determine mode
TRANSCRIPT
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8/3/2019 Determine Mode
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8/3/2019 Determine Mode
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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)
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8/3/2019 Determine Mode
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Overall Collapse (Mode I)
Collapse of plating together with stiffener as a unit
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8/3/2019 Determine Mode
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Overall Collapse (Mode I)
Collapse of plating together with stiffener as a unit
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
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8/3/2019 Determine Mode
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Overall Collapse (Mode I)
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
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8/3/2019 Determine Mode
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Overall Collapse (Mode I)
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)
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8/3/2019 Determine Mode
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9 9.5 10 10.5 11 11.5Am
0
100
200
300
400
500
xav(MPa)
Mode1-Area1(Am)
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8/3/2019 Determine Mode
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0 0.5 1 1.5 2 2.5UC
0
100
200
300
400
500
xav(M
Pa)
Mode1-Area1(UC)
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8/3/2019 Determine Mode
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0 0.5 1 1.5 2 2.5UC
0
100
200
300
400
500
xav(MPa)
Mode1-Area2(UC)
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8/3/2019 Determine Mode
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2 2
yb ybxb xb
Yeq Yeq Yeq Yeq
1
Overall Collapse (Mode I)
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
Collapse of plating together with stiffener as a unit
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8/3/2019 Determine Mode
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Overall Collapse (Mode I)
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
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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5 10 15 20 25 30 35Am
0
100
200
300
400
500
xav
Mode2-(Am)
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8/3/2019 Determine Mode
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Mode2-(UC)
0 0.5 1 1.5 2 2.5UC
0
100
200
300
400
500
xav(MPa)
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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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
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8/3/2019 Determine Mode
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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