2 Pressures and Forces due to Dry Bulk Cargo

2.1 Application

2.1.1 The pressures and forces due to dry cargo in bulk in a cargo hold are to be determined both for fully and partially filled cargo holds according to [2.4] and [2.5].

2.2 Hold definitions

2.2.1 Geometrical characteristics Figure 1 gives the main geometrical elements of a bulk carrier cargo hold.

Figure 1 : Definition of cargo hold parameters for bulk carrier

2.2.2 Fully and partially filled cargo holds

The definitions of a fully and partially filled dry bulk cargo holds are as follow:

a) Fully filled hold:
The dry bulk cargo density is such that the cargo hold is filled up to the top of the hatch coaming, as shown in Figure 2.
The upper surface of the cargo and its effective height in the hold h_C are to be determined in accordance with [2.3.1].
b) Partially filled hold:
The cargo density is such that the cargo hold is not filled up to the top of the hatch coaming, as shown in Figure 3 or Figure 4.
The upper surface of the cargo and its effective height in the hold hC are to be determined in accordance with [2.3.2].

2.3 Dry cargo characteristics

2.3.1 Definition of the upper surface of dry bulk cargo for full cargo holds

For a fully filled cargo hold as defined in [2.2.2], including non-prismatic holds, the effective upper surface of the cargo is an equivalent horizontal surface at h_C, in m, above inner bottom at centreline as shown in Figure 2.

The value of h_C is to be calculated at mid length of the cargo hold at the midship, is to be kept constant over the cargo hold region area and is determined as follows:

h_C = h_HPU + h₀

where:

S₀ : Shaded area, in m², above the lower intersection of topside tank and side shell or inner side, as the case may be, and up to the level of the intersection of the main deck with the hatch coaming, determined for the cargo hold at the midship as shown in Figure 2.

Figure 2 : Definition of effective upper surface of cargo for a full cargo hold

2.3.2 Definition of upper surface of dry bulk cargo for partially filled cargo holds

For any partially filled cargo hold, as defined in [2.2.2], including non-prismatic holds, the effective upper surface of the cargo is to be made of three parts:

One central horizontal surface of breadth B_H/2, in m, at a height h_C-CL, in m, above the inner bottom
A sloped surface at each side with an angle ψ/2, in degrees, between the central horizontal surface, and the side shell or inner hull, as shown in Figure 3, or the hopper plating, as shown in Figure 4, as the case may be.

The height of cargo surface h_C, in m, is to be calculated at mid length of the considered cargo hold and is to be taken as constant over the length of the hold as follows:

For

where:

h₁ : Height, in m, to be taken as:

For h₁ ≥ 0 as shown in Figure 3:
- h_{C – CL} = h_HPL + h₁ + h₂
- B₂ = B_H
For h₁ < 0 as shown in Figure 4
- h_{C – CL} = h₁₁ + h₂₂

h_C-CL : Height, in m, of the cargo surface at the centreline, as shown in Figure 3 and Figure 4

B₂ : Maximum breadth of the cargo, in m, as shown in Figure 3 and Figure 4

Figure 3 : Definition of the effective upper surface of cargo for a partially filled cargo hold when h₁ ≥ 0

Figure 4 : Definition of the effective upper surface of cargo for a partially filled cargo hold when h₁ < 0

2.3.3 Mass and density

The dry cargo mass and the density of the cargo are to be taken as follows:

For strength assessment in intact condition: the values defined in Table 1
For fatigue assessment: the values defined in Table 2
For strength assessment in flooded condition: the values defined in Table 3

Table 1 : Dry bulk cargo mass and density for strength assessment in intact condition

Ship type	Cargo mass Cargo density	Homogeneous loading condition		Alternate loading condition
		Fully filled hold	Partially filled hold	Fullyfilled hold	Partially filled hold
No BC notation	M	M = M_Full	N/A	N/A
	ρ_C	Maximum value specified in the loading manual
BC-C	M	M = M_Full	N/A	N/A
	ρ_C	but not less than 1.0
BC-B	M	M = M_Full	M = M_H	N/A
	ρ_C	but not less than 1.0	ρ_C = 3.0 ⁽¹⁾
BC-A	M	M = M_Full	M = M_H	M = M_HD + 0.1M_H	M = M_HD + 0.1M_H
	ρ_C	but not less than 1.0	ρ_C = 3.0 ⁽¹⁾		ρ_C = 3.0 ⁽¹⁾
(1) To be taken as 3.0 unless an alternative maximum cargo density is specified in the loading manual.

Table 2 : Dry bulk cargo mass and density for fatigue assessment

Ship type	Cargo mass Cargo density	Homogeneous loading condition (Fully filled hold)	Alternate loading condition (Partially filled hold)
No BC notation	M	M = M_H	N/A
No BC notation	ρ_C	ρ_C=maximum value specified in the loading manual
BC-C	M	M = M_H
BC-C	ρ_C
BC-B	M	M = M_H
BC-B	ρ_C
BC-A	M	M = M_H	M=M_HD
BC-A	ρ_C		ρ_C = 3.0 ⁽¹⁾
(1) To be taken as 3.0 unless an alternative maximum cargo density is specified in the loading manual.

