Section 2 Hull girder strength

2.1.1 The requirements for longitudinal strength of trimarans are contained within this Section.

2.1.2 Longitudinal strength calculations are to be carried out for all vessels, covering the range of load and ballast conditions proposed, in order to determine the required hull girder strength. Still water, static wave and dynamic bending moments and shear forces are to be calculated for both departure and arrival conditions.

2.2.1 In general, the effective sectional area of continuous longitudinal strength members, after deduction of openings, is to be used for the calculation of the midship section modulus.

2.2.2 Initially, the side hulls and deck structure extending outside the breadth of the main hull may only be considered effective if the cross-deck length is greater than 0,4L. Additional structure may be incorporated into the section modulus calculations if proven effective by a global finite element analysis. This analysis must be submitted to and approved by LR.

2.2.3 In general, sections are to be evaluated along the length of the ship to adequately represent structural transitions. If portions of the side hull and decks outside the breadth of the main hull are considered longitudinally effective according to Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation 2.2.2, additional sections are to be calculated at amidships of the side hull, at side hull terminations, and at any other appropriate sections to capture the transitions of the side hulls.

2.2.4 In addition to meeting the requirement of Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation 2.2.2, in order for the full breadth of the deck structure to be effective in longitudinal bending, the taper ratio, as depicted in Figure 3.2.1 Taper ratio of cross-deck connecting main hull to side hull, is to be 3:1 or greater

Figure 3.2.1 Taper ratio of cross-deck connecting main hull to side hull

2.2.5 Deck and side hull plating located forward of the position on the side hull corresponding to the 3:1 taper ratio is to be considered ineffective, see Figure 3.2.2 Ineffective plating for lower taper ratios.

Figure 3.2.2 Ineffective plating for lower taper ratios

2.2.6 Structural members which contribute to the overall hull girder strength are to be carefully aligned so as to avoid discontinuities resulting in abrupt variations of stresses and are to be kept clear of any form of opening which may affect their structural performance.

2.2.7 In general, short superstructures or deckhouses will not be accepted as contributing to the global longitudinal or transverse strength of the ship. However, where it is proposed to include substantial, continuous stiffening members, special consideration will be given to their inclusion on submission of the designer's/builder's calculations.

2.2.8 Where continuous deck longitudinal or deck girders are arranged above the strength deck, special consideration may be given to the inclusion of their sectional area in the calculation of the hull section modulus.

2.2.9 Adequate transition arrangements are to be fitted at the ends of effective continuous longitudinal strength members in the deck and bottom structures.

2.2.10 Structural material which is longitudinally continuous but which is not considered to be fully effective for longitudinal strength purposes will need to be specially considered. The global longitudinal strength assessment must take into account the presence of such material when it can be considered effective. The consequences of failure of such structural material and subsequent redistribution of stresses into or additional loads imposed on the remaining structure must be considered.

2.2.11 In particular, all longitudinally continuous material will be fully effective in tension whereas this may not be so in compression due to a low buckling capability. In this case, it may be necessary to derive and apply different hull girder section moduli to the hogging and sagging bending moment cases.

2.2.12 Openings in decks, longitudinal bulkheads and other longitudinal effective material having a length in the fore and aft directions exceeding 0,1B m or 2,5 m or a breadth exceeding 1,2 m or 0,04B m whichever is the lesser, are in all cases to be deducted from the sectional areas used in the section modulus calculation. B is as defined in Vol 1, Pt 1, Ch 1, 5.2 Principal particulars.

2.2.13 Openings smaller than stated in Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation 2.2.9, including manholes, need not be deducted provided they are isolated and the sum of their breadths or shadow area breadths, see Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation 2.2.14, in one transverse section does reduce the section modulus at deck or bottom by more than 3 per cent.

2.2.14 The expression 0,06 (B ₁ – b ₁), where B ₁ equals the breadth of the ship at the section considered and equals the sum of the breadths of deductible openings, may be used for deck openings in lieu of the 3 per cent limitation of reduction of section modulus in Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation 2.2.13.

2.2.15 Where calculating deduction-free openings, the openings are assumed to have longitudinal extensions as shown by the shaded areas in Figure 3.2.3 Isolated openings. The shadow area is obtained by drawing two tangent lines to an opening angle of 30°. The section to be considered is to be perpendicular to the centreline of the ship and is to result in the maximum deduction in each transverse space.

