Section 6 Combination of loads

6.1 Symbols

6.1.1 For the purposes of this Section, the following symbols apply:

= design vertical bending moment, in kNm
= permissible hull girder hogging and sagging still water bending moment envelopes for inspection/maintenance condition, in kNm, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder hogging and sagging still water bending moment envelopes for transit condition, in kNm, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder hogging and sagging still water bending moment envelopes for operational condition, in kNm, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder hogging and sagging still water bending moment envelopes for flooded condition, in kNm, see Table 2.6.1 Design load combinations
= vertical wave bending moment for a considered dynamic load case, in kNm, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.2.(a)
= design horizontal bending moment, in kNm
= horizontal wave bending moment for a considered dynamic load case, in kNm, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.2.(a)
= hogging vertical wave bending moment, in kNm, see Pt 10, Ch 2, 3.7 Dynamic hull girder loads 3.7.1.(a)
= sagging vertical wave bending moment, in kNm, see Pt 10, Ch 2, 3.7 Dynamic hull girder loads 3.7.1.(a)
= horizontal wave bending moment, in kNm, see Pt 10, Ch 2, 3.7 Dynamic hull girder loads 3.7.1.(a)
Q = design vertical shear force, in kN
= permissible hull girder positive and negative still water shear force limits for inspection/maintenance condition, in kN, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder positive and negative still water shear force limits for transit condition, in kN, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder positive and negative still water shear force limits for operational condition, in kN, see Pt 10, Ch 2, 2.1 Symbols and Table 2.6.1 Design load combinations
= permissible hull girder positive and negative still water shear force envelopes for flood condition, in kN, see Table 2.6.1 Design load combinations
= vertical wave shear force for a considered dynamic load case, in kN, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.2.(a)
= envelope positive vertical wave shear force, in kN, as defined in Pt 10, Ch 2, 3.7 Dynamic hull girder loads 3.7.2.(a)
= envelope negative vertical wave shear force, in kN, as defined in Pt 10, Ch 2, 3.7 Dynamic hull girder loads 3.7.2.(a)
= dynamic load combination factor for vertical wave bending moment for considered dynamic load case, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.2.(a)
= dynamic load combination factor for vertical wave shear force for considered dynamic load case, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.3.(a)
fβ = heading correction factor, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.1.(b)
= design sea pressure, in kN/m²

Table 2.6.1 Design load combinations

Global hull girder loads
Load component		Operation on-site		Inspection/maintenance		Transit		Flooded
Load component		S	S+D	S	S+D	S	S+D	S	S+D
		M_sw-perm-oper	M_sw-perm-oper+ M_wv	M_{sw-perm-maint}	M_{sw-perm-maint} + M_wv	M_sw-perm-sea	M_sw-perm-sea + M_wv	M_{sw-perm-flood}	M_{sw-perm-flood} + M_wv
		—	M_h	—	M_h	—	M_h	—	M_h
Q		Q_sw-perm-oper	Q_sw-perm-oper+ Q_wv	Q_{sw-perm-maint}	Q_{sw-perm-maint} + Q_wv	Q_sw-perm-sea	Q_sw-perm-sea + Q_wv	Q_{sw-perm-flood}	Q_{sw-perm-flood} + Q_wv
Local loads
Load component	Space type	Operation on-site		Inspection/maintenance		Transit		Flooded
Load component	Space type	S	S+D	S	S+D	S	S+D	S	S+D
External sea pressure	Exposed deck
External sea pressure	Hull envelope
Liquid pressure	Ballast tanks
	Cargo tanks/other tanks designed for liquid filling
	Fresh water and fuel/lube oil tanks
	Water tight boundaries/ void spaces
	Dry space
Deck loads	Dry space
NOTES
1. All the dynamic wave loads are to be adjusted by the factor. The value of is dependent on the operational condition, see Pt 10, Ch 2, 3.4 Return periods and probability factor, fprob.
2. The pressure in cargo tanks, and other tanks designed for liquid filling, that are stated in the unit’s Operations Manual as not to be loaded during transit may be taken as zero for the transit assessment.

