2 Stiffened and Unstiffened Panels

2.1 General

2.1.1 The plate panel of hull structure is to be modelled as stiffened or unstiffened panel. Method A and Method B as defined in Ch 8, Sec 1, [3] are to be used according to Table 1 and Figure 1 to Figure 9.

2.1.2 Average thickness of plate panel

Where the plate thickness along a plate panel is not constant, the panel used for the buckling assessment is to be modelled according to Ch 7 with a weighted average thickness taken as:

where:

A_i : Area of the i-th plate element.

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

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

Table 1 : Structural members

Structural elements	Assessment method	Normal panel definition
Longitudinal structure, see Figure 1, Figure 5 and Figure 7
Longitudinally stiffened panels Shell envelope Deck Inner hull Hopper tank side Longitudinal bulkheads	SP-A	Length: between web frames Width: between primary supporting members
Double bottom longitudinal girders in line with longitudinal bulkhead or connected to hopper tank side	SP-A	Length: between web frames Width: full web depth
Web of double bottom longitudinal girders not in line with longitudinal bulkhead or not connected to hopper tank side	SP-B	Length: between web frames Width: full web depth
Web of horizontal girders in double side space connected to hopper tank side	SP-A	Length: between web frames Width: full web depth
Web of horizontal girders in double side space not connected to hopper tank side	SP-B	Length: between web frames Width: full web depth
Web of single skin longitudinal girders or stringers	UP-B	Plate between local stiffeners/face plate/PSM
Transverse structure, see Figure 2, Figure 6 and Figure 8
Web of transverse deck frames including brackets	UP-B	Plate between local stiffeners/face plate/PSM
Verticalweb in double side space	SP-B	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	Plate between local stiffeners/face plate/PSM
Double bottom floors	SP-B	Length: full web depth Width: between primary supporting members
Vertical web frame including brackets	UP-B	Plate between vertical web stiffeners/face plate/PSM
Cross tie web plate	UP-B	Plate between vertical web stiffeners/face plate/PSM
Transverse oil-tight and watertight bulkheads, see Figure 3 and transverse wash bulkheads, see Figure 4
Regularly stiffened bulkhead panels inclusive the secondary buckling stiffeners perpendicular to the regular stiffener (such as carlings)	SP-A	Length: between primary supporting members Width: between primary supporting members
Irregularly stiffened bulkhead panels,e.g. web panels in way of hopper tank and bilge	UP-B	Plate between local stiffeners/face plate
Web plate of bulkhead stringers including brackets	UP-B	Plate between web stiffeners /face plate
Transverse corrugated bulkheads and cross deck, see Figure 9
Upper/lower stool including stiffeners	SP-A	Length: between internal web diaphragms Width: length of stool side
Stool internal web diaphragm	UP-B	Plate between local stiffeners /face plate / PSM
Cross deck	SP-A	Plate between local stiffeners/ PSM
Note 1: SP and UP stand for stiffened and unstiffened panel respectively. Note 2: A and B stand for Method A and Method B respectively.

2.1.3 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.

2.2 Stiffened panels

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

2.2.2 If the stiffener properties or stiffener spacing varies within the stiffened panel, the calculations 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 stiffener spacing at the considered location are to be assumed for the whole panel.

Figure 1 : Longitudinal plates for oil tankers

Figure 2 : Transverse web frames for oil tankers

Figure 3 : Transverse bulkhead for oil tankers

Figure 4 : Cross tie

Figure 5 : Longitudinal plates for single hull bulk carrier

Figure 6 : Transverse web frames for single hull bulk carrier

Figure 7 : Longitudinal plates for double hull bulk carrier

Figure 8 : Transverse web frames for double hull bulk carrier

Figure 9 : Corrugated bulkhead and cross deck for bulk carriers

2.3 Unstiffened panels

2.3.1 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 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 Modelling 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.
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 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, is to be taken as:
b = A ⁄ a
where:
A : Area of the plate, in mm²
a : length defined in (d), in mm
f) 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 in mm, defines the longitudinal direction for the capacity model.
c) The width of the model, , in mm, is to be taken as:
where:
A : Area of the plate, in mm²
d) The lengths of shorter side, b, and of the longer side, a, in mm, of the equivalent rectangular plate panel are to be taken as:
where:
e) 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 Reference stress

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

2.4.2 The reference stresses are to be calculated using the Stress based reference stresses as defined in App 1.

2.5 Lateral pressure

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

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

where:

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

P_i : Lateral pressure of the i-th plate element, in N/mm².

n : Number of finite elements in the buckling panel.

2.6 Buckling criteria

2.6.1 UP-A

The compressive buckling strength of UP-A is to satisfy the following criterion:

η_UP-A ≤ η_all

where:

η_UP-A : Maximum plate utilisation factor, calculated according to Method A as defined in Ch 8, Sec 5, [2.2].

2.6.2 UP-B

The compressive buckling strength of UP-B is to satisfy the following criterion:

η_UP-B ≤ η_all

where:

η_UP-B : Maximum plate utilisation factor, calculated according to Method B as defined in Ch 8, Sec 5, [2.2].

2.6.3 SP-A

The compressive buckling strength of SP-A is to satisfy the following criterion:

η_SP-A ≤ η_all

where:

η_SP-A : Maximum stiffened panel utilisation factor taken as the maximum of:

The overall stiffened panel capacity as defined in Ch 8, Sec 5, [2.1].
The plate capacity calculated according to Method A as defined in Ch 8, Sec 5, [2.2].
The stiffener buckling strength as defined in Ch 8, 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 the stiffener.

Note 1: The stiffener buckling capacity check can only be fulfilled when the overall stiffened panel capacity, as defined in Ch 8, Sec 5, [2.1], is satisfied.

2.6.4 SP-B

The compressive buckling strength of SP-B is to satisfy the following criterion:

η_SP-B ≤η_all

where:

η_SP-B : Maximum stiffened panel utilisation factor taken as the maximum of:

The overall stiffened panel capacity as defined in Ch 8, Sec 5, [2.1].
The plate capacity calculated according to Method B as defined in Ch 8, Sec 5, [2.2].
The stiffener buckling strength as defined in Ch 8, 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 the stiffener.

Note 1: The stiffener buckling capacity check can only be fulfilled when the overall stiffened panel capacity, as defined in Ch 8, 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:

η_opening ≤ η_all

where:

η_opening : Maximum web plate utilisation factor in way of openings, as defined in Ch 8, Sec 5, [2.4].