5 Fatigue Damage Calculation

5.1 General

5.1.1

The design fatigue life is divided into a number of time periods due to different loading conditions and due to limitation of the corrosion protection. It is assumed that the corrosion protection (i.e. coating system) is only effective for a limited number of years during which the structural details are protected, i.e. in-air environment. During the remaining part of the design life as specified in Table 5, the structural details are unprotected i.e. exposed to corrosive environment.

5.1.2

The elementary fatigue damage, given in [5.2], is the damage accumulated during a specific loading condition (j) associated with a specific environmental condition either protected condition, i.e. in-air environment, or unprotected condition, i.e. corrosive environment.

The combined fatigue damage, given in [5.3], is the combination of damage accumulated for a specific loading condition (j) for the in-air and corrosive environment time.

Total fatigue damage, given in [5.4], is the sum of the combined fatigue damages obtained for all loading conditions.

5.2 Elementary fatigue damage

5.2.1

The elementary fatigue damage for each fatigue loading condition (j) is to be calculated independently for both protected in-air environment and unprotected corrosive environment, based on the fatigue stress range obtained for the predominant load case as follows:

where:

N_D : Total number of wave cycles experienced by ship during the design fatigue life, taken as:

N_D = 31.557×10⁶ (f₀T_D) / (4 log L)

f₀ : Factor taking into account time in seagoing operations excluding time in loading and unloading, repairs, etc.

f₀ = 0.85.

α_(j) : Fraction of time in each loading condition given in Ch 9, Sec 1, Table 1 for oil tanker and in Ch 9, Sec 1, Table 3 for bulk carrier.

Δσ_{FS, (j)} : Fatigue stress range at the reference probability level of exceedance of 10^-2, in N/mm².

N_R : Number of cycles corresponding to the reference probability of exceedance of 10^-2.

N_R = 100.

ξ : Weibull shape parameter,

ξ = 1.

Γ(x) : Complete Gamma function.

K₂ : Constant of the design S-N curve, as given in Table 2 for in-air environment and in Table 3 for corrosive environment.

μ_(j) : Coefficient taking into account the change of inverse slope of the S-N curve, m,

For in-air environment:
For corrosive environment:
μ_(j) = 1.0

γ (a,x) : Incomplete Gamma function.

Δσ_q : Stress range, in N/mm², corresponding to the intersection of the two segments of design S-N curve at N = 10⁷ cycles, as given in Table 2.

Δm : Change in inverse slope of S-N curve at N=10⁷ cycles.

Δm = 2

5.3 Combined fatigue damage

5.3.1

The combined fatigue damage in protected in-air environment and unprotected corrosive environment for each loading condition (j) is to be calculated as follows:

where:

D_E,air(j) : The elementary fatigue damage for in-air environment for loading condition (j) given in [5.2.1].

D_E,corr(j) : The elementary fatigue damage for corrosive environment for loading condition (j) as calculated in [5.2.1].

Table 5 : Time in corrosive environment, T_C

Location of weld joint or structural detail	*Time in corrosive environment T_C,in years*
Water ballast tank	10
Oil cargo tank
Lower part ⁽¹⁾ of bulk cargo hold and water ballast cargo hold
Bulk cargo hold and water ballast cargo hold except lower part ⁽¹⁾	5
Void space Other areas	5
⁽¹⁾ Lower part means cargo hold part below a horizontal level located at a distance of 300 mm below the frame end bracket for holds of single side skin construction or 300 mm below the hopper tank upper end for holds of double side skin construction (see Pt 2, Ch 1, Sec 2, Figure 1).

5.4 Total fatigue damage

5.4.1

The total fatigue damage for all applicable loading conditions is calculated as follows:

where:

D_(j) : Combined fatigue damage for each applicable loading condition, as given in [5.3].

5.5 Fatigue life calculation

5.5.1 The fatigue life, T_F, is taken as:

otherwise.

where:

D_air : Total fatigue damage for all loading conditions in-air environment taken as:

D_corr : Total fatigue damage for all loading conditions in corrosive environment taken as:

5 Fatigue Damage Calculation

Table 5 : Time in corrosive environment, TC

Table 5 : Time in corrosive environment, T_C