Table 3 : Dry bulk cargo mass and density for strength assessment in flooded condition

Ship type	Cargo mass Cargo density	Homogeneous loading condition		Alternate loading condition
Ship type	Cargo mass Cargo density	Fully filled hold	Partially filled hold	Fully filled hold	Partially filled hold	Hold loaded with ρC≤1.78 t/m³ ⁽²⁾
No BC notation	M	M = M_H	N/A	N/A
No BC notation	ρ_C	ρ_C = maximum value specified in the loading manual	N/A	N/A
BC-C	M	M = M_H	N/A	N/A
BC-C	ρ_C		N/A	N/A
BC-B	M	M = M_H	M = M_H	N/A
BC-B	ρ_C		ρ_C= 3.0 ⁽¹⁾	N/A
BC-A	M	M = M_H	M = M_H	M = M_HD	M = M_HD	M = M_HD
BC-A	ρ_C		ρ_C= 3.0 ⁽¹⁾		ρ_C= 3.0 ⁽¹⁾	ρ_C= 1.78
(1) To be taken as 3.0 unless an alternative maximum cargo density is specified in the loading manual. (2) To be applied for bulk carriers that are required to carry cargoes with a density less than or equal to 1.78 t/m³.

2.3.4 FE application

The following process is to be applied for the bulk cargo pressure loads used in FE analysis:

a) Determine h_c according to [2.3.1] for fully filled cargo hold or [2.3.2] for partially filled cargo hold.
b) Determine the corresponding static pressure as defined in [2.4.2] and static shear pressure as defined in [2.5.2] using ρ_c and apply them in the FE model.
c) Calculate the actual mass of cargo, M_actual, in t.
d) Determine the effective cargo density, in t/m³:
e) Calculate the final pressure distribution and shear load using ρ_eff instead of ρ_c.

2.4 Dry bulk cargo pressures

2.4.1 Total pressure

The total pressure due to dry bulk cargo acting on any load point of a cargo hold boundary, in kN/m², is to be taken as:

P_in = P_bs For strength assessment of intact conditions for static (S) design load scenarios, given in Ch 4, Sec 7

P_in = P_bs + P_bd For strength assessment of intact conditions and fatigue assessment for static plus dynamic (S+D) design load scenarios, given in Ch 4, Sec 7

but not less than 0.

where:

P_bs : Static pressure due to dry bulk cargo, in kN/m², as defined in [2.4.2].

P_bd : Dynamic inertial pressure due to dry bulk cargo in cargo holds, in kN/m², as defined in [2.4.3].

Static and dynamic pressures as defined in [2.4.2] and [2.4.3] for FE analysis are to be determined using ρ_eff instead of ρ_c.

2.4.2 Static pressure

The dry bulk cargo static pressure P_bs, in kN/m², is to be taken as:

P_bs = ρ_C gK_C (z_C – z) but not less than 0.

2.4.3 Dynamic pressure

The dry bulk cargo dynamic pressure P_bd, in kN/m², for each load case is to be taken as:

P_bd = f_β ρ_C [0.25 a_X (x_G – x) + 0.25 a_Y (y_G – y) + f_dc K_C a_Z (z_C – z)] for z ≤ z_c

P_bd = 0 for z > z_c

2.5 Shear load

2.5.1 Application

For FE strength assessment, the following shear load pressures are to be considered in addition to the dry bulk cargo pressures defined in [2.4] when the load point elevation, z, is lower or equal to z_c:

For static (S) design load scenarios, given in Ch 4, Sec 7: Static shear load, P_bs-s, due to gravitational forces acting on hopper tanks and lower stools plating, as defined in [2.5.2].
For static plus dynamic (S+D) design load scenarios, given in Ch 4, Sec 7: The following dynamic shear load pressures:
- P_bs-s + P_bs-d for the hopper tank and the lower stool plating, as defined in [2.5.3].
- P_bs-dx for the inner bottom plating in the longitudinal direction, as defined in [2.5.4].
- P_bs-dy for the inner bottom plating in the transverse direction, as defined in [2.5.4].

Shear loads as defined in [2.5.2] to [2.5.4] for FE analysis are to be determined using ρ_eff instead of ρ_c.

2.5.2 Static shear load on the hopper tank and lower stool plating

The static shear load pressure, P_bs-s (positive downward to the plating) due to dry bulk cargo gravitational forces acting on hopper tank and lower stool plating, in kN/m², is to be taken as:

2.5.3 Dynamic shear load on the hopper tank and lower stool plating

The dynamic shear load pressure, P_bs-d (positive downward to the plating) due to dry bulk cargo forces on the hopper tank and lower stool plating, in kN/m², for each dynamic load case is to be taken as:

2.5.4 Dynamic shear load along the inner bottom plating for FE analyses

The dynamic shear load pressures, P_bs-dx in the longitudinal direction (positive to bow) due to dry bulk cargo forces acting along the inner bottom plating, in kN/m², for each dynamic load case is to be taken respectively as:

P_{bs – dx} = –0.75 f_β ρ_C a_X h_C

The dynamic shear load pressures, P_bs-dy in the transverse direction (positive to port) due to dry bulk cargo forces acting along the inner bottom plating, in kN/m², for each dynamic load case is to be taken respectively as

P_{bs – dy} = –0.75 f_β ρ_C a_y h_C

The dynamic shear load pressures P_bs-dx and P_bs-dy are only used for FE strength assessment.