Section 15 Requirements for ships with large deck openings
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Clasifications Register Rules and Regulations - Rules and Regulations for the Classification of Ships, July 2022 - Part 4 Ship Structures (Ship Types) - Chapter 8 Container Ships - Section 15 Requirements for ships with large deck openings

Section 15 Requirements for ships with large deck openings

15.1 Application

15.1.1 The combined stresses due to vertical bending moment, horizontal bending moment and torque are to be calculated as described in this Section.

15.2 Symbols and definitions

15.2.1 The following symbols and definitions are applicable to this Section unless otherwise stated:

Z Y = actual hull section modulus about the transverse neutral axis at the position considered, in m3
Z Z = actual hull section modulus about the vertical neutral axis at the position considered, in m3
ε = shear centre distance below baseline, in metres, may be taken as fε εm. Alternatively, the shear centre position along the length of the ship may be obtained by direct calculation. ε is taken as positive where the shear centre is below the baseline
εm = maximum shear centre distance below baseline of the ship in the midship region, in metres. εm is taken as positive where the shear centre is below the baseline
fε = longitudinal distribution factor of shear centre, to be taken as follows:
  • -1,0 at the aft end of L
  • 1,0 between engine room forward bulkhead and 0,8L from aft
  • -1,0 at the forward end of L

Intermediate values are to be determined by linear interpolation

M S = design still water bending moment at the section under consideration, in kN m
σC = combined stress at the position considered.

15.3 Design loadings

15.3.1 The design vertical wave bending moments, MWC1 and MWC2, at any position along the ship is defined as:

MWC1 = 0,05C0 C31 L2 B (Cb + 0,7) kN m
MWC2 = 0,05C0 C32 L2 B (Cb + 0,7) kN m
C31, C32 = vertical wave bending moment distribution coefficients depending on the longitudinal position from A.P. as defined in Table 8.15.1 Distribution of wave bending moments
C0 =

L, B, Cb are given in Pt 3, Ch 1, 6 Definitions

The sign convention is given in Figure 8.15.1 Sign conventions for hull girder loads

Table 8.15.1 Distribution of wave bending moments

Position C 31 C 32
Station 0 (A.P.) 0,000 0,000
  1 0,062 0,018
  2 0,158 0,017
  3 0,305 -0,008
  4 0,460 -0,058
  5 0,611 -0,137
  6 0,732 -0,235
  7 0,817 -0,350
  8 0,850 -0,458
  9 0,836 -0,548
  10 (mid – Lpp) 0,780 -0,607
  11 0,683 -0,615
  12 0,555 -0,571
  13 0,415 -0,498
  14 0,275 -0,404
  15 0,165 -0,302
  16 0,085 -0,208
  17 0,041 -0,132
  18 0,022 -0,074
  19 0,010 -0,028
  20 (F.P.) 0,000 -0,000

Note Intermediate values are to be determined by linear interpolation.



Figure 8.15.1 Sign conventions for hull girder loads

15.3.2 The design horizontal wave bending moments, MHC1 and MHC2, at any position along the ship are defined as:

MHC1 = 0,2033 C0 C41 L 2 T (Cb + 0,7) kN m
MHC2 = 0,2033 C0 C42 L2 T (Cb + 0,7) kN m
C41, C42 = horizontal wave bending moment distribution coefficients depending on the longitudinal position from A.P. as defined in Table 8.15.2 Distribution of horizontal wave bending moments and hydrodynamic torques

C 0 is defined in Pt 4, Ch 8, 15.3 Design loadings 15.3.1
L, T ,C b are given in Pt 3, Ch 1, 6 Definitions


The sign convention is given in Figure 8.15.1 Sign conventions for hull girder loads

Table 8.15.2 Distribution of horizontal wave bending moments and hydrodynamic torques

