S35

Buckling Strength Assessment of Ship
(Feb
2023)
(cont)
Structural Elements
S35
S35

TABLE OF CONTENTSSECTION 1

APPLICATION AND DEFINITIONS

1.
1.1
1.2

Application
GeneralApplication of this UR

2.
2.1
2.2
2.3
2.4

Terminology and Assumptions
Buckling
Net Scantling Approach
Structural Idealisation
Sign Convention

3.
3.1
3.2
3.3
3.4

Assessment Methods and Acceptance Criteria
Assessment Methods
Buckling Utilisation Factor
Allowable Buckling Utilisation Factor
Buckling Acceptance Criteria

SECTION 2

SLENDERNESS REQUIREMENTS

1.
1.1

GeneralIntroduction

2.
2.1

Stiffeners
Proportions of Stiffeners3.
3.1

Primary Supporting Members
Proportions and Stiffness

SECTION 3

BUCKLING REQUIREMENTS FOR HULL GIRDER PRESCRIPTIVEANALYSIS

1.
1.1
1.2
1.3

GeneralIntroduction
Definitions
Assumptions for Equivalent Plate Panels

2.
2.1
2.2
2.3
2.4
2.5

Buckling Criteria
Overall Stiffened Panel
PlatesStiffeners
Vertically Corrugated Longitudinal Bulkheads
Horizontally Corrugated Longitudinal Bulkheads

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S35
(cont)SECTION 4

BUCKLING REQUIREMENTS FOR DIRECT STRENGTH ANALYSIS OF
HATCH COVERS1.
1.1

GeneralIntroduction

2.
2.1
2.2
2.3
2.4
2.5
2.6

Stiffened and Unstiffened Panels
GeneralStiffened Panels
Unstiffened Panels
Reference Stress
Lateral Pressure
Buckling Criteria

SECTION 5

BUCKLING CAPACITY

1.
1.1

GeneralIntroduction

2.
2.1
2.2
2.3
2.4
2.5

Buckling Capacity of Plate Panels
Overall Stiffened Panels
PlatesStiffeners
Primary Supporting Members
Stiffened Panels with U-type Stiffeners3.
3.1

Buckling Capacity of Column Structures
Column Buckling of Corrugations

APPENDIX 1 STRESS BASED REFERENCE STRESSES
1.
1.1
1.2

Stress Based Method
Introduction
Stress Application

2.
2.1
2.2

Reference Stresses
Regular Panel
Irregular Panel and Curved Panel

Note:
1.

This UR is to be applied by IACS Societies to ships contracted for construction on orafter 1 July 2024.

2.

The “contracted for construction” date means the date on which the contract to build
the vessel is signed between the prospective owner and the shipbuilder. For further
details regarding the date of “contract for construction”, refer to IACS Procedural
Requirement (PR) No. 29.
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S35
(cont)SECTION 1

APPLICATION AND DEFINITIONS

Abbreviations
EPP
PSM
SP
UP
UR-S

Elementary Plate Panel, as defined in [2.3.1].
Primary Supporting Member.
Stiffened Panel, as defined in [2.3.3].
Unstiffened Panel, as defined in [2.3.3].
IACS Unified Requirements concerning Strength of Ships.

1.

Application

1.1

General1.1.1 Relevant Unified Requirements concerning Strength of Ships
This Unified Requirement (UR) establishes a general buckling assessment procedure as
illustrated in Figure 1 and is to be applied in conjunction with UR S21 for hatch cover
structures. UR S21 is referred to as Relevant UR-S hereafter in this UR.
Figure 1: Overview of applying this UR in conjunction with Relevant UR-S
Relevant
UR-S

Buckling checkrequirements

Working stresses& pressures
Safetyfactors

Slenderness& BUFs

HG prescriptive
analysis

HG cross-section,
plating , stiffener

Direct strength
analysis

SP, UP, PSM, etc.

--

StiffenerNet
scantlings

HG
Stress-based
requirements
UR S35
Buckling

HC

Buckling check
criteria

Slenderness
requirements

Note: BUF stands for Buckling Utilisation Factor, HC stands for Hatch Cover, and HG standsfor Hull Girder.
1.2

Application of this UR

1.2.1 Sections of this UR
The buckling checks are to be performed according to:- Sec 1 for general definitions regarding buckling capacity, allowable buckling utilisation
factors and buckling check criteria.
- Sec 2 for the slenderness requirements of longitudinal and transverse stiffeners.

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- Sec 3 for the prescriptive buckling requirements of plates, longitudinal and transverse
stiffeners, primary supporting members and other structures subject to hull girderstresses.

S35(cont)- Sec 4 for direct strength analysis (usually by finite element method) buckling
requirements of hatch cover structural members including plates, stiffeners and primary
supporting members.
- Sec 5 for the determination of buckling capacities of plate panels, stiffeners, primary
supporting members and column structures.
1.2.2 Buckling assessment with this UR
For the buckling assessment of a ship hull girder, a hatch cover or some structuralcomponent, the slenderness requirements as defined in Sec 2 and the buckling requirements
as defined in Sec 3 or Sec 4 are to be checked as per the requirements of the applicable
Relevant UR-S.
1.2.3 Alternative methods
This UR contains the general methods for the determination of buckling capacities of plate
panels, stiffeners, primary supporting members, and columns. For special cases not coveredin this UR, such as a whole plate structure with stiffeners in two directions (i.e., a stiffened
panel with both primary and secondary stiffeners), other more advanced methods, such as
finite element analysis methods, can be used as deemed appropriate by the Society.
2

Terminology and Assumptions

2.1

Buckling

2.1.1 Buckling strength
Buckling strength or capacity refers to the strength of a structure under in-plane
compressions and/or shear and lateral load. Buckling strength with consideration of thebuckling behaviour in [2.1.2] gives a lower bound estimate of ultimate capacity, or the
maximum load a structural member can carry without suffering major permanent set.
For each structural member, its buckling strength is to be taken as corresponding to the mostunfavourable or critical buckling mode.
2.1.2 Buckling behaviour
Buckling strength assessment takes into account both elastic buckling and post-buckling
behaviours. Post-buckling can consider the internal redistribution of loads depending on theload situation, slenderness and type of structure. Such as for the buckling assessment ofplates, generally its positive elastic post-buckling effect can be utilized.
As such, for slender structures, the calculated buckling strength is typically higher than theideal elastic buckling stress (minimum eigenvalue). Accepting elastic buckling of slender plate
panels implies that large elastic deflections and reduced in-plane stiffness may occur at
higher buckling utilisation levels.

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(cont)

2.2

Net Scantling Approach

2.2.1 General
Unless otherwise specified, all the scantling requirements, including slenderness
requirements, in this UR are based on net scantlings obtained by removing full corrosion
addition tc from the gross offered thicknesses.
2.2.2 Corrosion addition
Corrosion addition tc referred to in this UR is defined in the Relevant UR-S.
2.2.3 Stress calculation models
The structural models used for the calculation of stresses to be applied for bucklingassessment, which are usually based on net scantlings, are defined in the Relevant UR-S.
2.3

Structural Idealisation

2.3.1 Elementary plate panel
An elementary plate panel (EPP) is the unstiffened part of the plating between stiffeners
and/or primary supporting members. The plate panel length, a, and breadth, b, of the EPP
are defined respectively as the longest and shortest plate edges, as shown in Figure 2.
Figure 2: Elementary plate panel (EPP) definition

2.3.2 Standard types of stiffeners
Definitions of the cross-sectional dimensions of typical stiffener types are shown in Figure 3,
which are flat bars, bulb flats, angles, L2 and T bars. If applicable, other types of stiffeners
can be idealized to one of the typical types in Figure 3 for buckling check. For the U-type
stiffener which is usually fitted in some hatch covers, the definition of its cross-sectional
dimensions is shown in Figure 4.
Unless otherwise specified, the full span or full length 𝑙𝑙, in mm, of a stiffener is to be used forbuckling check, which equals to the spacing between primary supporting members.

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(cont)

Symbolic dimensions of the cross-sections are as below:
𝑏𝑏1
𝑏𝑏2
𝑏𝑏𝑓𝑓

Width of the attached plate enclosed by the U-type stiffener, in mm,
as shown in Figure 4.
Width of the attached plate between adjacent U-type stiffeners, in mm
as shown in Figure 4.
Width of the flange or face plate of the stiffener, in mm
as shown in Figure 3 and Figure 4.

𝑏𝑏𝑓𝑓−𝑜𝑜𝑜𝑜𝑜𝑜 Maximum distance, in mm, from mid thickness of the web to the flange edge, in mm, as
shown in Figure 3.
𝑑𝑑𝑓𝑓

Breadth of the extended part of the flange for L2 profiles, in mm, as shown in Figure 3.

𝑒𝑒𝑓𝑓Distance from attached plating to centre of flange, in mm, as shown in Figure 3. For its
detailed definition, refer to Sec 5, Symbols.

ℎ𝑤𝑤

Depth of stiffener web, in mm, as shown in Figure 3 and Figure 4.

𝑡𝑡𝑓𝑓

Net flange thickness, in mm.

𝑡𝑡𝑤𝑤

Net web thickness, in mm.

𝑡𝑡𝑝𝑝

Net thickness of plate, in mm.

Figure 3: Dimensions of typical stiffener cross sections

Flat

Bulb

Angle

T

L2

Figure 4: Dimensions of a U-type stiffener cross section

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(cont)

2.3.3 Stiffened panel (SP) and Unstiffened panel (UP)For a panel with relatively strong interactive effect between the stiffener and its attached plate,each stiffener with its attached plate as a whole is to be modelled as a stiffened panel (SP),so as to be able to consider both of its local and global buckling modes.
However, for an EPP, if its buckling strength can be checked without considering its
interactive effect with stiffeners fitted along its edges, it’s to be modelled as an unstiffened
panel (UP).
2.4

Sign Convention

2.4.1 Stresses
In this UR, compressive and shear stresses are to be taken as positive, tension stresses areto be taken as negative.
3.

Assessment Methods and Acceptance Criteria

3.1

Assessment Methods

3.1.1 Method A and Method B
The buckling assessment is to be carried out according to one of the following two methods
taking into account different boundary condition types:- Method A: All the edges of the EPP are forced to remain straight (but free to move in
the in-plane directions) due to the surrounding structure/neighbouring plates.
- Method B: The edges of the EPP are not forced to remain straight due to low in-plane
stiffness at the edges and/or no surrounding structure/neighbouring plates.
3.1.2 SP-A, SP-B, UP-A and UP-B models
For the buckling assessment of the stiffened panel (SP) and unstiffened panel (UP) structuralmodels defined in [2.3.3], with application of either Method A or Method B for the plate
buckling assessment, the following four buckling assessment models are established:- SP-A: a stiffened panel with application of Method A.
- SP-B: a stiffened panel with application of Method B.
- UP-A: an unstiffened panel with application of Method A.
- UP-B: an unstiffened panel with application of Method B.
3.2

Buckling Utilisation Factor

3.2.1 The utilisation factor, 𝜂𝜂 , is defined as the ratio between the applied loads and thecorresponding buckling capacity.

3.2.2 For combined loads, the utilisation factor, 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎 , is to be defined as the ratio of theapplied equivalent stress and the corresponding buckling capacity, as shown in Figure 5, andis to be taken as:
𝑊𝑊𝑎𝑎𝑎𝑎𝑎𝑎
1𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎 =
=
𝑊𝑊𝑈𝑈
𝛾𝛾𝑐𝑐
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(cont)

where:
𝑊𝑊𝑎𝑎𝑎𝑎𝑎𝑎 Equivalent applied stress. The actual applied stresses are given in Sec 3 and Sec 4
respectively for buckling assessment by prescriptive and direct strength analysis.
𝑊𝑊𝑈𝑈
𝛾𝛾𝑐𝑐

Equivalent buckling capacity. For plates and stiffeners, their respective buckling or
ultimate capacities are given in Sec 5.
Stress multiplier factor at failure.

For each typical failure mode, the corresponding buckling capacity of the panel is calculated
by applying the actual stress combination and then increasing or decreasing the stresses
proportionally until collapse occurs, i.e., when the increased or decreased stresses are on abuckling strength interaction curve or surface.

Figure 5 illustrates the buckling capacity and the buckling utilisation factor of a structuralmember subject to 𝜎𝜎𝑥𝑥 and 𝜎𝜎𝑦𝑦 stresses.
Figure 5: Illustration of buckling capacity and buckling utilisation factor

3.3

Allowable Buckling Utilisation Factor

3.3.1 The allowable buckling utilisation factor 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎 is to be taken according to the Relevant
UR-S.
3.4

Buckling Acceptance Criteria

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

where:
𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎
𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎
Buckling utilisation factor based on the applied stress, defined in [3.2.2].
Allowable buckling utilisation factor as defined in [3.3.1].
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S35
(cont)SECTION 2

SLENDERNESS REQUIREMENTS

Symbols
For symbols not defined in this section, refer to Sec 1, [2.3.2].
Specified minimum yield stress of the structural member being considered, in N/mm2.

𝑅𝑅𝑒𝑒𝑒𝑒1.

General1.1

Introduction

1.1.1 The stiffener elements except for U-type stiffeners are to comply with the applicable
slenderness and proportion requirements given in [2].
2.

Stiffeners

2.1

Proportions of Stiffeners

2.1.1 Net thickness of all stiffener types
The net thickness of stiffeners is to satisfy the following criteria:a)b)Stiffener web plate:𝑡𝑡𝑤𝑤 ≥ℎ𝑤𝑤 𝑅𝑅𝑒𝑒𝑒𝑒�
𝐶𝐶𝑤𝑤 235

𝑡𝑡𝑓𝑓 ≥

𝑏𝑏𝑓𝑓−𝑜𝑜𝑜𝑜𝑜𝑜 𝑅𝑅𝑒𝑒𝑒𝑒
�
𝐶𝐶𝑓𝑓
235

Flange:where:

𝐶𝐶𝑤𝑤 , 𝐶𝐶𝑓𝑓 : Slenderness coefficients given in Table 1.

If requirement b) is not fulfilled, the effective free flange outstand, in mm, used in strength
assessment including the calculation of actual net section modulus, is to be taken as:

235
𝑏𝑏𝑓𝑓−𝑜𝑜𝑜𝑜𝑜𝑜−𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐶𝐶𝑓𝑓 𝑡𝑡𝑓𝑓 �
𝑅𝑅𝑒𝑒𝑒𝑒Table 1: Slenderness coefficients

Type of Stiffener
Angle and L2 bars
T-barsBulb flats
Flat bars

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𝑪𝑪𝒘𝒘

75
75
45
22

𝑪𝑪𝒇𝒇

12
12
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S35
(cont)For built-up profile where the relevant yielding strength for the web of built-up profile without
the edge stiffener is acceptable, as an alternative the web can be assessed according to the
web requirements of Angle and L2 bars in Table 1, and the edge stiffener can be assessed
as a flat bar stiffener according to [2.1.1]. The requirement to flange in [2.1.2] shall still apply.
2.1.2 Net dimensions of angle and T-bars
The total flange breadth 𝑏𝑏𝑓𝑓 , in mm, for angle and T-bars is to satisfy the following criterion:
3.

Primary Supporting Members

3.1

Proportions and Stiffness

𝑏𝑏𝑓𝑓 ≥ 0.2ℎ𝑤𝑤

3.1.1 Proportions of web plate and flange
The scantlings of webs and flanges of primary supporting members are to comply with theRules of the Classification Society.

