Part 3 Hull Chapter 8 Buckling - DNV GL · 2015-09-29 · Buckling analysis according to Sec.4 is also applicable for beam analysis of structure elements subject to compressive and

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DNV GL AS

RULES FOR CLASSIFICATION

ShipsEdition October 2015

Part 3 Hull

Chapter 8 Buckling

FOREWORD

DNV GL rules for classification contain procedural and technical requirements related to obtainingand retaining a class certificate. The rules represent all requirements adopted by the Society asbasis for classification.

© DNV GL AS October 2015

Any comments may be sent by e-mail to [email protected]

If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of DNV GL, then DNV GL shallpay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to tentimes the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million.

In this provision "DNV GL" shall mean DNV GL AS, its direct and indirect owners as well as all its affiliates, subsidiaries, directors, officers,employees, agents and any other acting on behalf of DNV GL.

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Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 3Buckling

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CHANGES – CURRENT

This is a new document.

The rules enter into force 1 January 2016.

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CONTENTS

Changes – current...................................................................................................... 3

Section 1 General....................................................................................................... 61 Introduction............................................................................................6

1.1 Assumption......................................................................................... 62 Application..............................................................................................6

2.1 Scope................................................................................................. 63 Definitions.............................................................................................. 6

3.1 Assessment methods............................................................................ 73.2 Buckling utilisation factor...................................................................... 73.3 Buckling acceptance criteria.................................................................. 83.4 Allowable buckling utilisation factor........................................................ 9

Section 2 Slenderness requirements........................................................................ 111 Structural elements.............................................................................. 11

1.1 General............................................................................................. 112 Plates....................................................................................................11

2.1 Application.........................................................................................112.2 Net thickness of plate panels...............................................................11

3 Stiffeners.............................................................................................. 123.1 Proportions of stiffeners...................................................................... 12

4 Primary supporting members............................................................... 134.1 Proportions and stiffness..................................................................... 134.2 Web stiffeners of primary supporting members...................................... 15

5 Brackets................................................................................................165.1 Tripping brackets................................................................................165.2 End brackets......................................................................................165.3 Edge reinforcement............................................................................ 17

6 Pillars....................................................................................................186.1 Proportions of I-section pillars............................................................. 186.2 Proportions of box section pillars..........................................................186.3 Proportions of circular section pillars.....................................................18

7 Edge reinforcement in way of openings................................................187.1 Depth of edge stiffener....................................................................... 187.2 Proportions of edge stiffeners.............................................................. 19

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Section 3 Hull girder buckling.................................................................................. 201 General................................................................................................. 20

1.1 Scope............................................................................................... 201.2 Equivalent plate panel.........................................................................20

2 Hull girder stress..................................................................................212.1 General............................................................................................. 212.2 Stress combinations............................................................................22

3 Buckling criteria................................................................................... 223.1 Overall stiffened panel........................................................................ 223.2 Plates................................................................................................223.3 Stiffeners...........................................................................................233.4 Vertically corrugated longitudinal bulkheads...........................................233.5 Horizontally corrugated longitudinal bulkhead.........................................23

Section 4 Buckling requirements for direct strength analysis...................................241 General................................................................................................. 24

1.1 Scope............................................................................................... 242 Stiffened and unstiffened panels.......................................................... 24

2.1 General............................................................................................. 242.2 Stiffened panels................................................................................. 302.3 Unstiffened panels..............................................................................312.4 Reference stress.................................................................................332.5 Lateral pressure................................................................................. 332.6 Buckling criteria................................................................................. 33

3 Corrugated bulkhead............................................................................ 343.1 General............................................................................................. 343.2 Reference stress.................................................................................343.3 Overall column buckling.....................................................................343.4 Local buckling.................................................................................... 35

4 Vertically stiffened longitudinal plating in way of horizontal neutralaxis...................................................................................................... 36

4.1 Buckling criteria................................................................................. 365 Struts, pillars and cross ties.................................................................37

5.1 Buckling criteria................................................................................. 37

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SECTION 1 GENERAL

1 Introduction

1.1 Assumption

1.1.1 This chapter contains the strength criteria for buckling and ultimate strength of local supportingmembers, primary supporting members and other structures such as pillars, corrugated bulkheads andbrackets. These criteria shall be applied as specified in Ch.6 for hull local scantlings and in Ch.7 for finiteelement analysis.

1.1.2 For each structural member, the characteristic buckling strength shall be taken as the mostunfavourable/critical buckling failure mode.

1.1.3 Unless otherwise specified, the buckling strength of structural members in this chapter are based onnet scantling obtained by deducting tc from the gross offered thickness, where tc is defined in Ch.3.

1.1.4 In this chapter, compressive and shear stresses shall be taken as positive, tension stresses shall betaken as negative.

2 Application

2.1 Scope

2.1.1 The buckling checks shall be performed according to:

— Sec.2 for the slenderness requirements of plates, longitudinal and transverse stiffeners, primarysupporting members and brackets.

— Sec.3 for the hull girder buckling requirements of plates, longitudinal and transverse stiffeners, supportingmembers and other structures.

