2 Checking Criteria

2.1 General

2.1.1 The vertical hull girder ultimate bending capacity is to be checked for hogging and sagging conditions, for the following design load scenarios, as defined in Table 1:

For bulk carriers: design load scenario A, for seagoing, harbour/sheltered water and flooded conditions.
For oil tankers: design load scenario A, for seagoing and harbour/sheltered water conditions; and design load scenario B, for the operational seagoing homogeneous full load condition.

Table 1: Design load scenarios

Design load scenarios		Permissible still water bending moment, M_sw-U
A	S+D	M_sw-h or M_sw-s
	S	M_sw-p-h or M_sw-p-s
	A: S+D	M_sw-f
B	S+D	Maximum sagging still water bending moment for operational seagoing homogeneous full load condition ⁽¹⁾
⁽¹⁾ The maximum still water bending moment is to be taken from the departure condition with the ship homogeneously loaded at maximum draught and corresponding arrival and any mid-voyage conditions.

2.1.2 The vertical hull girder ultimate bending capacity at any hull transverse section is to satisfy the following criteria:

where:

M: Vertical bending moment, in kNm, to be obtained as specified in [2.2.1].

M_U : Vertical hull girder ultimate bending capacity, in kNm, to be obtained as specified in [2.3].

γ_R : Partial safety factor for the vertical hull girder ultimate bending capacity to be taken equal to:

γR = γ_M γ_DB

γ_M : Partial safety factor for the vertical hull girder ultimate bending capacity, covering material, geometric and strength prediction uncertainties; in general, to be taken equal to:

γ_M = 1.1

γ_DB : Partial safety factor for the vertical hull girder ultimate bending capacity, covering the effect of double bottom bending, to be taken equal to:

For hogging condition, except flooded conditions:
- γ_DB = 1.25 for empty cargo holds in alternate condition of BC-A bulk carriers,
- γ_DB = 1.10 for oil tankers, for BC-B and BC-C bulk carriers and loaded cargo holds in alternate condition of BC-A bulk carriers,
For sagging condition, except flooded condition: γ_DB = 1.0
For hogging and sagging condition, for flooded condition: γ_DB = 1.0

2.2 Hull girder ultimate bending loads

2.2.1 The vertical hull girder bending moment, M in hogging and sagging conditions, to be considered in the ultimate strength check is to be taken as:

M = γ_S M_{sw – U} + γ_W f_βM_wv

where:

M_sw-U : Permissible still water bending moment, in kNm, in hogging and sagging conditions at the hull transverse section considered as defined in Table 1.

M_wv : Vertical wave bending moment, in kNm, in hogging and sagging conditions at the hull transverse section considered as defined in Ch 4, Sec 4, [3.1].

γ_S : Partial safety factor for the still water bending moment, as defined in Table 2.

γ_W : Partial safety factor for the vertical wave bending moment, as defined in Table 2.

f_β : Heading correction factor, as defined in Sec 1, Hull Girder Yielding Strength, SYMBOLS

Table 2 : Partial safety factors

Design load scenarios	*γ_S*	*γ_W*
A	1.0	1.2
B	1.0	1.3

2.3 Hull girder ultimate bending capacity

2.3.1 The ultimate bending moment capacities of a hull girder transverse section, in hogging and sagging conditions, are defined as the maximum values of the curve of bending moment capacity versus the curvature χ of the transverse section considered (see Figure 1). The curvature χ is positive for hogging condition and negative for sagging condition.

Figure 1: Bending moment capacity versus curvature χ

The hull girder ultimate bending capacity, M_U, is to be calculated according to Ch 5, App 2.

2.3.2 The effective area for the hull girder ultimate strength capacity assessment is specified in Ch 5, App 2.