hcsr chapter 8_buckling

Harmonised Common Structural Rules Part 1, Chapter 8, Section 1

March 2011

Section 1 – General

1. Introduction

1.1 Assumption

1.1.1

This Chapter contains the strength criteria for buckling and ultimate strength of local supporting members,

primary supporting members and other structures such as pillars, corrugated bulkheads and brackets. These

criteria are to be applied as specified in Ch 6 for hull local scantlings and in Ch 7 for direct strength analysis.

1.1.2

For each structural member the characteristic buckling strength is to be taken as the most unfavourable / critical

buckling failure mode.

1.1.3

Unless otherwise specified, the scantling requirements of structural members in this Chapter are based on net

scantling obtained by removing tc from the gross offered thickness, where tc is defined in Ch 4.

1.1.4

In this Chapter, compressive and shear stresses are to be taken as positive, tension stresses are to be taken

negative unless otherwise specified.

2. Application

2.1 Scope

2.1.1

The buckling checks are to be performed according to:

Sec 2 for the slenderness requirements of plates, longitudinal and transverse stiffeners, primary supporting

members and brackets

Sec 3 for the prescriptive buckling requirements of plates, longitudinal and transverse stiffeners, supporting

members and other structures

Sec 4 for the buckling requirements of the FEM analysis for the plates, stiffened panels and other structures

Sec 5 for the buckling capacity of prescriptive and FEM buckling requirements.

2.1.2

Enlarged stiffeners, with or without web stiffening, used for Permanent Means of Access (PMA) are to comply

with the following requirements:

a) Slenderness requirements for primary supporting members as follows:

For enlarged stiffener web: Sec 2, [4.1.1] a), [5.1]

For enlarged stiffener flange: Sec 2, [4.1.1] b)

For stiffeners fitted on enlarged stiffener web: Sec2, [3.1.1] and [3.1.3]

Part 1, Chapter 8, Section 1 Harmonised Common Structural Rules

March 2011

b) Buckling strength of prescriptive requirements as follows:

For enlarged stiffener web, see Sec 3, [3.1]

For stiffeners fitted on enlarged stiffener web: Sec 3, [3.2]

c) All structural elements used for PMA are to be complied with for the buckling requirements of the FEM

analysis in Sec 4 when applicable

d) Buckling strength of longitudinal PMA platforms without stiffeners fitted on enlarged stiffener web is to be

checked using the criteria for local supporting members in Sec 2, [2.1] including Sec 2, [3.1.2] and [3.1.3]

and Sec 3, [3.2] provided shear buckling strength of web is verified in line with Sec 3, [3.1]

3. Definitions

3.1 General

3.1.1

“Buckling” is used as a generic term to describe the strength of structures, generally under in-plane compressions

and/or shear. The buckling strength or capacity can take into account the internal redistribution of loads

depending on the situation.

3.1.2 Method 1

Buckling capacity accepting local elastic plate buckling with load redistribution is referred to as Method 1.

Buckling capacity based on this principle gives a lower bound estimate of ultimate capacity, or the maximum

load the panel can carry without suffering major permanent set. Method 1 buckling capacity assessment utilizes

the positive elastic post-buckling effect for plates and accounts for load redistribution between the structural

components, such as between plating and stiffeners. For slender structures the capacity calculated using this

method is typically higher than the ideal elastic buckling stress (minimum Eigen-value). Accepting elastic

buckling of structural components in slender stiffened panels implies that large elastic deflections and reduced

in-plane stiffness will occur at higher buckling utilisation levels.

3.1.3 Method 2

Method 2 buckling capacity does not accept load redistribution between structural components and refers to the

minimum of value of the ideal elastic buckling stress and the Method 1 buckling capacity. Method 2 buckling

capacity normally equals the same strength as Method 1 for stocky panels, while it is the ideal elastic buckling

stress (minimum Eigen-value cut-off) for slender panels. By applying the ideal elastic buckling stress limitation,

large elastic deflections and reduced in-plane stiffness will be avoided at higher buckling utilisation levels.

3.2 Buckling utilisation factor

3.2.1

The utilisation factor, η, is defined as the ratio between the applied loads and the corresponding ultimate capacity

or buckling strength.

3.2.2

Astructural member is considered to have an acceptable buckling strength if it satisfies the following criterion:


March 2011

allact

where:

act : Actual buckling utilisation factor based on the applied design stress, defined in [3.2.3]

all : Allowable buckling utilisation factor defined in Sec 3 for prescriptive requirements and in Sec 4 for

FEM buckling requirements

3.2.3

For combined loads, the utilisation factor, ηact, is to be defined as the ratio of the applied equivalent stress and the

corresponding buckling capacity, as shown in Figure 1, and is to be taken as:

u

actact W

W

where:

actW : Applied equivalent stress due to the combined membrane stresses, in N/mm2

222 yxactW

x : Membrane stress applied in x direction, in N/mm2

y : Membrane stress applied in y direction, in N/mm2

: Membrane shear stress applied in xy plane, in N/mm2

uW : Equivalent buckling capacity, in N/mm2, to be taken as:

222ccycxuW

ccycx ,, : Critical stress, in N/mm², defined in Sec 5 [2.3] for plates and in [2.5] for stiffeners

The Figure 1 illustrates the buckling capacity and the buckling utilization factor of a structural member subject to

σx and σy stresses.

Figure 1: Example of buckling capacity and buckling utilisation factor

Harmonised Common Structural Rules Part1, Chapter 8, Section 2

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Section 2 – Slenderness requirements

Symbols

For symbols not defined in this section, refer to Ch 1, Sec 4.

bf-out : Maximum distance, in mm, from mid thickness of the web to the flange outstand based on gross

scantling, as shown in Figure 1

hw : Depth of stiffener web based on gross scantling, in mm, as shown in Figure 1

ReH : Specified minimum yield stress of the material, in N/mm2

s : Stiffener spacing, in mm

seff : Effective width of attached plate of stiffener, in mm, taken equal to

seff = 0.8 s

tf : Net flange thickness, in mm

tp : Net thickness of plate, in mm

tw : Net web thickness, in mm

1. Structural Elements

1.1 General

1.1.1

All structural elements are to comply with the applicable slenderness and proportion requirements given in [2] to

[4].

1.1.2

The structural idealisation and definitions are given in Ch 1, Sec 4.

2. Plates

2.1 Net thickness of plate panels

2.1.1

The net thickness of plate panels is to satisfy the following criteria:

235eH

p

R

C

st

where:

C : Slenderness coefficient as follows:

C = 100 for hull envelope and cargo and tank boundaries

C = 125 for other structures

Part1, Chapter 8, Section 2 Harmonised Common Structural Rules

Page 2 March 2011

3. Stiffeners

3.1 Proportions of stiffeners

3.1.1 Net thickness of all stiffener types

The net thickness of stiffeners is to satisfy the following criteria:

a) Stiffener web plate

235eH

w

ww

R

C

ht

b) Flange

235eH

f

outff

R

C

bt

where:

Cw, Cf : Slenderness coefficients given in Table 1

Figure 1: Stiffener scantling parameters

dw dw dw

bf-out

dw

Flat bars Bulb flats Angles T bars

bf-out

h h hh

Table 1: Slenderness coefficients

Type of Stiffener Cw Cf Angle bars 55 12

T-bars 65 12

Bulb bars 45 -

Flat bars 22 -

3.1.2 Net dimensions of angle and T-bars

The total flange breadth for angle and T-bars is to satisfy the following criterion:

wf hb 25.0

where:

bf : Total flange breadth, in mm

3.1.3 Stiffness of stiffeners

The net moment of inertia, in cm4, about the neutral axis parallel to the effective attached plate of stiffener, seff, is

not to be less than the minimum value given by:


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2352 eH

effstR

ACI

where:

: Length of stiffener between effective supports, in m

Aeff : Net sectional area of stiffener including effective attached plate, seff, in cm2

ReH : specified minimum yield stress of the material of the attached plate, in N/mm2

C : Slenderness coefficient taken as follows:

C = 1.43 for longitudinal stiffeners including sniped stiffeners

C = 0.72 for other stiffeners

4. Primary Supporting Members

4.1 Proportions and stiffness

4.1.1 Proportions of web plate and flange

The net thicknesses of the web plates and flanges of primary supporting members are to satisfy the following

criteria:

a) Web plate

235eH

w

ww

R

C

st

b) Flange

235eH

f

outff

R

C

bt

where:

sw : Plate breadth, in mm, taken as the spacing of the web stiffeners.

Cw : Slenderness coefficient for the web plate taken as

Cw = 100

Cf : Slenderness coefficient for the flange taken as

Cf = 12

4.1.2 Stiffness of transverse primary supporting members

The net moment of inertia for transverse primary supporting members, Ipsm, in cm4, supporting longitudinals

subject to axial compressive hull girder stress, is to comply, within its central half of the bending span, with the

following criterion:

stbdg

psm IsS

lI

3

4

300

where:

Ipsm : Net moment of inertia, in cm4, of transverse primary supporting member, with effective width of

attached plate equal to 0.8 S

lbdg : Bending span of transverse primary supporting member, in m, as defined in Ch 1, Sec 4

S : Spacing of transverse primary supporting members, in m

Ist : Moment of inertia of stiffeners within the central half of the bending span, in cm4, as given in [3.1.3].


