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Structural DesignAssessment

Primary Structure of Tankers

Guidance on direct calculations

May 2004

ShipRightDesign and construction

ABCD Lloyd’s Register Marine Business Stream 71 Fenchurch Street London EC3M 4BS Telephone 020 7709 9166 Telex 888379 LR LON G Fax 020 7488 4796

Lloyd's Register, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as the ‘Lloyd's Register Group’. The Lloyd's Register Group assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Lloyd's Register Group entity for the provision of this information or advice and in that case any responsibility. Lloyd’s Register Marine Business Stream is a part of Lloyd’s Register.

Lloyd’s Register,2004

Document History

Document Date: Notes:

October 1994 New document covering Primary Structure of Tankers

April 1996 Primary Structure of Bulk Carriers incorporated.

November 2001 Intranet user review version

July 2002 General release (Primary Structure of Bulk Carriers removed).

Notice 1 October 2002

Revisions as identified in ‘ History of Development up to January 2004’.

May 2004 Revisions as identified in ‘Structural Design Assessment – Primary structure of Tankers, Changes incorporated in May 2004 version’.

Primary Structure of Tankers, May 2004

Contents

Lloyd’s Register

Contents

Chapter 1 Introduction 1 Section 1 Application 1 2 Symbols 3 3 Direct calculation procedure report 4

Chapter 2 Primary Structure of Tankers 5 Section 1 Objectives 5 2 Structural modelling 5 3 Boundary conditions 15 3.1 General 3.2 Boundary conditions for local stress loadcases (symmetric loads) 3.3 Boundary conditions for local stress loadcases (asymmetric loads) 3.4 Boundary conditions for global stress loadcases (hull girder bending moments) 3.5 Boundary conditions for global stress loadcases (hull girder shear forces) 4 Loading conditions 27 4.1 General 4.2 Special loading and assessment conditions for ship with two oiltight longitudinal bulkheads and cross-tie arrangement in the centre tanks 4.3 Local stress load cases 4.4 Global stress load cases 4.5 Combination of load cases 5 Permissible stresses 38 6 Buckling acceptance criteria 40 7 Deflection of primary members 43


Chapter 1 SECTION 1

Lloyd's Register 1

Introduction

Section 1: Application

Section 2: Symbols Section 3: Direct calculation procedure report ■ Section 1: Application 1.1 The ShipRight Structural Design Assessment (SDA) procedure is mandatory for oil tankers greater than 190 m in length and for other tankers of abnormal hull form, or of unusual structural configuration or complexity. 1.2 When applied on a mandatory basis, the SDA procedure must be utilised in conjunction with both the ShipRight Fatigue Design Assessment (FDA) and Construction Monitoring (CM) procedures. 1.3 For tankers, other than those defined in 1.1, the SDA and/or FDA procedures may be applied on a voluntary basis. 1.4 The SDA procedure requires: • A detailed analysis of the ship’s structural response to applied static and quasi-dynamic loadings using finite

element analysis. • Sloshing analysis. When applicable, assessment of the strength of tank boundary structures against collapse due to

the dynamic loads imposed by the sloshing of liquids in partially filled tanks. • Other direct calculations as applicable. 1.5 This document details the SDA procedure for finite element analysis of the ship’s structure. The requirements for the sloshing analysis are given in the ShipRight SDA – Sloshing Loads and Scantling Assessment procedures manual. 1.6 The structural model and applied load cases detailed in this document will enable the following structural responses to be investigated: • Stresses in longitudinal primary members resulting from local loads and hull girder bending loads. • Stresses in transverse primary members including transverse bulkheads. • Buckling behaviour of primary structure. 1.7 The direct calculation of the ship’s structural response is to be based on a three-dimensional finite element analysis (3-D FEA) carried out in accordance with this procedure.


Chapter 1 SECTION 1

2 Lloyd’s Register

1.8 A detailed report of the calculations is to be submitted and must include the information detailed in Section 3. The report must show compliance with the specified required structural design criteria in Sections 5, 6 and 7. 1.9 If the computer programs employed are not recognised by Lloyd’s Register, full particulars of the programs will also require to be submitted, see Pt 3, Ch 1,3.1 of Lloyd’s Register’s Rules and Regulations for the Classification of Ships (hereinafter referred to as the Rules for Ships). 1.10 Lloyd’s Register may, in certain circumstances, require the submission of computer input and output in suitable electronic format to further verify the adequacy of the calculations carried out. 1.11 Where alternative procedures are proposed, these are to be agreed with Lloyd’s Register before commencement. 1.12 Tankers of unusual form or structural arrangements may need special consideration and additional calculations to those contained in this procedure may be required. 1.13 For tankers with two longitudinal bulkheads arrangement with a cross-tie in the centre tank, alternative assessment procedures are specified depending on the operational design requirement. Depending on the procedure followed, restrictions may be applied on the loading conditions permitted in service. Such restrictions are to be included in the Loading Manual, see para 4.3. 1.14 It is recommended that the designer consults with Lloyd’s Register on the SDA analysis requirements early on in the design cycle.


Chapter 1 SECTION 2

Lloyd's Register 3

■ Section 2: Symbols 2.1 For the purpose of this procedure the following definitions apply: L = Rule length, in metres, see Pt 3, Ch 1,6 of the Rules for Ships B = moulded breadth, in metres, see Pt.3, Ch 1,6 of the Rules for Ships D = depth of ship, in metres, see Pt 3, Ch 1,6 of the Rules for Ships kL, k = higher tensile steel factor, see Pt 3, Ch 2,1.2 of the Rules for Ships

MW = design vertical wave bending moment, including hog and sag factor, f2, and ship service factor, f1, see Pt 3, Ch 4,5 of the Rules for Ships

MWO = design vertical wave bending moment, excluding hogging and sagging factor and ship service factor, see Pt 3, Ch 4,5 of the Rules for Ships

f1 = the ship service factor, see Pt 3, Ch 4,5 of the Rules for Ships f2 = the hogging/sagging factor, see Pt 3, Ch 4,5 of the Rules for Ships

MS = Rule permissible still water bending moment, see Pt 3, Ch 4,5 of the Rules for Ships Ms = design still water bending moment, see Pt 3, Ch 4,5 of the Rules for Ships Msw = the still water bending moment distribution envelope to be applied to the FE models for stress and

buckling assessments. The values of Msw are to be greater than Ms and less or equal to MS. Msw are to be incorporated into the ship’s Loading Manual and loading instrument as the assigned permissible still water bending moment values. Msw is hereinafter referred as the permissible still water bending moment.

