Symbols

For symbols not defined in this section, refer to Ch 1, Sec 4

a_X, a_Y, a_Z:Longitudinal, transverse and vertical accelerations, in m/s², at x_G, y_G, z_G, as defined in Ch 4, Sec 3, [3.2].

B_H : Breadth of the cargo hold, in m, measured at mid-length of the cargo hold and at the mid height between the top of hopper tank and the bottom of topside tank, see Figure 1.

B_IB : Breadth of inner bottom, in m, measured at mid-length of the cargo hold, see Figure 1.

D₁ : Distance, in m, from the baseline to the freeboard deck at side amidships.

d_sc : Diameter, in m, of a steel coil.

f_cd : Factor for joint probability of occurrence of liquid cargo density and maximum sea state in 25 years design life, to be taken as:

For strength assessment with FE analysis of cargo tanks filled with liquid cargo:
- f_cd = 1.0 for ρ_L > 1.025 t/m³.
- f_cd = 0.88 for ρ_L = 1.025 t/m³.
For other cases:
- f_cd = 1.0.

f_dc : Dry cargo factor taken as:

f_dc = 1.0 for strength assessment,
f_dc = 0.5 for fatigue assessment.

f_β : Coefficient defined in Ch 4, Sec 4.

h_air : Height of air pipe or overflow pipe above the top of the tank, in m.

h_C : Height of bulk cargo, in m, from the inner bottom to the upper surface of bulk cargo, as defined in [2.3.1] or [2.3.2].

h_DB : Height, in m, of the double bottom at the centreline, measured at mid-length of the cargo hold, see Figure 1.

h_HPL : Vertical distance, in m, from the inner bottom at centreline to the upper intersection of hopper tank and side shell or inner side for double side bulk carriers, determined at mid length of the considered cargo hold, as shown in Figure 1.

h_HPL = 0 if there is no hopper tank.

h_HPU : Vertical distance, in m, from the inner bottom at centreline to the lower intersection of topside tank and side shell or inner side for double side bulk carriers, determined at mid length of the cargo hold at midship, as shown in Figure 1.

h_LS : Mean height, in m, of the lower stool, measured from the inner bottom.

h_max : Maximum permissible filling level, in m, taken as:

For ballast tanks: maximum tank height,
For cargo tanks with cargo density equal to ρ_L: maximum tank height
For cargo tanks with heavy liquid cargo density equal to ρ_part associated with a partially filled cargo tank: h_part as defined in Ch 10, Sec 4, [1.2.1].

K_C : Coefficient taken equal to:

for inner bottom, hopper tank, transverse and longitudinal bulkheads, lower stool, vertical upper stool, inner side and side shell.
K_C = 0 for topside tank, main deck and sloped upper stool.

K_C-f : Coefficient taken equal to:

: Distance, in m, between floors.

: Length of the cargo hold, in m, at the centreline between the transverse bulkheads. This is to be measured to the mid-depth of the corrugated bulkhead(s) if fitted.

: Distance, in m, between outermost dunnage per EPP in the ship X direction, see Figure 10.

: Length, in m, of a steel coil.

M : Mass, in t, of the bulk cargo being considered.

M_Full : Cargo mass, in t, in a cargo hold corresponding to the volume up to the top of the hatch coaming with a density of the greater of M_H/V_Full or 1.0 t/m³.

M_Full = 1.0 V_Full but not less than M_H.

M_H : Cargo mass, in t, in a cargo hold that corresponds to the homogeneously loaded condition at maximum draught with 50% consumables.

M_HD : Maximum allowable cargo mass, in t, in a cargo hold according to design loading conditions with specified holds empty at maximum draught with 50% consumables and all ballast water tanks in cargo hold region empty.

M_sc-ib : Equivalent mass of a steel coil, in t, on inner bottom, as defined in [4.3.1]

M_sc-hs : Equivalent mass of a steel coil, in t, on hopper side, as defined in [4.3.2].

n₁ : Number of tiers of steel coils.

n₂ : Number of load points per EPP of the inner bottom, see [4.1.3].

n₃ : Number of dunnages supporting one row of steel coils.