Page 4 March 2011

4.2 Web stiffeners of primary supporting members

4.2.1 Proportions of web stiffeners

The web and flange net thicknesses of web stiffeners fitted on primary supporting members are to satisfy the

requirements specified in [3.1.1] and [3.1.2].

4.2.2 Stiffness of web stiffeners

The net moment of inertia, in cm4, of web stiffener, Ist, fitted on primary supporting members, with effective

attached plate, seff, is not to be less than the values defined in Table 2.

Table 2: Stiffness criteria for web stiffening

Mode Minimum moment of inertia, in cm4 (a) web stiffeners parallel to compression stresses

s

l

2352 eH

effstR

ACI

(b) web stiffeners normal to compression stresses

l

s

52 102351000

21000

5.214.1

eH

wstRs

stsI

where: C Slenderness coefficient to be taken as

C = 1.43 for longitudinal stiffeners: both continuous and sniped stiffeners. C = 0.72 for other stiffeners

Length of web stiffener, in m. For web stiffeners welded to local supporting members, the length is to be measured between the flanges of the local supporting members. For sniped web stiffeners the length is to be measured between the lateral supports e.g. the total distance between the flanges of the primary supporting member as shown for Mode (b).

Aeff Net section area of web stiffener including effective attached plate, seff, in cm2 tw Net web thickness of the primary supporting member, in mm ReH Specified minimum yield stress of the material of the web plate of the primary supporting

member, in N/mm2

4.3 Edge reinforcement in way of openings

4.3.1 Depth of edge stiffener

If fitted, the depth of stiffener web, in mm, of edge stiffeners in way of openings is not to be less than:

235eH

stfw

RCh or 50 mm, whichever is greater

where:

stf : Length of stiffener between effective supports, in m


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C : Slenderness coefficient equal to:

C = 50

ReH : Specified minimum yield stress of the edge stiffener material, in N/mm2

4.3.2 Proportions of edge stiffeners

The net thickness of the web plate and flange of the edge stiffener is to satisfy the requirements specified in

[3.1.1] and [3.1.2].

5. Brackets

5.1 Tripping brackets

5.1.1 Minimum spacing

The unsupported length of the flange of the primary supporting member, in m, i.e. the distance between tripping

brackets, is not to be greater than:

eHw

f

ffb RA

A

ACbs

235

3

, but need not be less than sb-min

where:

bf : Flange breadth of primary supporting members, in mm

C : Slenderness coefficient taken as:

C = 0.022 for symmetrical flanges

C = 0.033 for asymmetrical flanges

Af : Net cross-sectional area of flange, in cm2

Aw : Net cross-sectional area of the web plate, in cm2

sb-min : Minimum unsupported flange length taken as:

sb-min = 3.0 m for the cargo tank/hold region, on tank/hold boundaries or the hull envelope including

external decks

sb-min = 4.0 m for other areas

5.1.2 Edge stiffening

Tripping brackets on primary supporting members are to be stiffened by a flange or edge stiffener if the effective

length of the edge, in mm, is greater than:

bb t75

where:

tb : Bracket net web thickness, in mm

5.2 End brackets

5.2.1 Proportions

The net web thickness of end brackets, in mm, subject to compressive stresses is not to be less than:


Page 6 March 2011

235eHb

b

R

C

dt

where:

db : Depth of brackets, in mm. as defined in Table 3

C : Slenderness coefficient as defined in Table 3

ReH : Specified minimum yield stress of the end bracket material, in N/mm2

Table 3: Buckling coefficient, C, for proportions of brackets

Mode C

(a) Brackets without edge stiffener

lbkt

dbkt

1620

b

bdC

where:

0.125.0 b

bd

(b) Brackets with edge stiffener

dbkt

C = 70

where: lb : Effective length of edge of bracket, in mm


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5.3 Edge reinforcement

5.3.1 Edge reinforcements of bracket edges

The depth of stiffener web, in mm, of edge stiffeners in way of bracket edges is not to be less than:

235eH

stfw


where:

stf : Length of edge stiffener between effective supports, in m

C : Slenderness coefficient taken as:

C = 75 for end brackets

C = 50 for tripping brackets

ReH : Specified minimum yield stress of the stiffener material, in N/mm2



[3.1.1] and [3.1.2].

6. Other structures

6.1 Pillars

6.1.1 Proportions of I-section pillars

For I-sections, the thickness of the web plate and the flange thickness are to comply with requirements specified

in [3.1.1] and [3.1.2].

6.1.2 Proportions of box section pillars

The thickness of thin walled box sections is to comply with the requirements specified in [3.1.1] a).

6.1.3 Proportions of circular section pillars

The net thickness, t, of circular section pillars, in mm, is to comply with the following criterion:

50

rt

where:

r : Mid thickness radius of the circular section, in mm

6.2 Edge reinforcement in way of openings

6.2.1 Depth of edge stiffener

When fitted as shown in Figure 2, the depth of stiffener web, in mm, of edge stiffeners in way of openings is not

to be less than:

235eH

stfw


where:


Page 8 March 2011

stf : Length of stiffener between effective supports, in m

C : Slenderness coefficient equal to:

C = 50

ReH : Specified minimum yield stress of the attached plate material of the edge stiffener, in N/mm2



[3.1.1] and [3.1.2].

Figure 2: Typical edge reinforcements

lsf


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Section 3 - Prescriptive Buckling Requirements

1. General

1.1 Scope

1.1.1

The requirements of this Section apply to structural members subject to hull girder stresses and to lateral

pressure.

1.1.2

The buckling checks have to be performed for the following structural elements:

Elementary plate panel

Longitudinal and transverse stiffeners

1.2 Equivalent plate panel

1.2.1

When the plate thickness varies over the width, la, in mm, of a plate panel, the buckling check is performed for

an equivalent plate panel width, having a thickness equal to the smaller plate thickness, t1. The width of this

equivalent plate panel, la’, in mm, is defined by the following formula:

5.1

2

121

'

t

tllla

where:

1l : Width of the part of the plate panel with the smaller plate thickness, 1t , in mm, as defined in Figure 1

2l : Width of the part of the plate panel with the greater plate thickness, 2t , in mm, as defined in Figure 1

Figure 1: Plate thickness change over the width

2. Hull Girder Stress

2.1 General

2.1.1

Buckling strength checks of structural members subjected to hull girder loads are to be based on the combination

of longitudinal stress, shear stress and lateral pressure.


Page 2 March 2011

2.1.2

The hull girder stresses are determined according to Ch 5, Sec [XXX] for intact conditions and in [XXX] for

flooded conditions.

2.1.3

When the shear stresses are not uniform over the width of the panel, the greater of the two following values is to

be used:

Mean value of τ

0.5 τmax

2.2 Stress combinations

2.2.1

Each elementary plate panel and longitudinal/transverse stiffeners are to satisfy the criteria defined in [3] with

the following stress combinations:

a) Longitudinal stiffening arrangement:

Stress combination 1 with nx , 0y and SF 7.0

Stress combination 2 with nx 7.0 , 0y and SF

b) Transverse stiffening arrangement:

Stress combination 1 with 0x , ny and SF 7.0

Stress combination 2 with 0x , ny 7.0 and SF

where:

n : Actual normal compressive stress in the elementary plate panel or stiffener resulting from hull girder

stress as defined in [2] , in N/mm2

SF : Actual shear stress, in N/mm2, as defined in [2]

3. Buckling Criteria

3.1 Plates

3.1.1

The buckling strength of elementary plate panels is to satisfy the following criterion:

1Plate

where:

Plate : Maximum plate utilisation factor calculated according to Method 1, as defined in Sec5, [2.3] with the

stress combinations defined in [2.2]

3.2 Stiffeners

3.2.1

The buckling strength of stiffeners is to satisfy the following criterion:


March 2011 Page 3

1Stiffener

where:

Stiffener : Maximum stiffener utilisation factor, as defined in Sec5, [2.5] with the stress combinations defined in

[2.2]


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Section 4 - Buckling requirements for direct strength analysis

Symbols

all : Allowable buckling utilisation factor, as defined in Table 1

1. General

1.1 Scope

1.1.1

The requirements of this Section apply for the buckling assessment of direct strength analysis subjected to

compressive stress, shear stress and lateral pressure.

1.1.2

All structural elements in the finite element analysis carried out according to Ch 7 are to be assessed

individually. The buckling checks have to be performed for the following structural elements:

Stiffened and un-stiffened panels

Web plate in way of openings

Corrugated bulkhead

Vertically stiffened side shell plating of single side skin bulk carrier

Struts, pillars and cross ties

1.2 Buckling assessment methods

1.2.1

The buckling check is to be performed using one of the two following methods:

Closed form method specified in Sec5, [2]

Semi-analytic method specified in Sec5, [3]

1.2.2

For the buckling assessment of the [single panel, ship], only one buckling method is to be used.