— Sec.4 for the buckling requirements of the direct analysis for the plates, stiffened panels and otherstructures. Buckling analysis according to Sec.4 is also applicable for beam analysis of structure elementssubject to compressive and shear stresses.

— the Society's document DNVGL-CG-0128, Buckling, for the buckling capacity.

2.1.2 StiffenerThe buckling check of the stiffeners referred to in this chapter is applicable to the stiffener fitted parallel tothe long edge of the plate panel.

2.1.3 Platforms for permanent means of access (PMA)Platforms for permanent means of access (PMA) without web stiffening shall be consider as enlargedstiffeners and shall comply with the following requirements:

— slenderness requirement for stiffeners as given in Sec.2 [3]— buckling strength for stiffeners as given in Sec.3 [3] and Sec.4 [2].

Platforms for permanent means of access (PMA) with web stiffening shall be considered as primary supportmembers (PSM) and shall comply with the following requirements:

— slenderness requirement for PMA as given in Sec.2 [4]— buckling strength of web plate as given in Sec.3 [3] and Sec.4 [2]— buckling strength of web stiffener as given in Sec.3 [3] and Sec.4 [2].

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3 Definitions

3.1 Assessment methodsThe buckling assessment is carried out according to one of the two methods taking into account differentboundary condition types:

— Boundary condition A: All the edges of the elementary plate panel are forced to remain straight (but freeto move in the in-plane directions) due to the surrounding structure/neighbouring plates. This method isapplicable to large continuous panels like bottom shell, side shell, deck inner hull and plane bulkheads.

— Boundary condition B: The edges of the elementary plate panel are not forced to remain straight due tolow in-plane stiffness at the edges and/or no surrounding structure/neighbouring plates.This method isapplicable to web of primary supporting members.

3.2 Buckling utilisation factor

3.2.1 The utilisation factor, η, is defined as the ratio between the applied loads and the correspondingultimate capacity or buckling strength.

3.2.2 For combined loads, the utilisation factor, ηact, shall be defined as the ratio of the applied equivalentstress and the corresponding buckling capacity, as shown in Figure 1, and shall be taken as:

where:

Wact = applied equivalent stress due to the combined membrane stress as defined in the Society'sdocument DNVGL-CG-0128, Buckling

Wu = equivalent buckling capacity as defined in the Society's documentDNVGL-CG-0128, Bucklingγc = stress multiplier factor at failure.

Figure 1 illustrates the buckling capacity and the buckling utilisation factor of a structural member subject toσx and σy stresses.

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Figure 1 Example of buckling capacity and buckling utilisation factor

3.3 Buckling acceptance criteria

3.3.1 A structural member is considered to have an acceptable buckling strength if it satisfies the followingcriterion:

where:

ηact = buckling utilisation factor based on the applied stress, defined in [3.2.2]ηall = allowable buckling utilisation factor as defined in [3.4].

3.3.2 Closed form method (CFM) is applicable for evaluation of buckling structural components given in Table1

Table 1 Closed Form Method (CFM)

Structural component Criterion Definitions / comments

Overall stiffened panel ηOverall < ηallηOverall is maximum utilization factor as defined in the Society'sdocument DNVGL-CG-0128 [3.2.1].

Plate ηPlate ≤ ηallηPlate is maximum utilization factor as defined in the Society'sdocumentDNVGL-CG-0128 ,[3.2.2].

Stiffener ηStiffener ≤ ηall

ηStiffener is maximum utilization factor as defined in the Society'sdocumentDNVGL-CG-0128 [3.2.3].

Note: This capacity check can only be fulfilled when the overallstiffened panel capacity, as defined in the Society's documentDNVGL-CG-0128 [3.2.1], is satisfied.

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ηFlange ≤ ηall

ηFlange = σbhd/σc is the maximum utilization factor for the flange ofthe corrugation.

σc is critical stress, in N/mm2, as defined in the Society'sdocument DNVGL-CG-0128 [3.2.2].Corrugation of vertically and

horizontally corrugated bulkheads

ηShear ≤ ηall

ηShear = τbhd/τc is the maximum shear utilization factor for theweb of the corrugation.

τc is critical shear stress, in N/mm2, as defined in the Society'sdocument DNVGL-CG-0128 [3.2.2].

Horizontally corrugatedlongitudinal bulkheads and

vertically corrugated bulkheadsexposed to high axial forces

η ≤ ηall

η is the overall column utilisation factor, defined in the Society'sdocument DNVGL-CG-0128 [3.3.1]. Each corrugation, within theextension of half flange, web and half flange must satisfy thiscriterion.

Struts, pillars and cross ties η ≤ ηallη is maximum buckling utilisation factor of struts, pillars or crossties, defined in the Society's document DNVGL-CG-0128 [3.3.1].

Web plate in way of openings ηOpening ≤ ηall

ηOpening is maximum web plate utilisation factor in way ofopenings, as defined in the Society's document DNVGL-CG-0128[3.2.4].

3.3.3 Semi analytical buckling code, PULS, can be used as an alternative to CFM for overall stiffened panel,plates and stiffeners.

Table 2 Semi analytical buckling code, PULS


Stiffened panel ηPanel ≤ ηallηPanel is the usage of the stiffened panel by the Society'sdocument DNVGL-CG-0128 Sec.4, PULS S3 panel.

