Khasiat Fadhilat (Isnad) Doa Haikal - Majmu' Syarif

Calculation of the strength characteristics of hull girder transverse sections

Ref: BV Rules 2005.

2.1	Hull girder transverse sections

2.1.1

General

Hull girder transverse sections are to be considered as being constituted by the members contributing to the hull girder longitudinal strength, i.e. all continuous longitudinal members below the strength deck defined in [2.2] , taking into account the requirements in [2.1.2] to [2.1.9] .
These members are to be considered as having (see also Ch 4, Sec 2 ):

• gross scantlings, when the hull girder strength characteristics to be calculated are used for the yielding checks in Ch 6, Sec 2
• net scantlings, when the hull girder strength characteristics to be calculated are used for the ultimate strength checks in Ch 6, Sec 3 and for calculating the hull girder stresses for the strength checks of plating, ordinary stiffeners and primary supporting members in Part B, Chapter 7 .

2.1.2

Continuous trunks and continuous longitudinal hatch coamings

Continuous trunks and continuous longitudinal hatch coamings may be included in the hull girder transverse sections, provided they are effectively supported by longitudinal bulkheads or primary supporting members.

2.1.3

Longitudinal ordinary stiffeners or girders welded above the decks

Longitudinal ordinary stiffeners or girders welded above the decks (including the deck of any trunk fitted as specified in [2.1.2] ) may be included in the hull girder transverse sections.

2.1.4

Longitudinal girders between hatchways

Where longitudinal girders are fitted between hatchways, the sectional area that can be included in the hull girder transverse sections is obtained, in m², from the following formula:
A_EFF = A_LG a
where:

ALG

:

Sectional area, in m2, of longitudinal girders

a

:

Coefficient: for longitudinal girders effectively supported by longitudinal bulkheads or primary supporting members: a = 1 for longitudinal girders not effectively supported by longitudinal bulkheads or primary supporting members and having dimensions and scantlings such that l0 / r £ 60: for longitudinal girders not effectively supported by longitudinal bulkheads or primary supporting members and having dimensions and scantlings such that l0 / r > 60: a = 0

l0

:

Span, in m, of longitudinal girders, to be taken as shown in Fig 1

r

:

Minimum radius of gyration, in m, of the longitudinal girder transverse section

s, b1

:

Dimensions, in m, defined in Fig 1 .

Figure 1 - Longitudinal girders between hatchways

2.1.5

Longitudinal bulkheads with vertical corrugations

Longitudinal bulkheads with vertical corrugations may not be included in the hull girder transverse sections.

2.1.6

Members in materials other than steel

Where a member contributing to the longitudinal strength is made in material other than steel with a Young's modulus E equal to 2,06 10⁵ N/mm², the steel equivalent sectional area that may be included in the hull girder transverse sections is obtained, in m², from the following formula:

where:

AM

:

Sectional area, in m2, of the member under consideration.

2.1.7

Large openings

Large openings are:

• elliptical openings exceeding 2,5 m in length or 1,2 m in breadth
• circular openings exceeding 0,9 m in diameter.

Large openings and scallops, where scallop welding is applied, are always to be deducted from the sectional areas included in the hull girder transverse sections.

2.1.8

Small openings

Smaller openings than those in [2.1.7] in one transverse section in the strength deck or bottom area need not be deducted from the sectional areas included in the hull girder transverse sections, provided that:
Sb_S £ 0,06 (B - Sb)
where:

SbS

:

Total breadth of small openings, in m, in the strength deck or bottom area at the transverse section considered, determined as indicated in Fig 2

Sb

:

Total breadth of large openings, in m, at the transverse section considered, determined as indicated in Fig 2

Where the total breadth of small openings Sb_S does not fulfil the above criteria, only the excess of breadth is to be deducted from the sectional areas included in the hull girder transverse sections.

2.1.9

Lightening holes, draining holes and single scallops

Lightening holes, draining holes and single scallops in longitudinals need not be deducted if their height is less than 0,25 h_W , without being greater than 75 mm, where h_W is the web height, in mm, defined in Ch 4, Sec 3 .
Otherwise, the excess is to be deducted from the sectional area or compensated.

