5 Strength Check

5.1 General

5.1.1 Application

The strength check is applicable to rectangular hatch covers subjected to a uniform pressure, designed with primary supporting members arranged in one direction or as a grillage of longitudinal and transverse primary supporting members.

In the latter case, i.e. when the hatch cover is arranged as a grillage of longitudinal and transverse primary supporting members, or when the Society deems it necessary, the stresses in the primary supporting members are to be determined by a grillage or a finite element analysis.

It is to be checked that stresses induced by concentrated loads are in accordance with the criteria in [5.4.4]. When FE analysis is carried out, the buckling assessment as described in [5.2.3], [5.3.4] and [5.4.6] can be made considering only the stresses given by the FE analysis.

The hatch covers fitted with U type stiffeners as shown in Figure 1 are to be checked by means of FE analysis. In transverse section of the stiffener, nodes are to be located at the connection between the web of the U type stiffener and the hatch cover plate as well as at the connection between the web and the flange of the U type stiffener. The buckling assessment as described in [5.2.3], [5.3.4] and [5.4.6] can be made considering only the stresses given by the FE analysis.

Figure 1 : Example of hatch cover fitted with U type stiffener

5.1.2 Hatch covers supporting containers

The scantlings of hatch covers supporting containers are to comply with the applicable requirements of the Society.

5.1.3 Hatch covers subjected to special cargoes

For hatch covers supporting special cargoes, stiffeners and primary supporting members are generally to be checked by direct calculations, taking into account the stiffener arrangements and their relative inertia. It is to be checked that stresses induced by special cargoes are in accordance with the criteria in [5.4.4].

5.2 Plating

5.2.1 Net thickness

The net thickness, in mm, of steel hatch cover top plating is not to be taken less than:

where:

σ : Normal stress, in N/mm², in the attached plating of primary supporting members, calculated according to [5.4.3] or determined through a grillage analysis or a finite element analysis.

5.2.2 Minimum net thickness

In addition to [5.2.1], the net thickness, in mm, of the plating forming the top of the hatch cover is not to be taken less than the greater of the following values:

t = 6

5.2.3 Buckling strength

The buckling strength of the hatch cover plating subjected to loading conditions as defined in [4.1] is to comply with the following formula:

η_Plate ≤ η_all

where:

η_Plate : Maximum plate utilisation factor calculated according to Method A, as defined in Pt 1, Ch 8, Sec 5, [2.2].

• For stresses obtained from beam theory, i.e. not calculated by means of finite element analysis:
  • σ_x or σ_y is selected for the uniaxial check of the plate in the direction parallel to the primary supporting member,
  • τ = 0.
• For stresses calculated by means of finite element analysis: σ_x, σ_y, τ obtained from FE analysis.

η_all : Allowable utilisation factor, as given in Table 3.

For hatch covers fitted with U type stiffeners, the buckling panels b₁, b₂ and c (see Figure 1) are to be assessed separately.

5.3 Stiffeners

5.3.1 For flat bar stiffeners, the ratio h_w /t_w is to comply with the following formula:

5.3.2 Minimum net thickness of web

The net thickness, in mm, of the stiffener web is to be taken not less than 4 mm.

5.3.3 Net section modulus and net shear sectional area

The net section modulus Z, in cm³, and the net shear sectional area A_shr, in cm², of a stiffener subject to lateral pressure are to be taken not less than given by the following formulae:

where:

ℓ_s : Stiffener span, in m, to be taken as the spacing, in m, of primary supporting members or the distance between a primary supporting member and the edge support, as applicable. When brackets are fitted at both ends of all stiffener spans, the stiffener span may be reduced by an amount equal to 2/3 of the minimum brackets arm length, but not greater than 10% of the gross span, for each bracket.

5.3.4 Buckling strength

The buckling strength of the hatch cover stiffeners subjected to loading conditions as defined in [4.1] is to comply with the following formula:

η_Stiffener ≤ η_all

where:

η_Stiffener : Maximum stiffener utilisation factor calculated according to Pt 1, Ch 8, Sec 5, [2.3].

• For uniaxial stresses obtained by beam theory, i.e. not calculated by means of finite element analysis:
  • σ_x : stiffener axial stress,
  • σ_y = 0,
  • τ = 0.
• For stresses calculated by means of finite element analysis:
  • σ_x : stiffener axial stress from FE analysis,
  • σ_y : stress perpendicular to the stiffener,
  • τ : shear stress in the attached plate.

η_all : Allowable utilisation factor, as given in Table 3.

The buckling strength of the hatch cover fitted with U type stiffeners subjected to loading conditions as defined in [4.1] is to be checked as detailed above, considering the U type as an equivalent T-bar profile as follows:

• Web height taken equal to d as defined in Pt 1, Ch 3, Sec 6, Figure 21.
• Web thickness equal to 2 t_w.
• Flange breadth taken as b₃, as shown on Figure 1.
• Flange thickness taken as t_f, as shown on Figure 1.
• Effective width of the attached plating, b_eff, taken as:
  • 
  • where:
  • C_x1,C_x2 : Reduction factor defined in Pt 1, Ch 8, Sec 5, Table 3 calculated for the EPP b1 and b2 according to case 1.

5.4 Primary supporting members

5.4.1 Application

The requirements in [5.4.3] to [5.4.5] apply to primary supporting members which may be analysed through isolated beam models.

Primary supporting members whose arrangement is of a grillage type and which cannot be analysed through isolated beam models are to be checked by direct calculations, using the checking criteria in [5.4.4].

5.4.2 Minimum net thickness of web

The web net thickness of primary supporting members, in mm, is not to be less than 6 mm.

5.4.3 Normal and shear stress for isolated beam

In case that grillage analysis or finite element analysis are not carried out, according to the requirements in [5.1.1], the maximum normal stress σ and shear stress τ, in N/mm², in the primary supporting members are to be taken as given by the following formulae:

where:

ℓ_m : Bending span, in m, of the primary supporting member.

5.4.4 Checking criteria

The normal stress σ and the shear stress τ, calculated according to [5.4.3] or determined through a grillage analysis or finite element analysis, as the case may be, are to comply with the following formulae:

σ ≤ σ_a

τ ≤ τ_a

5.4.5 Deflection limit

The net moment of inertia of a primary supporting member, when loaded by sea pressure, excluding the selfweight of the structure, is to be such that the deflection does not exceed μ ℓ_max.

where:

ℓ_max : Greatest span, in m, of primary supporting members.

5.4.6 Buckling strength of the web panels of the primary supporting members

The web of primary supporting members subject to loading conditions as defined in [4.1] is to be taken as:

η_Plate ≤ η_all

where:

η_Plate : Maximum plate utilisation factor calculated according to Method A, as defined in Pt 1, Ch 8, Sec 5, [2.2]. For web plate in way of opening, it is to be calculated according to Method A, as defined in Pt 1, Ch 8, Sec 5, [2.4].

• Shear stress obtained by beam theory (i.e. calculated according to [5.4.3] or determined through a grillage analysis), or
• σ_x, σ_y, τ obtained by FE analysis.

η_all : Allowable utilisation factor, as given in Table 3.

5.4.7 Slenderness criteria

For buckling stiffeners on webs of primary supporting members, the ratio h_w/t_w is to comply with the following formula:

5.5 Stiffeners and primary supporting members of variable cross section

5.5.1 The net section modulus Z, in cm³, of stiffeners and primary supporting members with a variable cross section is to be taken not less than the greater of the values given by the following formulae:

where:

Z_CS : Net section modulus, in cm³, for a constant cross section, complying with the checking criteria in [5.4.4].

ℓ₁ : Length of the variable section part, in m, as shown in Figure 2.

ℓ₀ : Span measured, in m, between end supports, as shown in Figure 2.

Z₁ : Net section modulus at end, in cm³, as shown in Figure 2.

Z₀ : Net section modulus at mid-span, in cm³, as shown in Figure 2.

Moreover, the net moment of inertia, in cm⁴, of stiffeners and primary supporting members with a variable cross section is to be taken not less than the greater of the values given by the following formulae:

I = I_CS

where:

I_CS : Net moment of inertia, in cm⁴, with a constant cross section complying with [5.4.5].

ϕ : Coefficient taken equal to:

I₁ : Net moment of inertia at end, in cm⁴, as shown in Figure 2.

I₀ : Net moment of inertia at mid-span, in cm⁴, as shown in Figure 2.

The use of these formulae is limited to the determination of the strength of stiffeners and primary supporting members in which abrupt changes in the cross section do not occur along their length.

Figure 2 : Variable cross section stiffener