Plate ηPlate ≤ ηall

ηPlate is the usage of the plate panel by the Society's documentDNVGL-CG-0128 Sec.4, PULS U3 panel. Not applicable if the plateis checked the stiffened panel option, PULS S3 panel.

Orthogonally stiffened panel ηPanel ≤ ηall

ηPanel is the usage of the stiffened panel with secondary bucklingstiffeners by the Society's document DNVGL-CG-0128 Sec.4,PULS S3 panel.

Irregular stiffened panel ηPlate ≤ ηall

ηPlate is the usage of the plate panel by the Society's documentDNVGL-CG-0128 Sec.4, PULS U3 panel. Alternatively PULS T1panel can be used.

Corrugation of vertically andhorizontally corrugated bulkheads

η ≤ ηall

η is maximum utilization factor for the corrugation as defined inthe Society's document DNVGL-CG-0128 Sec.4, PULS K3 Panel.

Alternatively, PULS U3 panel can be used.

Horizontally corrugatedlongitudinal bulkheads and

vertically corrugated bulkheadsexposed to high axial forces

η ≤ ηallη is utilization factor, defined in the Society's document DNVGL-CG-0128 Sec.4 PULS K3 panel.

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3.4 Allowable buckling utilisation factorThe allowable buckling utilisation factor is defined in Table 3.

Table 3 Allowable buckling utilisation factor ηall

Structural member Acceptance criteria Design loadscenario

ηall

AC-I S 0.80

AC-II S + D 1.00Plates and stiffeners/ stiffened panels

AC-III1) A, T 1.00

AC-I S 0.65

AC-II S + D 0.75Struts, pillars and cross-ties

AC-III1) A, T 0.75

AC-I S 0.72

AC-II S + D 0.90Corrugation of corrugated bulkheads

under lateral pressure from liquid loads.

AC-III1) A, T 0.90

1) For members of the collision bulkhead, AC-I shall be used.

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SECTION 2 SLENDERNESS REQUIREMENTSSymbols

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

bf-out = maximum distance, in mm, from the web to the flange edge as shown in Figure 1hw = depth of stiffener web, in mm, as shown in Figure 1ℓb = effective length of edge of bracket, in mm, as defined in Table 3ℓ = length of stiffener between effective supports, in mseff = effective width of attached plate of stiffener, in mm, taken equal to:

seff = 0.8 stf = net flange thickness, in mmtp = net thickness of plate, in mmtw = net web thickness, in mm.

1 Structural elements

1.1 GeneralAll structural elements shall comply with the applicable slenderness and proportion requirements given in [2]to [4]. These requirements may be based on a lower specified minimum yield stress value than the actualvalue provided that the requirements specified in Sec.3 and Sec.4 are satisfied for the lower value.

2 Plates

2.1 ApplicationBased on buckling control in accordance with Sec.3 and Sec.4, slenderness requirements according to [2.2]may be specially considered. The plate slenderness requirement does not apply to transversely stiffened bilgeplates and gunwale with radius.

2.2 Net thickness of plate panelsThe net thickness of plate panels, in mm, shall satisfy the following criteria:

where:

b = distance, in mm, between stiffeners at mid length of plate field, as shown in Ch.3 Sec.7 Figure 12C = slenderness coefficient taken as:

C = 100 for outer shell including strength deck except in superstructures, for vessels with lengthL>90 m

= 175 for internal structural members, except tank boundaries, in vessels with more than threecontinuous decks and for members in deck house/superstructure

= 125 for other structures not mentioned above.

Other values for C may be applicable for specific ship types, see Pt.5.

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3 Stiffeners

3.1 Proportions of stiffeners3.1.1 Net thickness of all stiffener typesThe net thickness of stiffeners shall satisfy the following criteria:

a) Stiffener web plate:

b) Flange:

where:

Cw, Cf = slenderness coefficients given in Table 1.

If requirement b) is not fulfilled the effective free flange out stand, in mm, used in strength assessment shallnot be taken greater than:

Figure 1 Stiffener scantling parameters

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Table 1 Slenderness coefficients

Type of profile Cw Cf

Angle bars 75 121)

T-bars 75 121)

Bulb bars 45 -

Flat bars 22 -

1) Cf = 22, non-continuous straight flanges with end bracket.

3.1.2 Net dimensions of angle and T-barsThe total flange breadth, in mm, for angle and T-bars shall satisfy the following criterion:

4 Primary supporting members

4.1 Proportions and stiffness4.1.1 Proportions of web plate and flangeThe net thicknesses of the web plates and flanges of primary supporting members shall satisfy the followingcriteria:

a) Web plate:

b) Flange:

where:

sw = plate breadth, in mm, taken as the spacing of the web stiffeners, see also the Society's documentDNVGL-CG-0128[3.2.4.2]

Cw = slenderness coefficient for the web plate taken as:

Cw = 100Cf = slenderness coefficient for the flange as shown in Table 1.

