Hull bending strength
5.1 Symbols
5.1.1 The symbols used in this Section are defined as follows:
f1 = ship service factor
f2 = wave bending moment factor
FB = local scantling reduction factor for hull members below the neutral axis, see 5.7
FD = local scantling reduction factor for hull members above the neutral axis, see 5.7
Imin = minimum moment of inertia, of the hull midship
section about the transverse neutral axis, in m4 Ms = design still water bending moment, sagging (nega-
tive) and hogging (positive), in kN m (tonne-f m), to be taken negative or positive according to the convention given in 5.3.2
Ms = maximum permissible still water bending moment, sagging (negative) and hogging (positive), in kN m (tonne-f m), see 5.5
Mw = design hull vertical wave bending moment amid- ships, sagging (negative) and hogging (positive), in kN m (tonne-f m), to be taken negative or positive according to the convention given in 5.3.2
Zc = actual hull section modulus, in m3, at continuous
strength member above strength deck, calculated with the lever specified in Ch 3,3.4
ZD, ZB = actual hull section moduli, in m3, at strength deck
and keel respectively, see Ch 3,3.4
Zmin = minimum hull midship section modulus about the transverse neutral axis, in m3
sÿ = permissible combined stress (still water plus wave), in N/mm2(kgf/mm2), see 5.6
sD, sB = maximum hull vertical bending stress at strength
deck and keel respectively, in N/mm2(kgf/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 Ch 3,2.6, above or below the neutral axis as appropriate.
5.2 Design vertical wave bending moments
5.2.1 The appropriate hogging or sagging design hull vertical wave bending moment at amidships is given by the following:
Mw = f1f2Mwo
where
Cb is to be taken not less than 0,60
C1 is given in Table 4.5.1
C2 = 1, (also defined in 5.2.2 at other positions along the length L)
f1 = ship service factor. To be specially considered depending upon the service restriction and in any event should be not less than 0,5. For unrestricted sea-going service f1= 1,0
f2 = –1,1 for sagging (negative) moment
f2 = 1,9Cb for hogging (positive) moment (Cb+ 0,7)
Mwo = 0,1C1C2L2B (C
b+ 0,7) kN m
(0,0102C1C2L2B (C
b+ 0,7) tonne-f m)
Consideration will be given to direct calculations of long-term vertical wave bending moments, see 2.6.
5.2.2 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.
5.2.3 For operation in sheltered water or short voyages a higher permissible still water bending moment can be assigned based on a reduced vertical wave bending moment given by:
(a) For operating in sheltered water:
Mw = 0,5f2Mwo
(b) For short voyages:
Mw = 0,8f2Mwo
These expressions can only be used in the expression for permissible still water bending moment, see 5.5, and the relevant loading conditions are to be included in the Loading Manual, see 8.1.
5.2.4 ‘Short voyages’ are defined as voyages of limited duration in reasonable weather. ‘Reasonable weather’ and ‘sheltered water’ are defined in Pt 1, Ch 2,2.
5.3 Design still water bending moments
5.3.1 The design still water bending moment, Ms, hogging and sagging is the maximum moment calculated from the loading conditions, given in 5.3.3, and is to satisfy the following relationship:
| Ms| £ | Ms|
5.3.2 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.
Part 3, Chapter 4
Section 5 Length L, in metres <90 90 to 300 >300 £350 >350 £500 Table 4.5.1 Factor C1 0,0412L + 4,0 10,75 10,75 –(
300 – L)
1,5 100 10,75 –(
L – 350)
1,5 100Longitudinal Strength
(e) Liquefied gas carriers:
(i) Homogeneous loading conditions for all approved cargoes.
(ii) Ballast conditions.
(iii) Cargo conditions where one or more tanks are empty or partially filled or where more than one type of cargo having significantly different densi- ties is carried.
(f) All ships:
(i) Any other loading condition likely to result in high bending moments and/or shear forces (including docking conditions, as appropriate).
5.4 Minimum hull section modulus
5.4.1 The hull midship section modulus about the transverse neutral axis, at the deck or the keel, is to be not less than:
Zmin = f1kLC1L2B (C
b+ 0,7) x 10–6 m3
and
f1 is to be taken not less than 0,5.
5.4.2 For materials to be included in the calculation of actual hull section properties, see Ch 3,3.
5.4.3 The midship section modulus for ships with a service restriction notation is to be not less than half the minimum value required for unrestricted service.
5.4.4 Scantlings of all continuous longitudinal members of the hull girder based on the minimum section modulus requirements given in 5.4.1 are to be maintained within 0,4L amidships. However, in special cases, based on considera- tion of type of ship, hull form and loading conditions, the scantlings may be gradually reduced towards the ends of the 0,4L part, bearing in mind the desire not to inhibit the vessel’s loading flexibility.
5.5 Permissible still water bending moments
5.5.1 The permissible still water bending moments sagging and hogging are to be taken as the lesser of the following: (a) | Ms| = FDsZDx 103– | M w| kN m (tonne-f m) (b) | Ms| = FBsZBx 103– | M w| kN m (tonne-f m) where
s = the permissible combined stress in N/mm2
(kgf/mm2) is given in 5.6 and F
Dand FBare defined
in 5.7.2. Mwis the design wave bending moment, sagging or hogging as appropriate, in accordance with 5.2.
