RULES FOR CLASSIFICATION Ships. Part 3 Hull Chapter 8 Buckling. Edition October 2015 DNV GL AS

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1 RULES FOR CLASSIFICATION Ships Edition October 2015 Part 3 Hull Chapter 8 The content of this service document is the subject of intellectual property rights reserved by ("DNV GL"). The user accepts that it is prohibited by anyone else but DNV GL and/or its licensees to offer and/or perform classification, certification and/or verification services, including the issuance of certificates and/or declarations of conformity, wholly or partly, on the basis of and/or pursuant to this document whether free of charge or chargeable, without DNV GL's prior written consent. DNV GL is not responsible for the consequences arising from any use of this document by others. The electronic pdf version of this document, available free of charge from is the officially binding version.

2 FOREWORD DNV GL rules for classification contain procedural and technical requirements related to obtaining and retaining a class certificate. The rules represent all requirements adopted by the Society as basis for classification. October 2015 Any comments may be sent by to rules@dnvgl.com 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 shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times 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, 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.

3 CHANGES CURRENT This is a new document. The rules enter into force 1 January Part 3 Chapter 8 Changes - current Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 3

4 CONTENTS Changes current...3 Section 1 General Introduction Assumption Application Scope Definitions Assessment methods utilisation factor acceptance criteria Allowable buckling utilisation factor... 9 Part 3 Chapter 8 Contents Section 2 Slenderness requirements Structural elements General Plates Application Net thickness of plate panels Stiffeners Proportions of stiffeners Primary supporting members Proportions and stiffness Web stiffeners of primary supporting members Brackets Tripping brackets End brackets Edge reinforcement Pillars Proportions of I-section pillars Proportions of box section pillars Proportions of circular section pillars Edge reinforcement in way of openings Depth of edge stiffener Proportions of edge stiffeners Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 4

5 Section 3 Hull girder buckling General Scope Equivalent plate panel Hull girder stress General Stress combinations criteria Overall stiffened panel Plates Stiffeners Vertically corrugated longitudinal bulkheads Horizontally corrugated longitudinal bulkhead...23 Part 3 Chapter 8 Contents Section 4 requirements for direct strength analysis General Scope Stiffened and unstiffened panels General Stiffened panels Unstiffened panels Reference stress Lateral pressure criteria Corrugated bulkhead General Reference stress Overall column buckling Local buckling Vertically stiffened longitudinal plating in way of horizontal neutral axis criteria Struts, pillars and cross ties criteria Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 5

6 SECTION 1 GENERAL 1 Introduction 1.1 Assumption 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 shall be applied as specified in Ch.6 for hull local scantlings and in Ch.7 for finite element analysis For each structural member, the characteristic buckling strength shall be taken as the most unfavourable/critical buckling failure mode Unless otherwise specified, the buckling strength of structural members in this chapter are based on net scantling obtained by deducting t c from the gross offered thickness, where t c is defined in Ch In this chapter, compressive and shear stresses shall be taken as positive, tension stresses shall be taken as negative. Part 3 Chapter 8 Section 1 2 Application 2.1 Scope The buckling checks shall 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 hull girder buckling requirements of plates, longitudinal and transverse stiffeners, supporting members and other structures. Sec.4 for the buckling requirements of the direct analysis for the plates, stiffened panels and other structures. analysis according to Sec.4 is also applicable for beam analysis of structure elements subject to compressive and shear stresses. the Society's document DNVGL-CG-0128,, for the buckling capacity Stiffener The buckling check of the stiffeners referred to in this chapter is applicable to the stiffener fitted parallel to the long edge of the plate panel Platforms for permanent means of access (PMA) Platforms for permanent means of access (PMA) without web stiffening shall be consider as enlarged stiffeners 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 support members (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]. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 6

7 3 Definitions 3.1 Assessment methods The buckling assessment is carried out according to one of the two methods taking into account different boundary condition types: Boundary condition A: All the edges of the elementary plate panel are forced to remain straight (but free to move in the in-plane directions) due to the surrounding structure/neighbouring plates. This method is applicable 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 to low in-plane stiffness at the edges and/or no surrounding structure/neighbouring plates.this method is applicable to web of primary supporting members. 3.2 utilisation factor The utilisation factor, η, is defined as the ratio between the applied loads and the corresponding ultimate capacity or buckling strength For combined loads, the utilisation factor, η act, shall be defined as the ratio of the applied equivalent stress and the corresponding buckling capacity, as shown in Figure 1, and shall be taken as: Part 3 Chapter 8 Section 1 W act W u γ c = applied equivalent stress due to the combined membrane stress as defined in the Society's document DNVGL-CG-0128, = equivalent buckling capacity as defined in the Society's documentdnvgl-cg-0128, = stress multiplier factor at failure. Figure 1 illustrates the buckling capacity and the buckling utilisation factor of a structural member subject to σ x and σ y stresses. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 7

8 Figure 1 Example of buckling capacity and buckling utilisation factor Part 3 Chapter 8 Section acceptance criteria A structural member is considered to have an acceptable buckling strength if it satisfies the following criterion: η act = buckling utilisation factor based on the applied stress, defined in [3.2.2] η all = allowable buckling utilisation factor as defined in [3.4] Closed form method (CFM) is applicable for evaluation of buckling structural components given in Table 1 Table 1 Closed Form Method (CFM) Structural component Criterion Definitions / comments Overall stiffened panel η Overall < η all η Overall is maximum utilization factor as defined in the Society's document DNVGL-CG-0128 [3.2.1]. Plate η Plate η all η Plate is maximum utilization factor as defined in the Society's documentdnvgl-cg-0128,[3.2.2]. Stiffener η Stiffener η all η Stiffener is maximum utilization factor as defined in the Society's documentdnvgl-cg-0128 [3.2.3]. Note: This capacity check can only be fulfilled when the overall stiffened panel capacity, as defined in the Society's document DNVGL-CG-0128 [3.2.1], is satisfied. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 8

9 Structural component Criterion Definitions / comments Corrugation of vertically and horizontally corrugated bulkheads Horizontally corrugated longitudinal bulkheads and vertically corrugated bulkheads exposed to high axial forces η Flange η all η Shear η all η η all η Flange = σ bhd /σ c is the maximum utilization factor for the flange of the corrugation. σ c is critical stress, in N/mm 2, as defined in the Society's document DNVGL-CG-0128 [3.2.2]. η Shear = τ bhd /τ c is the maximum shear utilization factor for the web of the corrugation. τ c is critical shear stress, in N/mm 2, as defined in the Society's document DNVGL-CG-0128 [3.2.2]. η is the overall column utilisation factor, defined in the Society's document DNVGL-CG-0128 [3.3.1]. Each corrugation, within the extension of half flange, web and half flange must satisfy this criterion. Struts, pillars and cross ties η η all η is maximum buckling utilisation factor of struts, pillars or cross ties, defined in the Society's document DNVGL-CG-0128 [3.3.1]. Web plate in way of openings η Opening η all openings, as defined in the Society's document DNVGL-CG-0128 η Opening is maximum web plate utilisation factor in way of [3.2.4]. Part 3 Chapter 8 Section 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 Structural component Criterion Definitions / comments Stiffened panel η Panel η all η Panel is the usage of the stiffened panel by the Society's document DNVGL-CG-0128 Sec.4, PULS S3 panel. Plate η Plate η all DNVGL-CG-0128 Sec.4, PULS U3 panel. Not applicable if the plate η Plate is the usage of the plate panel by the Society's document is checked the stiffened panel option, PULS S3 panel. Orthogonally stiffened panel η Panel η all stiffeners by the Society's document DNVGL-CG-0128 Sec.4, η Panel is the usage of the stiffened panel with secondary buckling PULS S3 panel. Irregular stiffened panel η Plate η all DNVGL-CG-0128 Sec.4, PULS U3 panel. Alternatively PULS T1 η Plate is the usage of the plate panel by the Society's document panel can be used. Corrugation of vertically and horizontally corrugated bulkheads Horizontally corrugated longitudinal bulkheads and vertically corrugated bulkheads exposed to high axial forces η η all η η all η is maximum utilization factor for the corrugation as defined in the Society's document DNVGL-CG-0128 Sec.4, PULS K3 Panel. Alternatively, PULS U3 panel can be used. η is utilization factor, defined in the Society's document DNVGL- CG-0128 Sec.4 PULS K3 panel. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 9

10 3.4 Allowable buckling utilisation factor The allowable buckling utilisation factor is defined in Table 3. Table 3 Allowable buckling utilisation factor η all Structural member Plates and stiffeners/ stiffened panels Struts, pillars and cross-ties Corrugation of corrugated bulkheads under lateral pressure from liquid loads. Acceptance criteria Design load scenario η all AC-I S 0.80 AC-II S + D 1.00 AC-III 1) A, T 1.00 AC-I S 0.65 AC-II S + D 0.75 AC-III 1) A, T 0.75 AC-I S 0.72 AC-II S + D 0.90 Part 3 Chapter 8 Section 1 1) For members of the collision bulkhead, AC-I shall be used. AC-III 1) A, T 0.90 Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 10

11 SECTION 2 SLENDERNESS REQUIREMENTS Symbols For symbols not defined in this section, refer to Ch.1 Sec.4. b f-out = maximum distance, in mm, from the web to the flange edge as shown in Figure 1 h w = depth of stiffener web, in mm, as shown in Figure 1 l b = effective length of edge of bracket, in mm, as defined in Table 3 l = length of stiffener between effective supports, in m s eff = effective width of attached plate of stiffener, in mm, taken equal to: s eff = 0.8 s t f = net flange thickness, in mm t p = net thickness of plate, in mm t w = net web thickness, in mm. 1 Structural elements 1.1 General All 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 actual value provided that the requirements specified in Sec.3 and Sec.4 are satisfied for the lower value. Part 3 Chapter 8 Section 2 2 Plates 2.1 Application Based 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 bilge plates and gunwale with radius. 2.2 Net thickness of plate panels The net thickness of plate panels, in mm, shall satisfy the following criteria: b = distance, in mm, between stiffeners at mid length of plate field, as shown in Ch.3 Sec.7 Figure 12 C = slenderness coefficient taken as: C = 100 for outer shell including strength deck except in superstructures, for vessels with length L>90 m = 175 for internal structural members, except tank boundaries, in vessels with more than three continuous 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. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 11

12 3 Stiffeners 3.1 Proportions of stiffeners Net thickness of all stiffener types The net thickness of stiffeners shall satisfy the following criteria: a) Stiffener web plate: b) Flange: Part 3 Chapter 8 Section 2 C w, C f = slenderness coefficients given in Table 1. If requirement b) is not fulfilled the effective free flange out stand, in mm, used in strength assessment shall not be taken greater than: Figure 1 Stiffener scantling parameters Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 12

13 Table 1 Slenderness coefficients Type of profile C w C f Angle bars ) T-bars ) Bulb bars 45 - Flat bars 22-1) C f = 22, non-continuous straight flanges with end bracket Net dimensions of angle and T-bars The total flange breadth, in mm, for angle and T-bars shall satisfy the following criterion: Part 3 Chapter 8 Section 2 4 Primary supporting members 4.1 Proportions and stiffness Proportions of web plate and flange The net thicknesses of the web plates and flanges of primary supporting members shall satisfy the following criteria: a) Web plate: b) Flange: s w C w = plate breadth, in mm, taken as the spacing of the web stiffeners, see also the Society's document DNVGL-CG-0128[ ] = slenderness coefficient for the web plate taken as: C w = 100 C f = 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 shall not be taken greater than: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 13

14 4.1.2 Deck transverse primary supporting members The net moment of inertia for deck transverse primary supporting members, in cm 4, supporting deck longitudinals subject to axial compressive hull girder stress, shall comply, within its central half of the bending span, with the following criterion: I psm-n50 l bdg S I st = net moment of inertia, in cm 4, of deck transverse primary supporting member, with effective width of attached plate equal to 0.8 S = unsupported bending span of deck transverse primary supporting member in m, as defined in Ch.3 Sec.7 or in case of a grillage structure the distance between connections to other primary support members = spacing of deck transverse primary supporting members, in m, as defined in Ch.3 Sec.7 = moment of inertia in cm 4 of longitudinal or stiffener necessary to satisfy the lateral buckling mode: Part 3 Chapter 8 Section 2 for for I = moment of inertia in cm 4 about the axis perpendicular to the expected direction of buckling A = cross sectional area in cm 2 Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 14

15 σ hg-cp = maximum compressive stress in deck in question based on Ch.5 Sec.3 [2] for ships without large deck 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], analysis as an equivalent where transverse primary supporting members are directly modelled. In such a case the allowable buckling utilisation factor shall be based on Sec.1 Table Web stiffeners of primary supporting members Proportions of web stiffeners The net thickness of web and flange of web stiffeners fitted on primary supporting members shall satisfy the requirements specified in [3.1.1] and [3.1.2] Bending stiffness of web stiffeners The net moment of inertia, in cm 4, of web stiffener, I st, fitted on primary supporting members, with effective attached plate, s eff, 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 cm 4 Part 3 Chapter 8 Section 2 Web stiffeners fitted along the PSM span A Web stiffeners fitted normal to the PSM span B 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. A eff = Net section area of web stiffener including effective attached plate, s eff, in cm 2. t w = Net web thickness of the primary supporting member, in mm. R eh = Specified minimum yield stress of the material of the web plate of the primary supporting member, in N/mm 2. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 15

16 5 Brackets 5.1 Tripping brackets Unsupported flange length Dimensions of tripping brackets shall be in accordance with Ch.3 Sec.6 [3.3]. The unsupported length of the flange of the primary supporting member, in m, i.e. the distance between tripping brackets, shall not be greater than every fourth spacing of stiffeners in general, not exceeding 4m Edge stiffening Tripping brackets on primary supporting members shall be stiffened by a flange or edge stiffener if the effective length of the edge, l b as defined in Table 3, in mm, is greater than: Part 3 Chapter 8 Section 2 t b = bracket net web thickness, in mm. 5.2 End brackets Proportions The net web thickness of end brackets, in mm, subject to compressive stresses shall not be less than: d b = depth of brackets, in mm, as defined in Table 3 C = slenderness coefficient as defined in Table 3 R eh = specified minimum yield stress of the end bracket material, in N/mm 2. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 16

17 Table 3 coefficient, C, for proportions of brackets Mode Brackets without edge stiffener C Part 3 Chapter 8 Section 2 Brackets with edge stiffener C = 70 Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 17

18 5.3 Edge reinforcement Edge reinforcements of bracket edges The depth of stiffener web, in mm, of edge stiffeners in way of bracket edges shall not be less than: C = slenderness coefficient taken as: C or 50 mm, whichever is greater. = 75 for end brackets = 50 for tripping brackets R eh = specified minimum yield stress of the stiffener material, in N/mm Proportions of edge stiffeners The 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]. Part 3 Chapter 8 Section 2 6 Pillars 6.1 Proportions of I-section pillars For I-sections, the thickness of the web plate and the flange thickness shall comply with requirements specified in [3.1.1] and [3.1.2]. 6.2 Proportions of box section pillars The 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 pillars The net thickness, t, of circular section pillars, in mm, shall comply with the following criterion: r = mid thickness radius of the circular section, in mm. 7 Edge reinforcement in way of openings 7.1 Depth of edge stiffener When fitted as shown in Figure 2, the depth of web, in mm, of edge stiffeners in way of openings shall not be less than: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 18

19 C = slenderness coefficient taken as: or 50 mm, whichever is greater. C = 50 R eh = specified minimum yield stress of the edge stiffener material, in N/mm Proportions of edge stiffeners The 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]. Part 3 Chapter 8 Section 2 Figure 2 Typical edge reinforcements Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 19