Tsc = scantling draught, in metres Cb = block coefficient, see Pt 3, Ch 1,6 of the Rules for Ships x = longitudinal distance, in metres, from amidships to the centre of gravity of the tank, x is positive

forward of amidships V = service speed, in knots, see Pt 3, Ch 1,6 of the Rules for Ships g = gravity constant ρ = density of sea-water (specific gravity to be taken as 1,025) h = local head for pressure evaluation ρc = density of cargo (specific gravity to be taken not less than 1,025) t = thickness of plating tc = thickness deduction for corrosion σcr = critical buckling stress corrected for plasticity effects σc = elastic critical buckling stress σo = specified minimum yield stress of material (special consideration will be given to steel where

σ0 ≥ 355 N/mm2, see Pt 3, Ch 2,1 of the Rules for Ships)

σL = L

235k

λ = factor against buckling σe = von Mises equivalent stress, given by

σe = σ σ σ σ τx y x y xy2 2 23+ − +

σx = direct stress in element x direction σy = direct stress in element y direction τxy = shear stress in element xy plane σ = total stress in local bending direction τ = mean shear stress over depth of web plate

2.2 Consistent units to be used throughout all parts of the analysis. Results presentation in N and mm preferred. 2.3 All Rule equations are to use units as defined in the Rules for Ships.


Chapter 1 SECTION 3


■ Section 3: Direct calculation procedure report 3.1 A report is to be submitted to Lloyd’s Register for approval of the primary structure of the ship and is to contain: • list of plans used including dates and versions; • detailed description of structural modelling including all modelling assumptions; • plots to demonstrate correct structural modelling and assigned properties; • details of material properties used; • details of boundary conditions; • details of all loading conditions reviewed with calculated SF and BM distributions; • details of applied loadings and confirmation that individual and total applied loads are correct; • plots and results that demonstrate the correct behaviour of the structural model to the applied loads; • summaries and plots of global and local deflections; • summaries and sufficient plots of von Mises, directional and shear stresses to demonstrate that the design criteria are

not exceeded in any member; • plate buckling analysis and results; • tabulated results showing compliance, or otherwise, with the design criteria; • proposed amendments to structure where necessary, including revised assessment of stresses and buckling

properties.


Chapter 2 SECTIONS 1 & 2

Lloyd's Register 5

Primary Structure of Tankers

Section 1: Objectives Section 2: Structural modelling Section 3: Boundary conditions Section 4: Loading conditions Section 5: Permissible stresses Section 6: Buckling acceptance criteria Section 7: Deflection of primary members

■ Section 1: Objectives 1.1 The objective of the structural analysis is to verify that the stress level and buckling capability of primary structures under the applied static and quasi-dynamic loads are within the acceptable limits.

■ Section 2: Structural modelling 2.1 In general, a 3-D finite plate element model of two-tank lengths located at about amidships is to be considered. The ends of the finite element (FE) model are to be located at the mid-tank position. A typical FE model is shown in Fig. 2.2.1 and Fig. 2.2.2. 2.2 This length of FE model is to enable the ship’s structure over the major cargo tank region to be assessed. If the cargo tank structure in the after and forward tank(s) is significantly different from the midships tank arrangement, then an extended or additional FE model is required. 2.3 The appropriate length of the FE model depends on the tank arrangement and is to be agreed with Lloyd’s Register at an early stage. 2.4 Unless there is asymmetry of the ship about the ship’s centreline, then only one side of the ship needs to be represented with appropriate boundary conditions imposed at the centreline. However, it is strongly recommended that both sides of the ship be modelled, as this will simplify the loading and analysis of asymmetrical loading conditions. The full depth of the ship is to be modelled. 2.5 The FE model of the ship structure is to be represented using a right handed Cartesian co-ordinate system with: X measured in the longitudinal direction, positive forward, Y measured in the transverse direction, positive to port from the centreline, Z measured in the vertical direction, positive upwards from the baseline.


Chapter 2 SECTION 2


2.6 Typical FE arrangements representing a double hull VLCC design with primary members are shown in Figs. 2.2.1 to 2.2.5. The proposed scantlings, excluding Owner’s extras or any additional thickness for ShipRight ES procedure are to be used throughout the FE model. The selected size and type of plate elements are to provide a satisfactory representation of the deflection and stress distribution within the structure. 2.7 In general the plate element mesh is to follow the primary stiffening arrangement as appropriate. The coarse mesh size should not be greater than: • transversely, one element between every longitudinal stiffener; • longitudinally, two elements between double bottom floors; • vertically, one element between longitudinal stiffeners; and • three or more elements over the depth of double bottom girders, floors and side transverses with adjacent structure

modelled to suit. • Reduced sized elements, in the order of 450mm x 450mm, are to be incorporated at stress concentrations such as

bracket toes, hopper knuckles, etc. 2.8 Where the mesh size of the coarse 3-D finite plate element model is insufficiently detailed to represent areas of localised higher stresses, these are to be investigated by means of separate local fine mesh models with boundary conditions derived from the main model. Alternatively, local fine mesh regions may be introduced into the main model. In general the requirements to use fine mesh models or fine mesh regions within the main model will be subject to the results from the main structural model. Proposals for follow-on fine mesh analysis should be submitted for approval. 2.9 The following structural items are to be investigated by fine mesh models unless it can be demonstrated by previous finite element investigation that the arrangements proposed are acceptable. • Hopper knuckle. • Transverse Stringer connections to inner skin structure and longitudinal bulkhead structure. • Secondary member end connection in way of primary members, which do not satisfy the relative deflection criteria

specified in section 7. 2.10 The mesh size in fine mesh regions is to be approximately 15t x 15t or 200 x 200 mm, whichever is the lesser, where t is the primary member thickness. The mesh size is not to be less than t x t. 2.11 In the coarse 3-D model, secondary stiffening members are to be modelled using line elements positioned in the plane of the plating having axial and bending properties (bars), which may be grouped as necessary. The bar elements are to have: • a cross-sectional area representing the stiffener area, excluding the area of attached plating (grouped as appropriate);

and • bending properties representing the combined attached plating and stiffener inertia (grouped as appropriate). 2.12 The permissible stresses and buckling criteria are based on membrane stress. However, the use of plate elements with bending properties may be preferred, as this can avoid the problems of low or zero stiffness for out-of-plane degrees of freedom associated with pure membrane elements and/or rod elements. In the latter case the membrane stress result is to be used for comparison with the acceptance stress criteria. 2.13 In general, the use of triangular plate elements is to be kept to a minimum. Where possible they should be avoided in areas where there are likely to be high stresses or a high stress gradient. These areas include: • in way of lightning /access holes; • in way of the connection between the corrugated bulkhead and inner bottom or stool; and • adjacent to knuckles or structural discontinuities.