= static sea pressure at considered draught, in kN/m², as defined in Pt 10, Ch 2, 2.3 Local static loads 2.3.2.(a)
= dynamic wave pressure for a considered dynamic load case, in kN/m², as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= green sea load for a considered dynamic load case, in kN/m², as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.5.(a)
= design tank pressure, in kN/m²
= tank testing pressure, in kN/m², as defined in Table 2.2.1 Static load pressures
= static tank pressure in the case of overfilling, in kN/m², as defined in Table 2.2.1 Static load pressures
= added overpressure due to liquid flow through air pipe or overflow pipe, in kN/m², as defined in Table 2.2.1 Static load pressures and Table 2.6.1 Design load combinations
= setting of pressure relief valve, in kN/m², as defined in Table 2.2.1 Static load pressures
= static tank pressure, in kN/m², as defined in Table 2.2.1 Static load pressures
= dynamic tank pressure for a considered dynamic load case, in kN/m², as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.6.(a)
= pressure in compartments and tanks in flooded or damaged condition, in kN/m², as defined in Table 2.2.1 Static load pressures
= static pressure on decks and inner bottom, in kN/m², as defined in Table 2.2.1 Static load pressures
= design deck pressure, in kN/m², as defined in Pt 10, Ch 2, 2.3 Local static loads 2.3.3
= envelope dynamic deck pressure on decks, inner bottom and hatch cover, in kN/m², as defined in Pt 10, Ch 2, 3.8 Dynamic local loads 3.8.5.(a)
= dynamic deck pressure on decks, inner bottom and hatch covers for a considered dynamic load case, in kN/m², as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.7.(a)
= dynamic wave pressure at bottom centreline, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.7.(a)
= kN/m²
= dynamic wave pressure at z = 0 and y = , as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.7.(a)
= kN/m²
= dynamic wave pressure at waterline, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.7.(a)
= kN/m²
= envelope maximum dynamic wave pressure, in kN/m², as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= pressure at still waterline for considered draught, in kN/m², see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= pressure at still waterline for considered draught, in kN/m², see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= load acting on supporting structures and securing systems for heavy units of cargo, equipment or structural components, in kN, as defined in Pt 10, Ch 2, 2.3 Local static loads 2.3.2.(a)
= dynamic load acting on supporting structures and securing systems for heavy units of cargo, equipment or structural components, in kN, as defined in Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.7.(b)
= envelope vertical dynamic load from heavy units, in kN, see Pt 10, Ch 2, 3.8 Dynamic local loads 3.8.6
= dynamic load combination factor for dynamic wave pressure, , at still waterline for considered dynamic load case, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= dynamic load combination factor for dynamic wave pressure, , at bilge for considered dynamic load case, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= dynamic load combination factor for dynamic wave pressure, , at centreline for considered dynamic load case, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= 0,8 + see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.5.(a)
= 0,5 + see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.5.(a)
= 1,0 at and forward of 0,2L from AE
= 0,8 at and aft of AE
intermediate values to be obtained by linear interpolation, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.5.(a)
= dynamic load combination factor for vertical acceleration for considered dynamic load case. is to be taken as appropriate to the tank location, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.6.(a)
= dynamic load combination factor for vertical acceleration for considered dynamic load case, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.6.(a)
= dynamic load combination factor for transverse acceleration for considered dynamic load case, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.6.(a)
= dynamic load combination factor for longitudinal acceleration for considered dynamic load case. is to be taken as most appropriate dependent on tank location, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.6.(a)
= distance from the deck to the still waterline at the applicable draught for the loading condition being considered, in metres, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.5.(a)
L = Rule length, in metres
= local breadth at the weather deck, in metres, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= local breadth at waterline for considered draught, in metres, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
= draught in the loading condition being considered, in metres, see Pt 10, Ch 2, 6.3 Application of dynamic loads 6.3.4.(a)
x = longitudinal coordinate, in metres
y = transverse coordinate, in metres
z = vertical coordinate, in metres
= longitudinal coordinate of reference point, in metres
= transverse coordinate of reference point, in metres
= vertical coordinate of reference point, in metres
= density of sea-water, 1,025 tonnes/m³
g = acceleration due to gravity, 9,81m/s².

6.2 General

6.2.1 Application.

The design load combinations given in Table 2.6.1 Design load combinations corresponding to the applicable static load scenarios given in Pt 10, Ch 2, 2.3 Local static loads are to be used as the basis for the scantling requirements and strength assessment (by FEM).
For each dynamic load case, the envelope load values as given in Pt 10, Ch 2, 3 Dynamic load components are multiplied with dynamic load combination factors to give simultaneously acting dynamic loads.
The procedures for calculating the simultaneously acting dynamic loads are given in Pt 10, Ch 2, 6.3 Application of dynamic loads. The dynamic loads for unrestricted worldwide transit are given in Pt 10, Ch 2, 7 Environmental loads for unrestricted worldwide transit condition. The dynamic loads for the site-specific load scenarios are given in Pt 10, Ch 2, 8 Environmental loads for site-specific load scenarios.

6.3 Application of dynamic loads

6.3.1 Dynamic load combination factors.

For scantling assessment, the dynamic load combination factors used for the calculations of the simultaneously acting dynamic loads are to be taken as given in:
- Pt 10, Ch 2, 7 Environmental loads for unrestricted worldwide transit condition for unrestricted worldwide transit;
- Pt 10, Ch 2, 7 Environmental loads for unrestricted worldwide transit condition for site-specific load scenarios.
For strength assessment by FEM, the dynamic load combination factors are to be taken as given in:
- Pt 10, Ch 2, 7 Environmental loads for unrestricted worldwide transit condition for unrestricted worldwide transit;
- Pt 10, Ch 2, 7 Environmental loads for unrestricted worldwide transit condition for site-specific load scenarios
The heading correction factor, , is to be taken as follows:
- For transit conditions using the worldwide environment, as defined in Table 2.3.3 Return periods for scantling requirements and strength assessment:
= 0,8 for beam sea dynamic load cases

= 1,0 for all other dynamic load cases
- For all other operational conditions, as defined in Table 2.3.3 Return periods for scantling requirements and strength assessment:
= 1,0 for beam sea dynamic load cases.

6.3.2 Vertical and Horizontal wave bending moment for a considered dynamic load case.

The simultaneously acting vertical wave bending moment, and horizontal wave bending moment, , are to be taken as:
- Vertical wave bending moment:
  = kNm for ≥ 0
  
  = — kNm for ≥ 0
- Horizontal wave bending moment:
= kNm

6.3.3 Vertical wave shear force for a considered dynamic load case.

The simultaneously acting vertical wave shear force, , is to be taken as:
= kNm for ≥ 0

= kNm for < 0.

6.3.4 Dynamic wave pressure distribution for a considered dynamic load case.

The simultaneously acting dynamic wave pressure, , is to be taken as follows, but not to be less than – g () below still waterline or less than 0 above still waterline:
- For the port and starboard side within the region with a defined bilge:
  =
  
  between centreline and start of bilge
  
  =
  
  between end of bilge and still waterline
  
  =
  
  for side shell above still waterline intermediate values of around the bilge are to be obtained by linear interpolation along the vertical distance.
- For the port and starboard side within the region without a defined bilge:
  =
  
  between bottom centreline and still waterline
  
  =
  
  above still waterline
  
  where
  
  = dynamic wave pressure at bottom centreline, to be taken as:
  
  = kN/m²
  
  = dynamic wave pressure at z = 0 and y = , to be taken as:
  
  = kN/m²
  
  = dynamic wave pressure at waterline, to be taken as:
  
  = kN/m²
Figure 2.6.1 Dynamic wave pressure for head sea dynamic load cases to Figure 2.6.3 Pressure distribution for wave crest and wave trough for forward and aft illustrate simultaneously acting dynamic wave pressures.

6.3.5 Green sea load of a considered dynamic load case.

The simultaneously acting green sea load on the weather deck,

is shown in Table 2.6.2 Green sea load.

Figure 2.6.1 Dynamic wave pressure for head sea dynamic load cases

Figure 2.6.2 Dynamic wave pressure for beam sea dynamic load cases

Figure 2.6.3 Pressure distribution for wave crest and wave trough for forward and aft

Table 2.6.2 Green sea load

Inclined green sea load, see Note

= max.

kN/m²

Uniformly distributed

= max.

kN/m²

NOTE

Inclined green sea load is obtained by linear interpolation between port side and starboard side, with load decreasing from port side to starboard side, with the maximum value at vessel side given by the formula and the minimum value at the opposite side taken as 34,3 kN/m². The assessment is then to be repeated, with loading decreasing from starboard side to port side.

6.3.6 Dynamic tank pressure for a considered dynamic load case.

The simultaneously acting dynamic tank pressure, , is to be taken as:
- For tanks in the cargo region:
  = kN/m²
- For tanks outside the cargo region:
  = kN/m²
where
= envelope dynamic tank pressure due to vertical acceleration, as defined in Pt 10, Ch 2, 3.8 Dynamic local loads 3.8.4.(a) with reference point taken as:
1. top of tank
2. top of air pipe/overflow for ballast tanks designed
  see Figure 2.6.4 Dynamic tank pressure in cargo tank (Left) and ballast tank (Right) due to positive and negative vertical tank acceleration, in kN/m²
= envelope dynamic tank pressure due to transverse acceleration, as defined in Pt 10, Ch 2, 3.8 Dynamic local loads 3.8.4.(b) with reference point taken as:
1. tank top towards port side for > 0
2. tank top towards starboard side for < 0
  see Figure 2.6.5 Dynamic tank pressure in cargo tank (Left) and ballast tank (Right) due to negative and positive transverse tank acceleration, in kN/m₂
= envelope dynamic tank pressure due to longitudinal acceleration, as defined in Pt 10, Ch 2, 3.8 Dynamic local loads 3.8.4.(c) with reference point taken as:
1. forward bulkhead for > 0
2. aft bulkhead of the tank for < 0,
  see Figure 2.6.6 Dynamic tank pressure in tanks due to positive and negative longitudinal acceleration, in kN/m²

NOTES

1. For a non-parallel tank, should be selected from either forward or aft bulkhead corresponding to the reference point . If the longitudinal load combination factor = 0, should be selected from the bulkhead with the greater breadth.

2. The vertical, transverse and longitudinal acceleration is to be taken at the centre of gravity of the tank under consideration.

Figure 2.6.4 Dynamic tank pressure in cargo tank (Left) and ballast tank (Right) due to positive and negative vertical tank acceleration

Figure 2.6.5 Dynamic tank pressure in cargo tank (Left) and ballast tank (Right) due to negative and positive transverse tank acceleration

6.3.7 Dynamic deck loads for a considered dynamic load case.

The simultaneously acting dynamic deck load for uniformly distributed load, , on the enclosed upper deck, where a forecastle or poop is fitted, and also on all lower decks, is to be taken as:
= kN/m²
The simultaneously acting dynamic vertical force for heavy units, , acting on supporting structures and securing systems for heavy units of cargo, equipment or structural components, is to be taken as:
= kN

Figure 2.6.6 Dynamic tank pressure in tanks due to positive and negative longitudinal acceleration