5.3.3 In general, the following loading conditions, based on amount of bunkers, fresh water and stores at departure and arrival, are to be considered. In design ballast conditions, partial filling of peak tanks is not acceptable unless means are provided to prevent the design partial filling levels being exceeded. Where the design ballast condition includes partial filling of the peak tanks, alarms are to be provided to indicate when the ballast water reaches its permitted level. Details of the arrangements to prevent overfilling are to be submitted for approval.
(a) General cargo ships, container ships, passenger ships, roll on-roll off ships and refrigerated cargo carriers:
(i) Homogeneous loading conditions, at maximum draught.
(ii) Ballast conditions.
(iii) 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.
(b) Bulk carriers, ore carriers and combination carriers (i) For ships of length, L, less than 150 m:
Alternate hold loading conditions at maximum draught, where applicable.
Homogeneous loading conditions at maximum draught.
Ballast conditions, including intermediate condi- tions associated with ballast exchange at sea. Special conditions, e.g. deck cargo conditions. For combination carriers, the conditions as specified in (c) for oil tankers are also to be considered.
(ii) For ships of length, L, 150 m or above:
Alternate light and heavy cargo loading condi- tions at maximum draught, where applicable. Homogeneous light and heavy cargo loading conditions at maximum draught.
Ballast conditions.
Short voyage conditions where the ship is loaded to maximum draught with reduced bunkers. Multiple port loading/unloading conditions, where applicable.
Deck cargo conditions, where applicable. Typical loading and discharging sequences from commencement to end of cargo operation, for homogeneous, alternate and part load condi- tions, where applicable.
Typical sequences for exchange of ballast at sea, where applicable.
For combination carriers the conditions as speci- fied in (c) for oil tankers are also to be considered. (c) Oil tankers:
(i) Homogeneous loading conditions (excluding dry and clean ballast tanks) and ballast or part loaded conditions.
(ii) Any specified non-uniform distribution of loading. (iii) Mid-voyage conditions relating to tank cleaning or other operations where these differ significantly from the ballast conditions.
(d) Chemical tankers:
(i) Conditions as specified for oil tankers.
(ii) Conditions for high density or segregated cargo.
RULES ANDREGULATIONS FOR THECLASSIFICATION OFSHIPS, July 2000
Part 3, Chapter 4
Section 5LLOYD’SREGISTER OFSHIPPING
Longitudinal Strength
5.6 Permissible hull vertical bending stresses
5.6.1 The permissible combined (still water plus wave) stress for hull vertical bending, s, is given by:
(a) Within 0,4L amidships
sÿ = N/mm2
(
kgf/mm2)
(b) for continuous longitudinal structural members outside 0,4L amidships
sÿ =
(
75 + 543 – 699( )
2)
N/mm2(
sÿ =(
75 + 543 – 699( )
2)
kgf/mm2)
where d is the distance, in metres, from the F.P. (for the fore end region) or from the A.P. (for the aft end region), as appro- priate, to the location under consideration.
Special consideration will be given to increasing the permissible stress outside 0,4L amidships to
N/mm2
(
kgf/mm2)
provided that sufficient buckling checks are carried out.
5.6.2 The requirements for ships of special or unusual design and for the carriage of special cargoes will be individually considered.
5.7 Local reduction factors
5.7.1 The maximum hull vertical bending stresses at deck, sD, and keel, sB, are given by the following, using the appropriate combination of bending moments to give sagging and hogging stresses:
sD = x 10–3 N/mm2 (kgf/mm2)
sB = x 10–3 N/mm2 (kgf/mm2)
Where the ship is always in the hogging condition, the sagging bending moment is to be specially considered.
5.7.2 Where the maximum hull vertical bending stress at deck or keel is less than the permissible combined stress, s, reductions in local scantlings within 0,4L amidships may be permitted. The reduction factors applicable in Part 4 are defined as follows:
For hull members above the neutral axis
FD =
For hull members below the neutral axis
FB =
In general the values of sDand sBto be used are the greater of the sagging or hogging stresses, and FDand FBare not to be taken less than 0,67 for plating and 0,75 for longitudinal stiffeners. sB s sD s | Ms+ Mw| ZB | Ms+ Mw| ZD 17,84 kL 175 kL 0,102 kL d L d L 1 kL d L d L 17,84 kL 175 kL
5.7.3 Where higher tensile steel is used in the hull struc- ture, the values of FDand FBfor the mild steel part are to be taken as not less than .
5.8 Hull moment of inertia
5.8.1 The hull midship section moment of inertia about the transverse neutral axis is to be not less than the following using the maximum total bending moment, sagging or hogging:
Imin = x 10–5 m4
where values of s are given in 5.6.1.
5.9 Continuous strength members above strength deck
5.9.1 Where trunk decks or continuous hatch coamings are effectively supported or deck longitudinals or girders are fitted above the strength deck, the modulus Zc is to be not less than Zmin. The scantling reduction factor, FD, referred to strength deck at side, is applicable and, in addition to the requirement given in 5.5.1, the permissible still water bending moments, sagging and hogging, are not to exceed:
| Ms| = sÿZc x 103– | M
w| kN m (tonne-f m)
where
Mwis the design wave bending moment sagging or hogging, as appropriate, in accordance with 5.2.