Chapter 2 SECTION 2

Lloyd's Register 7

2.14 Lightening holes, access openings, etc., in primary structure should be represented in high stress area, such as double bottom girders adjacent to transverse bulkheads and floor plates adjacent to the hopper knuckle. Additional mesh refinement may be necessary to model these openings but it may be sufficient to represent the effect of an opening by deleting the appropriate elements. 2.15 Lightening holes, access openings, etc., away from the above locations may be modelled by deleting the appropriate elements or may be take into account by applying a correction to the resulting shear stresses, see 5.5. 2.16 Face plates and plate panel stiffeners of primary members are to be represented by line elements with a cross-sectional area modified, where appropriate, in accordance with, Table 2.2.1 and Fig. 2.2.6.


Chapter 2 SECTION 2


Fig. 2.2.1 3-D Finite plate element model


Chapter 2 SECTION 2

Lloyd's Register 9

Fig. 2.2.2 3-D Finite plate element model


Chapter 2 SECTION 2


Fig. 2.2.3 Typical transverse frame


Chapter 2 SECTION 2

Lloyd's Register 11

Fig. 2.2.4 Typical transverse bulkhead horizontal girder


Chapter 2 SECTION 2


Fig. 2.2.5 Typical centreline girder


Chapter 2 SECTION 2

Lloyd's Register 13

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Effective area of face bars = b f tf

0,5b f

Effective Area of Face Bars

R

Effective area of symmetrical face bars

0

tf

Rt f

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Effective area of asymmetric face bars

0

Rt f

b f

R

b f

tf

Effective area of face bars = b f tf

b f

moss227

Fig. 2.2.6 Effective area of face bars


Chapter 2 SECTION 2


Table 2.2.1 Line element effective cross-section area Structure represented by line element Effective area, Ae

Primary member face bars Symmetrical Asymmetrical

Ae = 100% An Ae = 100% An

Curved bracket face bars (continuous)

Symmetrical Asymmetrical From Fig. 2.2.6

Straight bracket face bars (discontinuous)

Symmetrical Asymmetrical

Ae = 100% An Ae = 60% An

Straight portion

Symmetrical Asymmetrical

Ae = 100% An Ae = 60% An Straight bracket face bars

(continuous around toe curvature) Curved portion Symmetrical

Asymmetrical From Fig. 2.2.6

Flat bars Ae = 25% stiffener area

Web stiffeners - sniped both ends Other sections

A AYr

Ae P=

+

−

1 02

Flat bars Ae = 75% stiffener area

Web stiffeners - sniped one end, connected other end Other sections

A AY

r

Ae p=

+

−

12

02

Symbols

A = cross-section area of stiffener and associated plating An = average face bar area over length of line element Ap = cross-section area of associated plating I = moment of inertia of stiffener and associated plating Yo = distance of neutral axis of stiffener and associated plating from median plane of plate

r = radius of gyration = AI


Chapter 2 SECTION 3

Lloyd's Register 15

■ Section 3: Boundary conditions 3.1 General 3.1.1 The boundary conditions to be applied to the FE model are dependent on the extent of ship modelled and the load case to be analysed. Different boundary conditions need to be applied to analyse the local stress loadcases and global stress loadcases specified in Section 4. 3.1.2 The boundary conditions described in this section are suitable for the FE model of two cargo tank lengths (i.e. ½ tank + 1 tank + ½ tank). 3.1.3 A half breadth FE model may be used only if the structure is symmetrical about the ship’s centreline plane. However, for asymmetrical loading conditions, it is strongly recommended that both sides of the ship be modelled, as this will simplify the analysis procedure. 3.1.4 The boundary conditions described in this section are preferred. Alternative boundary conditions may be used, subject to Lloyd’s Register’s agreement, which should be obtained prior to commencement of the analysis. 3.1.5 Stress results derived from the region close to the boundary supports will be influenced by the imposed boundary conditions and may not be satisfactorily representative of the actual response of the structure. Therefore, these results may not be suitable for evaluating the structure. 3.1.6 The figures describing the boundary conditions indicate arrangement with one oiltight longitudinal bulkhead. For ships with more than one longitudinal oiltight bulkhead, constraints applied to lines K and P in Fig. 2.3.2 are to be applied to all longitudinal oiltight bulkheads. 3.2 Boundary conditions for local stress loadcases (symmetric loads) 3.2.1 The boundary conditions described in this section are to be applied to remove the effect of global hull girder bending from the FE model response induced by local loads. These boundary conditions are suitable for the analysis of the local stress loadcases that comprise symmetric loads. 3.2.2 The boundary conditions are summarised in Table 2.3.1. 3.2.3 Constraints at ends of model 3.2.3.1 The forward and aft ends of the model are to be constrained by means of rigid planes. The grid points relating to continuous longitudinal material at the model end are to be rigidly linked to an independent grid point in δx, θy and θz degrees of freedom. This independent point is to be located on the centre-line at a height close to the neutral axis (see Fig. 2.3.1). This independent point is not to be connected to the model except by the rigid links. The independent points at each end of the model are to be constrained in accordance with Table 2.3.1. 3.2.4 Transverse constraints 3.2.4.1 Transverse translation constraints, δy = 0, are to be applied to the gird points on the upper deck, at the intersection of longitudinal bulkhead with transverse bulkheads, i.e. points A and B in Fig.2.3.1. For ships with no centre line longitudinal oiltight bulkhead, the constraints are to be applied to the intersection of the transverse bulkheads with the centre line plane at the upper deck. 3.2.4.2 For a half-breadth FE model, see 3.2.6.


