Design Principles Hayward - engr.mun.ca

(Plastic) Design Principles

SAFEICE Dissemination Workshop

25 September 2007

Richard Hayward

SAFEICE Dissemination Workshop | Kotka, 25 September 2007 | No. 2

Content

Presentation of results reported in :

Deliverable 8-4 Principles of Plastic Design

Deliverable 9-2 Assessment of Risk Levels in Ice

Class Rules


Deliverable 8-4 Principles of Plastic Design

1. Why Plastic Design?2. Basic Collapse Mechanism3. Effect of Brackets4. Shear-Bending Interaction5. Shape Factors6. Energy Methods7. Acceptable Response Criteria?


1. Why Plastic Design?

Plastic design refers to design where the structural response of the structure is permitted to exceed the elastic limits of its material.

1. Elastic design requires excessively heavy structures to resist design ice loads.

2. An explicit consideration of plastic behaviour is required to determine the true margins of safety associated with extreme ice loads.


2/Yσσ = Yσσ =

2. Basic Collapse Mechanism : q = qY

N A

EI

LMw Y

Y32

2

=w

q

YMM =

Yσσ =

2/YMM =YMM =

Yqq =

M

2

12

L

M Y

YM12

2LqY

24

2LqY

w

2/YM


P.N.A = Axis

of Equal Areas

Yσσ < Yσσ =

2. Basic Collapse Mechanism : q = qEH

N A

EI

LMw P

EH32

~2

w

q

2

12

L

M P

PMM =

Yσσ =

2/PMM =PMM =

PMYqq =

EHqq =

M

2

12

L

M Y

yA

Z

ZM

P

PYP

2=

= σ

y

2

A

2

A

w

12

2LqEH

24

2LqEH2/PM


EI

LMw P

CH96

5~

2

2. Basic Collapse Mechanism : q = qcollapse

N A

EI

LMw P

collapse12

~2

EI

LMw P

p24

~2

w′

w

q q′

2

4

L

M P

2

16

L

M P

2

12

L

M P

PMM =

Yσσ = Yσσ = Yσσ =

PMM =PMM =

Yqq =

EHqq =

collapseqq = CHqq =′M M ′

2

12

L

M Y

w

w′

2/PM

2/PM

PM

24

2LqEH

8

2LqCH

12

2LqEH


Yσσ =Yσσ =

3. Effect of Brackets

N A

w

q

2

16

L

M P

PMM =

Yσσ =

PMM =PMM =

EHqq =

M

w

PM

12

2LqEHEHqq ⋅=′ 2PM⋅2

2

24

L

M P

%50+

PM12

2LqEH

12

2LqEH

• brackets dimensioned such that

three hinges form simultaneously

• reduction in effective span (and

hence bending moment) ignored

• 50% greater capacity, but more

sudden collapse

with

brackets

without brackets


4. Shear-Bending Interaction

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Shear Capacity N (Normalised)

Mo

men

t C

apac

ity

M (

No

rmal

ised

)

Case 1 : Full Plastic Section Modulus

Case 2 : Simple Reduced Plastic Section Modulus

Case 3 : Web Stress Reduced Plastic Section Modulus

ZpZpr =

2

1

−+=

fitted

required

webflangeA

AZZZpr

2

1

−=

fitted

required

A

AZpZpr


4. Shear-Bending (Symmetric) Interaction

- Effect of Web Stress Reduced Section Modulus -

1,0

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2,0

0,00,10,20,30,40,50,60,70,80,91,0

Arequired / Afitted

Pu

lt,

fix

ed

su

pp

ort

s / P

ult

, fr

ee s

up

po

rts

Aflange / Aweb = 0

Aflange / Aweb = 1

Aflange / Aweb = 2pinned-pinned B.C.

fixed-fixed B.C.