20 SECTION 3 HULL GIRDER BUCKLING Symbols For symbols not defined in this section, refer to Ch.1 Sec.4. η all = 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 This section applies to plate panels and stiffeners subject to hull girder compression and shear stresses. 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. Part 3 Chapter 8 Section The hull girder buckling strength requirements apply along the full length of the ship Design load sets The 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 to Ch.4 at the load calculation point (LCP) defined in Ch.3 Sec.7, and shall be applied together with the hull girder stress combinations given in [2.2]. 1.2 Equivalent plate panel When the plate thickness varies over the width b, of a plate panel, the buckling check shall be performed for an equivalent plate panel width, combined with the smaller plate thickness, t 1. The width of this equivalent plate panel, b eq, in mm, is defined by the following formula: l 1 = width of the part of the plate panel with the smaller plate thickness, t 1, in mm, as defined in [1.2.2] l 2 = width of the part of the plate panel with the greater plate thickness, t 2, in mm, as defined in [1.2.2]. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 20

21 Figure 1 Plate thickness change over the width In case of transverse butt weld, when a EPP is made with different thicknesses, the buckling check of the plate and stiffeners shall be made for each thickness considered constant on the EPP, the stresses and pressures being estimated for the EPP at the LCP. Part 3 Chapter 8 Section Materials When the plate panel is made of different materials, the minimum yield strength shall be used for the buckling assessment. 2 Hull girder stress 2.1 General Hull girder stress applicable for load components S The hull girder bending stresses, σ hg, in N/mm 2, for load component S shall be taken as: σ hg-sw = hull girder bending stress, in N/mm², due to vertical still water bending moment as defined in Ch.5 Sec.3 [2] for ships without large deck openings and in Ch.5 Sec.3 [3] for ships with large deck openings Hull girder stress applicable for load components S+D The hull girder bending stresses, σ hg, in N/mm 2, for load component S+D shall be taken as defined in Ch.5 Sec.3 [2] for ships without large deck openings and in Ch.5 Sec.3 [3] for ships with large deck openings The hull girder shear stresses, τ hg, in N/mm 2, are determined according to Ch.5 Sec.3[3]. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 21

22 2.2 Stress combinations Each elementary plate panel, and stiffeners, shall satisfy the criteria defined in [3] with the following stress combinations: a) Longitudinal stiffening arrangement: Stress combination 1 with: Stress combination 2 with: Part 3 Chapter 8 Section 3 b) Transverse stiffening arrangement: Stress combination 1 with: Stress combination 2 with: 3 criteria 3.1 Overall stiffened panel The buckling strength of overall stiffened panels shall satisfy the following criterion: η Overall η all η Overall = maximum utilisation factor as defined Sec.1 [3.3]. 3.2 Plates The buckling strength of elementary plate panels shall satisfy the following criterion: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 22

23 η Plate η all η Plate = maximum plate utilisation factor calculated according to SP-A, see Sec.1 [3.3]. For the determination of η Plate for vertically stiffened plating, the cases 12 and 16 in the Society's documentdnvgl-cg-0128sec.3 Table 3-3 corresponding to the shorter edge of the plate panel clamped, may be considered together with a mean σ y stress and ψ y =1, provided that the shorter edges are supported by longitudinal plating/decks and are located within 0.7z 1 from horizontal neutral axis. z 1 is the distance from the horizontal neutral axis to equivalent deck line or baseline respectively as defined in Ch.5 Sec.2 [1.6] 3.3 Stiffeners The buckling strength of stiffeners shall satisfy the following criterion: η Stiffener η all Part 3 Chapter 8 Section 3 η Stiffener = maximum stiffener utilisation factor, see Sec.1 [3.3]. 3.4 Vertically corrugated longitudinal bulkheads The shear buckling strength of vertically corrugated longitudinal bulkheads shall satisfy the following criterion: η Shear η all η Shear = maximum shear corrugated bulkhead utilisation factor as defined in Sec.1 [3.3]. 3.5 Horizontally corrugated longitudinal bulkhead Each corrugation, within the extension of half flange, web and half flange, shall satisfy the following criterion: η η all 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 used in way of stool with width exceeding 2 times the depth of the corrugation. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 23