Chapter 2 SECTION 3


3.2.5 Vertical constraints 3.2.5.1 Spring element method Grounded spring elements (i.e. spring elements with one end constrained in all 6 degrees of freedom) are to be applied to the grid points along the vertical part of the lines of intersection of the side shell, inner skin and longitudinal bulkhead(s) with transverse bulkheads, i.e. lines I, J, K, L, M, N, O, P, Q, R in Fig. 2.3.2. These spring elements are to have stiffness in δz degree of freedom only. The stiffness K of the spring elements are calculated as:

nLAGK

65

=

Where G = shear modulus of plate material A = shear area of the side shell, inner skin or longitudinal bulkhead(s) L = length of the cargo tank n = number of grid points to which the spring elements is applied to the side shell, inner skin or longitudinal bulkhead(s) For a half breadth FE model with a centreline longitudinal bulkhead, the values of spring stiffness to be applied to the lines of intersection of the transverse bulkheads with the centreline longitudinal bulkhead, i.e. lines K and P in Fig. 2.3.2, are to be calculated on the basis of half shear area of the longitudinal bulkhead. 3.2.5.2 Force balancing method As an alternative to the application of grounded spring elements as described in 3.2.5.1, balance of the model can be achieved by applying vertical forces to the grid points along the vertical part of the line of intersection of the side shell, inner skin and longitudinal bulkhead(s) with transverse bulkheads (i.e. lines I, J, K, L, M, N, O, P, Q, R in Fig. 2.3.2). A vertical constraint, δz = 0, is to be applied to a grid point at the intersection of the side shell and the upper deck at each transverse bulkhead position (i.e. points C, D, E and F in Fig. 2.3.1). Different values of force will require to be applied to each of the lines I, J, K, L, M, N, O, P, Q, R and these values will also be different for each load case. The vertical forces applied to each of the lines I, J, K, L, M, N, O, P, Q, R are to be derived for each load case considered. The sum of the nodal forces on each of the lines I, J, K, L, M, N, O, P, Q, R may be derived from a shear flow calculation or from the ratio of the shear area of the relevant member to the total shear are of the hull section. The total force along each line may be distributed evenly to the grid points. The total sum of these forces equals the out of balance vertical loads from each of the load cases. For a half breadth FE model, the calculation of the forces to be distributed to the grid points on the lines I, J, K, L, M, N, O, P, Q, R are to be based on the properties of the full hull section. Where a centreline longitudinal bulkhead exists, the forces to be applied to the lines of intersection of the transverse bulkheads with the centreline longitudinal bulkhead, i.e. lines K and P in Fig. 2.3.2, are to be taken as half of the calculated values. Alternative methods of calculating the applied vertical forces will be considered. 3.2.6 Additional centreline constraints for half-breadth model 3.2.6.1 For a half breadth FE model, symmetry boundary conditions are to be applied to the centreline plane of the FE model. Each grid point in the centreline plane is to be constrained in δy, θx and θz degrees of freedom (i.e. δy = θx = θz = 0).


Chapter 2 SECTION 3

Lloyd's Register 17

3.3 Boundary conditions for local stress loadcases (asymmetric loads) 3.3.1 The boundary conditions described in this section are suitable for the analysis of the local stress loadcases that comprise asymmetric local loads. 3.3.2 The boundary conditions are summarised in Table 2.3.2. 3.3.3 Constraints at ends of model 3.3.3.1 The constraints specified in 3.2.3 are to be applied to the ends of the FE model. 3.3.4 Transverse constraints 3.3.4.1 Grounded spring elements are to be applied to the grid points along the lines of intersection of the upper deck and bottom shell with the transverse bulkheads, i.e. lines S, T, U, and V in Fig. 2.3.2. These spring elements are to have stiffness in δy degree of freedom only. The stiffness K of the spring elements is to be calculated in accordance with the formula given in 3.2.5.1, where A is now representing the shear area of the deck or bottom shell. 3.3.4.2 For load cases which only involve asymmetric fill level of cargo tanks, the transverse constraints given in 3.2.4.1 may be used instead of those described in 3.3.4.1. For load case C2 in Fig. 2.4.1, in which asymmetric external pressure loads are applied, the grounded spring constraints specified in 3.3.4.1 are to be used. 3.3.4.3 For half breadth FE model, see 3.3.6. 3.3.5 Vertical constraints 3.3.5.1 The grounded spring element vertical constraints described in 3.2.5.1 are to be applied. 3.3.5.2 For load cases which only involve asymmetric fill level of cargo tanks, the force balancing vertical constraints given in 3.2.5.2 may be used as an alternative to 3.3.5.1. However, for load case C2 in Fig. 2.4.1, in which asymmetric external pressure loads are applied, the grounded spring constraints specified in 3.3.5.1 are to be used. 3.3.6 Additional centreline constraints for half-breadth model 3.3.6.1 For a half breadth FE model, the asymmetric load case needs to be divided into two sub loadcases where the symmetric and anti-symmetric components of the loads are applied separately. These symmetric load and anti-symmetric load sub loadcases are then applied to the FE model with symmetric and anti-symmetric boundary conditions respectively. The stress responses from the asymmetric load case are obtained by combining the results from the symmetric and anti-symmetric load subload cases. However, due to the complexity of this process, a half breadth FE model is not recommended for the analysis of asymmetric load cases and a full breadth model should be used. 3.3.6.2 The following boundary conditions are included for completeness: • For the anti-symmetric load sub loadcase, anti-symmetry boundary conditions are to be applied to the centreline

plane of the half breadth model. Each grid point in the centreline plane is to be constrained in δx, δz and θy degrees of freedom (i.e. δx = δz = θy =0).

• For the symmetric load sub loadcase, the boundary conditions specified in 3.2 are to be used. 3.4 Boundary conditions for global stress loadcases (hull girder bending moments) 3.4.1 These boundary conditions allow the FE model to deflect globally under the action of hull girder bending moments and are suitable for analysis of the global hull girder bending moment loadcases described in 4.4.1. The required bending moment is to be applied to the forward and aft ends of the model in accordance with the 3.4.3. No other loads are to be applied to the model.