If requirement b) is not fulfilled the effective free flange out stand, in mm, used in strength assessment shallnot be taken greater than:

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4.1.2 Deck transverse primary supporting membersThe net moment of inertia for deck transverse primary supporting members, in cm4, supporting decklongitudinals subject to axial compressive hull girder stress, shall comply, within its central half of thebending span, with the following criterion:

where:

Ipsm-n50 = net moment of inertia, in cm4, of deck transverse primary supporting member, with effectivewidth of attached plate equal to 0.8 S

ℓbdg = unsupported bending span of deck transverse primary supporting member in m, as defined inCh.3 Sec.7 or in case of a grillage structure the distance between connections to other primarysupport members

S = spacing of deck transverse primary supporting members, in m, as defined in Ch.3 Sec.7Ist = moment of inertia in cm4 of longitudinal or stiffener necessary to satisfy the lateral buckling

mode:

for

for

IA = moment of inertia in cm4 about the axis perpendicular to the expected direction of bucklingA = cross sectional area in cm2

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σhg-cp = maximum compressive stress in deck in question based on Ch.5 Sec.3 [2] for ships without largedeck openings and Ch.5 Sec.3 [3] for vessels with large deck openings.

Alternatively, semi-analytical buckling code (PULS) may be used according to the Society's document DNVGL-CG-0128 [4], Buckling analysis as an equivalent where transverse primary supporting members are directlymodelled. In such a case the allowable buckling utilisation factor shall be based on Sec.1 Table 3.

4.2 Web stiffeners of primary supporting members4.2.1 Proportions of web stiffenersThe net thickness of web and flange of web stiffeners fitted on primary supporting members shall satisfy therequirements specified in [3.1.1] and [3.1.2].

4.2.2 Bending stiffness of web stiffenersThe net moment of inertia, in cm4, of web stiffener, Ist, fitted on primary supporting members, with effectiveattached plate, seff, shall not be less than the minimum moment of inertia defined in Table 2.

Table 2 Stiffness criteria for web stiffeners

Stiffener arrangement Minimum moment of inertia of web stiffeners, in cm4

A

Web stiffeners fitted along the PSM span

B

Web stiffeners fitted normal to the PSM span

where:C = Slenderness coefficient to be taken as:

C = 0.72

Other values for C may be applicable for specific ship types, see Pt.5.ℓ = Length of web stiffener, in m.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.

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5 Brackets

5.1 Tripping brackets5.1.1 Unsupported flange lengthDimensions of tripping brackets shall be in accordance with Ch.3 Sec.6 [3.3]. The unsupported length ofthe flange of the primary supporting member, in m, i.e. the distance between tripping brackets, shall not begreater than every fourth spacing of stiffeners in general, not exceeding 4m.

5.1.2 Edge stiffeningTripping brackets on primary supporting members shall be stiffened by a flange or edge stiffener if theeffective length of the edge, ℓb as defined in Table 3, in mm, is greater than:

where:

tb = bracket net web thickness, in mm.

5.2 End brackets5.2.1 ProportionsThe net web thickness of end brackets, in mm, subject to compressive stresses shall not be less than:

where:

db = depth of brackets, in mm, as defined in Table 3C = slenderness coefficient as defined in Table 3ReH = specified minimum yield stress of the end bracket material, in N/mm2.

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Table 3 Buckling coefficient, C, for proportions of brackets

Mode C

Brackets without edge stiffener

where:

Brackets with edge stiffener

C = 70

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5.3 Edge reinforcement5.3.1 Edge reinforcements of bracket edgesThe depth of stiffener web, in mm, of edge stiffeners in way of bracket edges shall not be less than:

or 50 mm, whichever is greater.

where:

C = slenderness coefficient taken as:

C = 75 for end brackets= 50 for tripping brackets

ReH = specified minimum yield stress of the stiffener material, in N/mm2.

5.3.2 Proportions of edge stiffenersThe net thickness of the web plate and flange of the edge stiffener shall satisfy the requirements specified in[3.1.1] and [3.1.2].

6 Pillars

6.1 Proportions of I-section pillarsFor I-sections, the thickness of the web plate and the flange thickness shall comply with requirementsspecified in [3.1.1] and [3.1.2].

6.2 Proportions of box section pillarsThe thickness of thin walled box sections shall comply with the requirements specified in item (a) of [3.1.1].

6.3 Proportions of circular section pillarsThe net thickness, t, of circular section pillars, in mm, shall comply with the following criterion:

where:

r = mid thickness radius of the circular section, in mm.

7 Edge reinforcement in way of openings

7.1 Depth of edge stiffenerWhen fitted as shown in Figure 2, the depth of web, in mm, of edge stiffeners in way of openings shall not beless than:

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or 50 mm, whichever is greater.

where:

C = slenderness coefficient taken as:

C = 50ReH = specified minimum yield stress of the edge stiffener material, in N/mm2.

7.2 Proportions of edge stiffenersThe net thickness of the web plate and flange of the edge stiffener shall satisfy the requirements specified in[3.1.1] and [3.1.2].

Figure 2 Typical edge reinforcements

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SECTION 3 HULL GIRDER BUCKLINGSymbols

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

ηall = allowable buckling utilisation factor, as defined in Sec.1 [3.4]EPP = elementary Plate Panel as defined in Ch.3 Sec.7 [2.1]LCP = load calculation point as defined in Ch.3 Sec.7 [2.2] and Ch.3 Sec.7 [3.2].

1 General

1.1 Scope

1.1.1 This section applies to plate panels and stiffeners subject to hull girder compression and shearstresses. In addition the following structural members shall be checked:

— vertically corrugated longitudinal bulkheads subject to hull girder shear stresses— horizontally corrugated longitudinal bulkheads subject to hull girder compression and shear stresses.

1.1.2 The hull girder buckling strength requirements apply along the full length of the ship.

1.1.3 Design load setsThe buckling checks shall be performed for all design load sets defined in Ch.6 Sec.2 [2].For each design load set, for all dynamic load cases, the lateral pressure shall be determined according toCh.4 at the load calculation point (LCP) defined in Ch.3 Sec.7, and shall be applied together with the hullgirder stress combinations given in [2.2].

1.2 Equivalent plate panel

1.2.1 When the plate thickness varies over the width b, of a plate panel, the buckling check shall beperformed for an equivalent plate panel width, combined with the smaller plate thickness, t1. The width ofthis equivalent plate panel, beq, in mm, is defined by the following formula:

where:

ℓ1 = width of the part of the plate panel with the smaller plate thickness, t1, in mm, as defined in [1.2.2]ℓ2 = width of the part of the plate panel with the greater plate thickness, t2, in mm, as defined in

[1.2.2].

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Figure 1 Plate thickness change over the width

1.2.2 In case of transverse butt weld, when a EPP is made with different thicknesses, the buckling check ofthe plate and stiffeners shall be made for each thickness considered constant on the EPP, the stresses andpressures being estimated for the EPP at the LCP.

1.2.3 MaterialsWhen the plate panel is made of different materials, the minimum yield strength shall be used for thebuckling assessment.

2 Hull girder stress

2.1 General2.1.1 Hull girder stress applicable for load components SThe hull girder bending stresses, σhg, in N/mm2, for load component S shall be taken as:

where:

σhg-sw = hull girder bending stress, in N/mm², due to vertical still water bending moment as defined inCh.5 Sec.3 [2] for ships without large deck openings and in Ch.5 Sec.3 [3] for ships with largedeck openings.

2.1.2 Hull girder stress applicable for load components S+DThe hull girder bending stresses, σhg, in N/mm2, for load component S+D shall be taken as defined in Ch.5Sec.3 [2] for ships without large deck openings and in Ch.5 Sec.3 [3] for ships with large deck openings.

2.1.3 The hull girder shear stresses, τhg, in N/mm2, are determined according to Ch.5 Sec.3[3].

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2.2 Stress combinations

2.2.1 Each elementary plate panel, and stiffeners, shall satisfy the criteria defined in [3] with the followingstress combinations:

a) Longitudinal stiffening arrangement:

— Stress combination 1 with:


b) Transverse stiffening arrangement:



3 Buckling criteria

3.1 Overall stiffened panelThe buckling strength of overall stiffened panels shall satisfy the following criterion:

ηOverall ≤ ηall

where:

ηOverall = maximum utilisation factor as defined Sec.1 [3.3].

3.2 PlatesThe buckling strength of elementary plate panels shall satisfy the following criterion:

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ηPlate ≤ ηall

where:

ηPlate = maximum plate utilisation factor calculated according to SP-A, see Sec.1 [3.3].

For the determination of ηPlate for vertically stiffened plating, the cases 12 and 16 in the Society'sdocumentDNVGL-CG-0128Sec.3 Table 3-3 corresponding to the shorter edge of the plate panel clamped, maybe considered together with a mean σy stress and ψy=1, provided that the shorter edges are supported bylongitudinal plating/decks and are located within 0.7z1 from horizontal neutral axis. z1 is the distance fromthe horizontal neutral axis to equivalent deck line or baseline respectively as defined in Ch.5 Sec.2 [1.6]

3.3 StiffenersThe buckling strength of stiffeners shall satisfy the following criterion:

ηStiffener ≤ ηall

where:

ηStiffener = maximum stiffener utilisation factor, see Sec.1 [3.3].

3.4 Vertically corrugated longitudinal bulkheads

3.4.1 The shear buckling strength of vertically corrugated longitudinal bulkheads shall satisfy the followingcriterion:

ηShear ≤ ηall

where:

ηShear = maximum shear corrugated bulkhead utilisation factor as defined in Sec.1 [3.3].

3.5 Horizontally corrugated longitudinal bulkhead

3.5.1 Each corrugation, within the extension of half flange, web and half flange, shall satisfy the followingcriterion:

η ≤ ηall

where:

η = overall column utilisation factor, as defined in Sec.1 [3.3].

End constraints factor corresponding to pinned ends shall be applied except for fixed end support to be usedin way of stool with width exceeding 2 times the depth of the corrugation.

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SECTION 4 BUCKLING REQUIREMENTS FOR DIRECT STRENGTHANALYSISSymbols

ηall = allowable buckling utilisation factor, as defined in Sec.1 [3.4].