24 SECTION 4 BUCKLING REQUIREMENTS FOR DIRECT STRENGTH ANALYSIS Symbols η all = allowable buckling utilisation factor, as defined in Sec.1 [3.4]. 1 General 1.1 Scope The requirements given in this section apply for the buckling assessment in direct strength analysis for structural elements subjected to compressive stress, shear stress and lateral pressure Elements in the FE analysis carried out according to Ch.7shall be assessed individually. The buckling checks 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 to compressive stresses shall be checked: corrugation of vertically and horizontally corrugated bulkheads struts pillars cross-ties. Part 3 Chapter 8 Section Verification of buckling strength in accordance with the requirements in this section is also applicable for the structure analysed by beam elements when structural elements are subject to compressive and shear stresses Procedure for overall buckling of pillar and cross-tie and the procedure for buckling of plane and curved plate as well as for stiffened plate panels are given in the Society's documentdnvgl-cg-0128, analysis 2 Stiffened and unstiffened panels 2.1 General Boundary condition A and Boundary condition B as defined in Sec.1 [3.1]shall be used according to Table 1. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 24

25 Table 1 Boundary conditions for structural members Shell envelope Deck Inner hull Hopper tank side Longitudinal bulkheads Structural elements Assessment method Normal panel definition Double bottom longitudinal girders in line with longitudinal bulkhead or connected to hopper tank side Web of double bottom longitudinal girders not in line with longitudinal bulkhead or not connected to hopper tank side Web of horizontal girders in double side space connected to hopper tank side Longitudinal structures, see example Figure 1 SP-A SP-A SP-B 5) SP-A Length: between web frames Width: between primary supporting members Length: between web frames Width: full web depth Length: between web frames Width: full web depth Length: between web frames Width: full web depth Part 3 Chapter 8 Section 4 Web of horizontal girders in double side space not connected to hopper tank side Web of single skin longitudinal girders or stringers with regular mesh Web of single skin longitudinal girders or stringers with irregular mesh SP-B 5) SP-B 5) UP-B 5) Length: between web frames Width: full web depth Plate between local stiffeners/face plate/primary support member (PSM) Transverse structures, see example Figure 2 Web of transverse deck frames including brackets with regular mesh Web of transverse deck frames including brackets with irregular mesh SP-B 5) UP-B 5) Plate between local stiffeners/face plate/psm Vertical web in double side space SP-B 5) Length: full web depth Width: between primary supporting members Irregularly stiffened panels, e.g. web panels in way of hopper tank and bilge UP-B 5) Plate between local stiffeners/face plate/psm Double bottom floors SP-A 6) Length: full web depth Width: between primary supporting members Vertical web frame including brackets with regular mesh Vertical web frame including brackets with irregular mesh SP-B 5) UP-B 5) Cross tie web plate with regular mesh SP-B 5) Plate between vertical web stiffeners/face plate/ PSM Cross tie web plate with irregular mesh UP-B 5) PSM Plate between vertical web stiffeners/face plate/ Transverse bulkheads, see example Figure 3 Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 25

26 Structural elements Assessment method Normal panel definition Regularly stiffened bulkhead panels inclusive the secondary buckling stiffeners perpendicular to the regular stiffener (such as carlings) Irregularly stiffened bulkhead panels, e.g. web panels in way of hopper tank and bilge Web plate of bulkhead stringers including brackets with regular mesh Web plate of bulkhead stringers including brackets with irregular mesh Upper/lower stool including stiffeners SP-A UP-A SP-B 5) UP-B 5) Length: between primary supporting members Width: between primary supporting members Plate between local stiffeners/face plate Plate between web stiffeners /face plate Transverse corrugated bulkheads and cross deck, see example Figure 3 and Figure 4 Stool internal web diaphragm with regular mesh SP-A SP-B 5) Length: between internal web diaphragms Width: length of stool side Plate between local stiffeners /face plate / PSM Part 3 Chapter 8 Section 4 Stool internal web diaphragm with irregular mesh UP-B 5) 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 "inline support", i.e. the edge is free to pull in, boundary condition B (SP-B or UP-B) shall be applied. In other cases boundary 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 Average thickness of plate panel Where the plate thickness along a plate panel is not constant, the panel used for the buckling assessment shall be taken as the average thickness, in mm: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 26