Chapter 2 SECTION 3


3.4.2 The boundary conditions are summarised in Table 2.3.3. 3.4.3 Constraints at ends of model 3.4.3.1 Bending moment is to be applied to the forward and aft ends of the FE model. The end planes of the model are to be restrained to remain plane under the action of the applied bending moment whilst the cross-section is to be free to rotate. To achieve this objective, all grid points relating to continuous longitudinal material at the model ends are to be rigidly linked to an independent grid point in δx, θy and θz degrees of freedom. 3.4.3.2 The independent points are to be located on the centre-line at a height close to the neutral axis position. These independent points are not to be connected to the model except by the rigid links. The independent points are to be constrained in accordance with Table 2.3.3. The required vertical bending moment is to be applied to the independent grid point at each end of the model, see Fig. 2.3.3. 3.4.4 Transverse constraints 3.4.4.1 Transverse translation constraints, δy = 0, are to be applied to the gird points in the bottom shell, on the centreline, at the positions of the transverse bulkheads, see Fig. 2.3.4. 3.4.4.2 For a half breadth FE model, see 3.4.6. 3.4.5 Vertical constraints 3.4.5.1 Vertical translation constraints, δz = 0, are to be applied to the ends of the model, at the intersection points of the upper deck and the side shell, see Fig. 2.3.3. 3.4.6 Additional centreline constraints for half-breadth model 3.4.6.1 For a half breadth FE model, symmetry boundary conditions are to be applied to the centreline plane of the FE model. Each grid point in the centreline plane is to be constrained in δy, θx and θz degrees of freedom (i.e. δy = θx = θz =0). 3.5 Boundary conditions for global stress loadcases (hull girder shear forces) 3.5.1 These boundary are suitable for analysis of the global hull girder shear force loadcases described in 4.4.2. The required shear forces are to be applied to the fore end of the model. No other loads are to be applied to the model. 3.5.2 The boundary conditions are summarised in Table 2.3.4. 3.5.3 Constraints at ends of model 3.5.3.1 The boundary conditions for the local stress loadcases described in 3.2.3 are to be applied to the aft end of the model only. 3.5.3.2 Shear forces are to be applied to the fore end of the FE model by distributing vertical forces to the grid points along the vertical part of the side shell, inner skin and longitudinal bulkhead(s) in accordance with 4.4.2. The fore end of the model is to be free from constraints. 3.5.4 Transverse constraints 3.5.4.1 Transverse translation constraints, δy = 0, are to be applied to the gird points in the bottom shell, on the centreline, at the positions of the transverse bulkheads, as described in 3.4.4.


Chapter 2 SECTION 3

Lloyd's Register 19

3.5.5 Vertical constraints 3.5.5.1 Grounded spring elements with stiffness in δz degree of freedom are to be applied to the grid points along the vertical part of the side shell, inner skin and longitudinal bulkhead(s) at the aft end of the model. The stiffness K of the spring elements is to be calculated in accordance with the formula given in 3.2.5.1. 3.5.5.2 For a half breadth FE model with a centreline longitudinal bulkhead, the values of spring stiffness to be applied to the centreline longitudinal bulkhead are to be calculated based on half shear area of the longitudinal bulkhead. 3.5.6 Additional centreline constraints for half-breadth model 3.5.6.1 Symmetry boundary conditions as described in 3.4.6 are to be applied to the centreline plane of the FE model.


Chapter 2 SECTION 3


Table 2.3.1 Boundary conditions for local stress loadcases (symmetric loads)

Translation Rotation Location δx δy δz θx θy θz

Comments

Constraints at ends of model Aft end L - - - L L Fwd end L - - - L L Independent point aft end

Independent point fwd end -

See Fig.2.3.1

Transverse constraints

Points A, B - - - - - See Fig.2.3.1

Vertical constraints Lines I, J, K, L, M, N, O, P, Q, R

- - S -

- - See notes 1 & 2 and Fig.2.3.2

or Points C, D, E, F - - - - - See

Fig.2.3.2 Lines I, J, K, L, M, N, O, P, Q, R

- - F - - - See notes 3 & 4 and Fig.2.3.2

Additional centre line constraints for half-breadth model Centreline plane (symmetry) - - - -

Symbols constraint (fixed) constraint (fixed) may be required to remove mathematical singularities

- no constraint applied (free) L rigidly linked to independent point at neutral axis on centreline S application of grounded springs to grid points F application of forces to grid points Notes 1 Different values of spring stiffness are to be applied to each of the lines I, J, K, L, M, N, O, P, Q, R, see 3.2.5.1

2 For a half breadth FE model with a centreline longitudinal bulkhead, the calculation of the values of spring stiffness for applying to the lines K and P are to be based on half of the shear area of the longitudinal bulkhead, see 3.2.5.1.

3 Different values of force are to be applied to each of the lines, I, J, K, L, M, N, O, P, Q, R, and these values will be different for each load case considered, see 3.2.5.2.

4 For a half breadth FE model, the calculation of the forces for applying to the lines, I , J, K, L, M, N, O, P, Q, R, are to be based on the properties of the full hull section. Where a centreline longitudinal bulkhead exists, the forces to be applied to the lines, K and P, are to be taken as half of the calculated values, see 3.2.5.2.


Chapter 2 SECTION 3

Lloyd's Register 21

Table 2.3.2 Boundary conditions for local stress loadcases (asymmetric loads)


Comments

Constraints at ends of model Aft end L - - - L L Fwd end L - - - L L Independent point aft end

Independent point fwd end -

See Fig.2.3.1


Lines S, T, U, V - S - - - - See Fig.2.3.2

or Points A, B - - - - - See note 1 &

Fig.2.3.1 Vertical constraints Lines I, J, K, L, M, N, O, P, Q, R

- - S -

- - See note 2 & Fig.2.3.2

or Points C, D, E, F - - - - -

Lines I, J, K, L, M, N, O, P, Q, R

- - F - - -

See notes 1 & 3,

Figs.2.3.1 & 2.3.2

Symbols See Table 2.3.1. Notes 1 These constraints may only be used instead of grounded springs if the load case only involves asymmetric fill level

of cargo tanks. These constraints are not be used for asymmetric load case that involves asymmetric external pressure loads (i.e. load case C2 in Fig. 2.4.1).

2 See notes 1 and 2 of Table 2.3.1.

3 See notes 3 and 4 of Table 2.3.1.

4 For half breath FE model, see 3.3.6.


Chapter 2 SECTION 3


Table 2.3.3 Boundary conditions for global stress loadcases (hull girder bending moments) Translation Rotation Location

δx δy δz θx θy θz Comments

Constraints at ends of model Aft end L - - - L L Fwd end L - - - L L Independent point aft end M

Independent point fwd end - M

See Fig.2.3.3


Points K, L - - - - - See Fig.2.3.4

Vertical constraints Points G, H, I, J - - - - - Fig.2.3.3 Additional centre line constraints for half-breadth model Centreline plane (symmetry) - - -

Symbols M Bending moment applied to independent point

For other symbols, see Table 2.3.1.