1 General

1.1 Scope

1.1.1 The requirements given in this section apply for the buckling assessment in direct strength analysis forstructural elements subjected to compressive stress, shear stress and lateral pressure.

1.1.2 Elements in the FE analysis carried out according to Ch.7shall be assessed individually. The bucklingchecks shall be performed for the following structural elements:

— stiffened and unstiffened panels— web plate in way of openings— corrugated bulkheads— struts, pillars and cross ties.

This section applies to plate panels and stiffeners. In addition the following structural members subject tocompressive stresses shall be checked:

— corrugation of vertically and horizontally corrugated bulkheads— struts— pillars— cross-ties.

1.1.3 Verification of buckling strength in accordance with the requirements in this section is also applicablefor the structure analysed by beam elements when structural elements are subject to compressive and shearstresses.

1.1.4 Procedure for overall buckling of pillar and cross-tie and the procedure for buckling of plane and curvedplate as well as for stiffened plate panels are given in the Society's documentDNVGL-CG-0128, Bucklinganalysis

2 Stiffened and unstiffened panels

2.1 General

2.1.1 Boundary condition A and Boundary condition B as defined in Sec.1 [3.1]shall be used according toTable 1.

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Table 1 Boundary conditions for structural members

Structural elements Assessment method Normal panel definition

Longitudinal structures, see example Figure 1

Shell envelopeDeck

Inner hull

Hopper tank side

Longitudinal bulkheads

SP-ALength: between web framesWidth: between primary supporting members

Double bottom longitudinal girders in linewith longitudinal bulkhead or connected tohopper tank side

SP-ALength: between web framesWidth: full web depth

Web of double bottom longitudinal girdersnot in line with longitudinal bulkhead ornot connected to hopper tank side

SP-B5) Length: between web framesWidth: full web depth

Web of horizontal girders in double sidespace connected to hopper tank side SP-A

Length: between web framesWidth: full web depth

Web of horizontal girders in double sidespace not connected to hopper tank side SP-B5) Length: between web frames

Width: full web depth

Web of single skin longitudinal girders orstringers with regular mesh SP-B5)

Web of single skin longitudinal girders orstringers with irregular mesh UP-B5)

Plate between local stiffeners/face plate/Primarysupport member (PSM)

Transverse structures, see example Figure 2

Web of transverse deck frames includingbrackets with regular mesh SP-B5)

Web of transverse deck frames includingbrackets with irregular mesh UP-B5)

Plate between local stiffeners/face plate/PSM

Vertical web in double side space SP-B5) Length: full web depthWidth: between primary supporting members

Irregularly stiffened panels, e.g. webpanels in way of hopper tank and bilge UP-B5) Plate between local stiffeners/face plate/PSM

Double bottom floors SP-A6) Length: full web depthWidth: between primary supporting members

Vertical web frame including brackets withregular mesh SP-B5)

Vertical web frame including brackets withirregular mesh UP-B5)

Plate between vertical web stiffeners/face plate/PSM

Cross tie web plate with regular mesh SP-B5)

Cross tie web plate with irregular mesh UP-B5)Plate between vertical web stiffeners/face plate/PSM

Transverse bulkheads, see example Figure 3

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Structural elements Assessment method Normal panel definition

Regularly stiffened bulkhead panelsinclusive the secondary buckling stiffenersperpendicular to the regular stiffener(such as carlings)

SP-ALength: between primary supporting membersWidth: between primary supporting members

Irregularly stiffened bulkhead panels, e.g.web panels in way of hopper tank andbilge

UP-A Plate between local stiffeners/face plate

Web plate of bulkhead stringers includingbrackets with regular mesh SP-B5)

Web plate of bulkhead stringers includingbrackets with irregular mesh UP-B5)

Plate between web stiffeners /face plate

Transverse corrugated bulkheads and cross deck, see example Figure 3 and Figure 4

Upper/lower stool including stiffeners SP-ALength: between internal web diaphragmsWidth: length of stool side

Stool internal web diaphragm with regularmesh SP-B5)

Stool internal web diaphragm withirregular mesh UP-B5)

Plate between local stiffeners /face plate / PSM

Cross deck SP-A Plate between local stiffeners/ PSM

1) Note 1:

SP stands for stiffened panel.2) Note 2:

UP stands for unstiffened panel.3) Note 3:

A stands for Boundary condition A.4) Note 4:

B stands for Boundary condition B.5) Note 5:

For PSM web panels with one of the long edges along the face plate or along the attached plating without "in-line support", i.e. the edge is free to pull in, boundary condition B (SP-B or UP-B) shall be applied. In other casesboundary condition A (SP-A or UP-A) is applicable.

6) Note 6:

Typically the short plate edge is attached to the plate flanges and boundary condition A (SP-A or UP-A) is applicable.However in case of one of the long edges is without "in-line support" and is free to pull in, boundary condition B(SP-B or UP-B) shall be applied.

2.1.2 Average thickness of plate panelWhere the plate thickness along a plate panel is not constant, the panel used for the buckling assessmentshall be taken as the average thickness, in mm:

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where:

Ai = area of the i-th plate elementti = net thickness of the i-th plate elementn = number of finite elements defining the buckling plate panel.

2.1.3 Yield stress of the plate panelThe panel yield stress ReH_P is taken as the minimum value of the specified yield stresses of the elementswithin the plate panel.

Figure 1 Longitudinal plates, ore carrier

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SP-ASP-A

SP-A

SP-A

SP-A

SP-A

SP-A

Figure 2 Transverse web frames, ore carrier

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Figure 3 Transverse bulkhead, ore carrier

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Figure 4 Upper deck, ore carrier

2.2 Stiffened panels

2.2.1 To represent the overall buckling behaviour, each stiffener with attached plate shall be modelled as astiffened panel of the extent defined in Table 1.

2.2.2 If the stiffener properties or stiffener spacing varies within the stiffened panel, the calculations shallbe performed separately for all configurations of the panels, i.e. for each stiffener and plate between thestiffeners. Plate thickness, stiffener properties and stiffener spacing at the considered location shall beassumed for the whole panel.

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2.3 Unstiffened panels2.3.1 Irregular plate panelIn way of web frames, stringers and brackets, the geometry of the panel, i.e. plate bounded by webstiffeners/face plate, may not have a rectangular shape. In this case, an equivalent rectangular panel shall bedefined according to [2.3.2] for irregular geometry and [2.3.3] for triangular geometry and to be used for thebuckling assessment.

2.3.2 Modelling of an unstiffened panel with irregular geometryUnstiffened panels with irregular geometry shall be idealised to equivalent panels for plate bucklingassessment according to the following procedure:

a) The four corners closest to a right angle, 90 deg, 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.

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

d4d) A line joins 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 lengthof the line defines the length of the capacity model, a measured from one end point.

e) The length of shorter side, b in mm, shall be taken as:

where:

A= area of the plate, in mm²a= length defined in (d), in mm

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f) The stresses from the direct strength analysis shall be transformed into the local coordinate system of

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

2.3.3 Modelling of an unstiffened plate panel with triangular geometryUnstiffened panels with triangular geometry shall be idealised to equivalent panels for plate bucklingassessment according to the following procedure:

a) Medians are constructed as shown below.

b) The longest median is identified. This median the length of which is ℓ1 in mm, defines the longitudinal

direction for the capacity model.

c) The width of the model, ℓ2, in mm, shall be taken as:

where:

A = area of the plate, in mm²

d) The lengths of shorter side, b, and of the longer side, a, in mm, of the equivalent rectangular plate panelshall be taken as:

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where:

e) The stresses from the direct strength analysis shall be transformed into the local coordinate system

of the equivalent rectangular panel and shall be used for the buckling assessment of the equivalentrectangular panel.

2.4 Reference stress

2.4.1 The stress distribution shall be taken from the direct strength analysis and applied to the bucklingmodel. Method for calculation of stress based reference stresses is defined in Ch.7 Sec.4.

2.5 Lateral pressure

2.5.1 The lateral pressure applied to the direct strength analysis shall also be applied for the bucklingassessment.

2.5.2 Where the lateral pressure is not constant over a buckling panel defined by a number of finite plateelements, an average lateral pressure, N/mm2, is calculated using the following formula:

where:

Ai = area of the i-th plate element, in mm2

Pi = lateral pressure of the i-th plate element, in N/mm2

n = number of finite elements in the buckling panel.

2.6 Buckling criteriaThe compressive buckling strength shall satisfy the following criterion:

η ≤ ηall

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where η is the maximum of the relevant utilization factors:

ηUP-A = maximum plate utilisation factor for Boundary condition A, [2.1], see Sec.1 [3.3]ηUP-B = maximum plate utilisation factor for Boundary condition B, [2.1], see Sec.1 [3.3]ηSP-A = maximum stiffened panel utilisation factor taken as the maximum of:

— the overall stiffened panel capacity, see Sec.1 [3.3]— the plate capacity calculated according to Boundary Condition A, [2.1], see Sec.1 [3.3]— the stiffener buckling strength, see Sec.1 [3.3], considering separately the properties

(thickness, dimensions) and reference stresses of each EPP at both sides of the stiffenerηSP-B = maximum stiffened panel utilisation factor taken as the maximum of:

— the overall stiffened panel capacity, see Sec.1 [3.3]— the plate capacity calculated according to Boundary condition B, [2.1], see Sec.1 [3.3]— the stiffener buckling strength, see Sec.1 [3.3], considering separately the properties

(thickness, dimensions) and reference stresses of each EPP at both sides of the stiffenerηopening = maximum web plate utilisation factor in way of openings, see Sec.1 [3.3].

3 Corrugated bulkhead

3.1 General

3.1.1 Three buckling failure modes shall be assessed on corrugated 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 shall be assessed.

3.2.2 The membrane stresses at element centroid shall be used.

3.2.3 The maximum normal stress parallel to the corrugation and the maximum shear stress are definedaccording to the following methodology:

— element stresses shall be averaged over the width of the considered member (flange or web)— when the stress value at b/2 from ends cannot be obtained directly from FE element, the stress at this

location shall be obtained by interpolation on elements in this area. This interpolation shall be made onelements extending to a distance equal to 3b from the end of the corrugation. The normal stress parallelto the corrugation is interpolated at b/2 in accordance with the Society's document DNVGL-CG-0128,Buckling analysis, i.e. using the 2nd order polynomial curve. The shear stress at b/2 is obtained by linearinterpolation between the elements most close to b/2

where:

b = width of the considered member of the corrugation, i.e. flange or web.