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S35
(cont)SECTION 3

BUCKLING REQUIREMENTS FOR HULL GIRDER PRESCRIPTIVEANALYSIS

Symbols𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

Allowable buckling utilisation factor, as defined in Sec 1, [3.3.1].

1.

General1.1

Introduction

LCP Load Calculation Point, as defined in [1.2.1].

1.1.1 This section applies to plate panels including plane and curved plate panels, stiffeners
and corrugation of longitudinal corrugated bulkheads subject to hull girder compression andshear stresses.
1.1.2 The ship longitudinal extent where the buckling check is performed for structuralelements subject to hull girder stresses is to be in accordance with the Relevant UR-S.
1.1.3 Design load sets: The buckling check is to be performed for all design load setscorresponding to the design loading conditions defined in the Relevant UR-S with the mostunfavourable pressure combinations.
For each design load set, for all static and dynamic load cases, the lateral pressure is to be
determined at the load calculation point defined in [1.2.1], and is to be applied together withthe hull girder stress combinations defined in the Relevant UR-S.
1.2

Definitions

1.2.1 Load calculation point
The load calculation points (LCP) for both elementary plate panels (EPP) and stiffeners aredefined as follows:a) LCP for hull girder stresses of EPP
The hull girder stresses for EPP are to be calculated at the load calculation points defined inTable 1.
Table 1: Load calculation points (LCP) coordinates for plate buckling assessment
Hull girder bending stress

LCP
coordinates

Non horizontal platingx coordinate

Mid-length of the EPP

y coordinate

Both upper and lower
ends of the EPP (points
A1 and A2 in Figure 1)

z coordinate

Horizontal plating

Hull girder shear
stressOutboard and inboard
ends of the EPP (points
A1 and A2 in Figure 1)

Mid-point of EPP(point B in Figure 1)

Corresponding to x and y values

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Figure 1: LCP for plate buckling assessment

S35(cont)b) LCP for hull girder stresses of longitudinal stiffeners
The hull girder stresses for longitudinal stiffeners are to be calculated at the following load
calculation point:- at the mid length of the considered stiffener.
- at the intersection point between the stiffener and its attached plate.
c) LCP for pressure of horizontal stiffeners
The load calculation point for the pressure is located at:- Middle of the full length, 𝑙𝑙, of the considered stiffener.

- The intersection point between the stiffener and its attached plate.
d)

LCP for pressure of non-horizontal stiffeners

The lateral pressure, P is to be calculated as the maximum between the value obtained at
middle of the full length, 𝑙𝑙, and the value obtained from the following formulae:

𝑃𝑃 =𝑝𝑝𝑈𝑈 +𝑝𝑝𝐿𝐿2

when the upper end of the vertical stiffener is below the lowest zero pressurelevel.

𝑙𝑙 𝑝𝑝

when the upper end of the vertical stiffener is at or above the lowest zeropressure level, see Figure 2.

𝑃𝑃 = 𝑙𝑙1 2𝐿𝐿
where:
𝑙𝑙1
𝑝𝑝𝑈𝑈 , 𝑝𝑝𝐿𝐿

Distance, in m, between the lower end of vertical stiffener and the lowest zeropressure level.
Lateral pressures at the upper and lower end of the vertical stiffener span l,respectively.

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Figure 2: Definition of pressure for vertical stiffeners

S35(cont)

1.3

Assumptions for Equivalent Plate Panels

1.3.1 Longitudinal stiffening with varying plate thickness
In longitudinal stiffening arrangement, when the plate thickness varies over the width 𝑏𝑏, of aplate panel, the buckling check is to be performed for an equivalent plate panel width,
combined with the smaller plate thickness, 𝑡𝑡1 . The width of this equivalent plate panel, 𝑏𝑏𝑒𝑒𝑒𝑒 , inmm, is defined by the following formula:
𝑡𝑡1 1.5
𝑏𝑏𝑒𝑒𝑒𝑒 = 𝑙𝑙1 + 𝑙𝑙2 � �
𝑡𝑡2
where:
𝑙𝑙1
𝑙𝑙2

Width of the part of the plate panel with the smaller plate thickness, 𝑡𝑡1 , in mm, as
defined in Figure 3.

Width of the part of the plate panel with the greater plate thickness, 𝑡𝑡2 , in mm, as
defined in Figure 3.

1.3.2 Transverse stiffening with varying plate thickness

In transverse stiffening arrangement, when an EPP is made with different thicknesses, thebuckling check of the plate and stiffeners is to be made for each thickness considered
constant on the EPP, the stresses and pressures being estimated for the EPP at the LCP.
1.3.3 Plate panel with different materials
When the plate panel is made of different materials, the minimum yield strength is to be used
for the buckling assessment.
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2.

Buckling Criteria

2.1

Overall Stiffened Panel

2.1.1 The buckling strength of overall stiffened panels is to satisfy the following criterion:𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:

𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 Maximum overall buckling utilisation factor as defined in Sec 5, [2.1].
2.2

Plates

2.2.1 The buckling strength of elementary plate panels is to satisfy the following criterion:𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:

Maximum plate buckling utilisation factor as defined in Sec 5, [2.2] where SP-A
model is to be used.

𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

For the determination of 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 of the vertically stiffened side shell plating of single side skinbulk carrier between hopper and topside tanks, the cases 12 and 16 of Sec 5, Table 3
corresponding to the shorter edge of the plate panel clamped are to be considered together
with a mean 𝜎𝜎𝑦𝑦 stress and 𝜓𝜓𝑦𝑦 = 1.
2.3

Stiffeners

2.3.1 The buckling strength of stiffeners or of side frames of single side skin bulk carriers is tosatisfy the following criterion:𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:
𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

Maximum stiffener buckling utilisation factor as defined in Sec 5, [2.3].

Note 1: This buckling check can only be fulfilled when the overall stiffened panel bucklingcheck, as defined in [2.1], is satisfied.
Note 2: The buckling check of the stiffeners is only applicable to the stiffeners fitted along thelong edge of the buckling panel.
2.4

Vertically Corrugated Longitudinal Bulkheads

The shear buckling strength of vertically corrugated longitudinal bulkheads is to satisfy thefollowing criterion:𝜂𝜂𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:
𝜂𝜂𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒

Maximum shear buckling utilisation factor, defined as𝜏𝜏𝑏𝑏ℎ𝑑𝑑𝜂𝜂𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒 =𝜏𝜏𝑐𝑐Page 14 of 51

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Shear stress, in N/mm2, in the bulkhead taken as the hull girder shear stress definedin the Relevant UR-S

𝜏𝜏𝑏𝑏ℎ𝑑𝑑𝜏𝜏𝑐𝑐

2.5

Shear critical stress, in N/mm2, as defined in Sec 5, [2.2.3].
Horizontally Corrugated Longitudinal Bulkheads

2.5.1 Each corrugation unit within the extension of half flange, web and half flange (i.e. single
corrugation as shown in grey in Figure 4) is to satisfy the following criterion:

where:

𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Overall column buckling utilisation factor, as defined in Sec 5, [3.1].
Figure 4: Single corrugation

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(cont)SECTION 4

BUCKLING REQUIREMENTS FOR DIRECT STRENGTH ANALYSIS OF
HATCH COVERS

Symbols
Yield stress of the plate panel, as defined in [2.1.3].

𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆

Yield stress of the stiffener, as defined in [2.1.3].

𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

Allowable buckling utilisation factor, as defined in Sec 1, [3.3.1].

Aspect ratio of the plate panel, as defined in the Symbol list of Sec 5.

𝛼𝛼1.

General1.1

Introduction

1.1.1 The requirements of this Section apply to the buckling assessment of hatch cover
structural members based on direct strength analysis (usually by finite element method) andsubjected to normal stress, shear stress and lateral pressure.
1.1.2 All structural elements in the direct strength analysis carried out according to theRelevant UR-S are to be assessed individually. The buckling checks are to be performed forthe following structural elements:- Stiffened and unstiffened panels.
- Web plate in way of openings.
2.

Stiffened and Unstiffened Panels

2.1

General2.1.1 The plate panel of a hatch cover structure is to be modelled as stiffened panel (SP) or
unstiffened panel (UP), with either Method A or Method B as defined in Sec 1, [3.1.1] to be
used for the calculation of the plate buckling capacity, which in combination is also equivalent
to use the buckling assessment models defined in Sec 1, [3.1.2].
2.1.2 Average thickness of plate panel
For FE analysis, where the plate thickness along a plate panel is not constant, the panel used
for the buckling assessment is to be modelled with a weighted average thickness taken as:𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎 =where:∑𝑛𝑛1 𝐴𝐴𝑖𝑖 𝑡𝑡𝑖𝑖
∑𝑛𝑛1 𝐴𝐴𝑖𝑖

𝐴𝐴𝑖𝑖: Area of the i-th plate element.

𝑛𝑛: Number of finite elements defining the buckling plate panel.

𝑡𝑡𝑖𝑖: Net thickness of the i-th plate element.

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2.1.3 Yield stress of the plate panel and stiffener
The panel yield stress 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃 is taken as the minimum value of the specified yield stressesof the elements within the plate panel.
The stiffener yield stress 𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆 is taken as the minimum value of the specified yieldstresses of the elements within the stiffener.
2.2

Stiffened Panels

2.2.1 For a stiffened panel (SP), each stiffener with attached plate is to be idealized as a
stiffened panel model of the extent defined in the Relevant UR-S.
2.2.2 If the stiffener properties or stiffener spacing varies within the stiffened panel, thecalculations are to be performed separately for all configurations of the panels, i.e. for each
stiffener and plate between the stiffeners. Plate thickness, stiffener properties and stiffenerspacing at the considered location are to be assumed for the whole panel.
2.3.1 The buckling check of the stiffeners of stiffened panels is only applicable to thestiffeners fitted along the longer side edges of the buckling panel.
2.3

Unstiffened Panels

2.3.1 Irregular plate panel
In way of web frames 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, for FE analysis, anequivalent rectangular panel is to be defined according to [2.3.2] for irregular geometry and[2.3.3] for triangular geometry and to comply with buckling assessment.
2.3.2 Equivalent EPP of an unstiffened panel with irregular geometry
Unstiffened panels with irregular geometry are to 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.

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.

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c)

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

d)A line joins the middle points of the chosen opposite edges (i.e. a mid-point is definedas 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, 𝑎𝑎, measured from one end point.

(cont)e)

The length of shorter side, 𝑏𝑏, in mm, is to be taken as:𝑏𝑏 =where:𝐴𝐴𝑎𝑎: Area of the plate, in mm²

𝐴𝐴: Length defined in (d), in mm.

𝑎𝑎f)
The stresses from the direct strength analysis are to be transformed into the local
coordinate system of the equivalent rectangular panel. These stresses are to be used for the
buckling assessment.
2.3.3 Modelling of an unstiffened plate panel with triangular geometry
Unstiffened panels with triangular geometry are to be idealised to equivalent panels for plate
buckling assessment 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 𝑙𝑙1 , in mm, defines
the longitudinal direction for the capacity model.

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c)

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(cont)

The width of the model, 𝑙𝑙2 , in mm, is to be taken as:𝑙𝑙2 =where:

𝐴𝐴
𝑙𝑙1

Area of the plate, in mm²

𝐴𝐴d)

The lengths of shorter side, 𝑏𝑏, and of the longer side, 𝑎𝑎, in mm, of the equivalent
rectangular plate panel are to be taken as:
𝑏𝑏 =

𝑙𝑙2
𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡

𝑎𝑎 = 𝑙𝑙1 𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡

where:

𝑙𝑙2
+ 0.6
𝑙𝑙1

e)

𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡 = 0.4

2.4

Reference Stress

The stresses from the direct strength analysis are to be transformed into the local
coordinate system of the equivalent rectangular panel and are to be used for the
buckling assessment of the equivalent rectangular panel.

2.4.1 The stress distribution is to be taken from the direct strength analysis according to theRelevant UR-S and applied to the buckling model.
2.4.2 For FE analysis, the reference stresses are to be calculated using the stress-basedreference stresses as defined in Appendix 1.
2.5

Lateral Pressure

2.5.1 The lateral pressure applied to the direct strength analysis is also to be applied to thebuckling assessment.
For FE analysis, where the lateral pressure is not constant over a buckling panel defined by anumber of finite plate elements, an average lateral pressure, N/mm2, is calculated using thefollowing formula:∑𝑛𝑛1 𝐴𝐴𝑖𝑖 𝑃𝑃𝑖𝑖
𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑛𝑛
∑1 𝐴𝐴𝑖𝑖
where:
𝐴𝐴𝑖𝑖

𝑃𝑃𝑖𝑖
𝑛𝑛

: Area of the 𝑖𝑖-th plate element, in mm2.

: Lateral pressure of the 𝑖𝑖-th plate element, in N/mm2.
: Number of finite elements in the buckling panel.
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2.6

Buckling Criteria

2.6.1 UP-A
The compressive buckling strength of UP-A is to satisfy the following criterion:𝜂𝜂𝑈𝑈𝑈𝑈−𝐴𝐴 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎
where:𝜂𝜂𝑈𝑈𝑈𝑈−𝐴𝐴

Plate buckling utilisation factor, equal to 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 as defined in Sec 5, [2.2] where UP-A
model is to be used.

2.6.2 UP-B
The compressive buckling strength of UP-B is to satisfy the following criterion:𝜂𝜂𝑈𝑈𝑈𝑈−𝐵𝐵 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:𝜂𝜂𝑈𝑈𝑈𝑈−𝐵𝐵

Plate buckling utilisation factor, equal to 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 as defined in Sec 5, [2.2] where UP-B
model is to be used.

2.6.3 SP-A
The compressive buckling strength of SP-A is to satisfy the following criterion:
𝜂𝜂𝑆𝑆𝑆𝑆−𝐴𝐴 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:𝜂𝜂𝑆𝑆𝑆𝑆−𝐴𝐴

Buckling utilisation factor of the stiffened panel, taken as the maximum of thebuckling utilisation factors calculated as below:- The overall stiffened panel buckling utilisation factor 𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 as defined in Sec 5,[2.1].
- The plate buckling utilisation factor 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 as defined in Sec 5, [2.2] where SP-A
model is to be used.

- The stiffener buckling utilisation factor 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 as defined in Sec 5, [2.3]considering separately the properties (thickness, dimensions), the pressures
defined in [2.5.2] and the reference stresses of each EPP at both sides of thestiffener.
Note 1: The stiffener buckling strength check can only be fulfilled when the overall stiffened
panel capacity check, as defined in Sec 5, [2.1], is satisfied.

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2.6.4 SP-B
The compressive buckling strength of SP-B is to satisfy the following criterion:
𝜂𝜂𝑆𝑆𝑆𝑆−𝐵𝐵 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎

where:𝜂𝜂𝑆𝑆𝑆𝑆−𝐵𝐵 Buckling utilisation factor of the stiffened panel, taken as the maximum of thebuckling utilisation factors calculated as below:- The overall stiffened panel buckling utilisation factor 𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 as defined in Sec 5,[2.1].
- The plate buckling utilisation factor 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 as defined in Sec 5, [2.2] where SP-B
model is to be used.