Table 2.3.4 Boundary conditions for global stress loadcases (hull girder shear forces)


Comments

Constraints at ends of model Aft end L - - - L L Fwd end - - F - - -

Independent point aft end


Points K, L - - - - - See Fig.2.3.4

Vertical constraints

Aft end - - S - - -

Additional centre line constraints for half-breadth model Centreline plane (symmetry) - - -

Symbols F Application of vertical forces to the grid points along the vertical part of the side shell, inner skin and

longitudinal bulkhead(s) to represent shear forces, see 3.5.3. The values of the total vertical force to be applied to each structural component are different and are dependent upon the shear area.

S Application of grounded springs to grid points along the vertical part of the side shell, inner skin and longitudinal bulkhead(s), see 3.5.5. The values of the spring stiffness to be applied to each structural component are different and are dependent upon the shear area.

For other symbols, see Table 2.3.1.


Chapter 2 SECTION 3

Lloyd's Register 23

Fig. 2.3.1 Locations for application of constraints for local stress load cases

(symmetric loadcases see Table 2.3.1, asymmetric loadcases, see Table 2.3.2)

C

D

A

E

F

B

Independent point

N.A

N.A

N.A

N.A

Independent point


Chapter 2 SECTION 3


Fig. 2.3.2 Locations for application of constraints for local stress load cases

(symmetric loadcases see Table 2.3.1, asymmetric loadcases, see Table 2.3.2)

I J

LM

NO

Q R

K

P

S

T

S

T

U

V

J

L

O

Q


Chapter 2 SECTION 3

Lloyd's Register 25

Fig. 2.3.3 Boundary conditions for global stress load cases (hull girder bending moments)

δz = 0

δz = 0

δz = 0

δz = 0

G

I

H

J

Independent point

M

N.A

N.A

M

N.A

N.A


Chapter 2 SECTION 3


Fig. 2.3.4 Boundary conditions for global stress load cases (hull girder bending moments)

K

L

δy = 0

δy = 0


Chapter 2 SECTION 4

Lloyd's Register 27

■ Section 4: Loading conditions 4.1 General 4.1.1 The loading conditions which are likely to impose the most onerous local and global load regimes are to be investigated by structural analysis. 4.1.2 Where specified loading conditions agreed between the Shipbuilder and Shipowner are not covered by the loading conditions given in these guidance notes, then these additional loading conditions are to be examined. Full details of all proposed loading conditions are to be submitted at an early stage for consideration. 4.2 Special loading and assessment conditions for ship with two oiltight longitudinal bulkheads and cross-tie arrangement in the centre tanks 4.2.1 Standard loading conditions to be used in the assessment are as described in paragraph 4.3. 4.2.2 However, additional requirements are applicable to ships with two oiltight longitudinal bulkheads and a cross-tie arrangement in the centre tanks. 4.2.3 The reason for these additional load cases is that the loading conditions shown in Fig. 2.4.1(a) are symmetrical with respect to the transverse distribution of tank fillings. For tankers with two oiltight longitudinal bulkheads and a cross-tie arrangement in the centre tanks, it is possible that unequal fillings of transversely paired wing cargo tanks would result in a more onerous structural response. 4.2.4 For ships, which are not intended to operate in sea-going or sheltered water conditions with unequal filling levels in transversely paired side wing cargo tanks, the additional load cases specified in Fig. 2.4.2 are to be examined using the stress and buckling criteria given in 5.2 and 6.10. This is to cater for possible accidental discharge of one side wing cargo tank during operations in sheltered water conditions. Such ships will have to comply with the following restrictions, which are to be clearly stated in the Loading Manual. (a) The ship is not to be operated in sea-going or sheltered water conditions with a difference in filling height in

transversely paired tanks exceeding 5% of the tank depth. (b) In cargo operations in sheltered water conditions the difference in filling height between transversely paired wing

tanks is not to exceed 25% of the tank depth. (c) Wing cargo tank testing is always to be carried out with both port and starboard wing cargo tanks full. Strict control

is to be exercised to ensure that the difference in filling levels during filling and discharging does not exceed 25% of the depth of the tank.

4.2.5 If any asymmetrical filling of transversely paired side wing cargo tanks is envisaged in either sea-going, sheltered water or tank testing conditions, the additional loading conditions specified in Fig. 2.4.2 are to be examined to verify satisfaction of the stress and buckling criteria given in Tables 2.5.1 and 2.6.2. 4.3 Local stress load cases 4.3.1 The standard loading conditions to be applied to the structural model are shown in Figs. 2.4.1. Fig. 2.4.1(a), (b) and (c) specify the standard loading conditions for tankers with two oiltight longitudinal bulkheads, one centreline oiltight longitudinal bulkhead and no oiltight longitudinal bulkheads respectively. 4.3.2 The loading conditions shown in Fig. 2.4.1(a) are symmetrical with respect to the transverse distribution of tank fillings. For tankers with two oiltight longitudinal bulkheads and a cross-tie arrangement in the centre-tanks, it is possible that unequal fillings of transversely paired wing cargo tanks would result in more onerous structural response. In this case additional analysis is required, see 4.2.


Chapter 2 SECTION 4


4.3.3 The conditions of operation for asymmetrical loading are to be clearly stated in the Ship’s Loading Manual. If the ship is not intended to operate in such loading conditions, a note is to be included in the Loading Manual stating that these loading conditions are not permitted. For designs with two oiltight longitudinal bulkheads and cross-tie in centre tank, see 4.2. 4.3.4 Loads arising from liquids in tanks are to be applied as equivalent pressure loads to all contacted surfaces. The design specific gravity of the cargo is not to be taken as less than 1,025. Fuel oil tanks and/or other tanks in the double bottom in way of cargo tanks are to be included in the model. 4.3.5 The additional pressure on the external plating due to a wave crest is to be applied as local loads in accordance with the pressure head distribution given in Fig.2.4.3. 4.4 Global stress load cases 4.4.1 Global hull girder bending moments 4.4.1.1 The following global hull girder bending moments are to be considered: • Maximum permissible still water bending moment (sagging and hogging). • Combined maximum permissible still water and Rule design vertical wave bending moment (sagging and hogging). 4.4.1.2 Stress responses are to be determined by applying a suitable bending moment to the model ends, using the boundary conditions given in 3.4. No other loads are to be applied to the FE model. This bending moment should be applied as a separate load case. 4.4.2 Global hull girder shear forces 4.4.2.1 For the cargo loaded conditions specified in Fig. 2.4.1 (a) 3, (b) 3 and (c) 1 with all tanks abreast empty, the structure is also to be assessed against the combination of local loads (see 4.3) and global shear loads. 4.4.2.2 The shear forces to be applied to the FE model are the summation of global design wave shear forces (see Pt 3, Ch 4,6 of the Rules for Ships) and maximum permissible still water shear force assigned to the ship minus the maximum shear force developed in the local loads case. Both positive and negative shear forces are to be considered. No other loads are to be applied to the FE model. 4.4.2.3 The shear forces are to be represented by vertical forces distributed to the grid points along the vertical part of the side shell, inner skin and longitudinal bulkhead(s) and applied to the fore end of the FE model. The vertical force, f, at each nodal points of a structural component is to be calculated as:

where F is the total shear force A is the total shear area of structural components a is the shear area of each structural component n is the number of grid points on each structural component 4.4.2.4 The boundary conditions to be applied to the FE model are described in 3.5. This shear force should be applied as a separate load case. 4.4.3 Alternative method may be used to apply the global hull girder loads. In this case, the proposed method should be submitted for Lloyd’s Register’s agreement prior to commencement of the analysis.

nAaFf =


Chapter 2 SECTION 4

Lloyd's Register 29

4.5 Combination of Load Cases 4.5.1 The stresses derived from the local stress load cases are to be combined with the stresses derived from the global stress load cases, in accordance with Tables 2.5.1 and 2.6.2, for checking compliance with the permissible stress and buckling criteria. 4.5.2 For cargo loaded and ballast conditions, the local stresses are to be combined with the global stresses arising from the application of combined maximum assigned still water moment (Msw) and Rule vertical wave design bending moment (Mw). For tank testing conditions, the local stresses may be combined with the global stresses arising from the application of maximum assigned still water bending moment only. Both hogging and sagging bending moments are to be considered for stress combination to give maximum stresses for comparison with the permissible stress criteria and buckling assessment. 4.5.3 For the cargo loaded conditions specified in Fig. 2.4.1 (a) 3, (b) 3 and (c) 1, compliance with the permissible stress criteria is also to be verified for the combined local stress and global stress from the application of design wave shear force and maximum permissible still water shear force. Both positive and negative global shear forces are to be considered for stress combination to give maximum stresses for comparison with the permissible stress and buckling criteria.


Chapter 2 SECTION 4


Fig. 2.4.1 – Part (a) Standard load cases

Tankers with two oiltight longitudinal bulkheads (see continuation)


Chapter 2 SECTION 4

Lloyd's Register 31

Fig. 2.4.1 – Part (a) Standard load cases

Tankers with two oiltight longitudinal bulkheads (see continuation)


Chapter 2 SECTION 4


(only required for asymmetrical centreline bulkhead arrangement)

Fig. 2.4.1 – Part (b) Standard load cases

Tankers with one centreline oiltight longitudinal bulkhead (see continuation)


Chapter 2 SECTION 4

Lloyd's Register 33

Fig. 2.4.1 – Part (b) Standard load case

Tankers with one centreline oiltight longitudinal bulkhead (see continuation)


Chapter 2 SECTION 4


Additional internal head above top of tanks in metres: h1 = 0,125D1 + R(b1-0,6B) minimum value of h1=h2 h2 = 0,125D1 External draught in metres: T1 = 0,4D+0,5RB T2 = 0,4D-0,5RB Where

R =

−

+

127054,00,10,45 L

BL

L, B, D = see Ch 1,2 D1 = see Note 1 b1 = largest horizontal distance, in metres, from the tank corner at top of tank, either side to mid point of span of member concerned. See also Pt 4, Ch 9,6.2 of the Rules for Ships.

Fig. 2.4.1 – Part (c) Standard load cases

Tankers with no oiltight longitudinal bulkheads (see continuation)


Chapter 2 SECTION 4

Lloyd's Register 35

Fig. 2.4.1 – Part (c) Standard load cases

Tankers with no oiltight longitudinal bulkheads (conclusion)

NOTES 1. All tanks which are loaded are to include an additional internal head measured above the top of the tank as follows:

1.1 2,45 m in tank test conditions.

1.2 D1/8 m in cargo and ballast conditions (except condition 2(c)). D1 is the moulded depth of the ship in metres, but is not to be taken greater than 16,0 m.

2. The specific gravity in loaded tanks is not to be taken as less than 1,025.

3. Where applicable, the additional wave head, in metres, is to be applied as given in Fig. 2.4.3.

4. Transverse bulkheads are to be examined with the loading applied to each side of the bulkhead in turn. Where the structural model only includes one transverse bulkhead, two separate load cases will be required.

5. For designs having two longitudinal oiltight bulkheads and cross-ties in the centre tank, wing cargo tank testing is always to be carried out with both port and starboard cargo tanks full. Strict control is to be exercised to ensure that the difference in levels during filling and discharge does not exceed 25 per cent of the depth of the tank. This restriction is to be included as a Note in the Loading Manual. However, this restriction will not apply if the additional load cases indicated in Fig. 2.4.2 have been analysed and the stress and buckling capability comply with Table 2.5.1 and Table 2.6.2 (see also 4.2).

6. For single hull tankers the loading conditions will be specially considered.


Chapter 2 SECTION 4


(a) Tankers with two oiltight longitudinal bulkheads with a cross-tie in the centre tank

Fig. 2.4.2

Additional load cases

NOTES See Notes of Fig. 2.4.1


Chapter 2 SECTION 4

Lloyd's Register 37

Scantlingdraught

hw

2

hw

2hw

2

hwhw

where hw = 4,6 10-2 L e-0,0044L m for L< 227 m hw = 3,846 m for L ≥ 227 m L = Rule length, in metres, as defined in Pt 3, Ch 1,6 of the Rules for Ships e = base of natural logarithm 2,7183

