ExplosionHavk

dearmeltedUrban and Civil

Nov 25, 2013 (3 years and 9 months ago)

82 views

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



1

Resistance to Accidental
Explosions



General principles

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



2

Outline


Classification of explosion loads


Dynamic response based on SDOF analogy


Dynamic response charts


ISO
-
damage (pressure
-
impulse) diagram


Resistance curves for beams, girders and plates


Ductility limitations


Verification of simple design methods




NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



3

Simple
(SDOF)

vs. advanced
methods


SDOF methods


Biggs’ (1964)


(
Elastic
-
plastic/rigid plastic methods, component analysis…)


Early Design



Screening of scenarios


Codes (NORSOK, IGN(UK)…



Advanced Methods


NLFEA


Large
-
scale simulations feasible


Detail Engineering


Critical Scenarios


Quality of analysis?


0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
Impulse I/(RT)
Pressure F/R
Pressure asymptote
Impulsive asymptote
Iso-damage curve for y
max
/y
elastic
= 10
Elastic-perfectly plastic resistance
Iso
-
damage curve for
blast loading

USFOS
Non-linear static and dynamic analysis

Blast loading

Transient dynamic analyses
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



4



Impulsive domain

-


t
d
/T< 0.3


Response independent of load magnitude


Dynamic domain

-

0.3 < t
d
/T < 3


Quasi
-
static domain

-

3 < t
d
/T



EXPLOSION

Classification of response



w
R
w
dw
max
w
max


1
0
F
max
Rise time small



max
max
w
w
R
F

Rise time large


I
m
R
w
dw
eq
w
max


2
0
,


I
F
t
dt
t
d


0
=
impuls
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



5


Conservation of momentum





EXPLOSION

Impulsive domain

-

t
d
/T< 0.3


F
eq
(t)

m
eq

k
eq
(y)

Y(t
d
)

t

F
eq
(t)

y(t)

t
d







d
d
t
d eq
0
eq eq
y t 0
1 I
y t F t dt
m m

 

R(y)= k
eq
(y)∙y







Conservation of energy
















max
max
0
0
2
2
2
2
1
2
1
y
eq
y
eq
d
eq
dy
y
R
m
I
dy
y
R
m
I
t
y
m

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



6


Rise time small (1)




External work Strain energy


EXPLOSION

Quasi
-
static domain

-

t
d
/T> 3


F
eq
(t)

m
eq

k
eq
(y)

Y(t
d
)

t

F
eq
(t)

y(t)

t
d



max
y
eq,max max
0
F y R y dy


R(y)= k
eq
(y)∙y







Rise time large (2)



Static solution




eq,max max
F R y

t

F
eq
(t)

y(t)

t
d

(1)

(2)

t
rise

t
rise

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



7

Explosion response
-
1 DOF analogy

)
(
t
f
y
k
y
m




Dynamic equilibrium

(x)

=
displacement shape function
y(t)
= displacement amplitude


2
2
i
i
i
M
dx
x
m
m







=
generalized mass






i
i
i
F
dx
x
t
p
t
f



)
(
)
(
=
generalized load





dx
x
EI
k
xx
2
,

=
generalized elastic bending stiffness
k

0
=
generalized plastic bending stiffness

(
fully developed mechanism)





dx
x
N
k
x
2
,

=
generalized membrane stiffness

(
fully plastic: N = N
P
)
m
= distributed mass
M
i

= con
centrated mass
p
= explosion pressure
F
i
= concentrated load (e.g. support reactions)
x
i
= position of concentrated mass/load
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



8

Dynamic equilibrium
-

alternative formulation


)
(
t
F
Ky
y
M
k
lm






l
m
lm
k
k
k




= load
-
mass transformation factor

M
m
k
m




= mass transformation factor

F
f
k
l




= load transformation factor






i
i
M
mdx
M


= total mass





i
i
F
pdx
F



= total load

m
k
k
K




= characteristic stiffness


NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



9

EXPLOSION

SDOF analogy


Biggs’ method

f(t)

t

f(t)

F
eq
(t)

m
eq

k
eq
(y)

y









eq eq eq eq
m y t c y t k y F t
  
Dynamic equilibrium:

y(t)

t

y
max

)
(
t
F
Ky
y
M
k
lm




Load
-
mass
transformation
factor

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



10

Development of explosion response charts






m,u u m,c c
k M k M y K y y F(t)
  
l l

Dynamic equilibrium



Explosion load history


Solve dynamic equation


numerical integration


Determine maximum
deformation y
max



Perform analysis for
different duration and load
amplitude



F
(t)

t

t

0,00
0,05
0,10
0,15
0,20
0,000
0,005
0,010
0,015
Time [secs]
Displacement [m]
Shell - plate
Shell - stiffener
beam
R
el
/F
max
= 0.31
R
el
/F
max
= 0.59
F
max

R
(
y
)

y

R
el

y
el

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



11

EXPLOSION

Classification of resistance curves

R

R

R

R

w

w

w

w

K
1

K
1

K
1

K
1

K
3

K
2

K
2

K
2

Elastic

Elastic
-
plastic

(determinate)