- The stiffener buckling utilisation factor 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 as defined in Sec 5, [2.3]considering separately the properties (thickness, dimensions), the pressures
defined in [2.5.2] and the reference stresses of each EPP at both sides of thestiffener.
Note 1: The stiffener buckling strength check can only be fulfilled when the overall stiffened
panel capacity check, as defined in Sec 5, [2.1], is satisfied.
2.6.5 Web plate in way of openings
The web plate of primary supporting members with openings is to satisfy the following
criterion:𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝜂𝜂𝑎𝑎𝑎𝑎𝑎𝑎
where:

𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 Maximum web plate utilisation factor in way of openings, calculated with the definitionin Sec 1, [3.2.2] and the stress multiplier factor at failure 𝛾𝛾𝑐𝑐 which can be calculated
following the requirements in Sec 5, [2.4].

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(cont)SECTION 5

BUCKLING CAPACITY

Symbols
𝐴𝐴𝑝𝑝

Net sectional area of the stiffener attached plating, in mm2, taken as:
𝐴𝐴𝑝𝑝 = 𝑠𝑠𝑡𝑡𝑝𝑝

𝐴𝐴𝑠𝑠

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

𝑏𝑏

Length of the shorter side of the plate panel, in mm.

𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1

Effective width of the attached plating of a stiffener, in mm, without the shear lag
effect taken as:𝑎𝑎𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒

Length of the longer side of the plate panel, in mm.
Effective width of the attached plating of a stiffener, in mm, as defined in [2.3.5].

- For 𝜎𝜎𝑥𝑥 > 0- For prescriptive assessment:𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 =𝐶𝐶𝑥𝑥1 𝑏𝑏1 + 𝐶𝐶𝑥𝑥2 𝑏𝑏2
2- For FE analysis:
𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 = 𝐶𝐶𝑥𝑥 𝑏𝑏- For 𝜎𝜎𝑥𝑥 ≤ 0
𝑏𝑏𝑓𝑓

𝑏𝑏1 , 𝑏𝑏2

𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 = 𝑏𝑏

Breadth of the stiffener flange, in mm.
Width of plate panel on each side of the considered stiffener, in mm. For stiffened
panels fitted with U-type stiffeners, 𝑏𝑏1 and 𝑏𝑏2 are as defined in Sec 1, Figure 4.

𝐶𝐶𝑥𝑥1 , 𝐶𝐶𝑥𝑥2 Reduction factor defined in Table 3 calculated for the EPP1 and EPP2 on each sideof the considered stiffener according to case 1.
𝑑𝑑

Length of the side parallel to the cylindrical axis of the cylinder corresponding to thecurved plate panel as shown in Table 4, in mm.

𝑑𝑑𝑓𝑓

Breadth of the extended part of the flange for L2 profiles, in mm, as shown in Sec 1,
Figure 3.

𝑒𝑒𝑓𝑓

Distance from attached plating to centre of flange, in mm, as shown in Sec 1, Figure
3 to be taken as:𝑒𝑒𝑓𝑓 = ℎ𝑤𝑤

for flat bar profile.

𝑒𝑒𝑓𝑓 = ℎ𝑤𝑤 + 0.5𝑡𝑡𝑓𝑓

for angle, L2 and T profiles.

𝑒𝑒𝑓𝑓 = ℎ𝑤𝑤 − 0.5𝑡𝑡𝑓𝑓

for bulb profile.

𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 Coefficient defined in [2.2.4].

𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 Coefficient defined in [2.2.5].
ℎ𝑤𝑤

Depth of stiffener web, in mm, as shown in Sec 1, Figure 3.

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𝑙𝑙

Span, in mm, of stiffener equal to spacing between primary supporting members
or span of side frame equal to the distance between the hopper tank and top wingtank in way of the side shell.

𝑅𝑅

Radius of curved plate panel, in mm.

𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆

Specified minimum yield stress of the stiffener in N/mm2.

𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃
𝑆𝑆

Specified minimum yield stress of the plate in N/mm2.
Partial safety factor, unless otherwise specified in the Relevant UR-S, to be taken as
1.0.

𝑡𝑡𝑝𝑝

Net thickness of plate panel, in mm.

𝑡𝑡𝑓𝑓

Net flange thickness, in mm.

𝑡𝑡𝑤𝑤

Net stiffener web thickness, in mm.

𝑥𝑥-axis Local axis of a rectangular buckling panel parallel to its long edge.

𝑦𝑦-axis Local axis of a rectangular buckling panel perpendicular to its long edge.

𝛼𝛼

Aspect ratio of the plate panel, defined in Table 3 to be taken as: 𝛼𝛼 =
1−𝜓𝜓
𝛼𝛼

𝑎𝑎
𝑏𝑏

𝛽𝛽

Coefficient taken as: 𝛽𝛽 =𝜎𝜎𝑥𝑥

Normal stress applied on the edge along 𝑥𝑥-axis of the buckling panel, in N/mm2.

𝜔𝜔

𝜎𝜎𝑦𝑦
𝜎𝜎1

𝜎𝜎2

𝜎𝜎𝐸𝐸

Coefficient taken as: 𝜔𝜔 = 𝑚𝑚𝑚𝑚𝑚𝑚( 3, 𝛼𝛼)

Normal stress applied on the edge along 𝑦𝑦-axis of the buckling panel, in N/mm2.

Maximum normal stress along a panel edge, in N/mm2.
Minimum normal stress along a panel edge, in N/mm2.

Elastic buckling reference stress, in N/mm2 to be taken as:- For the application of the limit state of plane plate panels according to [2.2.1]:
𝜎𝜎𝐸𝐸 =

𝑡𝑡𝑝𝑝 2𝜋𝜋 2 𝐸𝐸��
12(1 − 𝜈𝜈 2 ) 𝑏𝑏

- For the application of the limit state of curved plate panels according to [2.2.6]:
𝜎𝜎𝐸𝐸 =

𝑡𝑡𝑝𝑝 2𝜋𝜋 2 𝐸𝐸��
12(1 − 𝜈𝜈 2 ) 𝑑𝑑

𝜏𝜏

Applied shear stress, in N/mm2.

𝜓𝜓Edge stress ratio to be taken as: 𝜓𝜓 = 𝜎𝜎2

𝜏𝜏𝑐𝑐
𝛾𝛾

𝛾𝛾𝑐𝑐

𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺

Buckling strength in shear, in N/mm2, as defined in [2.2.3].
𝜎𝜎

1Stress multiplier factor acting on loads. When the factor is such that the loads reachthe interaction formulae, 𝛾𝛾 = 𝛾𝛾𝑐𝑐 .
Stress multiplier factor at failure.

Stress multiplier factor of global elastic buckling capacity.

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1.

General1.1

Introduction

1.1.1 This section contains the methods for determination of the buckling capacities of plate
panels, stiffeners, primary supporting members and columns.
1.1.2 For the application of this section, the stresses 𝜎𝜎𝑥𝑥 , 𝜎𝜎𝑦𝑦 and 𝜏𝜏 applied on the structuralmembers are defined in:- Sec 3 for hull girder prescriptive buckling requirements.
- Sec 4 for direct strength analysis buckling requirements of hatch covers.
1.1.3 Buckling capacity
The buckling capacity is calculated by applying the actual stress combination and thenincreasing or decreasing the stresses proportionally until the interaction formulae defined in[2.1.1], [2.2.1] and [2.3.4] are equal to 1.0, respectively.
1.1.4 Buckling utilisation factor
The buckling utilisation factor of the structural member is equal to the highest utilisation factor
obtained for the different buckling modes.
1.1.5 Lateral pressure
The lateral pressure is to be applied and considered as constant for the calculation ofbuckling capacities as defined in [1.1.3].
2.

Buckling Capacity of Plate Panels

2.1

Overall Stiffened Panels

2.1.1 The elastic stiffened panel limit state is based on the following interaction formula,which sets a precondition for the buckling check of stiffeners in accordance with [2.3.4]:
𝛾𝛾𝑐𝑐

𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺=1with the corresponding buckling utilization factor defined as𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 =1𝛾𝛾𝑐𝑐

where the stress multiplier factors of global elastic buckling capacity, 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 , are to be calculated
based on the following formulae:
𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 = 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏+𝜏𝜏 for 𝜏𝜏 ≠ 0 and (𝜎𝜎𝑥𝑥 > 0 or 𝜎𝜎𝑦𝑦 > 0)𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 = 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏
𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 = 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏

for 𝜏𝜏 = 0 and (𝜎𝜎𝑥𝑥 > 0 or 𝜎𝜎𝑦𝑦 > 0)for 𝜏𝜏 ≠ 0 and (𝜎𝜎𝑥𝑥 ≤ 0 and 𝜎𝜎𝑦𝑦 ≤ 0)
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where 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏+𝜏𝜏 , 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 and 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 are stress multiplier factors of the global elastic buckling
capacity for different load combinations as defined in [2.1.2], [2.1.3] and [2.1.4], respectively.
For the calculation of 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏+𝜏𝜏 , 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 and 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 , neither 𝜎𝜎𝑥𝑥 nor 𝜎𝜎𝑦𝑦 shall be taken less than0.
𝜎𝜎𝑥𝑥 , 𝜎𝜎𝑦𝑦𝜏𝜏Applied normal stress to the plate panel, in N/mm2, to be taken as defined in [2.2.7].
Applied shear stress, in N/mm2, to be taken as defined in [2.2.7].

2.1.2 The stress multiplier factor 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 for the stiffened panel subjected to biaxial loads istaken as:𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 =where:
𝑁𝑁𝑥𝑥

𝜋𝜋 2 [𝐷𝐷11 𝐿𝐿4𝐵𝐵2 + 2(𝐷𝐷12 + 𝐷𝐷33 )𝑛𝑛2 𝐿𝐿2𝐵𝐵1 𝐿𝐿2𝐵𝐵2 + 𝑛𝑛4 𝐷𝐷22 𝐿𝐿4𝐵𝐵1 ]𝐿𝐿2𝐵𝐵1 𝐿𝐿2𝐵𝐵2
𝐿𝐿2𝐵𝐵2 𝑁𝑁𝑥𝑥 + 𝑛𝑛2 𝐿𝐿2𝐵𝐵1 𝑁𝑁𝑦𝑦

Load per unit length applied on the edge along 𝑥𝑥-axis of the stiffened panel, in
N/mm, taken as
𝑁𝑁𝑥𝑥 = 𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎 (𝐴𝐴𝑝𝑝 + 𝐴𝐴𝑠𝑠 )/𝑠𝑠

For stiffened panels fitted with U-type stiffeners, stiffener spacing 𝑠𝑠 is taken as:
𝑠𝑠 = 𝑏𝑏1 + 𝑏𝑏2

𝑁𝑁𝑦𝑦
𝐿𝐿𝐵𝐵1
𝐿𝐿𝐵𝐵2

where 𝑏𝑏1 and 𝑏𝑏2 are as defined in Sec 1, Figure 4.

Load per unit length applied on the edge along 𝑦𝑦 axis of the stiffened panel, in
N/mm, taken as 𝑁𝑁𝑦𝑦 = 𝑐𝑐𝜎𝜎𝑦𝑦 𝑡𝑡𝑝𝑝

Stiffener span, in mm, distance between primary supporting members, i.e. 𝐿𝐿𝐵𝐵1 = 𝑙𝑙.
Specially, for vertically stiffened side shell of single side skin bulk carriers, 𝐿𝐿𝐵𝐵1 = 0.8𝑙𝑙.

Total width of stiffened panel between lateral supports, in mm, taken as 6 times of thestiffener spacing, i.e. 6s.

𝑛𝑛

Number of half waves along the direction perpendicular to the stiffener axis. The
factor 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 is to be minimized with respect to the wave parameters 𝑛𝑛, i.e. to betaken as the smallest value larger than zero.

𝑐𝑐

Factor taking into account the normal stress distribution in the attached plating acting
perpendicular to the stiffener’s axis:
𝑐𝑐 = 0.5(1 + 𝜓𝜓)𝜓𝜓

𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎

𝑐𝑐 =12(1 − 𝜓𝜓)for 0 ≤ 𝜓𝜓 ≤ 1
for 𝜓𝜓 < 0Edge stress ratio for case 2 according to Table 3.
Average stress for both plate and stiffener, taken as:
𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎 = 𝜎𝜎𝑥𝑥 − 𝜈𝜈𝜈𝜈𝜎𝜎𝑦𝑦 𝐴𝐴𝑠𝑠 /(𝐴𝐴𝑝𝑝 + 𝐴𝐴𝑠𝑠 ) ≥ 0
for 𝜎𝜎𝑥𝑥 > 0 𝑎𝑎𝑎𝑎𝑎𝑎 𝜎𝜎𝑦𝑦 > 0
for 𝜎𝜎𝑥𝑥 ≤ 0 or 𝜎𝜎𝑦𝑦 ≤ 0
𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎 = 𝜎𝜎𝑥𝑥
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𝐷𝐷11 , 𝐷𝐷12 , 𝐷𝐷22 , 𝐷𝐷33 Bending stiffness coefficients, in Nmm, of the stiffened panel, defined ingeneral as:
𝐸𝐸𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒 104⎫
𝑠𝑠⎪⎪
𝐸𝐸𝑡𝑡𝑝𝑝3 𝜈𝜈𝐷𝐷12 =⎪
2
12(1 − 𝜈𝜈 )𝐸𝐸𝑡𝑡𝑝𝑝3⎬
𝐷𝐷22 =
12(1 − 𝜈𝜈 2 ) ⎪⎪𝐸𝐸𝑡𝑡𝑝𝑝3⎪
𝐷𝐷33 =
12(1 + 𝜈𝜈) ⎭𝐷𝐷11 =For stiffened panels fitted with U-type stiffeners, 𝐷𝐷12 and 𝐷𝐷22 are defined as:
3
𝐸𝐸𝑡𝑡𝑝𝑝3𝑏𝑏12
𝑡𝑡𝑤𝑤
�1.2 + 4.8 × 𝑀𝑀𝑀𝑀𝑀𝑀 �1.0,
𝐷𝐷22 =
� × 𝑀𝑀𝑀𝑀𝑀𝑀 �1.0, � � ��
12(1 − 𝜈𝜈 2 )ℎ𝑤𝑤 (𝑏𝑏1 + 𝑏𝑏2 )𝑡𝑡𝑝𝑝

𝐷𝐷12 = 𝜈𝜈𝐷𝐷22ℎ𝑤𝑤 is the breadth of U-type stiffener web as defined in Sec 1, Figure 4.

Moment of inertia, in cm4, of the stiffener including the effective width of theattached plating, same as 𝐼𝐼 defined in [2.3.4].

𝐼𝐼𝑒𝑒𝑒𝑒𝑒𝑒

2.1.3 The stress multiplier factor 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 for the stiffened panel subjected to pure shear load
is taken as:𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 =𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 =where:

4

3 𝐷𝐷
�𝐷𝐷11
22
2

(𝐿𝐿𝐵𝐵1⁄2) 𝑁𝑁𝑥𝑥𝑥𝑥(𝐷𝐷12 +𝐷𝐷33 )2(𝐷𝐷12 +𝐷𝐷33 )2−
0.6
� 𝑓𝑓𝑓𝑓𝑓𝑓 𝐷𝐷11 𝐷𝐷22 ≥ (𝐷𝐷12 + 𝐷𝐷33 )2
𝐷𝐷11 𝐷𝐷22
𝐷𝐷11 𝐷𝐷22

�8.125 + 5.64�

𝐷𝐷 𝐷𝐷
𝐷𝐷 2 𝐷𝐷 2
�2𝐷𝐷11 (𝐷𝐷12 +𝐷𝐷33 )�8.3 + 1.525 (𝐷𝐷 11+𝐷𝐷22 )2 − 0.493 (𝐷𝐷 11+𝐷𝐷22 )4 �
2
(𝐿𝐿𝐵𝐵1⁄2) 𝑁𝑁𝑥𝑥𝑥𝑥
12
33
12
33

𝑓𝑓𝑓𝑓𝑓𝑓 𝐷𝐷11 𝐷𝐷22 < (𝐷𝐷12 + 𝐷𝐷33 )2

𝑁𝑁𝑥𝑥𝑥𝑥 = 𝜏𝜏𝑡𝑡𝑝𝑝

2.1.4 The stress multiplier factor 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏+𝜏𝜏 for the stiffened panel subjected to combined loads
is taken as:
1111𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏+𝜏𝜏 = 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 2 �−
+�
+4
�
2
𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏
2
𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 2𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏

where 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝑏𝑏𝑏𝑏 and 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺,𝜏𝜏 are as defined in [2.1.2] and [2.1.3], respectively.

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2.2

Plates

2.2.1 Plate limit state
The plate limit state is based on the following interaction formulae:
𝑒𝑒0

𝑒𝑒0

𝑒𝑒

𝑒𝑒

𝛾𝛾𝑐𝑐1 𝜎𝜎𝑦𝑦 𝑆𝑆 0𝛾𝛾𝑐𝑐1 𝜎𝜎𝑥𝑥 𝑆𝑆 2 𝛾𝛾𝑐𝑐1 𝜎𝜎𝑦𝑦 𝑆𝑆 2
𝛾𝛾𝑐𝑐1 |𝜏𝜏|𝑆𝑆 0𝛾𝛾𝑐𝑐1 𝜎𝜎𝑥𝑥 𝑆𝑆 𝑒𝑒0
� − 𝐵𝐵 �
� �
�
� +�
� +�
� =1
𝜎𝜎𝑐𝑐𝑐𝑐𝜎𝜎𝑐𝑐𝑐𝑐𝜏𝜏𝑐𝑐
𝜎𝜎𝑐𝑐𝑐𝑐𝜎𝜎𝑐𝑐𝑐𝑐2222𝛾𝛾𝑐𝑐2 𝜎𝜎𝑥𝑥 𝑆𝑆 𝛽𝛽𝑝𝑝0.25
𝛾𝛾𝑐𝑐2 |𝜏𝜏|𝑆𝑆 𝛽𝛽𝑝𝑝0.25
��+�
= 1 𝑓𝑓𝑓𝑓𝑓𝑓 𝜎𝜎𝑥𝑥 ≥ 0�𝜏𝜏𝑐𝑐
𝜎𝜎𝑐𝑐𝑐𝑐𝛾𝛾𝑐𝑐3 𝜎𝜎𝑦𝑦 𝑆𝑆 𝛽𝛽𝑝𝑝0.25
𝛾𝛾𝑐𝑐3 |𝜏𝜏|𝑆𝑆 𝛽𝛽𝑝𝑝0.25+�= 1 𝑓𝑓𝑓𝑓𝑓𝑓 𝜎𝜎𝑦𝑦 ≥ 0���𝜎𝜎𝑐𝑐𝑐𝑐𝜏𝜏𝑐𝑐𝛾𝛾𝑐𝑐4 |𝜏𝜏|𝑆𝑆
=1
𝜏𝜏𝑐𝑐

with

𝛾𝛾𝑐𝑐 = 𝑀𝑀𝑀𝑀𝑀𝑀( 𝛾𝛾𝑐𝑐1 , 𝛾𝛾𝑐𝑐2 , 𝛾𝛾𝑐𝑐3 , 𝛾𝛾𝑐𝑐4 )and the corresponding buckling utilization factor defined as𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 =where:
𝜎𝜎𝑥𝑥 , 𝜎𝜎𝑦𝑦
𝜏𝜏

1
𝛾𝛾𝑐𝑐

Applied normal stress to the plate panel, in N/mm2, to be taken as defined in [2.2.7].

Applied shear stress to the plate panel, in N/mm2.
Ultimate buckling stress, in N/mm2, in direction parallel to the longer edge of the𝜎𝜎𝑐𝑐𝑐𝑐buckling panel as defined in [2.2.3].

𝜎𝜎𝑐𝑐𝑐𝑐buckling panel as defined in [2.2.3].

𝜏𝜏𝑐𝑐

Ultimate buckling stress, in N/mm2, in direction parallel to the shorter edge of the
Ultimate buckling shear stress, in N/mm2, as defined in [2.2.3].

𝛾𝛾𝑐𝑐1 , 𝛾𝛾𝑐𝑐2 , 𝛾𝛾𝑐𝑐3 , 𝛾𝛾𝑐𝑐4
𝐵𝐵

𝑒𝑒0

𝛽𝛽𝑝𝑝

: Stress multiplier factors at failure for each of the above different limit

states. 𝛾𝛾𝑐𝑐2 and 𝛾𝛾𝑐𝑐3 are only to be considered when 𝜎𝜎𝑥𝑥 ≥ 0 and 𝜎𝜎𝑦𝑦 ≥ 0 respectively.

Coefficient given in Table 1

Coefficient given in Table 1
Plate slenderness parameter taken as:𝛽𝛽𝑝𝑝 =

𝑏𝑏 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃
�
𝐸𝐸
𝑡𝑡𝑝𝑝

Table 1: Definition of coefficients 𝑩𝑩 and 𝒆𝒆𝟎𝟎

Applied stress

𝜎𝜎𝑥𝑥 ≥ 0 and 𝜎𝜎𝑦𝑦 ≥ 0
𝜎𝜎𝑥𝑥 < 0 or 𝜎𝜎𝑦𝑦 < 0𝑩𝑩

0.7 − 0.3 𝛽𝛽𝑝𝑝 ⁄𝛼𝛼
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𝒆𝒆𝟎𝟎

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2.2.2 Reference degree of slenderness
The reference degree of slenderness is to be taken as:
𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃
𝜆𝜆 = �
𝐾𝐾𝜎𝜎𝐸𝐸

where:
𝐾𝐾

Buckling factor, as defined in Table 3 and Table 4.

2.2.3 Ultimate buckling stresses
The ultimate buckling stresses of plate panels, in N/mm2, are to be taken as:

𝜎𝜎𝑐𝑐𝑐𝑐 = 𝐶𝐶𝑥𝑥 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

𝜎𝜎𝑐𝑐𝑐𝑐 = 𝐶𝐶𝑦𝑦 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

The ultimate buckling stress of plate panels subject to shear, in N/mm2, is to be taken as:𝜏𝜏𝑐𝑐 = 𝐶𝐶𝜏𝜏

where:

𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

𝐶𝐶𝑥𝑥 , 𝐶𝐶𝑦𝑦 , 𝐶𝐶𝜏𝜏

√3

Reduction factors, as defined in Table 3- For the 1st Equation of [2.2.1], when 𝜎𝜎𝑥𝑥 < 0 or 𝜎𝜎𝑦𝑦 < 0, the reduction factors areto be taken as:
𝐶𝐶𝑥𝑥 = 𝐶𝐶𝑦𝑦 = 𝐶𝐶𝜏𝜏 = 1.
- For other cases:- For SP-A and UP-A, 𝐶𝐶𝑦𝑦 is calculated according to Table 3 by using1
𝑐𝑐1 = �1 − � ≥ 0𝛼𝛼- For SP-B and UP-B, 𝐶𝐶𝑦𝑦 is calculated according to Table 3 by using
𝑐𝑐1 = 1

- For vertically stiffened single side skin of bulk carrier, 𝐶𝐶𝑦𝑦 is calculated
according to Table 3 by using1
𝑐𝑐1 = �1 − � ≥ 0𝛼𝛼- For corrugation of corrugated bulkheads, 𝐶𝐶𝑦𝑦 is calculated according to Table 3
by using
1
𝑐𝑐1 = �1 − � ≥ 0𝛼𝛼The boundary conditions for plates are to be considered as simply supported, see cases 1, 2
and 15 of Table 3. If the boundary conditions differ significantly from simple support, a more
appropriate boundary condition can be applied according to the different cases of Table 3
subject to the agreement of the Society.

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2.2.4 Correction factor 𝑭𝑭𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍

The correction factor 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 depending on the edge stiffener types on the longer side of thebuckling panel is defined in Table 2. An average value of 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 is to be used for plate panels
having different edge stiffeners. For stiffener types other than those mentioned in Table 2, thevalue of 𝑐𝑐 is to be agreed by the Society. In such a case, value of 𝑐𝑐 higher than thosementioned in Table 2 can be used, provided it is verified by buckling strength check ofpanel using non-linear FE analysis and deemed appropriate by the Society.
Table 2: Correction factor 𝑭𝑭𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍
𝑭𝑭𝒍𝒍𝒍𝒍𝒍𝒍𝒍𝒍
Structural element types

Unstiffened Panel

Stiffener not fixed at both ends
Flat bar (1)Angle and L2
profiles𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑐𝑐 �

T profile
Stiffener
fixed atboth ends

1.0

N/A

1.0

N/A

𝑡𝑡𝑤𝑤
𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑐𝑐 + 1 𝑓𝑓𝑓𝑓𝑓𝑓>1
𝑡𝑡𝑝𝑝

Bulb profile

Stiffened
Panel

𝒄𝒄

Girder of highrigidity (e.g. bottom
transverse)

3

𝑡𝑡𝑤𝑤
𝑡𝑡𝑤𝑤
≤1
� + 1 𝑓𝑓𝑓𝑓𝑓𝑓
𝑡𝑡𝑝𝑝
𝑡𝑡𝑝𝑝
1.4

-

U-type profile
fitted on hatch
cover(2)
-

0.10
0.30
0.40
0.30
N/A

Plate on which the U-type profile isfitted, including EPP 𝑏𝑏1 and EPP 𝑏𝑏2- For 𝑏𝑏2 < 𝑏𝑏1: 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1- For 𝑏𝑏2 ≥ 𝑏𝑏1:
3
𝑏𝑏1
𝑡𝑡𝑤𝑤
𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = �1.55 − 0.55 � �1 + 𝑐𝑐 � � �
𝑏𝑏2
𝑡𝑡𝑝𝑝

0.2

Other plates of the U-type profile:𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1(1) 𝑡𝑡𝑤𝑤 is the net web thickness, in mm, without the correction defined in [2.3.2].
(2) 𝑏𝑏1 , 𝑏𝑏2 and 𝑡𝑡𝑤𝑤 are defined in Sec.1, Figure 4.
2.2.5 Correction factor 𝑭𝑭𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕

The correction factor 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is to be taken as:- For transversely framed EPP of single side skin bulk carrier, between the hopper and
top wing tank:- 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1.25 when the two adjacent frames are supported by one tripping bracket
fitted in way of the adjacent plate panels.

- 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1.33 when the two adjacent frames are supported by two tripping brackets
each fitted in way of the adjacent plate panels.
- 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1.15 elsewhere.

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S35

S35
(cont)- For the attached plate of a U-type stiffener fitted on a hatch cover:𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑀𝑀𝑀𝑀𝑀𝑀(3 − 0.08(𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡0 − 6)2 , 1.0) ≤ 2.25
where:

3
𝑏𝑏2
6𝑏𝑏22
𝑡𝑡𝑤𝑤
𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡0 = 𝑀𝑀𝑀𝑀𝑀𝑀 � + 2
� � , 6� for EPP 𝑏𝑏2
𝑏𝑏1 𝜋𝜋 ℎ𝑤𝑤 (𝑏𝑏1 + 𝑏𝑏2 ) 𝑡𝑡𝑝𝑝
3
𝑏𝑏1
6𝑏𝑏12
𝑡𝑡𝑤𝑤
𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡0 = 𝑀𝑀𝑀𝑀𝑀𝑀 � + 2
� � , 6� for EPP 𝑏𝑏1
𝑏𝑏2 𝜋𝜋 ℎ𝑤𝑤 (𝑏𝑏2 + 𝑏𝑏1 ) 𝑡𝑡𝑝𝑝

with 𝑏𝑏1 , 𝑏𝑏2 and ℎ𝑤𝑤 as defined in Sec.1, Figure 4.

Coefficient 𝐹𝐹 defined in Case 2 of Table 3 is to be replaced by the following formula:
𝐹𝐹 = �1 − �𝐾𝐾𝑦𝑦− 1��𝜆𝜆2𝑝𝑝 � 𝑐𝑐1 ≥ 0
0.91𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡- For other cases: 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1.
2.2.6

Curved plate panels

This requirement for curved plate limit state is applicable when 𝑅𝑅⁄𝑡𝑡𝑝𝑝 ≤ 2500. Otherwise, therequirement for plate limit state given in [2.2.1] is applicable.
The curved plate limit state is based on the following interaction formula:
1.25

1.25

𝛾𝛾𝑐𝑐 𝜎𝜎𝑎𝑎𝑎𝑎 𝑆𝑆��
𝐶𝐶𝑎𝑎𝑎𝑎 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

𝛾𝛾𝑐𝑐 𝜎𝜎𝑡𝑡𝑡𝑡 𝑆𝑆
𝛾𝛾𝑐𝑐 𝜎𝜎𝑡𝑡𝑡𝑡 𝑆𝑆
𝛾𝛾𝑐𝑐 𝜎𝜎𝑎𝑎𝑎𝑎 𝑆𝑆− 0.5 ����+�
�
𝐶𝐶𝑡𝑡𝑡𝑡 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃
𝐶𝐶𝑎𝑎𝑎𝑎 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃 𝐶𝐶𝑡𝑡𝑡𝑡 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 =1𝛾𝛾𝑐𝑐with the corresponding buckling utilization factor defined aswhere:
𝜎𝜎𝑎𝑎𝑎𝑎𝜎𝜎𝑡𝑡𝑡𝑡2𝛾𝛾𝑐𝑐 𝜏𝜏√3𝑆𝑆+�
� = 1.0𝐶𝐶𝜏𝜏 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃

Applied axial stress to the cylinder corresponding to the curved plate panel, in N/mm2.
In case of tensile axial stresses, 𝜎𝜎𝑎𝑎𝑎𝑎 = 0.
Applied tangential stress to the cylinder corresponding to the curved plate panel, in
N/mm2. In case of tensile tangential stresses, 𝜎𝜎𝑡𝑡𝑡𝑡 = 0.

𝐶𝐶𝑎𝑎𝑎𝑎 , 𝐶𝐶𝑡𝑡𝑡𝑡 , 𝐶𝐶𝜏𝜏 Buckling reduction factor of the curved plate panel, as defined in Table 4.

The stress multiplier factor, 𝛾𝛾𝑐𝑐 , of the curved plate panel need not be taken less than the
stress multiplier factor, 𝛾𝛾𝑐𝑐 , for the expanded plane panel according to [2.2.1].

