2

3 3 3 3 3

2

4 4

0

3,

16 16

2

816

m m m

omx y x y

omx y xav x y

om xav

C A C A C A C

Am B L m B LC E E C E E

L B L B

A m B L m B m B m LC E E D H D

L B L t L LB Bm B LB

C A pL t

22 4 4

1 23 3 3 3

22 2 4 2 2 2

3 3 3

2

4 4

3,16 16

( )8

16

om

omxav rex rey

om xav

EAE m b a m b aC Ca b a b

EA m b a m b a D m mb aC

a b a b t ab a mb

m B abC A p

L t


6/20


Determine value of Am in terms ofxav

9 9.5 10 10.5 11 11.5

Am

0

100

200

300

400

500

xav

(MPa)

0 0.5 1 1.5 2 2.5

UC

0

100

200

300

400

500

xav

(MPa)


7/20

9 9.5 10 10.5 11 11.5Am

0

100

200

300

400

500

xav(MPa)

Mode1-Area1(Am)


8/20

0 0.5 1 1.5 2 2.5UC

0

100

200

300

400

500

xav(M

Pa)

Mode1-Area1(UC)


9/20

0 0.5 1 1.5 2 2.5UC

0

100

200

300

400

500

xav(MPa)

Mode1-Area2(UC)


10/20

2 2

yb ybxb xb

Yeq Yeq Yeq Yeq

1


2 22 2

xb xav 2

2 22

yb 2

( 2 )

8 2 1

( 2 )

8 2 1

eqx m m om mx x y

x y

y m m om eq mx y x

x y

tm E A A A A mE

L L B

E A A A t A mE

B L B

Yp Ys

Yeq Yx 313.6sx sx

sx sx

Bt n A

Bt n A

Yx

Yeq Yy

Yx Yy

for longitudinally stiffened panels

for transversely stiffened panels

( ) / 2 for orthogonally stiffened panels

Yeq=equivalent yield stress



11/20


teq=equivalent plate thickness

eq eq

eq2

x yt t

t

s ss seq eq

,y yx x

x y

n An At t t t

B L

2 22 2

xb xav 2

3 205800 ( 2 6.882) 19.265 3205800 0.3

8 2550 2 1 0.09 2550 3400m m m

A A A

2 2

yb ybxb xb

Yeq Yeq Yeq Yeq

1


12/20

Biaxial Compressive Collapse (Mode II)

- Thick plating and under predominant biaxial compressive stress

- Mode of collapse

plate stiffener interaction yields at the corner of plating between stiffener.

22 4 4

1 23 3 3 3

22 2 4 2 2 2

3 3 3

2

4 4

3,

16 16

( )8

16( )

om

om

xav rex rey

om xav rex rey

EAE m b a m b aC C

a b a b

EA m b a m b a D m mb a

C a b a b t ab a mb

m b a abC A p

a b t

22 4 4

1 23 3 3 3

22 2 4 2 2 2

3 3 3

2

4 4

3,16 16

8

16

om

omxav

om xav

EAE m b a m b aC C

a b a b

EA m b a m b D m mb aC

a b a t ab a mb

m b abC A p

a t


13/20

Biaxial Compressive Collapse (Mode II)

2 2

max av 2

( 2 ) 2cos

8

m m om t x x x

m EA A A b

a b

- Thick plating and under predominant biaxial compressive stress

- Mode of collapse

plate stiffener interaction yields at the corner of plating between stiffener.

2 2 2

max maxmax max

Y Y Y Y Y

1y yx x av

2 2 2

max maxmax max

Y Y Y Y Y

1y yx x av

2 2

max av 2( 2 )

8m m om

x x x m EA A Aa

2

max 2

( 2 ) 2cos

8

m m om t y x

EA A A m a

b a

2

max 2

( 2 )

8

m m omy

EA A A

b


14/20

5 10 15 20 25 30 35Am

0

100

200

300

400

500

xav

Mode2-(Am)


15/20

Mode2-(UC)

0 0.5 1 1.5 2 2.5UC

0

100

200

300

400

500

xav(MPa)


16/20

Beam-Column-type Collapse (Mode III)

Effective width of plating between longitudinals:

2 2

min minmax max

Y Y Y Y

1y yx x

Yeu

xu

b

b

2

1.0 1

2 / 1/ 1

euforb

b for

Plate adge at mid-span:

229.5xu


17/20

Beam-Column-type Collapse (Mode III)

Effective width of plating between longitudinals:

PSC at mid-span:

850 313.62.074

16 205800

Ypb

t E

0.18 459eb L mm

2850 16 235 10 90 15 17,300p w f

A A A A mm

2459 16 235 10 90 15 11,044e pe w f A A A A mm

20.5 ( 0.5 ) ( 0.5 )65.325

e w w f w f

p

e

b t A t h A t h t z mm

A

22 2 33 3

12 2 12 2 12 2

102919130.6

f f fe w w we pe p w p f w p

b t tb t t h t hI A z A z t A t h z

maxmaxp xav p

e

Mz

I

max 2 maxqM C M

2 2 2

8

[1 sec( / 2)]C kLk L

2

max 8qqL

M

maxmax ( )s xav w f p

e

Mt h t z

I


18/20

Collapse by Local Buckling of Stiffener Web (Mode IV)

L WIV u u su

s

x x xx

x

bt A

bt A

L euu Yx

b

b

22W W w

E u w 2

w12(1 )

x

tEk

h

2W w w

w u 2

w

x

h tk

D


19/20

Collapse by Tripping of Stiffener (Mode V)

L euu Yx

b

b

2 2 2 2 2T w f f w 4

E 2 2 21,2,3...

p p

(J J ) 3( 1) 1min

12m

a G EI h m Sqa

I a I I m

L TV u u s

s

x x xxu

x

bt A

bt A


20/20

Gross Yielding (Mode VI)

21 3

M MM M

VI VI VI VI VI

u u u u u

1

cc c

y yx x

x x y y

VI

M ux x

VI

u Y eux

b

b

2

1.0 1

2 / 1/ 1

euforb

b for

Determine Mode

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