Figure 2 - Calculation of Σb and ΣbS

2.2	Strength deck

2.2.1

The strength deck is, in general, the uppermost continuous deck.
In the case of a superstructure or deckhouses contributing to the longitudinal strength, the strength deck is the deck of the superstructure or the deck of the uppermost deckhouse.

2.2.2

A superstructure extending at least 0,15 L within 0,4 L amidships may generally be considered as contributing to the longitudinal strength. For other superstructures and for deckhouses, their contribution to the longitudinal strength is to be assessed on a case by case basis, through a finite element analysis of the whole ship, which takes into account the general arrangement of the longitudinal elements (side, decks, bulkheads).
The presence of openings in the side shell and longitudinal bulkheads is to be taken into account in the analysis. This may be done in two ways:

• by including these openings in the finite element model
• by assigning to the plate panel between the side frames beside each opening an equivalent thickness, in mm, obtained from the following formula:
  
  
  where (see Fig 3 ):

  lP

  :

  Longitudinal distance, in m, between the frames beside the opening

  h

  :

  Height, in m, of openings

  IJ

  :

  Moment of inertia, in m4, of the opening jamb about the transverse axis y-y

  AJ

  :

  Shear area, in m2, of the opening jamb in the direction of the longitudinal axis x-x

  Figure 3 - Side openings

  G

  :

  Coulomb's modulus, in N/mm2, of the material used for the opening jamb, to be taken equal to: for steels: G = 8,0.104 N/mm2 for aluminium alloys: G = 2,7.104 N/mm2.

2.3	Section modulus

2.3.1

The section modulus at any point of a hull transverse section is obtained, in m³, from the following formula:

where:

IY

:

Moment of inertia, in m4, of the hull transverse section defined in [2.1] , about its horizontal neutral axis

z

:

Z co-ordinate, in m, of the calculation point with respect to the reference co-ordinate system defined in Ch 1, Sec 2, [4]

N

:

Z co-ordinate, in m, of the centre of gravity of the hull transverse section defined in [2.1] , with respect to the reference co-ordinate system defined in Ch 1, Sec 2, [4] .

2.3.2

The section moduli at bottom and at deck are obtained, in m³, from the following formulae:

• at bottom:
  
• at deck:
  

where:

IY, N

:

Defined in [2.3.1]

VD

:

Vertical distance, in m: in general: VD = zD - N where: zD : Z co-ordinate, in m, of strength deck, defined in [2.2] , with respect to the reference co-ordinate system defined in Ch 1, Sec 2, [4] if continuous trunks or hatch coamings are taken into account in the calculation of IY , as specified in [2.1.2] : where: yT, zT : Y and Z co-ordinates, in m, of the top of continuous trunk or hatch coaming with respect to the reference co-ordinate system defined in Ch 1, Sec 2, [4] ; yT and zT are to be measured for the point which maximises the value of VD if longitudinal ordinary stiffeners or girders welded above the strength deck are taken into account in the calculation of IY , as specified in [2.1.3] , VD is to be obtained from the formula given above for continuous trunks and hatch coamings. In this case, yT and zT are the Y and Z co-ordinates, in m, of the top of the longitudinal stiffeners or girders with respect to the reference co-ordinate system defined in Ch 1, Sec 2, [4] .

2.4	Moments of inertia

2.4.1

The moments of inertia I_Y and I_Z , in m⁴, are those, calculated about the horizontal and vertical neutral axes, respectively, of the hull transverse sections defined in [2.1] .

2.5	First moment

2.5.1

The first moment S, in m³, at a level z above the baseline is that, calculated with respect to the horizontal neutral axis, of the portion of the hull transverse sections defined in [2.1] located above the z level.

2.6	Structural models for the calculation of normal warping stresses and shear stresses

2.6.1

The structural models that can be used for the calculation of normal warping stresses, induced by torque, and shear stresses, induced by shear forces or torque, are:

• three dimensional finite element models
• thin walled beam models

representing the members which constitute the hull girder transverse sections according to [2.1] .