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S35
Figure 1: Transverse stiffened bilge plating

S35(cont)

Table 3: Buckling factor and reduction factor for plane plate panels
Aspectratio
𝜶𝜶

𝐾𝐾𝑥𝑥 = 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

Buckling factor K

8.4
𝜓𝜓 + 1.1

𝜓𝜓 ≤ −1

𝐾𝐾𝑥𝑥 = 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 [7.63 − 𝜓𝜓(6.26 − 10 𝜓𝜓)]1 ≥ 𝜓𝜓 ≥ 0

𝐾𝐾𝑥𝑥 = 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 [5.975(1 − 𝜓𝜓)2 ]
1 2
�
𝛼𝛼 2
𝐾𝐾𝑦𝑦 =(1 − 𝜓𝜓) 2.4
� 2 + 6.9𝑓𝑓1 �
1 + 𝜓𝜓 +100
𝛼𝛼𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ∙ 2 �1 +𝛼𝛼 ≤ 6 𝑓𝑓1 = (1 − 𝜓𝜓)(𝛼𝛼 − 1)
𝛼𝛼 > 6
𝐾𝐾𝑦𝑦 =

𝑓𝑓1 = 0.6 �1 −6𝜓𝜓𝛼𝛼

� �𝛼𝛼 +

14

� but

𝛼𝛼
0.35

not greater than 14.5 −𝛼𝛼 2

1
𝑓𝑓1 = 0.6 � + 14𝛽𝛽�𝛽𝛽
but not greater than
14.5 − 0.35𝛽𝛽2

𝛼𝛼 > 6(1 − 𝜓𝜓)4𝑎𝑎≤ 𝜓𝜓 < 03200𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (1 + 𝛽𝛽2 )2(1 − 𝑓𝑓3 )(100 + 2.4𝛽𝛽2 + 6.9𝑓𝑓1 + 23𝑓𝑓2 )1−

2

Reduction factor C

When 𝜎𝜎𝑥𝑥 ≤ 0, 𝐶𝐶𝑥𝑥 = 1

0 > 𝜓𝜓 > −1

1

Stressratio𝝍𝝍

1 ≥ 𝜓𝜓 ≥ 0

Case

When 𝜎𝜎𝑥𝑥 > 0,
𝐶𝐶𝑥𝑥 = 1for 𝜆𝜆 ≤ 𝜆𝜆𝑐𝑐
1
0.22𝐶𝐶𝑥𝑥 = 𝑐𝑐 � − 2 � for 𝜆𝜆 > 𝜆𝜆𝑐𝑐
𝜆𝜆

𝜆𝜆where:
𝑐𝑐 = (1.25 − 0.12𝜓𝜓) ≤ 1.25
𝑐𝑐
0.88
�
𝜆𝜆𝑐𝑐 = �1 + �1 −2
𝑐𝑐When 𝜎𝜎𝑦𝑦 ≤ 0, 𝐶𝐶𝑦𝑦 = 1
When 𝜎𝜎𝑦𝑦 > 0
1𝐶𝐶𝑦𝑦 = 𝑐𝑐 � −where:𝜆𝜆

𝑅𝑅+𝐹𝐹 2 (𝐻𝐻−𝑅𝑅)
𝜆𝜆2

�𝑐𝑐 = (1.25 − 0.12𝜓𝜓) ≤ 1.25
𝜆𝜆
𝑅𝑅 = 𝜆𝜆 �1 − � for 𝜆𝜆 < 𝜆𝜆𝑐𝑐
𝑐𝑐
𝑅𝑅 = 0.22 for 𝜆𝜆 ≥ 𝜆𝜆𝑐𝑐
𝜆𝜆𝑐𝑐 = 0.5𝑐𝑐 �1 + �1 −

0.88
𝑐𝑐

�

𝑓𝑓2 = 𝑓𝑓3 = 0

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S35

3(1 − 𝛹𝛹) ≤ 𝛼𝛼 ≤6(1 − 𝛹𝛹)
1.5(1 − 𝛹𝛹) ≤ 𝛼𝛼 < 3(1 − 𝛹𝛹)

𝑓𝑓1 =

𝐾𝐾

−1�

𝜆𝜆𝑝𝑝

� 𝑐𝑐1 ≥ 0

𝜆𝜆2𝑝𝑝 = 𝜆𝜆2 − 0.5 for 1 ≤ 𝜆𝜆2𝑝𝑝 ≤ 3
𝑐𝑐1 as defined in [2.2.3]

𝑓𝑓2 = 𝑓𝑓3 = 0

𝐻𝐻 = 𝜆𝜆 −𝑇𝑇 = 𝜆𝜆 +1− (2 − 𝜔𝜔𝜔𝜔)4𝛽𝛽
2−9(𝜔𝜔𝜔𝜔 − 1)( − 𝛽𝛽)32𝜆𝜆𝑐𝑐�𝑇𝑇+√𝑇𝑇 2 −4�14 1+
15𝜆𝜆 3≥ 𝑅𝑅

𝑓𝑓2 = 𝑓𝑓3 = 0

For 𝛼𝛼 > 1.5
1

𝜔𝜔 4

1

𝑓𝑓1 = 2 � − 16 �1 − � � � − 1�
𝛽𝛽

1 − 𝛹𝛹 ≤ 𝛼𝛼 < 1.5(1 − 𝛹𝛹)

𝑓𝑓2 = 3𝛽𝛽 − 23

𝛽𝛽𝑓𝑓3 = 0For 𝛼𝛼 ≤ 1.5

1.5
1
𝑓𝑓1 = 2 �
− 1� � − 1�
1 − 𝜓𝜓
𝛽𝛽

𝑓𝑓2 =𝜓𝜓(1 − 16𝑓𝑓42 )1 − 𝛼𝛼𝑓𝑓3 = 00.75(1 − 𝛹𝛹) ≤ 𝛼𝛼 < 1 − 𝛹𝛹

𝑓𝑓4 = (1.5 − 𝑀𝑀𝑖𝑖𝑖𝑖(1.5, 𝛼𝛼))2

𝑓𝑓1 = 0

𝑓𝑓2 = 1 + 2.31(𝛽𝛽 − 1)
4−48 � − 𝛽𝛽� 𝑓𝑓42
3𝑓𝑓

𝑓𝑓3 = 3𝑓𝑓4 (𝛽𝛽 − 1) − � 4 −1.81

𝑓𝑓4 = (1.5 − 𝑀𝑀𝑖𝑖𝑖𝑖(1.5, 𝛼𝛼))2

𝐾𝐾𝑦𝑦 = 5.972𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
where

4𝑎𝑎
3

(cont)

1
𝑓𝑓1 = − 1𝛽𝛽𝜓𝜓 < 1 −S35�

𝐹𝐹 = �1 − 0.912

𝛼𝛼−1
1.31

�

𝛽𝛽2
1 − 𝑓𝑓3

𝑓𝑓5
1 + 3𝜓𝜓
+�
𝑓𝑓3 = 𝑓𝑓5 �
1.81
5.24
9
(1 + Max(−1, 𝜓𝜓))2
𝑓𝑓5 =
16

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S35
Aspectratio
𝜶𝜶0 > 𝜓𝜓 > −1 1 ≥ 𝜓𝜓 ≥ 0

3Stressratio
𝝍𝝍

𝐾𝐾𝑥𝑥 =

Buckling factor K11 ≥ 𝜓𝜓 ≥ −14

1 3 − 𝜓𝜓
�𝛼𝛼 2
2𝛼𝛼 < 1.64
6

1 ≥ 𝜓𝜓 ≥ 0

𝐾𝐾𝑥𝑥 =

𝐾𝐾𝑦𝑦 =0.75
𝜆𝜆

for 𝜆𝜆 > 0.75

𝐶𝐶𝑥𝑥 = 1 for 𝜆𝜆 ≤ 0.7
𝐶𝐶𝑥𝑥 = 21

𝜆𝜆 +0.51

4(0.425 + 𝛼𝛼 2 )(3𝜓𝜓 + 1)𝛼𝛼 215𝜓𝜓(1 − 3.42𝜓𝜓) 2𝛼𝛼

𝐾𝐾𝑦𝑦 = (0.425 + 𝛼𝛼 2 )1(3 − 𝜓𝜓)2𝛼𝛼 2

𝛼𝛼For UP-A:
𝐶𝐶𝑦𝑦 = 1 for 𝜆𝜆 ≤ 0.75
𝐶𝐶y =

0.75
𝜆𝜆

for 𝜆𝜆 > 0.75

For UP-B:

𝐶𝐶y = 1 for 𝜆𝜆 ≤ 0.7
𝐶𝐶y = 21

𝜆𝜆 +0.51

8—for 𝜆𝜆 > 0.7

1+ 0.56 + 0.13𝛼𝛼 2
𝛼𝛼 2𝐾𝐾𝑦𝑦 = 4(0.425 + 𝛼𝛼 2 )(1 + 𝜓𝜓) 2 −7

𝐶𝐶𝑥𝑥 = 1 for 𝜆𝜆 ≤ 0.75
For UP-B:

𝐾𝐾𝑥𝑥 = 1.28—

For UP-A:

𝐶𝐶𝑥𝑥 =

𝛼𝛼 ≥ 1.64

𝐾𝐾𝑥𝑥 = �0.425 +5Reduction factor C

4(0.425 + 1/𝛼𝛼 2 )3𝜓𝜓 + 1

𝐾𝐾𝑥𝑥 = 4 �0.425 + 2� (1 + 𝜓𝜓) −𝛼𝛼5𝜓𝜓(1 − 3.42𝜓𝜓)

0 > 𝜓𝜓 ≥ −1

(cont)Case1 ≥ 𝜓𝜓 ≥ −1

S35

𝐾𝐾𝑦𝑦 = 1 +for 𝜆𝜆 > 0.7

0.56 0.13
+ 4
𝛼𝛼 2
𝛼𝛼

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S35

S35
(cont)Case
9

Stress Aspect
ratio
ratio
𝜶𝜶
𝝍𝝍
—

Buckling factor K

𝐶𝐶𝑥𝑥 = 1 for 𝜆𝜆 ≤ 0.83

𝐾𝐾𝑥𝑥 = 6.97

1

0.22

𝐶𝐶𝑥𝑥 = 1.13 � − 2 �𝜆𝜆𝜆𝜆
for 𝜆𝜆 > 0.83

10—Reduction factor C

𝐾𝐾𝑦𝑦 = 4 +2.07 0.67
+ 4
𝛼𝛼 2
𝛼𝛼

𝛼𝛼 ≥ 4

𝐾𝐾𝑥𝑥 = 4

𝐶𝐶𝑦𝑦 = 1 for 𝜆𝜆 ≤ 0.83
1

0.22

𝐶𝐶𝑦𝑦 = 1.13 � − 2 �𝜆𝜆𝜆𝜆
for 𝜆𝜆 > 0.83

11—

𝛼𝛼 < 412—

𝐶𝐶𝑥𝑥 = 1 for 𝜆𝜆 ≤ 0.83
1

0.22

𝐶𝐶𝑥𝑥 = 1.13 � − 2 �𝜆𝜆𝜆𝜆
for 𝜆𝜆 > 0.83

44 − 𝛼𝛼
𝐾𝐾𝑥𝑥 = 4 + 2.74 ��3For 𝛼𝛼 < 2𝐶𝐶𝑦𝑦 = 𝐶𝐶𝑦𝑦2

𝐾𝐾𝑦𝑦 = 𝐾𝐾𝑦𝑦 determined as per case 2

For 𝛼𝛼 ≥ 2𝐶𝐶𝑦𝑦 = �1.06 +1� 𝐶𝐶10𝛼𝛼 𝑦𝑦2

where:
𝐶𝐶𝑦𝑦2 ∶ 𝐶𝐶𝑦𝑦 determined as
per case 213—𝛼𝛼 ≥ 4𝛼𝛼 < 414—

𝐾𝐾𝑥𝑥 = 6.97

𝐶𝐶𝑥𝑥 = 1 for 𝜆𝜆 ≤ 0.83

44 − 𝛼𝛼
𝐾𝐾𝑥𝑥 = 6.97 + 3.1 ��
3

6.97 3.1 4 − 1/𝛼𝛼 4
𝐾𝐾𝑦𝑦 = 2 + 2 �
�
𝛼𝛼
𝛼𝛼
3

Page 34 of 51

1

0.22

𝐶𝐶𝑥𝑥 = 1.13 � − 2 �𝜆𝜆𝜆𝜆
for 𝜆𝜆 > 0.83

𝐶𝐶𝑦𝑦 = 1 for 𝜆𝜆 ≤ 0.83
1

0.22

𝐶𝐶𝑦𝑦 = 1.13 � − 2 �𝜆𝜆𝜆𝜆
for 𝜆𝜆 > 0.83

IACS Req. 2023

S35

S35
(cont)Case
15

Stressratio𝝍𝝍

Aspectratio
𝜶𝜶－Buckling factor K

𝐾𝐾𝜏𝜏 = √3 �5.34 +Reduction factor C

4
�
𝛼𝛼 2

16

－

4 7.15
𝐾𝐾𝜏𝜏 = √3 �5.34 + Max � 2 , 2.5 ��𝛼𝛼 𝛼𝛼𝐶𝐶𝜏𝜏 =

𝐾𝐾𝜏𝜏 = 𝐾𝐾𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏15 𝑟𝑟

17－𝐶𝐶𝜏𝜏 = 1 for 𝜆𝜆 ≤ 0.84
0.84
𝜆𝜆

for 𝜆𝜆 > 0.84

𝐾𝐾𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏15 : 𝐾𝐾𝜏𝜏 according to case 15

𝑟𝑟 : Opening reduction factor taken as
𝑑𝑑𝑏𝑏
𝑑𝑑𝑎𝑎
𝑟𝑟 = �1 − � �1 − �
𝑎𝑎
𝑏𝑏
with

𝑑𝑑𝑎𝑎
𝑑𝑑𝑏𝑏
≤ 0.7 𝑎𝑎𝑎𝑎𝑎𝑎
≤ 0.7
𝑎𝑎
𝑏𝑏

18
－

𝐾𝐾𝜏𝜏 = √3 �0.6 +

4
�
𝑎𝑎 2
𝐶𝐶𝜏𝜏 = 1 for 𝜆𝜆 ≤ 0.84

19－

𝐾𝐾𝜏𝜏 = 8𝐶𝐶𝜏𝜏 =0.84
𝜆𝜆

for 𝜆𝜆 > 0.84

Edge boundary conditions:
Plate edge free
Plate edge simply supported
Plate edge clamped
Note 1: Cases listed are general cases. Each stress component (𝜎𝜎𝑥𝑥 , 𝜎𝜎𝑦𝑦 ) is to be understood in local coordinates.

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Table 4: Buckling factor and reduction factor for curved plate panel with 𝑹𝑹/𝒕𝒕𝒑𝒑 ≤ 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐
Case
1

2

3

4

Aspect ratio

𝑑𝑑
𝑅𝑅≤ 0.5�
𝑅𝑅
𝑡𝑡𝑝𝑝

Buckling factor K

𝐾𝐾 = 1 +Reduction factor C

For general application:

2 𝑑𝑑2
3 𝑅𝑅𝑡𝑡𝑝𝑝𝑑𝑑
𝑅𝑅> 0.5�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 = 0.267

𝑑𝑑
𝑅𝑅≤ 1.63�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 =

𝑑𝑑

�𝑅𝑅𝑡𝑡𝑝𝑝

𝑑𝑑 2

𝑅𝑅𝑡𝑡𝑝𝑝𝐶𝐶𝑎𝑎𝑎𝑎 = 1 for 𝜆𝜆 ≤ 0.25

𝐶𝐶𝑎𝑎𝑎𝑎 = 1.233 − 0.933𝜆𝜆for 0.25 < 𝜆𝜆 ≤ 1

𝑑𝑑

𝑡𝑡𝑝𝑝

�3 − � � ≥ 0.4

+3

𝑅𝑅

𝑅𝑅

𝐶𝐶𝑡𝑡𝑡𝑡 = 1.274 − 0.686𝜆𝜆for 0.4 < 𝜆𝜆 ≤ 1.2

𝐶𝐶𝑡𝑡𝑡𝑡 =

2

𝑑𝑑
𝑅𝑅
≤�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 =

𝑑𝑑
𝑅𝑅
>�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 = 0.3

𝑑𝑑
𝑅𝑅≤ 8.7�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 = √3�28.3 +𝑑𝑑
𝑅𝑅> 8.7�
𝑅𝑅
𝑡𝑡𝑝𝑝

𝐾𝐾 = √3

0.6𝑑𝑑

�𝑅𝑅𝑡𝑡𝑝𝑝+

For curved single fields, e.g. bilge
strake, which are bounded byplane panels as shown in Figure 1:
0.65
𝐶𝐶𝑎𝑎𝑎𝑎 = 2 ≤ 1.0
𝜆𝜆𝐶𝐶𝑡𝑡𝑡𝑡 = 1 for 𝜆𝜆 ≤ 0.4

𝑑𝑑2
𝑅𝑅 2
+ 2.25 � �
2𝑅𝑅
𝑑𝑑𝑡𝑡𝑝𝑝

𝐾𝐾 = 0.3

𝑅𝑅𝑡𝑡𝑝𝑝𝐶𝐶𝑎𝑎𝑎𝑎 = 0.2/𝜆𝜆2 for 𝜆𝜆 > 1.5

For general application:(𝑅𝑅𝑡𝑡𝑝𝑝 )0.175
𝑑𝑑0.35𝑑𝑑
𝑅𝑅> 1.63�
𝑡𝑡𝑝𝑝
𝑅𝑅

𝑑𝑑 2

𝐶𝐶𝑎𝑎𝑎𝑎 = 0.3/𝜆𝜆3 for 1 < 𝜆𝜆 ≤ 1.5

𝑅𝑅𝑡𝑡𝑝𝑝
�𝑅𝑅𝑡𝑡𝑝𝑝− 0.3 2𝑑𝑑
𝑑𝑑

0.65
for 𝜆𝜆 > 1.2
𝜆𝜆2

For curved single fields, e.g. bilge
strake, which are bounded byplane panels as shown in Figure 1:
0.8
𝐶𝐶𝑡𝑡𝑡𝑡 = 2 ≤ 1.0
𝜆𝜆
As in load case 2.

2

𝑅𝑅2
𝑑𝑑2
+ 0.291 ��2𝑅𝑅
𝑑𝑑𝑡𝑡𝑝𝑝0.67𝑑𝑑3
𝑅𝑅1.5 𝑡𝑡𝑝𝑝1.5

0.28𝑑𝑑2

𝑅𝑅 �𝑅𝑅𝑡𝑡𝑝𝑝

𝐶𝐶𝜏𝜏 = 1 for 𝜆𝜆 ≤ 0.4

𝐶𝐶𝜏𝜏 = 1.274 − 0.686𝜆𝜆for 0.4 < 𝜆𝜆 ≤ 1.2
𝐶𝐶𝜏𝜏 =

0.65
for 𝜆𝜆 > 1.2
𝜆𝜆2

Explanations for boundary conditions:- - - - - - - - - - - - Plate edge free.
——————— Plate edge simply supported.
Plate edge clamped.

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2.2.7 Applied normal and shear stresses to plate panels
The normal stress, 𝜎𝜎𝑥𝑥 and 𝜎𝜎𝑦𝑦 , in N/mm2, to be applied for the overall stiffened panel capacity
and the plate panel capacity calculations as given in [2.1.1] and [2.2.1] respectively, are to betaken as follows:- For FE analysis, the reference stresses as defined in Sec.4 [2.4].
- For prescriptive assessment of the overall stiffened panel capacity and the plate
panel capacity, the axial or transverse compressive stresses calculated according to
the Relevant UR-S, at load calculation points of the considered stiffener or theconsidered elementary plate panel, as defined in item a) and item b) of Sec 3, [1.2.1]
respectively. However, in case of transverse stiffening arrangement, the transverse
compressive stress used for the assessment of the overall stiffened panel capacity is
to be taken as the compressive stress calculated at load calculation points of thestiffener attached plating, as defined in item a) of Sec 3, [1.2.1].
- For grillage analysis where the stresses are obtained based on beam theory, thestresses taken as:
𝜎𝜎𝑥𝑥𝑥𝑥 + 𝜈𝜈𝜎𝜎𝑦𝑦𝑦𝑦
𝜎𝜎𝑥𝑥 =
1 − 𝜈𝜈 2
Where
𝜎𝜎𝑥𝑥𝑥𝑥 , 𝜎𝜎𝑦𝑦𝑦𝑦

𝜎𝜎𝑦𝑦 =

𝜎𝜎𝑦𝑦𝑦𝑦 + 𝜈𝜈𝜎𝜎𝑥𝑥𝑥𝑥
1 − 𝜈𝜈 2

Stress, in N/mm2, from grillage beam analysis respectively along 𝑥𝑥 or 𝑦𝑦
axis of the plate attached to the PSM web.

The shear stress 𝜏𝜏, in N/mm2, to be applied for the overall stiffened panel capacity and theplate panel capacity calculations as given in [2.1.1] and [2.2.1] respectively, are to be taken as
follows:- For FE analysis, the reference shear stresses as defined in Sec 4, [2.4].
- For prescriptive assessment of the plate panel capacity, the shear stresses
calculated according to the Relevant UR-S, at load calculation points of theconsidered elementary plate panel, as defined in item a) of Sec 3, [1.2.1].
- For prescriptive assessment of the overall stiffened panel capacity, the shear
stresses calculated according to the Relevant UR-S, at the following load calculation
point:- At the middle of the full span, 𝑙𝑙, of the considered stiffener.
- At the intersection point between the stiffener and its attached plating.
- For grillage beam analysis, 𝜏𝜏 = 0 in the plate attached to the PSM web.

2.3

Stiffeners

2.3.1 Buckling modes
The following buckling modes are to be checked:- Stiffener induced failure (SI).
- Associated plate induced failure (PI).
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2.3.2 Web thickness of flat bar
For accounting the decrease of the stiffness due to local lateral deformation, the effective
web thickness of flat bar stiffener, in mm, is to be used in [2.1] and [2.3.4] for the calculation of
the net sectional area, 𝐴𝐴𝑠𝑠 , the net section modulus, 𝑍𝑍, and the moment of inertia, 𝐼𝐼, of thestiffener and is taken as:
𝑡𝑡𝑤𝑤_𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑡𝑡𝑤𝑤 �1 −2.3.3 Idealisation of bulb profile

𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1
2𝜋𝜋 2 ℎ𝑤𝑤 2� � �1 −
��
3
𝑠𝑠
𝑠𝑠

Bulb profiles are to be considered as equivalent angle profiles. The net dimensions of theequivalent built-up section are to be obtained, in mm, from the following formulae.
′ℎ𝑤𝑤 = ℎ𝑤𝑤
−

′
ℎ𝑤𝑤
+2
9.2

′
𝑏𝑏𝑓𝑓 = 𝛼𝛼 �𝑡𝑡𝑤𝑤
+

𝑡𝑡𝑓𝑓 =

′
ℎ𝑤𝑤
−2
9.2

′
ℎ𝑤𝑤
− 2�
6.7

′
𝑡𝑡𝑤𝑤 = 𝑡𝑡𝑤𝑤

where:′′, 𝑡𝑡𝑤𝑤ℎ𝑤𝑤

𝛼𝛼

Net height and thickness of a bulb section, in mm, as shown in Figure 2.
Coefficient equal to 𝛼𝛼 = 1.1 +𝛼𝛼 = 1.02′ �
�120−ℎ𝑤𝑤

3000′
for ℎ𝑤𝑤≤ 120′
for ℎ𝑤𝑤> 120

Figure 2: Idealisation of bulb stiffener

Bulb flat

Equivalent angle bar

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2.3.4 Ultimate buckling capacity
When 𝜎𝜎𝑎𝑎 + 𝜎𝜎𝑏𝑏 + 𝜎𝜎𝑤𝑤 > 0 while initially setting 𝛾𝛾 = 1, the ultimate buckling capacity for stiffeners
is to be checked according to the following interaction formula:𝛾𝛾𝑐𝑐 𝜎𝜎𝑎𝑎 + 𝜎𝜎𝑏𝑏 + 𝜎𝜎𝑤𝑤
𝑆𝑆 = 1
𝑅𝑅𝑒𝑒𝑒𝑒with the corresponding buckling utilization factor defined as𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =where:
𝜎𝜎𝑎𝑎

𝜎𝜎𝑥𝑥

𝑅𝑅𝑒𝑒𝑒𝑒
𝜎𝜎𝑏𝑏
𝑍𝑍

𝑀𝑀2

1
𝛾𝛾𝑐𝑐

Effective axial stress, in N/mm2, at mid span of the stiffener, acting on the stiffener with
its attached plating.
𝑠𝑠𝑡𝑡𝑝𝑝 + 𝐴𝐴𝑠𝑠
𝜎𝜎𝑎𝑎 = 𝜎𝜎𝑥𝑥
𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 𝑡𝑡𝑝𝑝 + 𝐴𝐴𝑠𝑠

Nominal axial stress, in N/mm2, acting on the stiffener with its attached plating.
- For FE analysis, 𝜎𝜎𝑥𝑥 is the FE corrected stress as defined in [2.3.6] in the attachedplating in the direction of the stiffener axis.
- For prescriptive assessment, 𝜎𝜎𝑥𝑥 is the axial stress calculated according to Sec 3, [2.2.1]
at load calculation point of the stiffener, as defined in Sec 3, [1.2.1].
- For grillage beam analysis, 𝜎𝜎𝑥𝑥 is the stress acting along the 𝑥𝑥-axis of the attached
buckling panel.
Specified minimum yield stress of the material, in N/mm2- 𝑅𝑅𝑒𝑒𝑒𝑒 = 𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆 for stiffener induced failure (SI).
- 𝑅𝑅𝑒𝑒𝑒𝑒 = 𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃 for plate induced failure (PI).

Bending stress in the stiffener, in N/mm2:
𝑀𝑀0 + 𝑀𝑀1 + 𝑀𝑀2
𝜎𝜎𝑏𝑏 =
1000𝑍𝑍Net section modulus of stiffener, in cm3, including effective width of plating according
to [2.3.5], to be taken as:- The section modulus calculated at the top of stiffener flange for stiffener induced
failure (SI).
- The section modulus calculated at the attached plating for plate induced failure (PI).
Bending moment, in Nmm, due to eccentricity of sniped stiffeners, to be taken as- 𝑀𝑀2 = 0 for continuous stiffeners- 𝑀𝑀2 = 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑤𝑤𝑛𝑛𝑛𝑛 𝛾𝛾𝛾𝛾𝑥𝑥 (𝐴𝐴𝑝𝑝 + 𝐴𝐴𝑠𝑠 ) for stiffeners sniped at one or both ends.

𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 Coefficient to account for the end effect of the stiffener sniped at one or both ends, tobe taken as- 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = −1.2 for stiffener induced failure (SI)- 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1.2 for plate induced failure (PI).

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M1

Bending moment, in Nmm, due to the lateral load P:|𝑃𝑃|𝑠𝑠𝑙𝑙 2- 𝑀𝑀1 = 𝐶𝐶𝑖𝑖 24×103(cont)- 𝑀𝑀1 = 𝐶𝐶𝑖𝑖𝑃𝑃

𝐶𝐶𝑖𝑖
𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶𝑆𝑆𝑆𝑆- 𝑀𝑀1 = 𝐶𝐶𝑖𝑖 14.2×103

for sniped stiffener
for stiffener sniped at one end and continuous at the other end

Lateral load, in kN/m2.
- For FE analysis, 𝑃𝑃 is the average pressure as defined in Sec 4, [2.5.2] in theattached plating.
- For prescriptive assessment, 𝑃𝑃 is the pressure calculated at load calculation point of
the stiffener, as defined in Sec 3, [1.2.1].
Pressure coefficient:- 𝐶𝐶𝑖𝑖 = 𝐶𝐶𝑆𝑆𝑆𝑆 for stiffener induced failure (SI).
- 𝐶𝐶𝑖𝑖 = 𝐶𝐶𝑃𝑃𝑃𝑃 for plate induced failure (PI).
Plate induced failure pressure coefficient:
𝐶𝐶𝑃𝑃𝑃𝑃 = 1

if the lateral pressure is applied on the side opposite to the stiffener.

𝐶𝐶𝑃𝑃𝑃𝑃 = −1 if the lateral pressure is applied on the same side as the stiffener.

Stiffener induced failure pressure coefficient:

𝐶𝐶𝑆𝑆𝑆𝑆 = −1 if the lateral pressure is applied on the side opposite to the stiffener.
𝐶𝐶𝑆𝑆𝑆𝑆 = 1

𝑀𝑀0|𝑃𝑃|𝑠𝑠𝑙𝑙 2

8×103|𝑃𝑃|𝑠𝑠𝑙𝑙 2

for continuous stiffener

if the lateral pressure is applied on the same side as the stiffener.

Bending moment, in Nmm, due to the lateral deformation w of stiffener:𝛾𝛾
𝑤𝑤 with precondition 𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 − 𝛾𝛾 > 0
𝑀𝑀0 = 𝐹𝐹𝐸𝐸 𝐶𝐶𝑠𝑠𝑠𝑠𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 − 𝛾𝛾 0

𝛾𝛾𝐺𝐺𝐺𝐺𝐺𝐺 Stress multiplier factor of global elastic buckling capacity as defined in [2.1].
𝐹𝐹𝐸𝐸
𝐼𝐼

𝑡𝑡𝑝𝑝
𝐶𝐶𝑠𝑠𝑠𝑠

Ideal elastic buckling force of the stiffener, in N.
𝜋𝜋 2
𝐹𝐹𝐸𝐸 = � � 𝐸𝐸𝐸𝐸 ⋅ 104𝑙𝑙

Moment of inertia, in cm4, of the stiffener including effective width of attached plating
according to [2.3.5]. 𝐼𝐼 is to comply with the following requirement:
𝑠𝑠𝑡𝑡𝑝𝑝3𝐼𝐼 ≥12 ⋅ 104
Net thickness of plate, in mm, to be taken as- For prescriptive requirements: the mean thickness of the two attached plating
panels,- For FE analysis: the thickness of the considered EPP on one side of the stiffener.
Deformation reduction factor to account for global slenderness, to be taken as:
1- 𝐶𝐶𝑠𝑠𝑠𝑠 = 1 − 𝜆𝜆4𝐺𝐺
for 𝜆𝜆𝐺𝐺 ≤ 1.56
12
4
- 𝐶𝐶𝑠𝑠𝑠𝑠 = 3 /𝜆𝜆𝐺𝐺
for 𝜆𝜆𝐺𝐺 > 1.56
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(cont)𝜆𝜆𝐺𝐺

The reference degree of global slenderness of the stiffened panel, to be taken as𝛾𝛾𝜆𝜆𝐺𝐺 = �𝛾𝛾𝑅𝑅𝑅𝑅𝑅𝑅 with 𝛾𝛾𝑅𝑅𝑅𝑅𝑅𝑅 =𝐺𝐺𝐺𝐺𝐺𝐺Min (𝑅𝑅𝑒𝑒𝑒𝑒_𝑃𝑃 , 𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆 )2 +𝜎𝜎 2 −𝜎𝜎2�𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎
𝑥𝑥,𝑎𝑎𝑎𝑎 𝜎𝜎𝑦𝑦 +3𝜏𝜏𝑦𝑦

𝜎𝜎𝑥𝑥,𝑎𝑎𝑎𝑎 Average stress for both plate and stiffener as defined in [2.1.2].
𝜎𝜎𝑦𝑦

Applied transverse stress to the plate panel as defined in [2.1.1].

