4 Primary Supporting Members

4.1 Application

4.1.1 The requirements of this section apply to the strength check of primary supporting members in cargo hold structures, subjected to lateral pressure for ships having a length L less than 150 m.

4.1.2 As an alternative to [4.1.1], the strength check may be verified by direct strength assessment deemed as appropriate by the Society.

4.2 Design load sets

4.2.1 Application

Design load sets as given in Table 3 are to be considered for primary supporting members on cargo hold boundaries of bulk carriers less than 150 m in length.

4.2.2 Loading conditions

The severest loading conditions from the loading manual or otherwise specified by the designer are to be considered for the calculation of P_in in design load sets BC-11 to BC-12.

If primary supporting members support deck structure or tank/watertight boundaries, applicable design load sets in Pt 1, Ch 6, Sec 2, Table 1 are also to be considered.

Table 3 : Design load sets for primary supporting members in cargo hold region

Item	Design load set	Load component	Draught	Design load	Loading condition
Bulk cargo hold assigned as ballast hold	WB-4	P_in– P_ex ⁽¹⁾	T_BAL-H ⁽³⁾	S+D	Heavy ballast condition
Bulk cargo hold assigned as ballast hold	WB-6	P_in	-	S	Harbour/test condition
Bulk cargo hold	BC-11	P_in– P_ex ⁽¹⁾	T_SC	S+D	Cargo loading condition
Bulk cargo hold	BC-12	P_in– P_ex ⁽¹⁾	-	S	Harbour condition
Compartments not carrying liquids	FD-1 ⁽²⁾	P_in	T_SC	S+D	Flooded condition
Compartments not carrying liquids	FD-2 ⁽²⁾	P_in		S	Flooded condition
(1) P_ex is to be considered for external shell only. (2) FD-1 and FD-2 are not applicable to external shell. (3) Minimum draught among heavy ballast conditions is to be used.

4.3 Centre girders and side girders

4.3.1 Net web thickness

The net thickness of girders in double bottom structure, in mm, is not to be less than the greater of the value t₁ and t₂ specified in the followings according to each location:

where |x - x_c| is less than 0.25 ℓ_DB, |x - x_c| is to be taken as 0.25 ℓ_DB.

where:

P : Design pressure in kN/m², for the design load set being considered according to Pt 1, Ch 6, Sec 2, [2.1.3], calculated at mid-point of a floor located midway between transverse bulkheads or transverse bulkhead and toe of stool, where fitted.

S : Distance between the centres of the two spaces adjacent to the centre or side girder under consideration, in m.

d₀ : Depth of the solid floor at the point under consideration in m.

d₁ : Depth of the opening, if any, at the point under consideration in m.

C₁ : Coefficient given in Table 4 depending on B_DB /ℓ_DB. For intermediate values of B_DB /ℓ_DB, C₁ is to be obtained by linear interpolation.

a : Depth of girders at the point under consideration, in m. However, where horizontal stiffeners are fitted on the girder, a is the distance from the horizontal stiffener under consideration to the bottom shell plating or inner bottom plating, or the distance between the horizontal stiffeners under consideration.

S₁ : Spacing, in m, of vertical stiffeners or floors.

C’₁ : Coefficient given in Table 5 depending on S₁ /a. For intermediate values of S₁ /a, C’₁ is to be determined by linear interpolation.

H : Value obtained from the following formulae:

Where the girder is provided with an unreinforced opening:
In other cases:
H = 1.0.

Table 4 : Coefficient C₁

B_DB /ℓ_DB	0.4 and under	0.6	0.8	1.0	1.2	1.4	1.6 and over
C₁	0.5	0.71	0.83	0.88	0.95	0.98	100

Table 5 : Coefficient C'₁

S₁ /a	0.3 and under	0.4	0.5	0.6	0.7	0.8	0.9	1.0	1.2	1.4 and over
C’₁	64	38	25	19	15	12	10	9	8	7

4.4 Floors

4.4.1 Net web thickness

The net thickness of floors in the double bottom structure, in mm, is not to be less than the greatest of values t₁ and t₂ specified in the following according to each location:

where |x - x_c| is less than 0.25 ℓ_DB, |x - x_c| is to be taken as 0.25 ℓ_DB and where |y| is less than B’_DB/4, |y| is to be taken as B’_DB/4.

where:

S : Spacing of solid floors, in m.

d₀ : Depth of the solid floor at the point under consideration in m.

d₁ : Depth of the opening, if any, at the point under consideration in m.

B’_DB : Distance between toes of hopper tanks at the position of the solid floor under consideration, in m.