1.2.3 [Alternative method

Alternative method different than those defined in [1.2.1] used for the buckling assessment needs the prior

agreement of the HP.

The conditions for the approval are stated in the TB of these Rules]

Note: Upon Decision of HP

1.3 Allowable buckling utilisation factor

1.3.1 General structural elements

The allowable buckling utilisation factor is defined in Table 2.


Page 2 March 2011

Table 1: Allowable buckling utilisation factor

Structural component ηall, Allowable buckling utilisation factor Stiffened and un-stiffened panels Vertically stiffened side shell plating of single side skin bulk carrier Web plate in ways of openings

1.00 for load combination: S+D 0.80 for load combination: S

Struts, pillars and cross-ties 0.75 for load combination: S+D 0.65 for load combination: S

Corrugated bulkheads 0.90 for load combination: S+D 0.72 for load combination: S

1.3.2 Corrugated bulkhead

Where a lower stool is not fitted to a transverse or longitudinal corrugated bulkhead, the allowable buckling

utilisation factor in Table 2 is to be reduced by 10% for the corrugation and below supporting structure within

the extent defined as follows:

Full height of the corrugation

Supporting structure for a transverse corrugated bulkhead - longitudinally within half a web frame space

forward and aft from each side of the bulkhead

Supporting structure for a longitudinal corrugated bulkhead – transversely within three longitudinal stiffener

spacing from each side of the bulkhead.

2. Stiffened and un-stiffened panels

2.1 General

2.1.1

The hull structure is to be modelled as stiffened or un-stiffened panel. Method 1 and Method 2 as defined in

Sec 1, [3.1] are to be used according to Table 1 and Figure 1 to Figure 4.

Table 2: Structural members

Structural Elements Idealisation Assessment method

Normal panel definition

Longitudinal structure,( see Figure 1: ) Longitudinally stiffened panels Shell envelope Deck Inner hull Hopper tank side Longitudinal bulkheads

SP M1 Length: between web frames Width: between primary supporting members (PSM)

Double bottom longitudinal girders in line with longitudinal bulkhead or connected to hopper tank side

SP M1 Length: between web frames Width: full web depth

Web of horizontal girders in double side space connected to hopper tank side


Web of double bottom longitudinal girders not in line with longitudinal bulkhead or not connected to hopper tank side



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Web of horizontal girders in double side space not connected to hopper tank side


Web of single skin longitudinal girders or stringers

UP M2 Between local stiffeners/face plate/PSM

Transverse structure, see Figure 2: Web of transverse deck frames including brackets


Vertical web in double side space SP M2 Length: full web depth Width: between primary supporting members

All irregularly stiffened panels, e.g. Web panels in way of hopper tank and bilge


Double bottom floors SP M2 Length: full web depth Width: between primary supporting members

Vertical web frame including brackets

UP M2 Between vertical web stiffeners/face plate/PSM

Cross tie web plate UP M2 Between vertical web stiffeners/face plate/PSM

Transverse Oil-tight and Watertight bulkheads, (see Figure 3: and Transverse wash bulkheads,( see Figure 4: All regularly stiffened bulkhead panels

SP M1 Length: between primary supporting members Width: between primary supporting members

All irregularly stiffened bulkhead panels, e.g. web panels in way of hopper tank and bilge

UP M1 Between local stiffeners/face plate

Web plate of bulkhead stringers including brackets

UP M2 Between web stiffeners /face plate

Transverse Corrugated bulkheads

Upper/lower stool including stiffeners

SP M1 Length: between internal web diaphragms Width: length of stool side

Stool internal web diaphragm UP M2 Between local stiffeners /face plate / PSM Notes

1) SP stands for stiffened panel

2) US stands for un-stiffened panel

3) M1 stands for Method 1

4) M2 stands for Method 2

2.1.2

Where the plate thickness along a panel is not constant, the [lowest – weighted average] thickness of finite plate

elements modelled according to Ch 7 is to be used for the panel buckling assessment.

The weighted average thickness is to be taken as:

i

n

ii

n

avr

A

tAt

1

1

where:

iA : Area of the ith plate element

it : Net thickness of the ith plate element

n : Number of finite elements defining the buckling panel


Page 4 March 2011

2.1.3

The panel yield stress ReH_Plate is taken as the minimum value of the specified yield stresses of the elements

within the panel.


March 2011 Page 5

SP - M1

SP - M1

SP - M1

SP - M1 SP - M1SP - M1

SP - M1

SP - M1

SP - M1

SP - M1Alternativeprocedurefor curved

panel

SP - M2SP - M2SP - M1

SP - M1

SP - M1

SP - M1

SP - M1

SP - M1SP - M1

SP - M1

SP - M1 SP - M1 SP - M1

SP -

M2

SP -

M2

SP -

M1

Notes

1) SP – M1 denotes stiffened panel – buckling strength assessed using Method 1

2) SP – M2 denotes stiffened panel – buckling strength assessed using Method 2

Figure 1: Buckling Assessment for longitudinal strength

AlternativeProcedure

for opening

AlternativeProcedure for

Cross-tiepillar buckling

SP-M2

UP-M2

UP-M2

SP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2UP-M2

UP-M2UP-M2UP-M2

SP-M2

SP-M2SP-M2UP-M2

UP-M2

SP-M2

Notes

1) SP – M1 denotes Stiffened Panel – buckling strength assessed using Method 1

2) UP – M2 denotes Un-stiffened Panel – buckling strength assessed using Method 2


Figure 2: Transverse Web Frames


Page 6 March 2011

SP - M1

SP - M1

SP - M1

SP - M1

SP - M1

SP - M1

SP - M1 SP - M1

SP -

M1

SP - M1 SP - M1 SP - M1UP - M2

UP - M2

SP -

M1

SP -

M1

SP -

M1

SP -

M1

SP -

M1

SP -

M1

Notes

1) SP – M1 denotes Stiffened Panel – buckling strength assessed using Method 1.


Figure 3: Transverse Bulkhead

SP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2

UP-M2UP-M2

UP-M2UP-M2UP-M2

SP-M2

SP-M1UP-M2

UP-M2

SP-M1

SP-M2

SP-M1

SP-M1

SP-M1

UP-M2UP-M2

Notes




Figure 4: Cross Tie


March 2011 Page 7

Notes

1) M2 denotes buckling strength assessed using Method 2

Figure 5: Transverse Web Frames for single hull bulk carrier

UP- M2 UP-

M2

UP- M2

UP- M2

UP- M2

UP- M2

SP- M2 UP-

M2

UP- M2

SP- M2

SP- M2

SP- M2


Page 8 March 2011

Notes



Figure 6: Longitudinal plates for single hull bulk carrier

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

UP- M1

SP- M2

SP- M2

SP- M2

SP- M2

SP- M2

SP- M2

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

Alternative Procedure for

vertically stiffened side shell plating


March 2011 Page 9

Notes


Figure 7: Transverse Web Frames for double hull bulk carrier

Alternative Procedure for opening

Alternative Procedure for opening

SP- M2

SP- M2

SP- M2

SP- M2

UP- M2

SP- M2

SP- M2

UP- M2


Page 10 March 2011

Notes



Figure 8: Longitudinal plate for double hull bulk carrier

2.2 Stiffened panels

2.2.1

To correctly model the overall buckling behaviour, each stiffener with attached plate is to be represented as a

stiffened panel of the extent defined in Table 1 and hence assumed to be part of a larger structural entity.

M1

UP- M1

SP- M1

SP- M1

SP- M1

SP- M2

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M1

SP- M2

SP- M2

SP- M2


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2.2.2

If the plate thickness or stiffener properties or stiffener spacing varies within the stiffened panel, the calculations

are to be performed separately for all configurations of the panel: for each stiffener and plate between the

stiffeners. Plate thickness, stiffener properties and stiffener spacing at the considered location are to be assumed

for the whole panel.

2.3 Un-stiffened panels

2.3.1

In way of web frames, stringers and brackets, the geometry of the panel (i.e. plate bounded by web

stiffeners/face plate) may not have a rectangular shape. In this case, an equivalent rectangular panel is to be

defined according to Figure 5 for irregular geometry and Figure 6 for triangular geometry.

2.3.2

The equivalent rectangular panel the dimensions of which are la and la, is to be comply with the buckling

assessment.