𝑤𝑤0

Assumed imperfection, in mm, to be taken as:
𝑤𝑤0 = 𝑙𝑙 /1000.

𝜏𝜏

𝜎𝜎𝑤𝑤

Applied shear stress to the plate panel as defined in [2.1.1].

Stress due to torsional deformation, in N/mm2, to be taken as:- For stiffener induced failure (SI)- For 𝜎𝜎𝑎𝑎 > 0

𝜎𝜎𝑤𝑤 = 𝐸𝐸𝑦𝑦𝑤𝑤 𝑒𝑒𝑓𝑓 𝛷𝛷0 �- For 𝜎𝜎𝑎𝑎 ≤ 0

𝜎𝜎𝑤𝑤 = 0𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡 𝜋𝜋 21� �𝛾𝛾𝜎𝜎 − 1� with precondition 𝜎𝜎𝐸𝐸𝐸𝐸 − 𝛾𝛾𝛾𝛾𝑎𝑎 > 0
𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡
1 − 𝜎𝜎 𝑎𝑎
𝐸𝐸𝐸𝐸- For plate induced failure (PI)

𝑦𝑦𝑤𝑤

-

𝛷𝛷0
𝜎𝜎𝐸𝐸𝐸𝐸

𝜎𝜎𝑤𝑤 = 0

Distance, in mm, from centroid of stiffener cross section to the free edge of stiffener
flange, to be taken as:𝑡𝑡
𝑦𝑦𝑤𝑤 = 2𝑤𝑤
for flat bar
𝑦𝑦𝑤𝑤 = 𝑏𝑏𝑓𝑓 −2 +𝑡𝑡 𝑏𝑏 2
ℎ𝑤𝑤 𝑡𝑡𝑤𝑤
𝑓𝑓 𝑓𝑓

2𝐴𝐴𝑠𝑠

𝑦𝑦𝑤𝑤 = 𝑏𝑏𝑓𝑓−𝑜𝑜𝑜𝑜𝑜𝑜 + 0.5𝑡𝑡𝑤𝑤 −𝑦𝑦𝑤𝑤 =𝑏𝑏𝑓𝑓
2

for angle and bulb profiles

2 +𝑡𝑡 �𝑏𝑏 2 −2𝑏𝑏 𝑑𝑑 �
ℎ𝑤𝑤 𝑡𝑡𝑤𝑤
𝑓𝑓 𝑓𝑓
𝑓𝑓 𝑓𝑓

for T profile.

2𝐴𝐴𝑠𝑠

for L2 profile

Coefficient taken as:
𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝛷𝛷0 =10−4
𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡 ℎ𝑤𝑤: Reference stress for torsional buckling, in N/mm2, to be taken as:
𝐸𝐸 𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡 𝜋𝜋 21𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡 2
𝜎𝜎𝐸𝐸𝐸𝐸 = ��
� 𝐼𝐼𝜔𝜔 ∙ 102 +𝐼𝐼𝑇𝑇 + �� 𝜀𝜀 ∙ 10−4 �
𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡 𝜋𝜋2(1 + 𝜈𝜈)𝐼𝐼𝑝𝑝𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡

𝐼𝐼𝑝𝑝

Net polar moment of inertia of the stiffener, in cm4, about point C as shown in Sec 1,
Figure 3, as defined in Table 5.

𝐼𝐼𝑇𝑇

Net St. Venant’s moment of inertia of the stiffener, in cm4, as defined in Table 5.

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𝐼𝐼𝜔𝜔𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡

Net sectorial moment of inertia of the stiffener, in cm6, about point C as shown in
Sec 1, Figure 3, as defined in Table 5.
Stiffener span, distance equal to spacing between primary supporting members, i.e.
𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑙𝑙. When the stiffener is supported by tripping brackets, 𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡 should be taken as the
maximum spacing between the adjacent primary supporting members and fitted tripping
brackets.

𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡 Number of half waves, taken as a positive integer so as to give smallest reference
stress for torsional buckling.
Degree of fixation, in mm2, to be taken as:

𝜀𝜀

3𝑏𝑏

2ℎ

- 𝜀𝜀 = � 𝑡𝑡 3 + 𝑡𝑡 3𝑤𝑤�
𝑝𝑝
𝑡𝑡𝑝𝑝3

𝐴𝐴𝑤𝑤

𝐴𝐴𝑓𝑓

𝐼𝐼𝑝𝑝
𝐼𝐼𝑇𝑇
𝐼𝐼𝜔𝜔

- 𝜀𝜀 = �3b�𝑤𝑤

−1

for bulb, angle, L2 and T profiles;
for flat bars.

: Net web area, in mm2.

: Net flange area, in mm2.
Table 5: Moments of inertia
Flat bars
3
ℎ𝑤𝑤
𝑡𝑡𝑤𝑤
3 ⋅ 104

(1)

3
𝑡𝑡𝑤𝑤
ℎ𝑤𝑤 𝑡𝑡𝑤𝑤
�1 − 0.63 �4
3 ⋅ 10ℎ𝑤𝑤

Bulb, angle, L2 and T profiles
𝐴𝐴𝑤𝑤 (𝑒𝑒𝑓𝑓 − 0.5𝑡𝑡𝑓𝑓 )2+ 𝐴𝐴𝑓𝑓 𝑒𝑒𝑓𝑓2 � 10−4�33𝑏𝑏𝑓𝑓 𝑡𝑡𝑓𝑓3(𝑒𝑒𝑓𝑓 − 0.5𝑡𝑡𝑓𝑓 )𝑡𝑡𝑤𝑤
𝑡𝑡𝑓𝑓
𝑡𝑡𝑤𝑤
−
0.63
+
�1
�
�1 − 0.63 �
44
3 ⋅ 10𝑒𝑒𝑓𝑓 − 0.5𝑡𝑡𝑓𝑓
3 ⋅ 10𝑏𝑏𝑓𝑓(2)

For bulb, angle and L2 profiles :2

𝐴𝐴𝑓𝑓3 + 𝐴𝐴3𝑤𝑤
3 3
ℎ𝑤𝑤
𝑡𝑡𝑤𝑤
36 ⋅ 1062
𝑒𝑒𝑓𝑓2 𝐴𝐴𝑓𝑓 𝑏𝑏𝑓𝑓2 + 𝐴𝐴𝑤𝑤 𝑡𝑡𝑤𝑤
�𝐴𝐴𝑓𝑓 �𝑏𝑏𝑓𝑓 − 2𝑑𝑑𝑓𝑓 � + 𝐴𝐴𝑤𝑤 𝑡𝑡𝑤𝑤 �
+
�
−
6
6
36 ∙ 1010
3
4�𝐴𝐴𝑓𝑓 + 𝐴𝐴𝑤𝑤 �

For T profile:− 𝐴𝐴𝑓𝑓 𝑑𝑑𝑓𝑓 �𝑏𝑏𝑓𝑓 − 𝑑𝑑𝑓𝑓 ��𝑏𝑏𝑓𝑓3 𝑡𝑡𝑓𝑓 𝑒𝑒𝑓𝑓2
12 ⋅ 106(1) 𝑡𝑡𝑤𝑤 is the net web thickness, in mm.
𝑡𝑡𝑤𝑤_𝑟𝑟𝑟𝑟𝑟𝑟 as defined in [2.3.2] is not to be used in this table.
(2) df is to be taken as 0 for bulb and angle profiles.

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2.3.5 Effective width of attached plating
The effective width of attached plating of stiffeners, 𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 , in mm, is to be taken as:- For 𝜎𝜎𝑥𝑥 > 0:

- For FE analysis,
𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑀𝑀𝑀𝑀𝑀𝑀(𝐶𝐶𝑥𝑥 𝑏𝑏, 𝜒𝜒𝑠𝑠 𝑠𝑠)- For prescriptive assessment,𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑀𝑀𝑀𝑀𝑀𝑀 �- For 𝜎𝜎𝑥𝑥 ≤ 0:
where:
χs𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 = 𝜒𝜒𝑠𝑠 𝑠𝑠: Effective width coefficient to be taken as:𝜒𝜒𝑠𝑠 =

 eff

𝐶𝐶𝑥𝑥1 𝑏𝑏1 + 𝐶𝐶𝑥𝑥2 𝑏𝑏2, 𝜒𝜒𝑠𝑠 𝑠𝑠�
2ℓ𝑒𝑒𝑒𝑒𝑒𝑒1.12≤ 1.0 for
≥1
1.75
𝑠𝑠
1+
ℓ𝑒𝑒𝑒𝑒𝑒𝑒 1.6�𝑠𝑠 �𝜒𝜒𝑠𝑠 = 0.407ℓ𝑒𝑒𝑒𝑒𝑒𝑒for𝑠𝑠ℓ𝑒𝑒𝑒𝑒𝑒𝑒<1
𝑠𝑠: Effective length of the stiffener, in mm, taken as:ℓ𝑒𝑒𝑒𝑒𝑒𝑒 =𝑙𝑙√3for stiffener fixed at both ends.

ℓ𝑒𝑒𝑒𝑒𝑒𝑒 = 0.75𝑙𝑙 for stiffener simply supported at one end and fixed at the other.

ℓ𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑙𝑙

for stiffener simply supported at both ends.

2.3.6 FE corrected stresses for stiffener capacity

When the reference stresses σ x and σ y obtained by FE analysis according to Sec 4, [2.4]are both compressive, σ x is to be corrected according to the following formulae:- If 𝜎𝜎𝑥𝑥 < 𝜈𝜈𝜎𝜎𝑦𝑦
𝜎𝜎𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 = 0- If 𝜎𝜎𝑥𝑥 ≥ 𝜈𝜈𝜎𝜎𝑦𝑦
𝜎𝜎𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 = 𝜎𝜎𝑥𝑥 − 𝜈𝜈𝜎𝜎𝑦𝑦

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2.4

Primary Supporting Members

2.4.1 Web plate in way of openings
The web plate of primary supporting members with openings is to be assessed for bucklingbased on the combined axial compressive and shear stresses.
The web plate adjacent to the opening on both sides is to be considered as individual
unstiffened plate panels as shown in Table 6.
The interaction formulae of [2.2.1] are to be used with:
𝜎𝜎𝑥𝑥 = 𝜎𝜎𝑎𝑎𝑎𝑎
𝜎𝜎𝑦𝑦 = 0𝜏𝜏 = 𝜏𝜏𝑎𝑎𝑎𝑎

where:
𝜎𝜎𝑎𝑎𝑎𝑎Weighted average compressive stress, in N/mm2, in the area of web plate being
considered, i.e. P1, P2, or P3 as shown in Table 6.

For the application of Table 6, the weighted average shear stress is to be taken as:- Opening modelled in primary supporting members:𝜏𝜏𝑎𝑎𝑎𝑎 Weighted average shear stress, in N/mm2, in the area of web plate being considered,i.e. P1, P2, or P3 as shown in Table 6.
- Opening not modelled in primary supporting members:𝜏𝜏𝑎𝑎𝑎𝑎 Weighted average shear stress, in N/mm2, given in Table 6.

2.4.2 Reduction factors of web plate in way of openings

The reduction factors, 𝐶𝐶𝑥𝑥 or 𝐶𝐶𝑦𝑦 in combination with, 𝐶𝐶𝜏𝜏 of the plate panel(s) of the web
adjacent to the opening is to be taken as shown in Table 6.
2.4.3 The equivalent plate panel of web plate of primary supporting members crossed byperpendicular stiffeners is to be idealised as shown in Figure 3.
Figure 3: Web plate idealization

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The correction of panel breadth is applicable also for other slot configurations provided thatthe web or collar plate is attached to at least one side of the passing stiffener.
Table 6: Reduction factors
Configuration(1)𝑪𝑪𝒙𝒙 , 𝑪𝑪𝒚𝒚(a) Without edge
reinforcements:(2)Separate
reduction
factors are to be
applied to areas
P1 and P2 usingcase 3 or case 6
in Table 3, withedge stressratio:
𝜓𝜓 = 1.0(b) With edge reinforcements:

Separate
reduction
factors are to be
applied forareas P1 andP2 using Cx forcase 1 or Cy forcase 2 in Table
3 with stressratio:
𝜓𝜓 = 1.0(c) Example of hole in web:

Openingmodelled in
PSM

𝑪𝑪𝝉𝝉

Opening
not modelled in
PSM
Separate
When case 17 of
reduction factors Table 3 isare to beapplicable:
applied to areas A common
P1 and P2 using reduction factor is tocase 18 or case be applied to areas
19 in Table 3.
P1 and P2 usingcase 17 in Table 3
with:𝜏𝜏𝑎𝑎𝑎𝑎 = 𝜏𝜏𝑎𝑎𝑎𝑎 (𝑤𝑤𝑤𝑤𝑤𝑤)
When case 17 ofTable 3 is notapplicable:
Separate reduction
factors are to be
applied to areas P1
and P2 using case18 or case 19 inTable 3 with:
Separate
reduction
factors are to be
applied forareas P1 andP2 using case
15 in Table 3.

𝜏𝜏𝑎𝑎𝑎𝑎 = 𝜏𝜏𝑎𝑎𝑎𝑎 (𝑤𝑤𝑤𝑤𝑤𝑤)ℎ/ (ℎ − ℎ0)

Separate reduction
factors are to be
applied to areas P1
and P2 using case
15 in Table 3 with:𝜏𝜏𝑎𝑎𝑎𝑎 = 𝜏𝜏𝑎𝑎𝑎𝑎 (𝑤𝑤𝑤𝑤𝑤𝑤)ℎ/ (ℎ − ℎ0)

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

Where:hHeight, in m, of the web of the primary supporting member in way of the opening.

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(cont)Height in m, of the opening measured in the depth of the web.

h0𝜏𝜏𝑎𝑎𝑎𝑎 (𝑤𝑤𝑤𝑤𝑤𝑤) Weighted average shear stress, in N/mm2, over the web height h of the primary
supporting member.
Note (1)

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

Note (2)For a PSM web panel with opening and without edge reinforcements as shown in
configuration (a), the applicable buckling assessment method depends on its
specific boundary conditions. If one of the long edges along the face plate oralong the attached plating is not subject to "inline support", i.e. the edge is free topull in, Method B should be applied. In other cases, typically such as when the
short plate edge is attached to the plate flanges, Method A is applicable.

2.5

Stiffened Panels with U-type Stiffeners

2.5.1 Local plate buckling
For stiffened panels with U-type stiffeners, local plate buckling is to be checked for each of
the plate panels EPP 𝑏𝑏1 , 𝑏𝑏2 , 𝑏𝑏𝑓𝑓 and ℎ𝑤𝑤 (see Sec 1, Figure 4) separately as follows:- The attached plate panels EPP 𝑏𝑏1 and 𝑏𝑏2 are to be assessed using SP-A model, wherein the calculation of buckling factors 𝐾𝐾𝑥𝑥 as defined in Case 1 of Table 3, the correction
factor 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 for U-type stiffeners as defined in Table 2 is to be used; and in thecalculation of 𝐾𝐾𝑦𝑦 as defined in Case 2 of Table 3, the 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 for U-type stiffeners as
defined in [2.2.5] is to be used.

- The face plate and web plate panels 𝑏𝑏𝑓𝑓 and ℎ𝑤𝑤 are to be assessed using UP-B modelwith 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1 and 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 1.

2.5.2 Overall stiffened panel buckling and stiffener buckling

For a stiffened panel with U-type stiffeners, the overall buckling capacity and ultimate
capacity of the stiffeners are to be checked with warping stress 𝜎𝜎𝑤𝑤 = 0, and with bending
moment of inertia including effective width of attached plating being calculated based on thefollowing assumptions:- The two web panels of a U-type stiffener are to be taken as perpendicular to theattached plate with thickness equal to 𝑡𝑡𝑤𝑤 and height equal to the distance between theattached plate and the face plate of the stiffener.

- Effective width of the attached plating, 𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 , taken as the sum of the 𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒 calculated for
the EPP 𝑏𝑏1 and 𝑏𝑏2 respectively according to SP-A model.

- Effective width of the attached plating of a stiffener without shear lag effect, 𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 , taken
as the sum of the 𝑏𝑏𝑒𝑒𝑒𝑒𝑒𝑒1 calculated for the EPP 𝑏𝑏1 and 𝑏𝑏2 respectively.

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3.

Buckling capacity of column structures

3.1

Column Buckling of Corrugations

3.1.1 Buckling utilisation factor
The column buckling utilisation factor, 𝜂𝜂, for axially compressed corrugations is to be taken as:𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =where:
𝜎𝜎𝑎𝑎𝑎𝑎𝜎𝜎𝑐𝑐𝑐𝑐𝜎𝜎𝑎𝑎𝑎𝑎𝜎𝜎𝑐𝑐𝑐𝑐Average axial compressive stress in the member, in N/mm2.
Minimum critical buckling stress, in N/mm2, taken as:- 𝜎𝜎𝑐𝑐𝑐𝑐 = 𝜎𝜎𝐸𝐸 for 𝜎𝜎𝐸𝐸 ≤ 0.5𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆
𝑅𝑅

𝜎𝜎𝐸𝐸

- 𝜎𝜎𝑐𝑐𝑐𝑐 = �1 − 𝑒𝑒𝑒𝑒_𝑆𝑆 � 𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆 for 𝜎𝜎𝐸𝐸 > 0.5𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆
4𝜎𝜎𝐸𝐸

Elastic column compressive buckling stress, in N/mm2, according to [3.1.2].

𝑅𝑅𝑒𝑒𝑒𝑒_𝑆𝑆 Specified minimum yield stress of the considered member, in N/mm2. For built-up
members, the lowest specified minimum yield stress is to be used.

3.1.2 Elastic column buckling stress
The elastic compressive column buckling stress, 𝜎𝜎𝐸𝐸 in N/mm2 of members subject to axial
compression is to be taken as:
𝜎𝜎𝐸𝐸 = 𝜋𝜋 2 𝐸𝐸𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒
where:
𝐼𝐼𝐴𝐴

𝑙𝑙𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝐼𝐼
−4
2 10
𝐴𝐴𝑙𝑙𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

Net moment of inertia about the weakest axis of the cross section, in cm4.
Net cross-sectional area of the member, in cm2.
Unsupported length of the member, in m.

𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 End constraint factor, corresponding to simply supported ends is to be applied except
for fixed end support to be used in way of stool with width exceeding 2 times the depthof the corrugation, taken as:- 𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 = 1.0 where both ends are simply supported.

- 𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 = 2.0 where one end is simply supported and the other end is fixed.

- 𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 = 4.0 where both ends are fixed.

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APPENDIX 1 STRESS BASED REFERENCE STRESSES
Symbols
Length, in mm, of the longer side of the plate panel as defined in Sec 5.

𝑎𝑎𝑏𝑏

Length, in mm, of the shorter side of the plate panel as defined in Sec 5.

𝐴𝐴𝑖𝑖

𝑛𝑛

Area, in mm2, of the 𝑖𝑖-th plate element of the buckling panel.

Number of plate elements in the buckling panel.

𝜎𝜎𝑥𝑥𝑥𝑥Actual stress, in N/mm2, at the centroid of the 𝑖𝑖-th plate element in 𝑥𝑥 direction,
applied along the shorter edge of the buckling panel.

𝜎𝜎𝑦𝑦𝑦𝑦Actual stress, in N/mm2, at the centroid of the 𝑖𝑖-th plate element in 𝑦𝑦 direction,
applied along the longer edge of the buckling panel.

𝜓𝜓Edge stress ratio as defined in Sec 5.

𝜏𝜏𝑖𝑖Actual membrane shear stress, in N/mm2, at the centroid of the 𝑖𝑖-th plate element of
the buckling panel.

1.1

Introduction

1.

Stress Based Method

1.1.1 This section provides a method to determine stress distribution along edges of theconsidered buckling panel by second-order polynomial curve, by linear distribution using leastsquare method and by weighted average approach. This method is called Stress based
Method. The reference stress is the stress components at centre of plate element transferred
into the local system of the considered buckling panel.
1.1.2 Definition: A regular panel is a plate panel of rectangular shape. An irregular panel isplate panel which is not regular, as detailed in Sec 4, [2.3.1].
1.2

Stress Application

1.2.1 Regular panel
The reference stresses are to be taken as defined in [2.1] for a regular panel when thefollowing conditions are satisfied:- At least, one plate element centre is located in each third part of the long edge a of aregular panel and- This element centre is located at a distance in the panel local 𝑥𝑥 direction not less than𝑎𝑎⁄4 to at least one of the element centres in the adjacent third part of the panel.

Otherwise, the reference stresses are to be taken as defined in [2.2] for an irregular panel.
1.2.2 Irregular panel and curved panel

The reference stresses of an irregular panel or of a curved panel are to be taken as defined in[2.2].
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2.

Reference Stresses

2.1

Regular Panel

2.1.1 Longitudinal stress
The longitudinal stress 𝜎𝜎𝑥𝑥 applied on the shorter edge of the buckling panel is to be
calculated as follows:- For plate buckling assessment, the distribution of σ x ( x) is assumed as second orderpolynomial curve as:𝜎𝜎𝑥𝑥 = 𝐶𝐶𝑥𝑥 2 + 𝐷𝐷𝐷𝐷 + 𝐸𝐸

The best fitting curve 𝜎𝜎𝑥𝑥 (𝑥𝑥) is to be obtained by minimising the square error Π
considering the area of each element as a weighting factor.
𝛱𝛱 = ∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 �𝜎𝜎𝑥𝑥𝑥𝑥 − (𝐶𝐶𝑥𝑥𝑖𝑖2 + 𝐷𝐷𝑥𝑥𝑖𝑖 + 𝐸𝐸)�2

The unknown coefficients C, D and E must yield zero first derivatives, 𝜕𝜕𝜕𝜕 withrespect to C, D and E, respectively.
𝑛𝑛⎧𝜕𝜕𝜕𝜕 = 2 � 𝐴𝐴 𝑥𝑥 2 �𝜎𝜎 − �𝐶𝐶𝑥𝑥 2 + 𝐷𝐷𝑥𝑥 + 𝐸𝐸�� = 0
𝑖𝑖 𝑖𝑖
𝑥𝑥𝑥𝑥
𝑖𝑖
𝑖𝑖
⎪ 𝜕𝜕𝜕𝜕
𝑖𝑖=1
⎪
𝑛𝑛
⎪
𝜕𝜕𝜕𝜕
= 2 � 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 �𝜎𝜎𝑥𝑥𝑥𝑥 − �𝐶𝐶𝑥𝑥𝑖𝑖2 + 𝐷𝐷𝑥𝑥𝑖𝑖 + 𝐸𝐸�� = 0⎨ 𝜕𝜕𝜕𝜕
𝑖𝑖=1𝑛𝑛⎪⎪ 𝜕𝜕𝜕𝜕
⎪= 2 � 𝐴𝐴𝑖𝑖 �𝜎𝜎𝑥𝑥𝑥𝑥 − �𝐶𝐶𝑥𝑥𝑖𝑖2 + 𝐷𝐷𝑥𝑥𝑖𝑖 + 𝐸𝐸�� = 0
𝜕𝜕𝜕𝜕
⎩
𝑖𝑖=1

The unknown coefficients C, D and E can be obtained by solving the 3 above equations.

𝜎𝜎𝑥𝑥1 =
𝜎𝜎𝑥𝑥2 =
If −

1 𝑏𝑏
𝑏𝑏 2
𝑏𝑏
� 𝜎𝜎𝑥𝑥 (𝑥𝑥)𝑑𝑑𝑑𝑑 = 𝐶𝐶 + 𝐷𝐷 + 𝐸𝐸
3
𝑏𝑏 0
2

𝑏𝑏
1 𝑎𝑎
𝑏𝑏 2
� 𝜎𝜎𝑥𝑥 (𝑥𝑥)𝑑𝑑𝑑𝑑 = �𝑎𝑎2 − 𝑎𝑎𝑎𝑎 + � 𝐶𝐶 + �𝑎𝑎 − � 𝐷𝐷 + 𝐸𝐸
2
3
𝑏𝑏 𝑎𝑎−𝑏𝑏

𝐷𝐷
𝑏𝑏
<
2𝐶𝐶
2

𝜎𝜎𝑥𝑥3 =

or −

𝐷𝐷
𝑏𝑏
> 𝑎𝑎 − , 𝜎𝜎𝑥𝑥3 is to be ignored. Otherwise, 𝜎𝜎𝑥𝑥3 is taken as:
2𝐶𝐶2

1 𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚
𝑏𝑏 2
𝐷𝐷 2
�
𝜎𝜎𝑥𝑥 (𝑥𝑥)𝑑𝑑𝑑𝑑 =
𝐶𝐶 −
+ 𝐸𝐸
12
4𝐶𝐶
𝑏𝑏 𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚

where:

𝑏𝑏 𝐷𝐷
𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚 = − −
2 2𝐶𝐶
𝑏𝑏 𝐷𝐷
𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚 = −2 2𝐶𝐶Page 49 of 51

IACS Req. 2023

S35

S35
(cont)The longitudinal stress is to be taken as:
𝜎𝜎𝑥𝑥 = 𝑀𝑀𝑀𝑀𝑀𝑀( 𝜎𝜎𝑥𝑥1 , 𝜎𝜎𝑥𝑥2 , 𝜎𝜎𝑥𝑥3 )The edge stress ratio is to be taken as:𝜓𝜓𝑥𝑥 = 1- For overall stiffened panel buckling and stiffener buckling assessments, the longitudinal
stress 𝜎𝜎𝑥𝑥 applied on the shorter edge of the attached plate is to be taken as:
𝜎𝜎𝑥𝑥 =∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜎𝜎𝑥𝑥𝑥𝑥∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖

The edge stress ratio 𝜓𝜓𝑥𝑥 for the stress 𝜎𝜎𝑥𝑥 is equal to 1.0.

2.1.2 Transverse stress

The transverse stress 𝜎𝜎𝑦𝑦 applied along the longer edges of the buckling panel is to be
calculated by extrapolation of the transverse stresses of all elements up to the shorter edgesof the considered buckling panel.
Figure 1: Buckling panel

The distribution of 𝜎𝜎𝑦𝑦 (𝑥𝑥) is assumed as straight line. Therefore: 𝜎𝜎𝑦𝑦 (𝑥𝑥) = 𝐴𝐴 + 𝐵𝐵𝐵𝐵

The best fitting curve 𝜎𝜎𝑦𝑦 (𝑥𝑥) is to be obtained by the least square method minimising thesquare error Π considering area of each element as a weighting factor.
2𝛱𝛱 = ∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 �𝜎𝜎𝑦𝑦𝑦𝑦 − (𝐴𝐴 + 𝐵𝐵𝑥𝑥𝑖𝑖 )�

The unknown coefficients C and D must yield zero first partial derivatives, 𝜕𝜕𝜕𝜕 withrespect to C and D, respectively.
𝑛𝑛𝜕𝜕𝜕𝜕
= 2 � 𝐴𝐴𝑖𝑖 �𝜎𝜎𝑦𝑦𝑦𝑦 − (𝐴𝐴 + 𝐵𝐵𝑥𝑥𝑖𝑖 )� = 0
𝜕𝜕𝜕𝜕
𝑖𝑖=1
𝑛𝑛

𝜕𝜕𝜕𝜕
= 2 � 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 �𝜎𝜎𝑦𝑦𝑦𝑦 − (𝐴𝐴 + 𝐵𝐵𝑥𝑥𝑖𝑖 )� = 0
𝜕𝜕𝜕𝜕
𝑖𝑖=1

The unknown coefficients A and B are obtained by solving the 2 above equations and are
given as follow:
�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜎𝜎𝑦𝑦𝑦𝑦 ��∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖2 � − (∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 )�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 𝜎𝜎𝑦𝑦𝑦𝑦 �𝐴𝐴 =2�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 ��∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖2 � − �∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 �Page 50 of 51

IACS Req. 2023

S35

S35
(cont)

𝐵𝐵 =(∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 )�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 𝜎𝜎𝑦𝑦𝑦𝑦 � − (∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 )�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜎𝜎𝑦𝑦𝑦𝑦 �2�∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 ��∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖2 � − �∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝑥𝑥𝑖𝑖 �

The transverse stress is to be taken as:
𝜎𝜎𝑦𝑦 = 𝑚𝑚𝑚𝑚𝑚𝑚( 𝐴𝐴, 𝐴𝐴 + 𝐵𝐵𝐵𝐵)

The edge stress ratio is to be taken as:𝜓𝜓𝑦𝑦 =

𝑚𝑚𝑚𝑚𝑚𝑚( 𝐴𝐴, 𝐴𝐴 + 𝐵𝐵𝐵𝐵)
for 𝜎𝜎𝑦𝑦 > 0
𝑚𝑚𝑚𝑚𝑚𝑚( 𝐴𝐴, 𝐴𝐴 + 𝐵𝐵𝐵𝐵)𝜓𝜓𝑦𝑦 = 1 𝑓𝑓𝑓𝑓𝑓𝑓 𝜎𝜎𝑦𝑦 ≤ 0.

2.1.3 Shear stress

The shear stress 𝜏𝜏 is to be calculated using a weighted average approach, and is to be taken
as:∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜏𝜏𝑖𝑖𝜏𝜏 = 𝑛𝑛∑𝑖𝑖=1 𝐴𝐴𝑖𝑖
2.2

Irregular Panel and Curved Panel

2.2.1 Reference stresses
The longitudinal, transverse and shear stresses are to be calculated using a weighted
average approach. They are to be taken as:∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜎𝜎𝑥𝑥𝑥𝑥
𝜎𝜎𝑥𝑥 =∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖
𝜎𝜎𝑦𝑦 =∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜎𝜎𝑦𝑦𝑦𝑦∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖

∑𝑛𝑛𝑖𝑖=1 𝐴𝐴𝑖𝑖 𝜏𝜏𝑖𝑖𝜏𝜏 = 𝑛𝑛∑𝑖𝑖=1 𝐴𝐴𝑖𝑖

The edge stress ratios are to be taken as𝜓𝜓𝑥𝑥 = 1𝜓𝜓𝑦𝑦 = 1
End ofDocument

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IACS Req. 2023