C₂ : Coefficient given in Table 6 depending on B_DB /ℓ_DB. For intermediate values of B_DB /ℓ_DB, C₂ is to be obtained by linear interpolation.

a : Depth of the solid floor at the point under consideration, in m. However, where horizontal stiffeners are fitted on the floor, a is the distance from the horizontal stiffener under consideration to the bottom shell plating or the inner bottom plating or the distance between the horizontal stiffeners under consideration.

S₁ : Spacing, in m, of vertical stiffeners or girders.

C’₂ : Coefficient given in Table 7 depending on S₁ /d₀. For intermediate values of S₁ /d₀, C’₂ is to be determined by linear interpolation.

H : Value obtained from the following formulae:

Where openings with reinforcement or no opening are provided on solid floors:

Where slots without reinforcement are provided:
without being taken less than 1.0.
Where slots with reinforcement are provided:
H =1.0.

Where openings without reinforcement are provided on solid floors:

Where slots without reinforcement are provided:
without being taken less than
where slots with reinforcement are provided:

d₂ : Depth of slots without reinforcement provided at the upper and lower parts of solid floors, in m, whichever is greater.

Table 6 : Coefficient C₂

B_DB /ℓ_DB	0.4 and under	0.6	0.8	1.0	1.2	1.4	1.6 and over
C₂	0.48	0.47	0.45	0.43	0.40	0.37	0.34

Table 7 : Coefficient C'₂

S₁/d₀	0.3 and under	0.4	0.5	0.6	0.7	0.8	0.9	1.0	1.2	1.4 and over
C'₂	64	38	25	19	15	12	10	9	8	7

4.5 Stringer of double side structure

4.5.1 Net web thickness

The net thickness of stringers in double side structure, in mm, is not to be less than the greater of the value t₁ and t₂ specified in the followings according to each location:

where |x - x_c| is under 0.25 ℓ_DS, |x - x_c| is to be taken as 0.25 ℓ_DS.

where:

P : Design pressure in kN/m², for the design load set being considered according to Pt 1, Ch 6, Sec 2, [2.1.3], as measured vertically at the upper end of hopper tank, longitudinally at the centre of ℓ_DS.

S : Breadth of part supported by stringer, in m.

d₀ : Depth of stringers, in m.

d₁ : Depth of opening, if any, at the point under consideration, in m.

ℓ_DS : Length of the double side structure between the transverse bulkheads under consideration, in m.

h_DS : Height of the double side structure between the upper end of hopper tank and the lower end of topside tank located midway between transverse bulkheads of hold under consideration, in m.

C₃ : Coefficient given in Table 8 depending on h_DS/ℓ_DS. For intermediate values of h_DS/ℓ_DS, C₃ is to be obtained by linear interpolation.

a : Depth of stringers at the point under consideration, in m. However, where horizontal stiffeners are fitted on the stringer, a is the distance from the horizontal stiffener under consideration to the side shell plating or the longitudinal bulkhead of double side structure or the distance between the horizontal stiffeners under consideration.

S₁ : Spacing, in m, of transverse stiffeners or web frames.

C’₃ : Coefficient given in Table 9 depending on S₁/a. For intermediate values of S₁/a, C’₃ is to be obtained by linear interpolation.

H : Value obtained from the following formulae:

Where the stringer is provided with an unreinforced opening:
In other cases
H=1.0

Table 8 : Coefficient C₃

h_DS /ℓ_DS	0.5 and under	0.6	0.7	0.8	0.9	1.0	1.1	1.2	1.3 and over
C₃	0.16	0.23	0.30	0.36	0.41	0.44	0.47	0.50	0.54

Table 9 : Coefficient C'₃

S₁ /a	0.3 and under	0.4	0.5	0.6	0.7	0.8	0.9	1.0	1.2	1.4 and over
C'₃	64	38	25	19	15	12	10	9	8	7

4.6 Transverse web in double side structure

4.6.1 Net web thickness

The net thickness of transverse webs in double side structure, in mm, is not to be less than the greater of the value t₁ and t₂ specified in the followings according to each location:

where z - z_BH is greater than 0.4 h’_DS , z - z_BH is to be taken as 0.4 h’_DS .

where:

S : Breadth of part supported by transverses, in m.

d₀ : Depth of transverses, in m.

d₁ : Depth of opening at the point under consideration, in m.

C₄ : Coefficient given in Table 10 depending on h_DS/ℓ_DS. For intermediate values of h_DS/ℓ_DS, C₄ is to be obtained by linear interpolation.

z_BH : Z coordinate, in m, of the upper end of hopper tank with respect to the reference coordinate system defined in Pt 1, Ch 1, Sec 4, [3.6].

h_DS : As defined in the requirements of [4.5.1].

h’_DS : Height of the double side structure between the upper end of hopper tank and the lower end of topside tank at the position under consideration, in m.

ℓ_DS : As defined in the requirements of [4.5.1].

a : Depth of transverses at the point under consideration, in m. However, where vertical stiffeners are fitted on the transverse, a is the distance from the vertical stiffener under consideration to the side shell or the longitudinal bulkhead of double side hull or the distance between the vertical stiffeners under consideration.

S₁ : Spacing, in m, of horizontal stiffeners or stringers.

C’₄ : Coefficient given in Table 11 depending on S₁ /a. For intermediate values of S₁ /a, C’₄ is to be obtained by linear interpolation.

H : Value obtained from the following formulae:

Where the transverse is provided with an unreinforced opening:
In other cases:
H = 1.0.

α : The greater of a or S₁, in m.

Table 10 : Coefficient C₄

h_DS /ℓ_DS	0.5 and under	0.6	0.7	0.8	0.9	1.0	1.1	1.2	1.3 and over
C₄	0.62	0.61	0.59	0.55	0.52	0.49	0.46	0.43	0.41

Table 11 : Coefficient C'₄

S₁ /a	0.3 and under	0.4	0.5	0.6	0.7	0.8	0.9	1.0	1.2	1.4 and over
C'₄	64	38	25	19	15	12	10	9	8	7

4.7 Primary supporting member in bilge hopper tanks and topside tanks

4.7.1 Boundary conditions

The requirements of this sub-article apply to primary supporting members considered as clamped at both ends. For boundary conditions deviated from the above, the yielding check is to be considered on a case-bycase basis.

4.7.2 Net section modulus, net shear sectional area and web thickness

The net section modulus Z, in cm³, the net shear sectional area A_shr, in cm², and the net web thickness t_w, in mm, subjected to lateral pressure are not to be less than the values obtained from the following formulae:

P : Design pressure in kN/m², for the design load set being considered according to Pt 1, Ch 6, Sec 2, [2.1.3], calculated at the mid-point of span ℓ of a web frame located midway between transverse bulkheads of holds.

S : Spacing of primary supporting members, in m.

ℓ_bdg : Effective bending span, in m, of primary supporting members, measured between the supporting members as defined in Pt 1, Ch 3, Sec 7, [1.1.6].

ℓ_shr : Effective shear span, in m, of primary supporting members, measured between the supporting members as defined in Pt 1, Ch 3, Sec 7, [1.1.7].

f_bdg : Bending moment factor:

For continuous primary supporting members and where end connections are fitted consistent with idealisation of the primary supporting members as having fixed ends and is not to be taken higher than:
f_bdg = 10.
For primary supporting members with reduced end fixity, the yield check is to be considered on a case-by-case basis.

C_s-pr : Permissible bending stress coefficient for primary supporting members taken equal to:

C_s-pr = 0.70 for AC-S.
C_s-pr = 0.85 for AC-SD.

h_w : Web height, in mm.

C₅ : Coefficient defined in Table 12 according to s₁ and d₀. For intermediate values of s₁ /d₀, coefficient C₅ is to be obtained by linear interpolation.

s₁ : Spacing of stiffeners or tripping brackets on web plate, in m.

d₀ : Spacing of stiffeners parallel to shell plate on web plate, in m.

Table 12 : Coefficient C₅

s₁ /d₀	0.3 and under	0.4	0.5	0.6	0.7	0.8	0.9	1.0	1.5	2.0 and over
C₅	60.0	40.0	26.8	20.0	16.4	14.4	13.0	12.3	11.1	10.2

4 Primary Supporting Members

Table 3 : Design load sets for primary supporting members in cargo hold region

Table 4 : Coefficient C1

Table 5 : Coefficient C'1

Table 6 : Coefficient C2

Table 7 : Coefficient C'2

Table 8 : Coefficient C3

Table 9 : Coefficient C'3

Table 10 : Coefficient C4

Table 11 : Coefficient C'4

Table 12 : Coefficient C5

Table 4 : Coefficient C₁

Table 5 : Coefficient C'₁

Table 6 : Coefficient C₂

Table 7 : Coefficient C'₂

Table 8 : Coefficient C₃

Table 9 : Coefficient C'₃

Table 10 : Coefficient C₄

Table 11 : Coefficient C'₄

Table 12 : Coefficient C₅