Page 12 March 2011

(a) The four corners closest to a right angle, 90degrees, in the bounding polygon for the plate are identified

(b) The distances along the plate bounding polygon between the corners are calculated, i.e. the sum of all

the straight line segments between the end points

d4

d2

d1

d3

(c) The pair of opposite edges with the smallest total length is identified, i.e. minimum of d1+d3 and d2+d4

(d) A line is joined between the middle points of the chosen opposite edges (i.e. a mid point is defined as

the point at half the distance from one end). This line defines the longitudinal direction for the capacity

model. The length of the line defines the length of the capacity model, l1 or d2 measured from one end point.

l1

(e) The length of shorter side, la, and aspect ratio α of capacity model are to be taken as

1/ lAl pla

1l

la

where:

Apl : Area of the plate

l1 : length defined in (d)

l2la

(f) The stresses from the direct strength analysis are to be resolved into the local coordinate system of the

equivalent rectangular panel. These stresses are to be used for the buckling assessment.

Figure 9: Modelling of an Un-stiffened Panel with Irregular Geometry


March 2011 Page 13

(a) Medians are constructed as shown below.

(b) The longest median is identified. This median, l1, defines the longitudinal direction for the capacity

model.

l1

(c) The width of the model, l2, is to be taken as:

12 / lAl pl

where:

Apl : Area of the plate

l2

(d) The length of shorter side, la, and aspect ratio α of capacity model are to be taken as

tria C

ll 2

2

2

1triC

l

l

where:

6.04.01

2 l

lCtri

(e) The stresses from the direct strength analysis are to be resolved into the local coordinate system of the

equivalent rectangular panel and are to be used for the buckling assessment of the equivalent rectangular

panel.

Figure 10: Modelling of an Un-stiffened Panel with Triangular Geometry


Page 14 March 2011

2.4 Reference stress

2.4.1

The stress distribution is to be taken from the direct strength analysis and applied to the buckling model.

2.4.2

The reference stresses are to be calculated using one of the two following methods:

Stress based reference stresses as defined in Appendix 1

Displacement based reference stresses as defined in Appendix 2

2.5 Lateral pressure

2.5.1

The lateral pressure applied to the direct strength analysis is also to be applied to the buckling assessment.

2.5.2

Where the lateral pressure is not constant over a buckling panel defined by a number of finite plate elements, an

average lateral pressure, N/mm², is calculated using the following formula:

i

n

ii

n

avr

A

PAP

1

1

where:

iA : Area of the ith plate element, in m²

iP : Lateral pressure of the ith plate element, in N/mm²

n : Number of finite elements in the buckling panel

2.6 Buckling criteria

2.6.1 Un-stiffened panel - Method 1

The compressive buckling strength of un-stiffened panel - Method 1 is to satisfy the following criterion:

allUP 1

where:

1UP : Plate ultimate capacity calculated according to Method 1 as defined in Sec 5, [2.3] or Sec 5, [3].

2.6.2 Un-stiffened panel - Method 2

The compressive buckling strength of un-stiffened panel - Method 2 is to satisfy the following criterion:

allUP 2

where:

2UP : Plate buckling utilisation factor, as defined in Sec 5, [3] or taken as the maximum of

1UP : Plate ultimate capacity calculated according to Method 1as defined in Sec 5, [2.3],

Elastic : Plate elastic capacity calculated according to Method 2 as defined in Sec 5, [2.3].


March 2011 Page 15

2.6.3 Stiffened panel - Method 1

The compressive buckling strength of stiffened panel - Method 1 is to satisfy the following criterion:

allSP 1

where:

1SP : Stiffened panel buckling utilisation factor calculated as defined in Sec 5, [3] or taken as the maximum

of:

the overall stiffened panel capacity as defined in Sec 5, [2.2],

the plate capacity calculated according to Method 1 as defined in Sec 5, [2.3],

the longitudinal stiffener buckling strength as defined in Sec 5, [2.5].

2.6.4 Stiffened panel - Method 2

The compressive buckling strength of stiffened panel - Method 2 is to satisfy the following criterion:

allSP 2

where:

2SP : Stiffened panel buckling utilisation factor calculated as defined in Sec 5, [3] or taken as the maximum

of:

1SP as defined in [2.6.3],

the plate capacity according to Method 2 as defined in Sec 5, [2.3],

2.6.5 Web plate in way of openings

The web plate of primary supporting members with openings is to satisfy the following criterion:

allopening

where:

opening : Web plate capacity utilisation factor in way of openings, as defined in Sec 5, [2.4].

3. Corrugated bulkhead

3.1 General

3.1.1

Three buckling failure modes are to be assessed on vertically or horizontally corrugated longitudinal or

transverse bulkheads:

corrugation overall column buckling

corrugation flange panel buckling

corrugation web panel buckling

3.2 Reference stress

3.2.1

Each corrugation flange and web panel is to be assessed.


Page 16 March 2011

3.2.2

The membrane stresses at element centroid are used.

3.2.3

The maximum normal stress parallel to the corrugation and the maximum shear stress are defined according to

the following methodology:

Averaging element stresses is to be done over the flange width

The “interpolation” is to be applied where the stresses value at s/2 from lower end cannot be obtained

directly from an element

After averaging the stresses over the flange width, and after obtaining the stress at s/2 from lower end, the

maximum stresses are to be used for compliance with the buckling criteria

where:

s : flange breath of the corrugation.

3.2.4

Where more than one plate thicknesses are used for flange panel, maximum stress is to be obtained for each

thickness range and to be checked with the buckling criteria for each thickness.

3.3 Overall column buckling

3.3.1

The overall buckling failure mode of corrugated bulkheads subjected to axial compression is to be checked for

column buckling (e.g. horizontally corrugated bulkheads, vertically corrugated bulkheads subject to localized

vertical forces).

Table 3: Application of overall column buckling for corrugated bulkhead

Corrugation orientation

Horizontal Vertical

Longitudinal bulkhead Required Required, only if subject to localized vertical forces (e.g. crane loads) Transverse bulkhead Required

3.3.2

Each corrugation unit (one corrugation space) within the extension of half flange, web and half flange is to

satisfy the following criterion :

allOverall

where:

Overallr : Overall column utilisation factor, as defined in Sec 5, [4.1].

3.3.3

End constraint factor endf corresponding to pinned ends is to be applied except for fixed end support to be used in

way of stool with width exceeding 2 times the depth of the corrugation.


March 2011 Page 17

3.4 Local buckling

3.4.1

The compressive buckling strength of a unit flange and a unit web of corrugation bulkheads is to satisfy the

following criterion :

allCorr

where:

Corr : Unit flange or unit web utilisation factor, as defined in Sec 5, [4.2.1].

Two stress combinations are to be considered:

The maximum normal stress parallel to the corrugation plus the shear stress and the stress perpendicular to

corrugation at the location where the maximum normal stress parallel to the corrugation occurs

The maximum shear stress plus the normal stress parallel to the corrugation and the stress perpendicular to

corrugation at the location where the maximum shear stress occurs

4. Vertically stiffened side shell plating of single side skin bulk carrier


4.1.1

The compressive buckling strength of the vertically stiffened side shell plating of single side skin bulk carrier is

to satisfy the following criterion :

allvss

where:

vss : Vertically stiffened side shell plating buckling utilisation factor of single side skin bulk carrier

The interaction curve of Sec 5, [2.3.1] is to be used with the following stress combinations:

a) Pure vertical stress:

The maximum vertical stress of stress elements is used with 1 and 1 .

b) Maximum vertical stress combined with longitudinal and shear stress:

The maximum vertical stress in the buckling panel plus the shear and longitudinal stresses at the location

where the maximum vertical stress occurs is used with 2 and 1 .

The plate thickness to be considered in the buckling strength check is the one where the maximum

vertical stress occurs.

c) Maximum shear stress combined with longitudinal and vertical stress:

The maximum shear stress in the buckling panel plus the longitudinal and vertical stresses at the location

where maximum shear stress occurs is used with 2 and 1 .

The plate thickness to be considered in the buckling strength check is the one where the maximum shear

stress occurs.

d) Distributed longitudinal stress associated with vertical and shear stress:

The actual size of the buckling panel is used to define .


Page 18 March 2011

The actual edge factor for longitudinal stress is to be used. The average values for vertical and shear

stresses are to be used.

The plate thickness to be considered in the buckling strength check is the minimum thickness of the

buckling panel.

5. Struts, pillars and cross ties


5.1.1

The compressive buckling strength of struts, pillars and cross ties is to satisfy the following criterion:

allPillar

where:

Pillar : Buckling capacity utilisation factor of struts, pillars or cross ties, as defined in Sec 5, [4.1]


March 2011 Page 1

Section 5 - Buckling Capacity

Symbols


E : Modulus of elasticity as defined in Ch 3, in N/mm2

: Poisson coefficient as defined in Ch 3

pt : Net thickness of plate panel, in mm

al : Length of the shorter side of the plate panel as defined in Table 1, in mm

stfl : Span of stiffener equal to spacing between primary support members, in mm

s : Spacing between stiffeners, in mm

: Aspect ratio of the panel, defined in Table 1

effb : Effective width of attached plating

PlateeHR _ : Specified minimum yield stress of the plate in N/mm2

StiffenereHR _ : Specified minimum yield stress of the stiffener in N/mm2

G : Shear modulus

)1(2

E

endf : End constraint factor, taken as:

1.0 where both ends are pinned

2.0 where one end is pinned and the other end is fixed

4.0 where both ends are fixed

A pillar end may be considered fixed when effective brackets are fitted. These brackets are to be

supported by structural members with greater bending stiffness than the pillar

For cross tie, fend is to be taken equal to 2.0

x : Compressive stress applied on the edge along x axis of the buckling panel, in N/mm2

y : Compression stress applied on the edge along y axis of the buckling panel, in N/mm2

: Applied shear stress, in N/mm2

cx : Buckling strength due to compression applied on the short edge of the buckling panel, in N/mm2

cy : Buckling strength due to compression applied on the long edge of the buckling panel, in N/mm2

c : Buckling strength in shear, in N/mm2

: Stress multiplier; load proportionality factor

c : stress multiplier at collapse

wt : Net stiffener web thickness, in mm


Page 2 March 2011

ft : Net flange thickness, in mm

wh : Depth of stiffener web, in mm, excluded the flange thickness

fb : Breadth of the stiffener, in mm

fe: Distance from connection to plate to centre of flange, in mm

)5.0( fw th

for Bulb profile

)5.0( fw th

for Angle and Tee profile

Figure 1: Stiffener cross sections

Note: Measurements of breadth, bf and depth, hw are based on gross scantlings.

1. General

1.1 Scope

1.1.1

This Section contains the methods for definition of buckling utilisation factors, determination of the buckling

capacity and other measures necessary to control buckling of plate panels, longitudinal and transverse stiffeners,

primary support members, struts, pillar, cross ties and corrugated bulkhead.

1.2 Definitions for usage factor and buckling capacities

1.2.1

The utilisation factor is defined as the ratio between the applied loads and the corresponding ultimate capacity or

buckling strength.

For each typical failure mode, the corresponding capacity of the panel is calculated by applying the actual stress

combination and then increasing or decreasing the stresses proportionally until collapse.

xccx

yccy

cc

hw t w

t p

h w

bf

hwtw

hw

bf

t f

ef

C C C C

bf


March 2011 Page 3

cyxc

yx

ccycx

yx

u

actact W

W

1

)( 2222

222

222

222

2. Closed form method

2.1 General

2.1.1

This part contains the formulations for the determination of the buckling capacity for the prescriptive buckling

requirements and for the buckling requirements in finite element analysis by using the closed form method

approach.

2.1.2

The collapse is obtained when the interaction formulae defined in [2.2.1], [2.3.1], [2.4.1] and [2.5.3] are equal to 1.0.

2.1.3

The buckling utilisation factor of the structural member is equal to the highest utilisation factor obtained for the

different calculated failure modes.

2.1.4

The lateral pressure is kept constant in the stiffener buckling strength.

2.2 Overall stiffened panel capacity

2.2.1

The elastic stiffened panel state limit is based on the following interaction formulae:

Ask Richard to write the formulae

2.3 Plate capacity

2.3.1

The state limit for the plate between stiffeners is based on the following interaction formula:

1321

e

ccy

y

cx

x

e

cy

y

e

cx

x B

where:

Method 1 Method 2

yx , and Actual stress Actual stress.

When x or y are in tension, the

respective value is to be taken

equal to 0.


Page 4 March 2011

cx, cy

and c Ultimate critical stresses defined in [2.3.4] Elastic Critical stresses defined in

[2.3.2]

1e 2

1

2 2e

3e 2

B xand

ypositive

(compressive

stress)

1200

120120

1

p

a

p

a

p

a

t

lfor

t

lfor

t

l

B

0

xor

ynegative

(tensile stress)

1

2.3.2 Elastic critical stresses

The elastic critical stresses of plate panels subject to compression or shear, respectively, are to be taken as:

Excx K

Eycy K

Ec K

KKK yx ,, : Buckling factors, as defined in Tables 1 and 2

E : Reference stress, in N/mm2

2

2

2

112

a

p

l

tE

2.3.3

The reference degree of slenderness is to be taken as:

E

PlateeH

K

R

_

2.3.4 Ultimate critical stresses

The ultimate critical stresses of plate panels subject to compression or shear, respectively, are to be taken as:

PlateeHxcx RC _

PlateeHRCycy _

3

_ PlateeHc

RC


March 2011 Page 5

where:

CCC yx ,,: Reduction factors, as defined in Tables 1 and 2.

where 0x (tensile stress), 1xC .

where 0y (tensile stress), 1yC .

The boundary conditions for plates are to be considered as simply supported (cases 1, 2 and 5 of Table 1). If the

boundary conditions differ significantly from simple support, more appropriate boundary condition can be

applied according to cases 3, 4 and 7 to 10 of Table 1.


March 2011 Page 6

Table 1: Buckling Factor and Reduction Factor for Plane Plate Panels

Case Stress ratio ψ Aspect ratio α Buckling factor K Reduction factor C 1 01

1

1.1

4.8

longx FK

1xC for c

2

22.01

cC x

for c where:

25.1)12.025.1( c

c

cc

88.011

2

10 )1026.6(63.7 longx FK

1 2)1(975.5 longx FK

2 01 1

)1.1(

1.211

2

2

yK

2

2 )(1

RHFR

cC y

Where:

25.1)12.025.1( c )/1( cR for c

22.0R for c

ccc /88.0115.0

0/191.0

1 12

c

KF p

5.022 p and

31 2 p 11 c for σy due to direct loads (3)

0)/11(1 c for σy due to bending (in general) (2) 01 c for σy due to bending in extreme load

cases (e.g. watertight bulkheads.)

RTTc

λλH

)4(

22

3

1

15

14

T

10

5.11 1.1

)1(1.211

2

2

yK

)109.13(2

5.1

1.1

)1(1.211

2

2

yK

2

287.187.5(

)106.82

1

4

)1(31

975.5

12

yK

4

)1(3

9675.31

2

yK

87.11

5375.04

t

x x

· la

la

· x· x

t

· y

y

y

· l a

la

· y


March 2011 Page 7

Case Stress ratio ψ Aspect ratio α Buckling factor K Reduction factor C 3 01

0

13

)/1425.0(4 2

xK

1xC for 7.0

51.0

12

xC

for 7.0

10

)1()/1425.0(4 2 xK

)42.31(5

4

11 0 2

31425.0

2

xK

5

-

3KK

1C for 84.0

84.0

C for 84.0

1

2

434.5

K

10

2

34.54

K

6

-

K = K’ r K’ = K according to Case 5 r = opening red. factor

a

b

a

a

l

d

l

dr 11

7.0a

a

l

d

and 7.0

a

b

l

d

t

· x

x x

la

· l a

· x

t

· x

la

· l a

· x

x x

t

la

· l a

t

la

· l a

d b

da


March 2011 Page 8

Case Stress ratio ψ

Aspect ratio α

Buckling factor K Reduction factor C

7

-

64.1 28.1xK

1xC for 7.0

51.0

12

xC for

7.0

64.1 2

13.056.01

xK

8

-

3

2

97.6xK

1xC for 83.0

2

22.0113,1

xC for

83.0

3

2

22

55.21

xK

9

-

4 4xK

14 74.2

3

44

4

xK

1 267.007.2

4

xK

10

-

4 97.6xK

14 3

3

497.6

4

xK

t

x x

· la

la

x

t

x x

· la

l

x

t

x x

· la

la

x


March 2011 Page 9

1 2

2407.2

4

xK

where: ψ the ratio between smallest and largest compressive stress as shown for Case 1 to 4

al length in mm, of the shorter side of the plate panel

Edge boundary conditions: - - - - - - - - - plate edge free

plate edge simply supported ▬▬▬▬▬ plate edge clamped Notes

(1) Cases listed are general cases. Each stress component (σx, σy ) is to be understood in local coordinates.

(2) c1 due to bending (in general) corresponds to straight edges (uniform displacement) of a plate panel integrated in a large structure.

This value is to be applied for hull girder buckling and buckling of web plate of primary supporting members in way of openings.

(3) c1 for direct loads corresponds to a plate panel with edges not restrained from pull-in which may result in non-straight edges

t

x x

· la

la

x


Page 10 March 2011

Table 2: Buckling and reduction factor for curved plate panel with R/t ≤ 2500 (1)

Case Aspect Ratio Buckling factor K Reduction factor C

1

General

t

R

R

la 5.0tR

lK a

2

3

21

1xC for 25.0

933.0233.1xC for 125.0 3/3.0 xC for 5.11 2/2.0 xC for 5.1

t

R

R

la 5.0

R

t

R

l

tR

lK aa 3267.0

2

tR

la2

4.0

Curved single field e.g. bilge strake

- - 0.165.02

xC

2a

2b

General t

R

R

la 63.1

35.0

175.0

3a

a

l

tR

tR

lK

1yC for 4.0

686.0274.1yC for 2.14.0

2

65.0

yC

for 2.1

t

R

R

la 63.1

22

2

2

25.23.0

tl

R

R

lK

a

a

Curved single field e.g. bilge strake

- - 0.18.02

yC

3

t

R

R

la 2

23.0

6.0

aa

a

l

tR

l

tR

tR

lK

as in load case 2a

t

R

R

la 2

22

2

2

291.03.0

tl

R

R

lK

a

a

4

t

R

R

la 7.8

3KK 5.0

5.15.1

367.03.28

tR

lK a

1C for 4.0 686.0274.1C for

2.14.0

2

65.0

C for 2.1 t

R

R

la 7.8 RtR

lK a

2

28.0

Explanations for boundary conditions - - - - - plate edge free ──── plate edge simply supported ▬▬▬ plate edge clamped Notes

(1) For curved plate fields with a very large radius the C-value need not to be taken less than for the expanded plane field.

(2) The parameters la, R and t must have the same unit, e.g. in mm.


March 2011 Page 11

2.3.5

The correction factor longF for boundary condition of stiffener on the longer side of the buckling panel is to be

taken as:

longF

c

Un-stiffened Panel 1.00 ---

Stiffened Panel Flat bar

11 cFt

tif long

p

w

11

3

p

wlong

p

w

t

tcF

t

tif

0.10

Bulb profile 0.30

Angle profile 0.40

Tee profile 0.30

Girder of high rigidity (e.g.

bottom transverse)

1.4 ---

An average value of longFis to be used for plate panels having different edge stiffeners.

2.4 Web plate of primary support members in way of openings

2.4.1

The web plate of primary support members with openings is to be assessed for buckling based on the combined

axial compressive and shear stresses.

The web plate adjacent to the opening on both sides is to be considered as individual unstiffened plate panels as

shown in Table 3.

The interaction curve of [2.3.1] is to be used with:

avx

0y

av

where:

av : Average compressive stress in the area of web plate being considered according to case 1, 2

or 3 in Table 1, in N/mm2

av : Average shear stress in the area of web plate being considered according to case 5 or 6 in

Table 1, in N/mm2

2.4.2

The reduction factors, xCor yC

in combination with C, of the plate panel(s) of the web adjacent to the

opening is to be taken as shown in Table 3.


Page 12 March 2011

Table 3: Reduction Factors

Mode Cx, Cy Cτ

(a) without edge reinforcements

P1

P2

avav av

av

Separate reduction factors are to be applied to areas P1 and P2 using Case 3 in Table 1, with edge stress ratio:

0.1

A common reduction factor is to be applied to areas P1 and P2 using Case 6 in Table 1 for area marked:

(b) with edge reinforcements

P2

P1 avav av

av

Separate reduction factors are to be applied for areas P1 and P2 using: Cx for Case 1 or Cy, for Case 2 in Table 1 with stress ratio

0.1

Separate reduction factors are to be applied for areas P1 and P2 using Case 5 in Table 1

(c) example of hole in web

P3

P1 P2

TB TB

av

avavav

avavav

av

Panels P1 and P2 are to be evaluated in accordance with (a). Panel P3 is to be evaluated in accordance with (b)

Note:

Web panels to be considered for buckling in way of openings are shown shaded and numbered P1, P2, etc.


March 2011 Page 13

2.5 Stiffeners

2.5.1

The following buckling modes shall be checked:

Buckling due to stiffener failure (SI)

Buckling failure initiated by the associated plate (PI)

The control point in [2.5.3] for SI is at the top of the stiffener and for PI at the plate/stiffener connection, both

taken at the mid span of the stiffener.

2.5.2

To take into account the decrease of stiffness due to local lateral deformation, the thickness web of flat bar

stiffener used in the stiffener buckling strength is reduced according to the following formula:

a

eff

a

wwreducedw l

b

l

htt 1

3

21

22

_

where:

effb : Effective breadth of attached plating of stiffeners in mm, as defined in [2.5.4]

2.5.3

The ultimate state limit for the stiffener buckling strength is based on the following interaction formulae:

1

SReH

warpingba

where:

a : Compressive axial effective stress acting on the post-buckled plate-stiffener combination, in N/mm2,

in way of the mid span of the stiffener

Speff

Spaxa Atb

Atl

eHR : Specified minimum yield stress of the material, in N/mm2

StiffenereHeH RR _ for stiffener induced collapse (SI)

PlateeHeH RR _ for plate induced failure (PI)

S : Safety factor, taken equal to:

S = 1.0 except for the case mentioned below

S = 1.1 for structures which are exclusively exposed to local loads (e.g. hatch covers, foundations)

S = 1.15 for bulk carrier stiffeners: longitudinal and transverse stiffeners of the hatchway coamings,

sloping plating of the topside tanks and hopper tanks, inner bottom, inner side if any, side shell of single

side skin construction and top and bottom stools of transverse bulkheads

net

ob Z

MM

10001

: Bending stress in the stiffener, in N/mm2

netZ : Net section modulus of stiffener, in cm3, including effective breadth of plating according to [2.5.4], to

be taken as:


Page 14 March 2011

For stiffener induced collapse (SI), the section modulus is to be calculated at the top of stiffener flange

For plate induced failure (PI), the section modulus is to be calculated at the attached plating

1M : Bending moment, in N.mm, due to the lateral load P

3

2

1 1024 stflsP

M for longitudinal stiffeners

3

2

1 108

)(

s

stf

c

nslPM

for transverse stiffeners

P : Lateral load, in kN/m2

sc : Factor for the boundary conditions of the transverse stiffener:

0.1sc

for simply supported stiffeners

0.2sc

for partially constraint stiffeners

n : Number of elementary plate panels breadths within the partial or total plate panel

0M : Bending moment, in N.mm, due to the lateral deformation w of stiffener

zf

zE Pc

wPFM 0

where: 0 zf Pc

EF : Ideal elastic buckling force of the stiffener, in N

42

2

10x

stf

Ex IEl

F

for longitudinal stiffeners

42

2

10yEy IEns

F


xI , yI

: Moment of inertia, in cm4, of the stiffener including effective width of attached plating according to

[2.5.4].

xIand yI

are to comply with the following requirement:

4

3

1012

tsI x


4

3

1012

tlI stf

y for transverse stiffeners


March 2011 Page 15

t : Net thickness of plate, to be taken as the mean thickness of the two attached plating panels, in mm

ZP : Nominal lateral load, in N/mm2, acting on the stiffener due to membrane stresses, x , y and 1 , in

the attached plating in way of the stiffener mid span:

1

2

22 ystf

xlp

Zx cl

s

s

tP


1

2

212

pstf

sstfyxl

stf

pZy tl

A

ns

lc

l

tP


p

saxl ts

A1

, in N/mm2

0)( 2

22

1_1

s

m

l

mERt

stfPlateeHp

1m , 2m : Coefficients taken equal to:

For longitudinal stiffener:

47.11 m 49.02 m for 0.2

s

lstf

96.11 m 37.02 m for 0.2

s

lstf

For transverse stiffener:

37.01 m 22

96.1

nm

for 5.0

s

lstf

49.01 m 22

47.1

nm

for 5.0

s

lstf

SA : Net sectional area of the stiffener without attached plating, in mm2

c : Factor taking into account the membrane stresses in the attached plating acting perpendicular to the

stiffener’s axis

)1(5.0 for 10

1

5.0

for 0

: Edge stress ratio for Case 2 according to Table 1

y : Membrane compressive stress in the attached plating acting perpendicular to the stiffener’s axis, in

N/mm2

: Shear membrane stress in the attached plating, in N/mm2

w : Deformation of stiffener, in mm, 10 www

0w : Assumed imperfection, in mm


Page 16 March 2011

10000stfl

w

For stiffeners sniped at both ends, w0 is not to be taken less than the distance from the midpoint of attached

plating to the neutral axis of the stiffener calculated with the effective width of the attached plating according to

[2.5.4].

1w : Deformation of stiffener at midpoint of stiffener span due to lateral load P, in mm. In case of

uniformly distributed load the w1, is to be taken as:

x

stf

IE

lsPw

7

4

1 10384

for longitudinal stiffener

27

4

1 10384

5

sy

stf

cIE

nslPw

for transverse stiffener

fc : Elastic support provided by the stiffener, in N/mm2

For longitudinal stiffener:

)1(2

2

px

stf

Ef cl

Fc

1101291.0

1

1

3

4

p

x

xa

px

ts

I

c

c

2

2

2

stf

stfxa l

s

s

lc

for slstf 2

22

21

s

lc stf

xa

for slstf 2

For transverse stiffener:

)1(2

2

pyEysf cns

Fcc

1101291.0

1

1

3

4

pstf

y

ya

py

tl

I

c

c

22

2

ns

l

l

nsc stf

stfya

for stflns 2

22

21

stfya l

nsc

for stflns 2


March 2011 Page 17

warping : Stress due to torsional deformation, in N/mm2

ET

stiffenereHstfscwarping Rl

zzEy

_

2

0'''

4.01

11)(

for stiffener induced collapse (SI)

0warping

for plate induced failure (PI)

'y : Horizontal distance from centroid of stiffener cross-section to reference point to be assessed (free edge point

of stiffener flange)

0' y for Flat bar

)(

2

)(fwf

fwff

' ttbA

ttbby

for Angle profile

2' fb

y for Tee profile

Note: Bulb profile is taken as with an equivalent angle profile.

'cz

: Vertical distance from centroid of stiffener cross-section to plate stiffener intersection

w

ffw

s

wwc h

tth

A

thz

2)(

2'

'Sz

: Vertical distance from centroid of stiffener cross-section to shear center of stiffener

)(2

'fw

s

wwS th

A

thz

w

stf

h

lΦ 001.00

ETσ : Reference stress for torsional buckling, in N/mm2

T

stfpET I

l

I

I

E385.0

102

22

pI: Net polar moment of inertia of the stiffener about point C as shown in Figure 1, defined in Table 4, in cm4

TI : Net St. Venant’s moment of inertia of the stiffener, defined in Table 4, in cm4

I : Net sectorial moment of inertia of the stiffener about point C as shown in Figure 1, defined in Table 4, in

cm6

: Degree of fixation

334

43

3

)5.0(4

4

3101

w

ff

p

stf

t

te

t

sI

l

wA: Net web area, in mm2


Page 18 March 2011

fA: Net flange area, in mm2

Table 4: Moments of inertia

Section property

Flat bars Bulb flats, angles and T bars

PI 4

3

103 ww th

422

103

)5.0(

ff

ffw eAteA

TI

w

www

h

tth63.01

103 4

3

f

fff

ff

wwff

b

ttb

te

ttte

63.01103

5.063.01

103

)5.0(

4

3

4

3

I 6

33

1036 ww th

for bulb flats and angles:

wf

wffff

AA

AAbeA 6.2

1012 6

22

for T bars:

6

23

1012 fff etb

2.5.4

The effective breadth of attached plating of stiffeners is to be taken as:

ssCb sxeff ,min 0.10056.04422.00673.00035.023

s

l

s

l

s

l effeffeffs

where:

xC : Average reduction factor for buckling of the two attached plate panels, according to Case 1 in Table 1

effl : Value taken as follows:

For longitudinal stiffeners:

stfeff ll , if simply supported at both ends

stfeff ll 6.0 , if fixed supported at both ends

For transverse stiffeners:

sleff , if simply supported at both ends

sleff 6.0

, if fixed supported at both ends


March 2011 Page 19

3. Semi-analytic buckling method

3.1 Scope

3.1.1

This part describes the semi-analytic buckling method and its application as required by the Rules in Sec 4. The

semi-analytic method is to be based on nonlinear analysis technique which predicts the complex behaviour of

rectangular shaped stiffened and un-stiffened panels.

3.1.2

The semi-analytic buckling method can also be applied for local structural configurations of more irregular and

complex shapes (e.g. fore and aft ship structures, web frames etc.) for more accurate strength assessments in

FEM buckling check.

3.1.3

The semi-analytic buckling method can also be applied for other structures such as corrugated bulkheads etc.

whenever appropriate.

3.1.4

The buckling strength assessments can be computed according to Method 1 (ultimate strength) or Method 2

(initial buckling strength) principles as defined in [1.2.2] and [1.2.3] respectively.

3.2 Effects accounted for

3.2.1

Typical failure modes of stiffened panels with open profiles are accounted for in the semi-analytic method.

These are

Plate buckling

Torsional /warping stiffener buckling

Stiffener web plate buckling

Lateral stiffener buckling. (global/overall buckling)

3.2.2

The semi-analytic method is to be capable of considering the following effects:

Non-linear geometrical behaviour

Material yielding

Initial deflections - geometrical imperfections/out-of flatness

Welding residual stresses

Interactions between buckling modes and structural elements; plates, stiffeners, girders etc.

Simultaneous acting loads; bi-axial compression/tension, shear and lateral pressure

Boundary conditions.

3.3 Assessment Criteria

3.3.1

A structure is considered to have an acceptable buckling strength if it satisfies the criteria given in Sec 1.


Page 20 March 2011

3.4 Application

3.4.1

The application of the stiffened panel and unstiffened panel with the Method 1 or Method 2, see Sec 4, [2.1].

3.4.2

Where the semi-analytic method is unable to correctly model the panel geometry, then an equivalent rectangular

panel is to be defined as described in Sec 4.

3.4.3

Where the panel between stiffeners consists of several plate thickness the weighted average thickness

may used for the thickness of the plating for assessment of the corresponding stiffener/plating

combination. Calculation of weighted average is to be in accordance with Sec 4, [2.2.2]. See Figure 2:

Figure 2: Capacity Model for Web Plate

1) Note

1) The correction of panel breadth is applicable also for other slot configurations provided that the

web or collar plate is attached to at least one side of the passing stiffener.

3.4.4

The local design pressure, and the deformations and bending/shear stresses it sets up in the stiffeners and plating, are to be coped with in the semi-analytic / numerical buckling method. Accordingly the local pressure effects should be eliminated from the in-plane design stresses in the buckling control.

4. Other structures

4.1 Struts, pillars and cross ties

4.1.1

The critical buckling stress for axially compressed struts, pillars and cross ties is to be taken as the lesser of the

column and torsional critical buckling stresses. The buckling utilisation factor, η, is to be taken as:

cr

av

where:

av : Average axial compressive stress in the member, in N/mm2

cr : Minimum critical buckling stress, in N/mm2

0.5hstf

hstf

Equivalent plate panel


March 2011 Page 21

Ecr for StiffenereHE R _5.0

StiffenereH

E

StiffenereHcr R

R_

_

41

for StiffenereHE R _5.0

E : Minimum elastic compressive buckling stress, in N/mm2, according to [4.1.2] to [4.1.3]

4.1.2

The elastic compressive column buckling stress, E , in N/mm2 of pillars subject to axial compression is to be

taken as:

42

2 10pillpill

endElA

IEf

where:

I : Net moment of inertia about the weakest axis of the cross-section, in cm4

pillA : Net cross-sectional area of the pillar, in cm2

pilll : Unsupported length of the pillar, in m

4.1.3

The elastic torsional buckling stress, ET , in N/mm2 , with respect to axial compression of pillars is to be taken

as:

42

2

10pillpol

warpend

pol

svET

lI

Ecf

I

GI

where:

svI : Net St. Venant’s moment of inertia, in cm4, see Table 5

polI : Net polar moment of inertia about the shear centre of cross section, in cm4

2

020 zyAII netzy

warpc : Warping constant, in cm6, see Table 6

pilll : Unsupported length of the pillar, in m

0y : Position of shear centre relative to the cross-sectional centroid, in cm, see Table 5

0z : Position of shear centre relative to the cross-sectional centroid, in cm, see Table 5

A : Net cross-sectional area, in cm2

yI : Net moment of inertia about y-axis, in cm4

zI : Net moment of inertia about z-axis, in cm4


Page 22 March 2011

4.1.4

The unsupported length of the cross tie, pilll , is to be taken as follows, in m:

For cross tie in centre tank: distance between the flanges of longitudinal stiffeners on the starboard and port

longitudinal bulkheads to which the cross tie’s horizontal stiffeners are attached

For cross tie in wing tank: distance between the flanges of longitudinal stiffeners on the longitudinal

bulkhead to which the cross tie’s horizontal stiffeners are attached, and the inner hull plating

4.1.5

For cross-sections where the centroid and the shear centre do not coincide, the interaction between the torsional

and column buckling mode is to be examined. The elastic torsional/column buckling stress, ETF , with respect

to axial compression is to be taken as:

ETEETEETEETF

4

2

1 2

where:

polI

Az 201

0z : Position of shear centre relative to the cross-sectional centroid, in cm, see Table 5

A : Net cross-sectional area, in cm2

polI : Net polar moment of inertia about the shear centre of cross section, in cm4

E : Elastic column compressive buckling stress, as defined in [4.1.2]

ET : Elastic torsional buckling stress, as defined in [4.1.3]

Table 5: Cross Sectional Properties

433 1023

1 wwtffsv tdtbI cm4

632

1024

ffwtwarp

tbdc

cm6

433 103

1 wwtffsv tdtbI cm4


March 2011 Page 23

y0 = 0 cm

12

0 105.0

ffwwt

wwt

tbtd

tdz

cm

63333

10144

4 wwtff

warp

tdtbc

cm6

43350 102

3

1 wwtffunetsv tdtbI

cm4

y0 = 0 cm

6/

105.0

2

10 1212

0ffuwwt

wwt

ffwwt

wwt

tbtd

td

tbtd

tdz

cm

632

10612

23

ffuwwt

ffuwwtwwtfuwarp tbtd

tbtdtdbc

cm6

43333

322

311 102

3

1 wwtffffffsv tdtbtbtbI cm4

y0 = 0 cm

332211

1233

2

10)5.0(

ffffffwwt

wwtfwtfso tbtbtbtd

tdtdbzz

cm

223

2122

1 102

owtf

ffofwarp zdI

bIzIc

cm6

4

21221

321

1 10)212

(

fffffff

btbttbI

cm4

423

22 10

12 ff

f

tbI

cm4

433

33 10

12 ff

f

tbI

cm4

1

31

3 10

ff

wtfs II

dIz

cm

Note:

All dimensions are in mm


Page 24 March 2011

4.2 Corrugated bulkhead

4.2.1

The buckling utilisation factor of a unit flange and a unit web of corrugation bulkheads is based on the combined

axial compressive and shear stresses.

The interaction curve of [2.3.1] is to be used with:

2

1


March 2011 Page 1

Appendix 1 – Stress based reference stresses

Symbols


al : Length of the shorter side of the plate panel as defined in Table 1, in mm

1. Stress based Buckling Assessment

1.1 Introduction

1.1.1

This section provides a method to determine stress distribution along edges of the considered buckling panel by

linear approximation using least square method. This method is called Stress Method.

Reference stress is stress components at center of plane element transferred into the local system of buckling

panel.

1.2 Axial and shear stress

The axial stress x applied on the short edge of the buckling panel and the shear stress are to be calculated

using a weighted average approach, given by:

n

i

n

xii

x

A

A

1

1

n

i

n

ii

A

A

1

1

where:

xi : Actual stress applied along the short edge of the buckling panel at the centroid of the ith plate element

of the panel, in N/mm2

i : Membrane shear stress at the centroid of the ith plate element of the panel, in N/mm2

Ai : Area of the ith plate element making up the panel, in mm2

n : Number of elements in the panel

The edge stress ratio ψx for the stress x is equal to 1.0.

1.3 Transverse stress

The transverse stress yapplied on the long edge of the buckling panel is to be calculated by extrapolation of

surrounding.


Page 2 March 2011

Figure 1: Buckling panel

The distribution of y x

is assumed as straight line also

y x C Dx

The best fitting curve y x

is to be obtained by minimizing the square error considering area of each

element as a weighting factor.

2

1

n

i iy ii

A C Dx

The unknown coefficients C and D must yield zero first derivatives, with respect to C and D, respectively.

1

1

2 0

2 0

n

i iy ii

n

i i iy ii

A C DxC

A x C DxD

The unknown coefficients C and D can therefore be obtained:

2

11

2

1

1111

2

11

2

1

111

2

1

n

iii

n

iii

n

ii

n

iiyi

n

iii

n

iiyii

n

ii

n

iii

n

iii

n

ii

n

iiyii

n

iii

n

iii

n

iiyi

xAxAA

AxAxAA

D

xAxAA

xAxAxAA

C

max ,y A A Ba

min ,

max ,y

A A Ba

A A Ba

uj σix

vj σiy

a

b

Harmonised Common Structural Rules Chapter 8, Appendix 2

July 2010 Page 1

Appendix 2 – Displacement Based Reference Stresses

Symbols

For symbols not defined in this Section, refer to Ch 1, Sec 4.

a : Length of the longer plate panel side

b : Length of the shorter plate panel side

x : Direction parallel to a, taken as the longitudinal direction

y : Direction parallel to b, taken as the transverse direction

C : Coefficient taken equal to:

)1(16 2

EC

: Poisson ratio

m : Coefficient taken equal to:

1m

1. Introduction

1.1

1.1.1

This Appendix provides a method to obtain the buckling stresses and edge stress ratios for elementary plate

panels (EPP) from a finite element calculation. This method is called “Displacement Method”.

2. Displacement method

2.1 General

2.1.1

As the mesh of the finite elements does not correspond, in general, to the buckling panels the nodal points of the

EPP can be mapped onto the FE-mesh and the displacements of these nodes can be derived from the FE-

calculation.

Whenever operations on displacements are performed, full numerical accuracy of the displacements should be

used.

2.1.2 Calculation of nodal displacements

Three different node locations are possible:

If a node of the buckling panel is located at an FE-node, then the displacements can be transferred directly.

If a node of the buckling panel is located on the edge of a plane stress element, then the displacements can

be linearly interpolated between the FE-nodes at the edge.

If a node of the buckling panel is located inside of an element, then the displacements can be obtained using

bi-linear interpolation of all nodes of the element.


July 2010 Page 2

2.1.3 Transformation in local system

The transformation of the nodal displacements from the global FE-system into the local system of the buckling

panel is performed by

guu

where:

u : Local displacement vector

gu : Global displacement vector

: Transformation matrix (2×3), of direction cosines of angles formed between the two sets of axes.

2.2 Calculation of buckling stresses and edge stress ratios

2.2.1

The displacements, derived at the corners of the elementary plate panel, are to be considered as input from which

the stresses at certain stress-points are derived. The locations and the numbering convention may be taken from

Fig 1.

The derived stresses at EPP stress nodes can be directly used as input for the buckling assessment according

Ch 8, Sec 5. The buckling load cases, which have to be considered in the FEM buckling assessment and defined

in Ch 7 are buckling load cases 1, 2 and 5 of Ch 8, Sec 5, Tab 1 and 1, 2a, 2b and 4 of Ch 8, Sec 5, Tab 2. In

special cases, other buckling load cases may be used for the buckling assessment by a hand calculation.

2.2.2 8-node buckling panel

Stress displacement relationship for a 8-node buckling panel (compressive stresses are positive)

(a) Displacement Nodes

EPP 1 EPP 2 EPP 3

a

b

1 2 3 4

5678

ui

vi

(b) Stress Nodes

EPP 1 EPP 2 EPP 3

a

b

1 2 3

456

iy

ix


July 2010 Page 3

Figure 1 8-node-buckling-panel

From the displacements of the EPP corner nodes the stresses of these nodes and on mid positions can be

obtained using:

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

6

*6

*6

5

*5

*5

4

*4

*4

3

*3

*3

2

*2

*2

1

*1

*1

/21/5/21/300000000/3/3/3/5

/10/42/6´/4200000000/6/6/10/6

/10/42/6/4200000000/6/6/10/6

00/21/4/21/40000/3/4/3/400

00/8/42/8/420000/8/6/8/600

00/8/42/8/420000/8/6/8/600

0000/21/3/21/5/3/5/3/30000

0000/6/42/10/42/10/6/6/60000

0000/6/42/10/42/10/6/6/60000

0000/3/3/3/5/21/5/21/30000

0000/6/6/10/6/10/42/6/420000

0000/6/6/10/6/10/42/6/420000

00/3/4/3/40000/21/4/21/400

00/8/6/8/60000/8/42/8/4200

00/8/6/8/60000/8/42/8/4200

/3/5/3/300000000/21/3/21/5

/10/6/6/600000000/6/42/10/42

/10/6/6/600000000/6/42/10/42

v

u

v

u

v

u

v

u

v

u

v

u

v

u

v

u

ambmambmambmambm

babbbaba

babababa

ambmambmambmambm

babababa

babababa

ambmambmambmambm

babababa

babababa

ambmambmambmambm

babababa

babababa

ambmambmambmambm

babababa

babababa

ambmambmambmambm

babababa

babababa

C

y

x

y

x

y

x

y

x

y

x

y

x

where:

Tyxyx ),,,,,,( 6

*6

*61

*1

*1

*

Tyxyx vuvuu ),,,,( 8811

In case of slightly warped buckling fields and underlying finite elements an appropriate warping correction

matrix has to be incorporated into the stress-displacement matrix, which provides balanced moments at the mid-

plane of the warped buckling field.

Handling nonlinear transversal stress distributions, in particular handling of extreme parabolic transversal

stress distribution causing buckling shape switch

If all 02/*6

*1 yy and 02/*

4*3 yy and 2/4/ *

5*2

*4

*3

*6

*1 yyyyyy then

4/25.0 *4

*3

*6

*1

*5

*2 yyyyyy

Linearization of transversal stress distribution

2/

2/

2.015.0

*,3

*,1

*,4

*,6

*,2

*,4

*,3

*,3

*,1

*,4

*,6

*,2

*,6

*,1

*,5

*,2

*,4

*,3

*,6

*,1

*,5

*,2

yyyyyyy

yyyyyyy

yyyyyyyy

If both *x and *

y are compressive stresses then the stresses x and y must be obtained as follows:

91.0/)3.0(

91.0/)3.0(**

**

xyy

yxx


July 2010 Page 4

Where compressive stress fulfils the condition xy 3.0 , then 0y and *xx

Where compressive stress fulfils the condition yx 3.0 , then 0x and *yy

This leads to the following stress vector:

Tyxyx ),,,,,,( 666111

The relevant buckling stresses can be obtained by:

LC 1: longitudinal compression

xlx

llx

xxxxxxl

xxxxxxll

xxxxxxl

thenif

/1

5.03

1

2/,2/,2/min,0

2/,2/,2/max

342516

435261

435261

LC 2: transverse compression

yty

tty

yyyyt

yyyyyyt

/1

5.02

1

)(2.0)(15.0

4631

526431

LC 5: shear

6

16

1

ii

hcsr chapter 8_buckling

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