Figure 3.2.3 Isolated openings

2.2.16 Isolated openings in longitudinals or longitudinal girders need not be deducted if their depth does not exceed 25 per cent of the web depth or 75 mm, whichever is the lesser.

2.2.17 Openings are considered isolated if they are spaced more than 1 m apart.

2.2.18 A reduction for drainage holes and scallops in beams and girder, etc. is not necessary so long as the global section modulus at deck or keel is reduced by no more than 0,5 per cent.

2.3.1 Higher tensile steel may be used for both deck and bottom structures or deck structure only. Where fitted for global strength purposes, it is to be used for the whole of the longitudinally continuous material for the following vertical distances:

1. z _htd below the line of deck at side

   

2. z _htb above the top of keel

   

   where

   F _D and F _B are not to be taken as less than k _g and are defined in Vol 1, Pt 6, Ch 3, 2.3 Higher tensile steel 2.3.2

   z _D, z _B and k _g and are defined in Vol 1, Pt 6, Ch 1, 1.3 Symbols and definitions.

2.3.2 Where the maximum hull vertical bending stress at the deck or keel is less than the permissible combined stress, σp, reductions in local scantlings within to 0,3L _R to 0,7L _R may be permitted. The reduction factors are defined as follows:

1. For hull members above the neutral axis

   

2. For hull member below the neutral axis

   

   where

   σ_D, σ_B and σ_ws are defined in Vol 1, Pt 6, Ch 1, 1.3 Symbols and definitions 1.3.1.

2.3.3 In general, the values of σ_D and σ_B to be used are the greater of the sagging or hogging stresses. F _D and F _B are not to be taken as less than 0,67 for plating and 0,75 for longitudinal stiffeners.

2.3.4 Where higher tensile steel is used in the hull structure, the values of F _D and F _B for the mild steel part are to be taken as not less than z/z _m

where

z and z _m are defined in Vol 1, Pt 6, Ch 1, 1.3 Symbols and definitions 1.3.1.

2.4.1 The effective geometric properties of all critical sections along the length of the ship are to be calculated directly from the dimensions of the section using only effective material elements which contribute to the global longitudinal strength irrespective of the grades of steel incorporated in the construction, see Vol 1, Pt 6, Ch 3, 2.2 Section modulus calculation.

2.4.2 Where higher tensile steel is fitted to satisfy global strength requirements, the extent of higher tensile steel is to be as specified in Vol 1, Pt 6, Ch 3, 2.3 Higher tensile steel. Where a mix of steel grades is used for plating and associated stiffeners, then the lower of the steel grades is to be used for the derivation of permissible stresses.

2.4.3 The longitudinal strength of the ship is to satisfy the following criteria for the hogging and sagging conditions:

where

σp	=	fσhg fhts σyd
fσhg	=	0,75 from 0,3LR to 0,7LR
	=	for continuous structural members aft of 0,3LR and forward of 0,7LR

Note that the σ_ws criteria may be relaxed if it can be demonstrated that either:

• A continuous fatigue monitoring system is to be adopted for the in-service life of the ship; or
• A fatigue design assessment procedure is applied which demonstrates that a higher limiting working stress coefficient, f _σws, may be applied.

σ_B, σ_D and σ_p are given in Table 3.2.1

f_hts, f_σhg, f_σws, M_wHog, M_wSag, M_tot, σ_yd and σ_ydMild are defined in Vol 1, Pt 6, Ch 1, 1.3 Symbols and definitions.

L_R is defined in Vol 1, Pt 1, Ch 1, 5.2 Principal particulars.

Component stress type	Nominal stress, N/mm2
Hull girder bending stress at strength deck, see Note 1
Hull girder bending stress at keel, see Note 1
Hull girder bending stress range, see Note 2
Note 1. The hogging and bending moments are to be considered. Note 2. The stress range at the keel or other longitudinally effective material should be used if it is greater than the stress range at the strength deck.

2.4.4 The design stress due to hull girder bending, σ_hg, for each structural member is given by:

2.4.5 Where different grades of steel are used then it should be ensured that the design stress in each structural member is less than the permissible hull vertical bending stress, i.e.

2.5.1 The hull midship section modulus about the transverse neutral axis, at the deck or the keel, is to be not less than:

2.6.1 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:

2.7.1 The shear strength of the vessel at any position along its length is to satisfy the following criteria: