5 Analysis Criteria

5.1 General

5.1.1 Evaluation areas

Verification of results against the acceptance criteria is to be carried out within the longitudinal extent of the mid-hold, as shown in Figure 21 and Figure 22.

Figure 21 : Longitudinal extent of evaluation area for oil tanker

Figure 22 : Longitudinal extent of evaluation area for bulk carrier

5.1.2 Structural members

The following structural elements within the evaluation area are to be verified with the criteria given in [5.2] and [5.3]:

All hull girder longitudinal structural members,
All primary supporting structural members and bulkheads within the mid-hold,
All structural members being part of the transverse bulkheads, such as:
- For oil tanker: stringer, buttress structure, stool tanks, partial girders together with attached transverse structures,
- For bulk carrier: stool tanks together with connected longitudinal girders and double bottom floors,
All structural members being part of the collision bulkhead, and extending to one web frame spacing forward of the collision bulkhead,
All structural members being part of the forward transverse bulkhead of the machinery space and all hull girder longitudinal structural members aft of this transverse bulkhead within the extent of 15% of the aftmost cargo hold length excluding slop tanks.

5.2 Yield strength assessment

5.2.1 Von Mises stress

For all plates of the structural members defined in [5.1.2], the von Mises stress, σ_vm, in N/mm², is to be calculated based on the membrane normal and shear stresses of the shell element. The stresses are to be evaluated at the element centroid of the mid-plane (layer), as follows:

where:

σ_x , σ_y : Element normal membrane stresses, in N/mm².

τ_xy : Element shear stress, in N/mm².

5.2.2 Axial stress in beams and rod elements

For beams and rod elements, the axial stress, σ_axial, in N/mm², is to be calculated based on axial force alone. The axial stress is to be evaluated at the middle of element length.

5.2.3 Coarse mesh permissible yield utilisation factors

The coarse mesh permissible yield utilisation factors, λ_yperm, given in Table 10, are based on the mesh sizes and element types described in [2.3] to [2.4].

The yield utilisation factor resulting from element stresses of each structural component are not to exceed the permissible values as given in Table 10.

Table 10 : Coarse mesh permissible yield utilisation factor

Structural component	Coarse mesh permissible yield utilisation factor, λ_yperm
Plating of all longitudinal hull girder structural members, primary supporting structural members and bulkheads. Face plate of primary supporting members modelled using shell or rod elements. Dummy rod of corrugated bulkhead	1.0 (load combination S+D) 0.8 (load combination S)
Corrugation of vertically corrugated bulkheads with lower stool and horizontally corrugated bulkhead, under lateral pressure from liquid loads, for shell elements only. Supporting structure in way of lower end of corrugated bulkheads without lower stool ⁽¹⁾.	0.90 (load combination S+D) 0.72 (load combination S)
Corrugation of vertically corrugated bulkheads without lower stool under lateral pressure from liquid loads and without lower stool, for shell elements only.	0.81 (load combination S+D) 0.65 (load combination S)
(1) Supporting structure for a transverse corrugated bulkhead refers to the structure in the longitudinal direction within half a web frame space forward and aft of the bulkhead, and within a vertical extent equal to the corrugation depth. Supporting structure for a longitudinal corrugated bulkhead refers to the structure in transverse direction within 3 longitudinal stiffener spacings from each side of the bulkhead, and within a vertical extent equal to the corrugation depth.

5.2.4 Yield criteria

The structural elements given in [5.1.2] are to comply with the following criteria:

λ_y ≤ λ_yperm

where:

λ_y: Yield utilisation factor.

for shell elements in general.
for rod or beam elements in general.

σ_vm : Von Mises stress, in N/mm².

σ_axial : Axial stress in rod or beam element, in N/mm².

λ_yperm : Coarse mesh permissible yield utilisation factors defined in Table 10.

The yield check criteria is to be based on axial stress for the following members:

The flange of primary supporting members,
The intersections between the flange and web of the corrugations, according to [5.2.5].

Where the von Mises stress of the elements in the cargo hold FE model in way of the area under investigation by fine mesh exceeds the yield criteria, average von Mises stress, obtained from the fine mesh analysis, calculated over an area equivalent to the mesh size of the cargo hold finite element model is to satisfy the yield criteria above.

In way of cut-outs, yield utilisation factor is to be obtained with shear stress correction, as given in [5.2.6].

5.2.5 Corrugation of corrugated bulkhead

The stress in corrugation of corrugated bulkheads is to be evaluated based on:

a) The von Mises stress, σ_vm, in shell elements on the flange and web of the corrugation.
b) The axial stress, σ_axial, in dummy rod elements, modelled with unit cross sectional properties at the intersection between the flange and web of the corrugation.

5.2.6 Shear stress correction for cut-outs

Except as indicated in [5.2.7], the element shear stress in way of cut-outs in webs is to be corrected for loss in shear area in accordance with the following formula. The corrected element shear stress is to be used to calculate the von Mises stress of the element for verification against the yield criteria.

where:

τ_cor : Corrected element shear stress, in N/mm².

h : Height of web of girder, in mm, in way of opening, see Table 1. Where the geometry of the opening is modelled, h is to be taken as the height of web of the girder deducting the height of the modelled opening.

t_mod-n50 : Modelled web thickness, in mm, in way of opening.

A_shr-n50 : Effective net shear area of web, in mm², taken as the web area deducting the area lost of all openings, including slots for stiffeners, calculated in accordance with Ch 3, Sec 7, [1.4.8].

τ_elem : Element shear stress, in N/mm², before correction.

5.2.7 Exceptions for shear stress correction for openings

Correction of element shear stress due to presence of cut-outs is not required for cases given in Table 11 provided λ_y/C_r complies with the criteria given in [5.2.4].

Table 11 : Exceptions for shear stress correction

Identification	Figure	Difference between modelled shear area and the modelled shear area in % of the modelled shear area	Reduction factor for yield criteria, C_r
Upper and lower slots for local support stiffeners fitted with lugs or collar plates		< 15%	0.85
Upper or lower slots for local support stiffeners fitted with lugs or collar plates		< 20%	0.80
In way of opening; upper and lower slots for local support stiffeners fitted with collar plates		< 40%	0.60
A_shr-n50 :Effective net shear area of the web, in mm², taken as the web area without the all opening areas and without the slots for stiffeners, in accordance with Ch 3, Sec 7, [1.4.8].

5.3 Buckling strength assessment

5.3.1 All structural elements in FE analysis carried out in accordance with this Section are to be assessed individually against the buckling requirements as defined in Ch 8, Sec 4.