3.2.4 Where more than one plate thickness is used for a flange panel, the maximum stress shall be obtainedfor each thickness range and to be checked with the buckling criteria for each thickness.Buckling criteria is given in [3.4.1].

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3.3 Overall column buckling

3.3.1 The overall buckling failure mode of corrugated bulkheads subjected to axial compression shall bechecked for column buckling, e.g. horizontally corrugated bulkheads and vertically corrugated bulkheadssubjected to local vertical forces.

Table 2 Application of overall column buckling for corrugated bulkhead

Corrugation Orientation

Horizontal Vertical

Longitudinal bulkhead Required

Transverse bulkhead Required

Required, when subjected to localvertical forces, e.g. crane loads

3.3.2 Each corrugation unit within the extension of half flange, web and half flange, i.e. single corrugation asshown in grey in Figure 5, shall satisfy the following criterion:

ηOverall ≤ ηall

where:

ηOverall = maximum overall column utilisation factor, see Sec.1 [3.3], considered as a pillar with anunsupported length taken as the length of the corrugation except for vertically corrugatedbulkheads where the length, ℓbdg, shall be applied as defined in Ch.3 Sec.6 [5.1.4].

Figure 5 Single corrugation

3.3.3 End constraint factor, fend corresponding to pinned ends shall be applied except for fixed end support tobe used in way of stool with width exceeding 2 times the depth of the corrugation.

3.4 Local buckling

3.4.1 The compressive buckling strength of a unit flange and a unit web of corrugation bulkheads shallsatisfy the following criterion:

ηCorr ≤ ηall

where:

ηCorr = maximum unit flange or unit web utilisation factor, see Sec.1 [3.3].

Two stress combinations shall be considered:

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— the maximum normal stress parallel to the corrugation plus the shear stress at the location where themaximum normal stress parallel to the corrugation occurs

— the maximum shear stress plus the normal stress parallel to the corrugation at the location where themaximum shear stress occurs.

The buckling assessment shall be performed for an aspect ratio α equal to 2, and for the thickness of themember where the maximum compressive/shear stress occurs (see [3.2.4]).

4 Vertically stiffened longitudinal plating in way of horizontalneutral axis

4.1 Buckling criteria4.1.1 PlatingThe compressive buckling strength for vertically stiffened longitudinal plating with the shorter edgessupported by longitudinal plating/decks and located within 0.7z1 from horizontal neutral axis, where z1 is thedistance from horizontal neutral axis to equivalent deck line or baseline respectively as defined in Ch.5 Sec.2[1.6], may be verified based on the following criterion:

ηvsp ≤ ηall

where:

ηvsp = maximum utilization factor calculated according to Method A as defined in the Society's documentDNVGL-CG-0128,Sec.3 [3.2.2.1] and considering the following boundary conditions and stresscombinations:

— 4 edges simply supported, ref. cases 1, 2 and 15 of the Society's document DNVGL-CG-0128,Table 3-3:

a) Pure vertical stress:

— The maximum vertical stress of stress elements is used with

α=1 and ψx=1.

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

— The maximum vertical stress in the buckling panel plus the shear and longitudinalstresses at the location where the maximum vertical stress occurs is used with

α=2 and ψx=ψy=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 verticalstresses at the location where maximum shear stress occurs is used with

α=2 and ψx=ψy=1.— The plate thickness to be considered in the buckling strength check is the one where the

maximum shear stress occurs.

— The 2 shorter edges of the plate panel clamped, ref. cases 11, 12 and 16 of the Society'sdocument DNVGL-CG-0128, Table 3-3:

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

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— The actual size of the buckling panel is used to define α.— The average values for longitudinal, vertical and shear stresses shall be used.— ψx=ψy1.— The plate thickness to be considered in the buckling strength check is based on Sec.3

[1.2.2].

Figure 6 Boundary condition/load combination (a), (b), (c) and (d) for vertically stiffenedlongitudinal plating in way of horizontal neutral axis

4.1.2 Vertical stiffenersThe buckling strength for vertical stiffeners attached to longitudinal plating within 0.7z1 from horizontalneutral axis, where z1 is the distance from horizontal neutral axis to equivalent deck line or baselinerespectively as defined in Ch.5 Sec.2 [1.6], shall satisfy the following criterion:

ηstiffener ≤ ηall

where:

ηstiffener = maximum stiffener utilization factor, as defined in the Society's document DNVGL-CG-0128,Sec.3 [3.2.3].

5 Struts, pillars and cross ties

5.1 Buckling criteria

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

ηPillar ≤ ηall

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where:

ηPillar = maximum utilisation factor of struts, pillars or cross ties, see Sec.1 [3.3].

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Part 3 Hull Chapter 8 Buckling - DNV GL · 2015-09-29 · Buckling analysis according to Sec.4 is also applicable for beam analysis of structure elements subject to compressive and

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