Elastic
-
plastic

(indeterminate)

Elastic
-
plastic

with membrane

K
2
=0

K
1

R

K
3

w

R
el

W
el


or y
el

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



12

Explosion response chart

maximum displacement versus load duration


Governing parameters:


Mechanisme resistance
vs. maximum load


R
el
/F
max


Load duration vs.
eigenperiod
t
d
/T


Membrane stiffness, if
any

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



13

EXPLOSION

Dynamic response chart for pressure pulse
-
[J.M.Biggs]

Triangular load
-

rise time = 0.3 t
d


NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



14

Development of ISO
-
damage curves from dynamic response
charts for a given pressure pulse

Example
y
allow
/y
el

=10

0.1
1
10
100
0.1
1
10
t
d
/T
y
max/
y
el
=0.1
= 0.7
= 0.6
= 0.5
R
el
/F
max
=0.05
= 0.3
= 1.1
= 1.0
= 0.9
R
el
/F
max
= 0.8
= 1.2
= 1.5
y
el
y
R
R
el
F
F
max
t
d
k
1
k
3
= 0.5k
1
=0.2k
1
=0.1k
1
k
3
= 0
k
3
= 0.1k
1
k
3
= 0.2k
1
k
3
= 0.5k
1
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



15

Example
y
allow
/y
el

=10

0.1
1
10
100
0.1
1
10
t
d
/T
y
max/
y
el
=0.1
= 0.7
= 0.6
= 0.5
R
el
/F
max
=0.05
= 0.3
= 1.1
= 1.0
= 0.9
R
el
/F
max
= 0.8
= 1.2
= 1.5
y
el
y
R
R
el
F
F
max
t
d
k
1
k
3
= 0.5k
1
=0.2k
1
=0.1k
1
k
3
= 0
k
3
= 0.1k
1
k
3
= 0.2k
1
k
3
= 0.5k
1
Pressure = F
max

Impulse =1/2F
maxt
t
d

Development of ISO
-
damage curves from dynamic
response charts for a given pressure pulse

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



16

EXPLOSION

Iso
-
damage curve for y
allow
/
yelastic

=10.
[W.Baker]


0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
Impulse I/(RT)
Pressure F/R
Pressure asymptote
Impulsive asymptote
Iso-damage curve for y
max
/y
elastic
= 10
Elastic-perfectly plastic resistance
Inadmissible domain

Admissible domain

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



17

EXPLOSION

Resistance curves


Beams and girders


Tabulated values for elastic
-
plastic behaviour


Resistance curves based on plastic thory


Plates


Elastic and plastic theory

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



18

Mass factor k
m
Load-mass factor
k
lm
Load case
Resistance
domain
Load
Factor
k
l
Concen-
trated
mass
Uniform
mass
Concen-
trated
mass
Uniform
mass
Maximum
resistance
R
el
Characteristic
stiffness
K
Dynamic reaction
V
Elastic
Plastic
bending
Plastic
membrane
0.64
0.50
0.50
0.50
0.33
0.33
0.78
0.66
0.66
8
M
L
p
8
M
L
p
384
5
3
EI
L
0
4
N
L
P
0
39
0
11
.
.
R
F

0
38
0
12
.
.
R
F
el

L
y
N
max
P
2
Elastic
Plastic
bending
Plastic
membrane
1.0
1.0
1.0
1.0
1.0
1.0
0.49
0.33
0.33
1.0
1.0
1.0
0.49
0.33
0.33
4
M
L
p
4
M
L
p
48
3
EI
L
0
4
N
L
P
0
78
0
28
.
.
R
F

0
75
0
25
.
.
R
F
el

L
y
N
max
P
2
Elastic
Plastic
bending
Plastic
membrane
0.87
1.0
1.0
0.76
1.0
1.0
0.52
0.56
0.56
0.87
1.0
1.0
0.60
0.56
0.56
6
M
L
p
6
M
L
p
56
4
3
.
EI
L
0
6
N
L
P
0
525
0
025
.
.
R
F

0
52
0
02
.
.
R
F
el

L
y
N
max
P
3
F=
pL
L
L/2
F
L/2
L/
3
L
/3
L/3
F/
2
F
/2
Transformation factors for beams with various boundary
and load conditions

NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



19

Transformation factors for beams with various boundary and
load conditions

Mass factor k
m
Load-mass factor
k
lm
Load case
Resistance
domain
Load
Factor
k
l
Concen-
trated
mass
Uniform
mass
Concen-
trated
mass
Uniform
mass
Maximum
resistance
R
el
Characteristic
stiffness
K
Dynamic reaction
V
Elastic
Elasto-
plastic
bending
Plastic
bending
Plastic
membrane
0.53
0.64
0.50
0.50
0.41
0.50
0.33
0.33
0.77
0.78
0.66
0.66
12
M
L
ps


8
M
M
L
ps
Pm



8
M
M
L
ps
Pm

384
3
EI
L
384
5
3
EI
L
307
3
EI
L






0
4
N
L
P
0
36
0
14
.
.
R
F

0
39
0
11
.
.
R
F
el

0
38
0
12
.
.
R
F
el

L
y
N
max
p
2
Elastic
Plastic
bending
Plastic
membrane
1.0
1.0
1.0
1.0
1.0
1.0
0.37
0.33
0.33
1.0
1.0
1.0
0.37
0.33
0.33


4
M
M
L
ps
Pm



4
M
M
L
ps
Pm

192
3
EI
L
0
4
N
L
P
0
71
0
21
.
.
R
F

0
75
0
25
.
.
R
F
el

L
y
N
max
P
2
F=
pL
L
F
L/2
L/
2
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



20

New Revision II: Transformation factors for
clamped beam with two concentrated loads


Mass factor k
m



Load
-
mass factor
k
lm



Load case



Resistance

domain



Load

Factor

k
l

Concen
-
trated
mass

Uniform
mass

Concen
-
trated
mass

Unifor
m
mass



Maximum
resistance

R
el



Characteristic
linear stiffness

K1



Dynamic reaction

V


L/
3
L
/3
L/3
F/
2
F
/2


Elastic


Elasto
-
plastic

bending



Plastic
bending



Plastic
membrane

080



0.87



1.0



1.0

0.64



0.76



1.0



1.0

0.41



0.52



0.56



0.56

0.80



0.87



1.0



1.0

0.51



0.60



0.56



0.56

9
ps
M
L



6
ps Pm
M M
L



6
ps Pm
M M
L


3
260
EI
L

3
56.4
EI
L


0


6
P
N
L


0.48 0.02
R F



0.52 0.02
el
R F



0.52 0.02
el
R F



L
y
N
max
P
3


NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



21

Transformation factors for beams with various boundary and load conditions

Mass factor k
m
Load-mass
factor
k
lm
Load case
Resistan
ce
domain
Load
Fact
or
k
l
Concen
-trated
mass
Unifor
m mass
Concen-
trated
mass
Unifor
m mass
Maximum
resistance
R
el
Characterist
ic stiffness
K
Dynamic
reaction
V
Elastic
Elasto-
plastic
Bending
Plastic
bending
Plastic
membra
ne
0.58
0.64
0.50
0.50
0.45
0.50
0.33
0.33
0.78
0.78
0.66
0.66
8
M
L
ps


4
2
M
M
L
ps
Pm



4
2
M
M
L
ps
Pm

185
3
EI
L
384
5
3
EI
L
160
3
EI
L






0
4
N
L
P
V
R
F
1
0
26
0
12


.
.
V
R
F
2
0
43
0
19


.
.
0
39
0
11
.
.
R
F
M
L
Ps


0
38
0
12
.
.
R
F
M
L
Ps


L
y
N
max
P
2
Elastic
Elasto-
plastic
Bending
Plastic
bending
Plastic
membra
ne
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.43
0.49
0.33
0.33
1.0
1.0
1.0
1.0
0.43
0.49
0.33
0.33
16
3
M
L
Ps


2
2
M
M
L
ps
Pm



2
2
M
M
L
ps
Pm

107
3
EI
L
48
3
EI
L
106
3
EI
L






0
4
N
L
P
V
R
F
1
0
25
0
07


.
.
V
R
F
2
0
54
0
14


.
.
0
78
0
28
.
.
R
F
M
L
Ps


0
75
0
25
.
.
R
F
M
L
Ps


L
y
N
max
P
2
Elastic
Elasto-
plastic
Bending
Plastic
bending
Plastic
membra
ne
0.81
0.87
1.0
1.0
0.67
0.76
1.0
1.0
0.45
0.52
0.56
0.56
0.83
0.87
1.0
1.0
0.55
0.60
0.56
0.56
6
M
L
Ps


2
3
M
M
L
ps
Pm



2
3
M
M
L
ps
Pm

132
3
EI
L
56
3
EI
L
122
3
EI
L






0
6
N
L
P
V
R
F
1
0
17
0
17


.
.
V
R
F
2
0
33
0
33


.
.
0
525
0
025
.
.
R
F
M
L
Ps


0
52
0
02
.
.
R
F
M
L
el
Ps


L
y
N
max
P
3
V
2
V
1
F=
pL
L
V
1
L/2
L/2
F
V
2
V
1
L/
3
L
/3
L/3
F/
2
F
/2
V
2
NUS July 12
-
14, 2005

Analysis and Design for Robustness of Offshore Structures

NUS


Keppel Short Course



22

Ductility ratios

( Ref: Interim Guidance Notes)

Table

A.6
-
3
Ductility ratios

beams with no axial restraint
Cross-section category
Boundary
conditions
Load
Class 1
Class 2
Class 3
Cantilevered
Concentrated
Distributed
6
7
4
5
2
2
Pinned
Concentrated
Distributed
6
12
4
8
2
3
Fixed
Concentrated
Distributed
6
4
4
3
2
2