Position C41 C42 C51 C 52 K31 K32
Station 0 (A.P.) 0,000 0,000 0,000 0,000 0,000 0,000
  1 –0,016 0,010 -0,181 0,124 0,101 –0,113
  2 –0,046 0,046 -0,343 0,349 0,211 –0,304
  3 –0,097 0,119 -0,439 0,593 0,276 –0,486
  4 –0,154 0,228 -0,433 0,794 0,277 –0,659
  5 –0,208 0,369 -0,387 0,898 0,214 –0,804
  6 –0,242 0,533 -0,285 0,959 0,089 –0,860
  7 –0,247 0,699 -0,123 0,930 –0,083 –0,801
  8 –0,217 0,846 0,086 0,849 –0,268 –0,662
  9 –0,153 0,948 0,189 0,723 –0,422 –0,404
  10 (mid – L pp) –0,072 0,997 0,245 0,586 –0,485 –0,090
  11 0,014 0,985 0,271 0,411 –0,447 0,232
  12 0,087 0,915 0,263 0,239 –0,338 0,483
  13 0,136 0,802 0,189 0,079 –0,227 0,734
  14 0,158 0,657 0,080 -0,081 –0,094 0,913
  15 0,151 0,502 -0,053 -0,099 0,067 0,998
  16 0,123 0,349 -0,131 -0,058 0,185 0,952
  17 0,083 0,214 -0,149 0,051 0,245 0,821
  18 0,043 0,106 -0,080 0,072 0,220 0,627
  19 0,013 0,034 -0,029 0,040 0,133 0,326
  20 (F.P.) 0,000 0,000 0,000 0,000 0,000 0,000

Note Intermediate values are to be determined by linear interpolation.

15.3.3 The design hydrodynamic torques, MWTC1 and MWTC2, at any position along the ship are defined as:

MWTC1 = MWTCB1 + MWTCQ1
MWTCB1 = 0,0728C0 C51 L B2 (Cb + 0,7) kN m
MWTCQ1 = –(0,65T + ) QHC1 kN m
MWTC2 = MWTCB2 + MWTCQ2
MWTCB2 = 0,0728C0 C52 L B2 (Cb + 0,7) kN m
MWTCQ2 = –(0,65T + ) QHC2 kN m
C51, C52 = hydrodynamic torque distribution coefficients depending on the longitudinal position from A.P. as defined in Table 8.15.2 Distribution of horizontal wave bending moments and hydrodynamic torques

C 0 is defined in Pt 4, Ch 8, 15.3 Design loadings 15.3.1

QHC1 = 0,8385 C0 K31 L T (Cb + 0,7) kN
QHC2 = 0,8385 C0 K32 L T (Cb + 0,7) kN
K31, K32 = horizontal wave shear force distribution coefficients depending on the longitudinal position from A.P. as defined in Table 8.15.2 Distribution of horizontal wave bending moments and hydrodynamic torques

L, B, T, Cb, are given in Pt 3, Ch 1, 6 Definitions.
ε is given in Pt 4, Ch 8, 15.2 Symbols and definitions 15.2.1


The sign convention is given in Figure 8.15.1 Sign conventions for hull girder loads

15.3.4 The value and distribution of static cargo torque, MSTC, are to be specified by the designer based on the intended operation of the ship and are not to be less than minimum design value of static cargo torque. The minimum design value of static cargo torque, MSTC, at any position along the ship is defined as:

MSTC = 15,7C6 Bs ηt + 0,7Nsd Ntd) kNm
ηs = the maximum number of stacks of containers over the breadth of the cargo hold
ηt = the maximum number of tiers of containers in the cargo hold amidships, excluding containers above the main deck or on the hatch covers
C6 = distribution coefficient depending on the length, Lpp, as defined in Table 8.15.3 Static cargo torque distribution factor
Nsd = the maximum number of stacks of containers over the breadth, B, on hatch covers or above the main deck
Ntd = the number of tiers of containers on hatch covers or above the main deck amidships, excluding containers in cargo holds

B is given in Pt 3, Ch 1, 6 Definitions.

Table 8.15.3 Static cargo torque distribution factor

Position Factor C6
Station 0 (A.P.) 0,0
  5 1,0
  15 1,0
  20 (F.P.) 0,0

Note Intermediate values are to be determined by linear interpolation.

15.4 Combined stress

15.4.1 Combined stress calculations are to be carried out at least at the following positions along the length of the ship:

  1. At the forward and aft ends of the engine room.

  2. At the forward and aft ends of the deck-house for multi-island designs.

  3. At the forward and aft transverse bulkhead positions of each cargo bay.

  4. At the forward and aft transverse bulkhead of fuel oil deep tanks.

  5. At any other sections where there are significant changes in cross-section properties.

15.4.2 The combined stress, σc, is to be less than the permissible stress given in Table 8.15.4 Permissible stress. σc, is to be taken as the greatest magnitude of the following stresses:

σc1 =
σc2 =
σ'c1 =
σ'c2 =

where

σ1 = σWC1 + σHC1 + σWTC1
σ2 = σWC2 + σHC2 + σWTC2
σ'1 = σWC1 - σHC1 - σWTC1
σ'2 = σWC2 - σHC2 - σWTC2

For σC1

f =
f =

where

MWC =

For σ'C1

f =

For σ'C2

f =

where

MWC' =
σSC = longitudinal stress due to hogging or sagging design still water bending moment M s
σWC1, σWC2 = longitudinal stress due to vertical wave bending moments
σHC1, σHC2 = longitudinal stress due to horizontal wave bending moments
σSTC = longitudinal warping stress due to static cargo torque
σWTC1, σWTC2 = longitudinal warping stress due to hydrodynamic torques
f fH, ffS = hogging and sagging vertical bending moment correction factors calculated in accordance with Pt 4, Ch 8, 16.6 Design vertical wave bending moments 16.6.1
MWC1, MWC2 = vertical bending moments defined in Pt 4, Ch 8, 15.3 Design loadings 15.3.1 at the longitudinal position considered

other symbols are as defined in Pt 4, Ch 8, 15.3 Design loadings and Pt 4, Ch 8, 15.4 Combined stress.

15.4.3 For ships with a beam greater than 32,26 m, longitudinal stresses are to be calculated using a finite element model of the entire hull in accordance with Part A of the LR’s ShipRight SDA procedure for container ships.

15.4.4 For ships with a beam less than or equal to 32,26 m, the longitudinal stresses may be obtained as follows:

σSC =
σWC =
σHC1 =
σHC2 =

σWTC1, σWTC2 and σSTC are to be evaluated by approved calculation procedures.

C 7 = coefficient for shear lag depending on vertical location of the point under consideration
= 0,6 at inboard edge of strength deck
= 1,0 at base line
= intermediate positions by interpolation

Z y and Z z are given in Pt 4, Ch 8, 15.2 Symbols and definitions 15.2.1.

15.4.5 At each section the stresses are to be calculated on the port and starboard sides, at:

  1. the inboard edge of the strength deck;

  2. the point on the bilge where the combined stress is greatest; and

  3. the top of continuous hatch coaming (where fitted).

15.4.6 Where the ship’s length is greater than 425 m or the ship’s beam is greater than 60 m, the vertical wave bending moments, horizontal wave bending moments and hydrodynamic torques are to be obtained from a direct calculation method. Alternatively, the hull stresses may be obtained using a probabilistic approach response-based analysis method considering the ship’s responses in wave environment. The analysis method is to be agreed with LR.

15.5 Permissible stress

15.5.1 The maximum tensile or compressive combined stress σc at any position along the length is not to be more than indicated in Table 8.15.4 Permissible stress.

Table 8.15.4 Permissible stress

Position Permissible combined stress,
N/mm2
Top of continuous hatch coaming
Elsewhere

15.5.2 The assessment of combined stress may conveniently be presented in the form of combined stress diagrams as indicated in Figure 8.15.2 Combined stress diagram for deck - Oblique sea.

Figure 8.15.2 Combined stress diagram for deck - Oblique sea


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