3 Dynamic Hull Girder Loads

3.1 Vertical wave bending moment

3.1.1 The vertical wave bending moments at any longitudinal position, in kNm, are to be taken as:

Hogging condition:

M_{wv – h} = 0.19 _{fnl – vh} f_m f_p C_w L² BC_B

Sagging condition:

M_{wv – s} = –0.19 f_{nl – vs} f_m f_p C_w L² BC_B

where:

f_nl-vh : Coefficient considering nonlinear effects applied to hogging, to be taken as:

f_nl-vh = 1.0 for strength and fatigue assessment.

f_nl-vs : Coefficient considering nonlinear effects applied to sagging, to be taken as:

for strength assessment.
f_nl-vs = 1.0 for fatigue assessment.

f_p : Coefficient to be taken as:

f_p = f_ps for strength assessment.
f_p = 0.9 [0.27 – (6 + 4f_T) L × 10^–5] for fatigue assessment.

f_m : Distribution factor for vertical wave bending moment along the ship’s length, to be taken as:

f_m = 0.0 for x ≤ 0
f_m = 1.0 for 0.4 L ≤ x ≤ 0.65 L
f_m = 0.0 for x ≥ L
Intermediate values of f_m are to be obtained by linear interpolation (see Figure 2).

Figure 2 : Distribution factor f_mm

3.2 Vertical wave shear force

3.2.1 The vertical wave shear forces at any longitudinal position, in kN, are to be taken as:

Q_{wv – pos} = 0.52 f_{q – pos} f_p C_w LBC_B

Q_{wv – neg} = –0.52 f_{q – neg} f_p C_w LBC_B

where:

f_p : Coefficient to be taken as:

f_p = f_ps for strength assessment.
f_p = 0.9 [0.27 – (17 – 8f_T) L × 10^–5] for fatigue assessment.

f_q-pos : Distribution factor along the ship length for positive wave shear force, to be taken as:

f_q-pos = 0.0 for x ≤ 0
f_q-pos = 0.92 f_{nl – vh} for 0.2 L ≤ x ≤ 0.3 L
f_q-pos = 0.7 for 0.4 L ≤ x ≤ 0.6 L
f_q-pos = 1.0 f_{nl – vs} for 0.7 L ≤ x ≤ 0.85 L
f_q-pos = 0.0 for x ≥ _L
Intermediate values of f_q-pos are to be obtained by linear interpolation (see Figure 3).

f_q-neg : Distribution factor along the ship length for negative wave shear force, to be taken as:

f_q-neg = 0.0 for x ≤ 0
f_q-neg = 0.92 f_{nl – vs} for 0.2L ≤ x ≤ 0.3 L
f_q-neg = 0.7 for 0.4L ≤ x ≤ 0.6 L
f_q-neg = 1.0 f_{nl – vh} for 0.7L ≤ x ≤ 0.85 L
f_q-neg = 0.0 for x ≥ L
Intermediate values of f_q-neg are to be obtained by linear interpolation, see Figure 4.

f_nl-vh, f_nl-vs:Coefficient considering nonlinear effects defined in [3.1.1].

Figure 3 : Distribution factor of positive vertical shear force f_q-pos

Figure 4 : Distribution factor of negative vertical shear force f_q-neg

3.3 Horizontal wave bending moment

3.3.1 The horizontal wave bending moment at any longitudinal position, in kNm, is to be taken as:

where:

f_nlh : Coefficient considering nonlinear effect to be taken as:

f_nlh = 0.9 for strength assessment
f_nlh = 1.0 for fatigue assessment

f_p : Coefficient to be taken as:

f_p = f_ps for strength assessment.
f_p = 0.9 ⋅ [(0.2 + 0.04f_T) + (11 – 8f_T) L x 10^–5] for fatigue assessment.

f_m : Distribution factor defined in [3.1.1].

3.4 Wave torsional moment

3.4.1 The wave torsional moment at any longitudinal position with respect to the ship baseline, in kNm, is to be taken as:

M_wt = f_p (M_wt1 + M_wt2)

where:

M_wt2 = 0.22 f_t2 C_w LB² C_B

f_t1, f_t2 : Distribution factors, taken as:

f_t1 = 0 for x < 0
for 0 ≤ x ≤ L
f_t1 = 0 for x > L
f_t2 = 0 for x < 0
for 0 ≤ x ≤ L
f_t2 = 0 for x > L

f_p : Coefficient to be taken as:

f_p = f_ps for strength assessment.
f_p = 0.9[0.2 + (5f_T – 4.25) B × 10^–4] for strength assessment.

3.5 Hull girder loads for dynamic load cases

3.5.1 General

The dynamic hull girder loads to be applied for the dynamic load cases defined in Ch 4, Sec 2, are given in [3.5.2] to [3.5.5].

3.5.2 Vertical wave bending moment

The vertical wave bending moment, M_wv-LC, in kNm, to be used for each dynamic load case in Ch 4, Sec 2, is defined in Table 1.

Table 1 : Vertical wave bending moment for dynamic load cases

Load combination factor	*M_wv-LC*
C_WV ≥ 0	f_β C_WV M_{wv – h}
C_WV < 0

where:

C_WV : Load combination factor for vertical wave bending moment, to be taken as specified in Ch 4, Sec 2.

M_wv-h, M_wv-s: Hogging and sagging vertical wave bending moment taking account of the considered design load scenario, as defined in [3.1.1].

3.5.3 Vertical wave shear force

The vertical wave shear force, Q_wv-LC, in kN, to be used for each dynamic load case in Ch 4, Sec 2, is defined in Table 2.

Table 2 : Vertical wave shear force for dynamic load cases

Load combination factor	*Q_wv-LC*
C_QW ≥ 0	f_β C_QW Q_{wv – pos}
C_QW < 0

where:

C_QW : Load combination factor for vertical wave shear force, to be taken as specified in Ch 4, Sec 2.

Q_wv-pos, Q_wv--neg : Positive and negative vertical wave shear force taking account of the considered design load scenario, as defined in [3.2.1].

3.5.4 Horizontal wave bending moment

The horizontal wave bending moment, M_wh-LC, in kNm, to be used for each dynamic load case defined in Ch 4, Sec 2, is to be taken as:

M_{wh – LC} = f_β C_WH M_wh

where:

C_WH : Load combination factor for horizontal wave bending moment, to be taken as specified in Ch 4, Sec 2.

M_wh : Horizontal wave bending moment taking account of the appropriate design load scenario, as defined in [3.3.1].

3.5.5 Wave torsional moment

The wave torsional moment, M_wt-LC, in kNm, to be used for each dynamic load case defined in Ch 4, Sec 2, is to be taken as:

M_{wt – LC} = f_β C_WT M_wt

where:

C_WT : Load combination factor for wave torsional moment, to be taken as specified in Ch 4, Sec 2.

M_wt : Wave torsional moment taking account of the appropriate design load scenario, as defined in [3.4.1].