5. Shape Factors

1,0

1,5

2,0

2,5

3,0

3,5

0,0 0,5 1,0 1,5 2,0

Web Height / Frame Spacing

Sh

ape

Fac

tor

= Z

p/Z

Af/Ap = 0,0

Af/Ap = 1,0Af/Ap = 0,25 Af/Ap = 0,5


6. Energy Methods

Longitudinal Framing

WorkInternalWorkExternal =

Mp

MprMpr

L

collapseq

L

Mprj

L

MpLqcollapse

24

4

2⋅+=

⋅j = number of rotationally-restrained supports


6. Energy Methods

Transverse Framing (Symmetric Load)


L

collapseq

j = number of rotationally-restrained supports

h

Mp

MprMpr

L

Mprj

L

Mp

L

hspacingqcollapse

24

4

21 ⋅+=

⋅−⋅⋅


−++

−+=

⋅−⋅⋅

xLxmp

xL

MpN

L

hspacingqcollapse

12

21

6. Energy Methods

Transverse Framing (Asymmetric Load)


L

collapseq

Mp

h

x

mp

mp

mp

mp

Nmp

N

mp

shear panel


6. Energy Methods

Transverse Framing (Asymmetric Load)

h/L 0.00.51.0An = Aw/Awsymmetric0.0 0.5 1.0 1.5 2.0

Zn

= Z

p/Z

psy

mm

etr

ic

0.0

1.0

2.0

3.0

4.0

5.0

6.0kz =

zp/Zp

0.025

0.05

0.750.10

0.20

0.30

( )

⋅−⋅

−⋅+

=

L

h

An

kzZn

212

175,51,1

87,0

−=

max1max

A

AnZZn


6. Energy Methods

Plating


∑∫∫=

=n

i

iiMdxdyyxwyxp1

0),(),( ϑl

w(x,y)1l 1ϑ

p (x,y)

x

y

I

I

I-I

Transverse Framing Longitudinal Framing


7. Acceptable Response Criteria?

1. Ultimate or collapse limit state (ULS)

• based on load carrying capacity or

ultimate strength

2. Serviceability limit state (SLS)

• based on the limits of deflections (or

vibration) for normal use



Sample Calculation

Flange = 150 x 17/18

Web = 250 x 17/18

Plate = 500 x 25

Length = 2000 mm, Load Height = 300 mm, ReH = 235 N/mm2



Finite Element Model

Symmetric Loading Asymmetric Loading



Transverse Framing

wp/L=0,10%

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30

Deflection, Permanent Set [mm]

Lin

e L

oad

[k

N/m

]

Symmetric Load

Asymmetric Load

Yield (FE Analysis)



Transverse Framing – Symmetric Loading

Design (Von Mises) Stresses Residual (Von Mises) Stresses



Transverse Framing – Asymmetric Loading

Design (Von Mises) Stresses Residual (Von Mises) Stresses



Transverse Framing – Asymmetric Loading

Design (Shear) Stresses Residual (Shear) Stresses



Plating (Transversely-Framed)

wp/s=0,86%

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 5 10 15 20 25 30 35 40


Lin

e L

oad

[k

N/m

]Restrained Edge Rotation

Unrestrained Edge Rotation

Yield (FE Analysis)



Plating (Longitudinally-Framed)

wp/s=1,24%

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40


Lin

e L

oad

[k

N/m

]Restrained Edge Rotation

Unrestrained Edge Rotation

Yield (FE Analysis)


Deliverable 9-2 Assessment of Risk Levels in

Ice Class Rules

1. Main Particulars of Ships Used in Assessment2. Assessment of Risks – Base Case3. Assessment of Risks – Influence of Load Height4. Assessment of Risks – Influence of Frame

Orientation5. A Structural Design Method for Ice Class Ships6. Recommendations for Further Development of Ice

Class Rules


1. Main Particulars of Ships Used in Assessment

100% Gulf of

Finland (assumed)

88% Gulf of Finland

12% Baltic Proper

57% Bay of Bothnia

21% Bothnian Sea

22% Baltic Proper

Operational

Profile

20,6°27,2°21,3°Frame Angle

20,0°16,5°19,0 °Waterline

Angle

360 mm (trans.)364 mm (trans.)370 mm (trans.)Frame Spacing

5000 kW13200 kW4119 kWPower

9000 t12000 t8250 tDisplacement

112 m155 m113 mLength

IAS/ULIASIASIce Class

TankerRo-RoChemical TankerType

KashiraArcturusKemira


2. Assessment of Risks

Base Case

Frame Spacing = 365 mm

Fra

me

Sp

an =

5 x

36

5 m

m σy = 235 N/mm2

Aflange/Aweb =0,50

kz = zp/Zp = 0,05

Afitted/Arequired = 1,0

Shape Factor = 1,25 (FSICR)

B.C. = Fixed-Fixed

Load Height = 300 mm



Base Case

FSICR (Kemira)

0510152025

Plate Thickness [mm], Plastic Section Modulus [100 cm3]

