4 Local Stiffener Stress

4.1 Stress due to stiffener bending

4.1.1 Stress due to dynamic pressure

The hot spot stress, in N/mm², due to local dynamic pressure in load case i1 and i2 for loading condition (j) is obtained from the following formula:

where:

P_{W, ik(j)} : Dynamic wave pressure, at the mid span, in kN/m², specified in Ch 4, Sec 5, [1.4], in load case i1 and i2 for loading condition (j).

P_{bd, ik(j)} : Dynamic dry bulk cargo pressure at the mid span, in kN/m², as specified in Ch 4, Sec 6, [2.4.1], in load case i1 and i2 for loading condition (j).

η_W, η_ld, η_bd: Pressure normal coefficients, taken as:

• η = 1 when the considered pressure is applied on the stiffener side,
• η = −1 otherwise.

f_NL : Correction factor for the non-linearity of the wave pressure taken as:

h_w : Water head equivalent to the pressure at waterline, in m, as defined in Ch 4, Sec 5.

x_e : Distance, in m, to the hot spot from the closest end of the span ℓ_bdg, as defined in Figure 2.

Z_eff-n50 : Net section modulus, in cm³, of the considered stiffener calculated considering an effective breadth b_eff of attached plating.

b_eff : Effective breadth, in mm, of attached plating specified at the ends of the span and in way of end brackets and supports, taken as:

Figure 2 : Definition of effective span and x_e for hot spot

4.1.2 Stress due to static pressure

The hot spot stress due to local static pressure, in N/mm², for loading condition (j) is obtained from the following formula:

where:

P_{ls, (j)} : Static liquid tank pressure, in kN/m², in loading condition (j) specified in Ch 4, Sec 6, [1.1.1].

P_{bs, (j)} : Static dry bulk cargo pressure, in kN/m², in loading condition (j) specified in Ch 4, Sec 6, [2.4.1].

4.2 Stress due to relative displacement

4.2.1 General

the additional hot spot stress due to the relative displacement is to be considered.

4.2.2 Relative displacement definition

Where the stress at the hot spot location, i.e. at the flange of longitudinal, due to relative displacement is in tension, the sign of the relative displacement is positive.

4.2.4 Oil tankers

The additional hot spot stress due to relative displacement for load case i1 and i2 of loading condition (j) for an oil tanker is to be accounted for either using finite element method as described in [4.2.6] or by applying a stress factor on the local dynamic stress component as described in the following:

where:

σ_{LD, ik(j)} : Local dynamic stress defined in [4.1.1].

K_d : Bending stress factor for longitudinal stiffeners caused by relative displacement between supports, shown on Figure 3, as given in Table 2.

Figure 3 : K_d factor in full load condition for oil tanker with two longitudinal bulkheads

4.2.5 Bulk carriers

The additional hot spot stress due to relative displacement for load case i1 and i2 of loading condition (j) for a bulk carrier is to be calculated using finite element method as described in [4.2.6].

4.2.6 Stress due to relative displacement derived using FE method

The following procedure is based on a cargo hold model complying with Ch 7, Sec 2, [2] to calculate the stress due to relative displacements. The stress due to relative displacements, in N/mm², for load case i1 and i2 of loading condition (j) for both locations “a” and “f” is to be calculated directly using the following expression:

σ_{dD, ik(j)} = (k = 1, 2)

where:

a, f : Suffix which denotes the location as indicated in Figure 4.

Aft, Fwd: Suffix which denotes the direction, afterward (Aft) or forward (Fwd), from the transverse bulkhead. as shown in Figure 4.

K_b : Stress concentration factor due to bending for the location ‘a’ or ‘f’ which may correspond to points ‘A’ or ‘B’ as defined in Table 4.

σ_dFwd-a,ik(j), σ_dAft-a,ik(j), σ_dFwd-f,ik(j), σ_dAft-f,ik(j): Additional stress at location ‘a’ and ‘f’, in N/mm², due to the relative displacement between the transverse bulkhead including swash bulkhead or floors in way of stool and the forward (Fwd) and afterward (Aft) transverse web or floor respectively for load case i1 and i2 of loading condition (j), taken as:

I_Fwd-n50, I_Aft-n50: Net moment of inertia, in cm⁴ , of forward (Fwd) and afterward (Aft) longitudinal.

Z_Fwd-n50, Z_Aft-n50: Net section modulus of forward (Fwd) and afterward (Aft) stiffener, in cm³.

ℓ_Fwd, ℓ_Aft : Span, in m, of forward (Fwd) and afterward (Aft) longitudinal, as shown in Figure 4.

x_eFwd, x_eAft: Distance, in m, as shown in Figure 2, to the hot spot in location ‘a’ or ‘f’ from the closest end of ℓ_Fwd and ℓ_Aft respectively.

δ_Fwd,ik(j), δ_Aft,ik(j): Relative displacement in the direction perpendicular to the attached plate, in mm, between the transverse bulkhead (including swash bulkhead or floor in way of stools) and the forward (Fwd) or afterward (Aft) transverse web (or floor) as shown in Figure 4.

Figure 4 : Definition of the relative displacement (example of the side longitudinal)

4.2.7 Stress due to relative displacement in still water

The additional hot spot stress, in N/mm², in still water, due to the relative displacement in the direction perpendicular to the attached plate between the transverse bulkhead including swash bulkhead or floor in way of stools and the adjacent transverse web or floor is to be obtained according to procedures of [4.2.4] and [4.2.5] for oil tankers and bulk carriers respectively, replacing dynamic local stress σ_LD and dynamic pressure with static local stress σ_LS and static pressure.