P_drop : Overpressure, in kN/m², due to sustained liquid flow through air pipe or overflow pipe in case of overfilling or filling during flow through ballast water exchange. It is to be defined by the designer, but not to be less than 25 kN/m².

P_PV : Design vapour pressure, in kN/m², but not less than 25 kN/m².

perm : Permeability of cargo, to be taken as:

perm = 0.3 for iron ore, coal cargoes and cement.
perm = 0 for steel coils and steel packed products.

R : Vertical coordinate of the ship rotation centre, defined in Ch 4, Sec 3.

s_C : Spacing of corrugations, in m, as defined in Ch 3, Sec 6, [10.4.2].

T_θ : Roll period, in s, as defined in Ch 4, Sec 3, [2.1.1].

V_Full : Volume, in m³, of cargo hold up to top of the hatch coaming, taken as:

V_Full = V_H + V_HC.

V_H : Volume, in m³, of cargo hold up to level of the intersection of the main deck with the hatch coaming excluding the volume enclosed by hatch coaming, see Figure 1.

V_HC : Volume, in m³, of the hatch coaming, from the level of the intersection of the main deck with the hatch side coaming to the top of the hatch coaming, determined for the cargo hold at midship, as shown in Figure 1.

V_TS : Total volume, in m³, of the portion of the lower bulkhead stools within the cargo hold length and inboard of the hopper tanks.

W : Mass, in t, of a steel coil.

x, y, z : X, Y and Z coordinates, in m, of the load point with respect to the reference coordinate system defined in Ch 4, Sec 1, [1.2.1].

x_G, y_G, z_G: X, Y and Z coordinates, in m, of the volumetric centre of gravity of the tank or fully filled cargo hold, i.e. V_Full, considered with respect to the reference coordinate system defined in Ch 4, Sec 1, [1.2].

In case of partially filled cargo hold, x_G, y_G, z_G to be taken as follows:
x_G, y_G: Volumetric centre of gravity of the cargo hold.
z_G = h_DB + h_C-cl / 2

z_top : Z coordinate of the highest point of tank, excluding small hatchways, in m.

z_C : Height of the upper surface of the cargo above the baseline in way of the load point, in m, to be taken as:

z_C = h_DB + h_C.

α : Angle, in deg, between panel considered and the horizontal plane.

ϕ : Pitch angle, in deg, defined in Ch 4, Sec 3, [2.1.2].

ψ : Assumed angle of repose, in deg, of bulk cargo (considered drained and removed); to be taken as:

ψ = 30° in general.
ψ = 35° for iron ore.
ψ = 25° for cement.

ρ_c : Density of bulk cargo, in t/m³, as defined in [2.3.3].

ρ_L : Density of liquid in the tank and ballast hold, in t/m³, but not less than:

For strength assessment:
- ρ_L = 1.025 for all liquids including oil cargoes. If a tank filled at 98% is intended to carry heavier liquid cargoes than 1.025 (i.e. ρ_max-LM > 1.025), then ρ_L = ρ_max-LM.
For fatigue assessment:
- ρ_L = 0.9 for liquid cargoes.
- ρ_L = 1.025 for all other liquids.

ρ_max-LM : Maximum liquid cargo density in t/m³, associated with a full tank at 98%, from any loading condition in the ship's loading manual or value specified by the designer.

ρ_part : Maximum permissible high liquid cargo density, in t/m³, associated with a partially filled cargo tank but not taken less than ρ_L considered for strength assessment.

ρ_slh : Liquid density, in t/m³, to be used for sloshing assessment, taken as:

ρ_slh = ρ_part for heavy liquid cargo density associated with partial filling of cargo tank
ρ_slh = ρ_L for all other cases

ρ_ST : Density of steel, in t/m3, to be taken as 7.85.

θ : Roll angle, in deg, defined in Ch 4, Sec 3, [2.1.1].

θ_h : Angle, in deg, between inner bottom plate and hopper sloping plate. in general θ_h is such that: