Section 6 Hull bending strength
Clasification Society 2024 - Version 9.40
Clasifications Register Rules and Regulations - Rules and Regulations for the Classification of Inland Waterways Ships, July 2022 - Part 3 Ship Structures (General) - Chapter 4 Longitudinal Strength - Section 6 Hull bending strength

Section 6 Hull bending strength

Parent topic: Chapter 4 Longitudinal Strength

6.1 Symbols

6.1.1 The symbols used in this Section are defined as follows:
f1 = ship service factor
f2 = wave bending moment factor
Ms = design still water bending moment, sagging (negative) and hogging (positive), in kN m, to be taken negative or positive according to the convention given in Pt 3, Ch 4, 6.3 Design still water bending moments
= maximum permissible still water bending moment, sagging (negative) and hogging (positive), in kN m
Mw = design hull vertical wave bending moment, sagging (negative) and hogging (positive), in kN m, to be taken negative or positive according to the convention given in Pt 3, Ch 4, 6.2 Design vertical wave bending moments
Zc = actual hull section modulus, in m3, at continuous strength member above strength deck, calculated with the lever specified in Pt 3, Ch 3, 3.4 Calculation of hull section modulus
ZD, ZB = actual hull section moduli, in m3, at strength deck and keel respectively, see Pt 3, Ch 3, 3.4 Calculation of hull section modulus
σ = permissible combined stress (still water plus wave), in N/mm2, see Pt 3, Ch 4, 6.5 Permissible hull vertical bending stresses
σD, σB = maximum hull vertical bending stress at strength deck and keel respectively, in N/mm2
z = vertical distance from the hull transverse neutral axis to the position considered, in metres
zM = vertical distance, in metres, from the hull transverse neutral axis to the minimum limit of higher tensile steel, as defined in Pt 3, Ch 3, 2.6 Vertical extent of higher tensile steel, above or below the neutral axis as appropriate.

6.2 Design vertical wave bending moments

6.2.1 The appropriate hogging or sagging design hull vertical wave bending moment at amidships is given by the following:

Mw = f1 f2 Mwo
where
Mwo = 0,1C1C2L2B(Cb + 0,7) kN m
= (0,0102C1C2L2B(Cb + 0,7) tonne-f m)
Cb = is to be taken not less than 0,60
C2 = 1 (also defined in Pt 3, Ch 4, 6.2 Design vertical wave bending moments 6.2.2 at other positions along the length L)
f1 = ship service factor. For Zone 3 f1 = 0,100, for Zone 2 f1 = 0,207, for Zone 1 f1 = 0,311
f2 = −1,1 for sagging (negative) moment
f2 = for hogging (positive) moment

Table 4.6.1 Wave bending moment factor

Length L, in meters Factor C1
< 90 0,0412L + 4,0
90 to 135
6.2.2 The longitudinal distribution factor, C2, of wave bending moment is to be taken as follows:
  • 0 at the aft end of L;
  • 1,0 between 0,4L and 0,65L from aft;
  • 0 at the forward end of L.

Intermediate values are to be determined by linear interpolation.

6.2.3 For harbour the condition, a higher permissible still water bending moment can be assigned based on a reduced vertical wave bending moment given by:
  1. For harbour condition,

Mw = 0,5f1f2Mwo

6.3 Design still water bending moments

6.3.1 The design still water bending moment, Ms, hogging and sagging is the maximum moment calculated from the loading conditions, given in Pt 3, Ch 4, 6.3 Design still water bending moments 6.3.3, and is to satisfy the following relationship:

6.3.2 Still water bending moments are to be calculated along the ship length. For these calculations, downward loads are to be taken as positive values and are to be integrated in the forward direction from the aft end of L. Hogging bending moments are positive.

6.3.3 In general, the following loading conditions, based on amounts of bunkers, fresh water and stores at departure and arrival, are to be considered:
  1. Homogeneous loading conditions, at maximum draught.
    1. For non-propelled carriers, the vessel is considered to be homogeneously loaded at its maximum draught, without supplies nor ballast.
    2. For self-propelled carriers, the vessel is considered to be homogeneously loaded at its maximum draught with 10 per cent of supplies (without ballast).
  2. Ballast conditions.
  3. Special loading conditions, e.g. container or light load conditions at less than the maximum draught, heavy cargo, empty holds or non-homogeneous cargo conditions, deck cargo conditions, etc. where applicable.
  4. Loading/unloading in two runs or in one run according to the defined loading sequence in Pt 3, Ch 4, 2.3 Longitudinal strength categories. The vertical wave bending moment for the harbour condition in Pt 3, Ch 4, 6.2 Design vertical wave bending moments 6.2.3 might be used in case.
  5. Any other loading condition likely to result in high bending moments and/or shear forces (including docking conditions, as appropriate).

6.3.4 Where the amount and disposition of consumables at any intermediate stage of the voyage are considered more severe, calculations for such intermediate conditions are to be submitted in addition to those for departure and arrival conditions. Also, where any ballasting and/or de-ballasting is intended during the voyage, calculations of the intermediate condition just before and just after ballasting and/or de-ballasting any tank are to be submitted and, where approved, included in the loading manual for guidance.

6.4 Permissible still water bending moments

6.4.1 The permissible still water bending moments sagging and hogging are to be taken as the lesser of the following:
  1. kN m
  2. kN m
where
σ = the permissible combined stress in N/mm2 as given in Pt 3, Ch 4, 6.5 Permissible hull vertical bending stresses. Mw is the design wave bending moment, sagging or hogging as appropriate, in accordance with Pt 3, Ch 4, 6.2 Design vertical wave bending moments.

6.5 Permissible hull vertical bending stresses

6.5.1 The permissible combined (still water plus wave) stress for hull vertical bending, σ, is given by:

  1. Longitudinal bending:

  2. In ships with continuous hatch coamings:

    Longitudinal bending at top of coaming

6.5.2 The permissible combined stress σc being the sum of stresses due to longitudinal bending and local loading (σc= σs + σb) is:

6.5.3 For additional maximum stress requirements, see respective ship type Chapter.

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