0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

IA

IAS

0,1 1 10 100 1000 10000

Return Period [Days]

0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Base Case

IACS (Kemira)

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

PC7

PC6

0,1 1 10 100 1000 10000


0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Base Case

RMRS (Kemira)

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

LU4

LU5

0,1 1 10 100 1000 10000


0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Base Case (Symmetric Bending Only)

RMRS (Kemira)

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

LU4

LU5

0,1 1 10 100 1000 10000 100000


0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Base Case - Kemira

270478217152360113020,5* RMRS

(LU5)

49940518531806122118,0IACS

(PC6)

1,6386526179534717,9FSICR

(IAS)

Frame

[Days]

Plate

[Days]

Frame

[kN/m2]

Plate

[kN/m2]

Frame

[cm3]

Plate

[mm]

Return PeriodCollapse LoadRequired Scantlings



Base Case - Arcturus

794340950155962616,7*RMRS

(LU4)

318124241512147199616,2IACS

(PC7)

131293985676242444520,8FSICR

(IA)

Frame

[Days]

Plate

[Days]

Frame

[kN/m2]

Plate

[kN/m2]

Frame

[cm3]

Plate

[mm]




Base Case - Kashira

254041144173275317,6*RMRS

(LU4)

22018916031571105616,8IACS

(PC7)

1,4463491176132417,7FSICR

(IA)

Frame

[Days]

Plate

[Days]

Frame

[kN/m2]

Plate

[kN/m2]

Frame

[cm3]

Plate

[mm]




Influence of Load Height


Fra

me

Sp

an =

5 x

36

5 m

m σy = 235 N/mm2

Aflange/Aweb =0,50

kz = zp/Zp = 0,05



B.C. = Fixed-Fixed





FSICR (Kemira)

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

IA

IAS

0,1 1 10 100 1000 10000


0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Load Height = 100 mm - Kemira

111

(270)

106

(4782)

1516

(1715)

1506

(2360)113020,5*

RMRS

(LU5)

192

(499)

22

(405)

1638

(1853)

1152

(1806)122118,0

IACS

(PC6)

1,3

(1,6)

22

(386)

465

(526)

1145

(1795)34717,9

FSICR

(IAS)

Frame

[Days]

Plate

[Days]

Frame

[kN/m2]

Plate

[kN/m2]

Frame

[cm3]

Plate

[mm]




Influence of Frame Orientation


Frame Span = 5 x 365 mm

σy = 235 N/mm2

Aflange/Aweb =0,50

kz = zp/Zp = 0,05



B.C. = Fixed-Fixed


Load adjusted by FSICR ca

factor:

44

547 FrameSpanca

⋅−=

0,1max =imum

6,0min =imum



Longitudinal Framing

FSICR (Kemira)

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[k

N/m

]

Frame Capacity

Plate Capacity

IA

IAS

0,1 1 10 100 1000 10000 100000


0

500

1000

1500

2000

2500

3000Measured

Gumbel I



Longitudinal Framing - Kemira

34

(270)

151

(4782)

1072

(1715)

1364

(2360)

1266

(1130)

22,3*

(20,5*)

RMRS

(LU5)

7,1

(499)

180

(405)

766

(1853)

1398

(1806)

905

(1221)

22,5

(18,0)

IACS

(PC6)

1,6

(1,6)

48

(386)

452

(526)

1143

(1795)

534

(347)

20,4

(17,9)

FSICR

(IAS)

Frame

[Days]

Plate

[Days]

Frame

[kN/m2]

Plate

[kN/m2]

Frame

[cm3]

Plate

[mm]



5. A Structural Design Method

for Ice Class Ships

0510152025


0

500

1000

1500

2000

2500

3000

Lin

e L

oad

[kN

/m]

Frame Capacity

Plate Capacity

0,1 1 10 100 1000 10000


Semi-Empirical Method


6. Recommendations for Further

Development of Ice Class Rules

Semi-empirical method needs further development with respect to

•different ice conditions

•different ship characteristics (especially bow shapes and frame

spacings/spans, i.e. loaded lengths)

•different design scenarios (i.e. other than continuous icebreaking)

•other hull areas (especially midbody and stern icebelts)

Response criteria needs further development with respect to

longitudinal frames (especially influence of adjacent frames)

(Plastic) Design Principles

SAFEICE Dissemination Workshop

25 September 2007

Richard Hayward

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Design Principles Hayward - engr.mun.ca