27 A i t i n = area of the i-th plate element = net thickness of the i-th plate element = number of finite elements defining the buckling plate panel Yield stress of the plate panel The panel yield stress R eh_p is taken as the minimum value of the specified yield stresses of the elements within the plate panel. Part 3 Chapter 8 Section 4 Figure 1 Longitudinal plates, ore carrier Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 27

28 SP-A SP-A SP-A SP-A Part 3 Chapter 8 Section 4 SP-A SP-A SP-A Figure 2 Transverse web frames, ore carrier Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 28

29 Part 3 Chapter 8 Section 4 Figure 3 Transverse bulkhead, ore carrier Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 29

30 Part 3 Chapter 8 Section 4 Figure 4 Upper deck, ore carrier 2.2 Stiffened panels To represent the overall buckling behaviour, each stiffener with attached plate shall be modelled as a stiffened panel of the extent defined in Table If the stiffener properties or stiffener spacing varies within the stiffened panel, the calculations shall be performed separately for all configurations of the panels, i.e. for each stiffener and plate between the stiffeners. Plate thickness, stiffener properties and stiffener spacing at the considered location shall be assumed for the whole panel. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 30

31 2.3 Unstiffened panels Irregular plate panel 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 shall be defined according to [2.3.2] for irregular geometry and [2.3.3] for triangular geometry and to be used for the buckling assessment Modelling of an unstiffened panel with irregular geometry Unstiffened panels with irregular geometry shall be idealised to equivalent panels for plate buckling assessment 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. Part 3 Chapter 8 Section 4 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 d 1 + d 3 and d 2 + d 4 d) 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 length of 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: A a = area of the plate, in mm² = length defined in (d), in mm Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 31

32 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 Modelling of an unstiffened plate panel with triangular geometry Unstiffened panels with triangular geometry shall be idealised to equivalent panels for plate buckling assessment according to the following procedure: a) Medians are constructed as shown below. Part 3 Chapter 8 Section 4 b) The longest median is identified. This median the length of which is l 1 in mm, defines the longitudinal direction for the capacity model. c) The width of the model, l 2, in mm, shall be taken as: 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 panel shall be taken as: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 32

33 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 equivalent rectangular panel. 2.4 Reference stress Part 3 Chapter 8 Section The stress distribution shall be taken from the direct strength analysis and applied to the buckling model. Method for calculation of stress based reference stresses is defined in Ch.7 Sec Lateral pressure The lateral pressure applied to the direct strength analysis shall also be applied for the buckling assessment Where the lateral pressure is not constant over a buckling panel defined by a number of finite plate elements, an average lateral pressure, N/mm 2, is calculated using the following formula: A i = area of the i-th plate element, in mm 2 P i = lateral pressure of the i-th plate element, in N/mm 2 n = number of finite elements in the buckling panel. 2.6 criteria The compressive buckling strength shall satisfy the following criterion: η η all Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 33

34 where η is the maximum of the relevant utilization factors: η UP-A = maximum plate utilisation factor for Boundary condition A, [2.1], see Sec.1 [3.3] η UP-B = maximum plate utilisation factor for Boundary condition B, [2.1], see Sec.1 [3.3] η SP-A = maximum stiffened panel utilisation factor taken as the maximum of: η SP-B 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 stiffener = 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 stiffener η opening = maximum web plate utilisation factor in way of openings, see Sec.1 [3.3]. 3 Corrugated bulkhead Part 3 Chapter 8 Section General 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 Each corrugation flange and web panel shall be assessed The membrane stresses at element centroid shall be used The maximum normal stress parallel to the corrugation and the maximum shear stress are defined according 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 on elements extending to a distance equal to 3b from the end of the corrugation. The normal stress parallel to the corrugation is interpolated at b/2 in accordance with the Society's document DNVGL-CG-0128, analysis, i.e. using the 2 nd order polynomial curve. The shear stress at b/2 is obtained by linear interpolation between the elements most close to b/2 b = width of the considered member of the corrugation, i.e. flange or web Where more than one plate thickness is used for a flange panel, the maximum stress shall be obtained for each thickness range and to be checked with the buckling criteria for each thickness. criteria is given in [3.4.1]. Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 34

35 3.3 Overall column buckling The overall buckling failure mode of corrugated bulkheads subjected to axial compression shall be checked for column buckling, e.g. horizontally corrugated bulkheads and vertically corrugated bulkheads subjected to local vertical forces. Table 2 Application of overall column buckling for corrugated bulkhead Longitudinal bulkhead Transverse bulkhead Horizontal Required Required Corrugation Orientation Vertical Required, when subjected to local vertical forces, e.g. crane loads Each corrugation unit within the extension of half flange, web and half flange, i.e. single corrugation as shown in grey in Figure 5, shall satisfy the following criterion: η Overall η all Part 3 Chapter 8 Section 4 η Overall = maximum overall column utilisation factor, see Sec.1 [3.3], considered as a pillar with an unsupported length taken as the length of the corrugation except for vertically corrugated bulkheads where the length, l bdg, shall be applied as defined in Ch.3 Sec.6 [5.1.4]. Figure 5 Single corrugation End constraint factor, f end corresponding to pinned ends shall be applied except for fixed end support to be used in way of stool with width exceeding 2 times the depth of the corrugation. 3.4 Local buckling The compressive buckling strength of a unit flange and a unit web of corrugation bulkheads shall satisfy the following criterion: η Corr η all η Corr = maximum unit flange or unit web utilisation factor, see Sec.1 [3.3]. Two stress combinations shall be considered: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 35

36 the maximum normal stress parallel to the corrugation plus the shear stress 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 at the location where the maximum shear stress occurs. The buckling assessment shall be performed for an aspect ratio α equal to 2, and for the thickness of the member where the maximum compressive/shear stress occurs (see [3.2.4]). 4 Vertically stiffened longitudinal plating in way of horizontal neutral axis 4.1 criteria Plating The compressive buckling strength for vertically stiffened longitudinal plating with the shorter edges supported by longitudinal plating/decks and located within 0.7z 1 from horizontal neutral axis, where z 1 is the distance 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: Part 3 Chapter 8 Section 4 η vsp η all η vsp = maximum utilization factor calculated according to Method A as defined in the Society's document DNVGL-CG-0128,Sec.3 [ ] and considering the following boundary conditions and stress combinations: 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 ψ x =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 α=2 and ψ x =ψ y =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 α=2 and ψ x =ψ y =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's document DNVGL-CG-0128, Table 3-3: a) Distributed longitudinal stress associated with vertical and shear stress: Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 36

37 The actual size of the buckling panel is used to define α. The average values for longitudinal, vertical and shear stresses shall be used. ψ x =ψ y 1. The plate thickness to be considered in the buckling strength check is based on Sec.3 [1.2.2]. Part 3 Chapter 8 Section 4 Figure 6 Boundary condition/load combination (a), (b), (c) and (d) for vertically stiffened longitudinal plating in way of horizontal neutral axis Vertical stiffeners The buckling strength for vertical stiffeners attached to longitudinal plating within 0.7z 1 from horizontal neutral axis, where z 1 is the distance from horizontal neutral axis to equivalent deck line or baseline respectively as defined in Ch.5 Sec.2 [1.6], shall satisfy the following criterion: η stiffener η all η stiffener = 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 criteria The compressive buckling strength of struts, pillars and cross ties shall satisfy the following criterion: η Pillar η all Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 37

38 η Pillar = maximum utilisation factor of struts, pillars or cross ties, see Sec.1 [3.3]. Part 3 Chapter 8 Section 4 Rules for classification: Ships DNVGL-RU-SHIP-Pt3Ch8. Edition October 2015 Page 38

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