Fig. 2.4.3 Pressure head distribution, Pw, for local wave crest


Chapter 2 SECTION 5


■ Section 5: Permissible stresses 5.1 The stresses resulting from the application of the standard and/or specified loading conditions are not to exceed the maximum permissible values given in Table 2.5.1. The assessment of the primary scantlings is to be based on the most severe criteria. 5.2 For the asymmetrical loading conditions specified in Fig. 2.4.2 for tankers with two oiltight longitudinal bulkheads and a cross-tie arrangement in the centre tanks, providing these conditions are not intended to be operated in sheltered water or sea-going conditions, the calculated direct stresses and combined stresses are not to exceed the yield stress of the material and the calculated shear stresses are not to exceed 0,58 of the tensile yield stress. For operation in sheltered water and sea-going conditions, the stress criteria given in Table 2.5.1 are to be complied with. See 4.2. 5.3 The permissible stress criteria in Table 2.5.1 are based on the recommended mesh size indicated in Section 2. 5.4 Where indicated in Table 2.5.1, the stresses derived from the local stress load cases are to be combined with the hull girder stresses in order to check compliance with the permissible stress criteria, see 4.5. Both hogging and sagging bending moments are to be considered when combining the hull girder bending moment load cases with local stress load cases, and both positive and negative shear forces are to be considered when combining the hull girder shear force load cases with the local stress load cases, to give maximum stress values for assessing against the permissible criteria. 5.5 The mean shear stress, τ, is to be taken as the average shear stress over the depth of the web of the primary member. Where openings are not represented in the structural model, both the mean shear stress, τ, and the element shear stress, τxy, are to be increased in direct proportion to the modelled web shear area divided by the actual web area. The revised τxy is to be used to calculate the combined equivalent stress, σe. Where the resulting stresses are greater than 90 per cent of the maximum permitted, a more detailed analysis using a fine mesh representing the opening may be required. 5.6 The structural items indicated in Table 2.5.1 are provided for guidance as to the most likely critical areas. All stresses for all parts of the model are to be examined for high values.


Chapter 2 SECTION 5

Lloyd's Register 39

Table 2.5.1 Maximum permissible membrane stresses

Permissible stresses Structural Item Applied stresses

σ τ σe

(a) Local stress and hull girder stress, see Note 2

– 0,46σ0 σ0 Longitudinal girders in double hull

See Note 1 (b) Local stress only – 0,35σ0 0,75σ0

Longitudinal girders in single hull:

Web plate Face plate

(a) Local stress and hull girder stress, see Note 2

0,83σ0 face plate only – 0,92σ0

See Note 1 (b) Local stress only – 0,35σ0 0,75σ0

(a) Local stress and hull girder stress, see Note 2 0,92σ0 see note 2.3 σ0

Plating of inner and outer hull and longitudinal bulkheads

See Notes 1 and 3 (b) Local stress only 0,63σ0 – 0,75σ0

Transverse structure excluding the toes of primary member brackets All local stresses

Web plate – 0,35σ0 0,75σ0

Face plate 0,75σ0 – –

See Note 5

Areas of stress concentration adjacent to welds including toes of primary member brackets See Note 4

All local stresses – – 245 N/mm2

Fine mesh regions

Average combined stress, σaverage and Average shear stress, τaverage See Note 6

All cases – 0,46σ0 σ0

Individual element, see 5.3 All cases – <1,2 τaverage <1,2 σaverage

NOTE 1. Scantlings are to be based on the most severe criteria. 2. Local stress and hull girder stress combination

2.1 For all cargo and ballast conditions, the hull girder bending stresses, corresponding to the combined maximum permissible still water bending moment (Msw) and Rule wave vertical bending moment (Mw), is to be added to the local stresses for checking compliance with the maximum permissible stress criteria.

2.2 For tank testing conditions, the hull girder bending stress may be based only on the maximum permissible still water bending moment, see 4.5.

2.3 For the cargo loaded conditions specified in Fig. 2.4.1 (a) 3, (b) 3 and (c) 1, compliance with the permissible shear stress criteria is also to be verified for the combined local stress and global stress from the application of design wave shear force and maximum permissible still water shear force. τxy in an individual element is not to exceed 0,46σ0 except where permitted by Note 3.

3. For side shell and longitudinal bulkhead plating in way of the ends of transverse bulkhead girders, τxy ≤ 0,57 N/mm2 (13,8/k kgf/mm2) taking into account both local and hull girder still water and wave shear stress.

4. No increase in permissible stress for higher tensile steel. A higher stress may be permitted if supported by appropriate fatigue calculations based on detailed finite plate element stresses where the full effect of asymmetry of configuration and face plates is taken into account.

5. Area of cross-ties not to be less than required by Pt 4, Ch 9,9.6.1 of Rules for Ships. 6. σaverage and τaverage are the average combined stress and shear stress respectively from elements being

assessed and the elements connected to its boundary nodes. However, averaging is not to be carried across a structural discontinuity or abutting structure.


Chapter 2 SECTION 6


■ Section 6: Buckling acceptance criteria 6.1 Plate panel buckling is to be investigated for the web plating of longitudinal girders and transverse primary structure including all stress components. Panel buckling is also to be investigated in the attached plating to primary members, e.g. deck, shell, inner hull and transverse and longitudinal bulkhead plating. 6.2 Panel buckling calculations are to be based on the proposed thickness reduced by the standard thickness deduction for corrosion given in Table 2.6.1. 6.3 The combined interaction of bi-axial compressive stresses, shear stresses and ‘in plane’ bending stresses are to be included in the buckling calculation. In general, the average stresses acting within the plate panel are to be used for the buckling calculation. 6.4 Where indicated in Table 2.6.2, the stresses derived from the local stress load cases are to be combined with the hull girder bending stresses for the assessment of panel buckling capability, see 4.4. Both hogging and sagging bending moments are to be considered when combining the hull girder bending moment load cases with local stress load cases, and both positive and negative shear forces are to be considered when combining the hull girder shear force load cases with the local stress load cases, to give maximum total stresses for the buckling check. 6.5 The stresses derived from the local load cases are to be increased by a factor equal to the original thickness divided by the thickness after the corrosion deduction given in 6.2. For hull girder stresses, this increase is not required. 6.6 The factors against buckling are to be derived using the computer program LR Buckle (ShipRight IS) or program ‘Buckling of flat rectangular plate panels’ (ShipRight Direct Calculation program no. 10403) or equivalent. 6.7 In calculating the factors against buckling, the edge restraint factor 'c,' defined in Pt 3, Ch 4,7 of the Rules for Ships, may be taken into account in calculating the critical buckling stress of wide panels subjected to compressive loading on the long edges. The edge restraint factor ‘c’ is not to be used in the calculation of the critical buckling stress for compression applied on the short edges. 6.8 When the calculated elastic critical buckling stress exceeds 50 per cent of the specified minimum yield stress, the buckling stress is to be adjusted for the effects of plasticity using the Johnson–Ostenfeld correction formula given below: σcr = σo (1 – σo/4σc) 6.9 The applied stresses which are to be included in the buckling calculation, and the required minimum factor against buckling, λ, are given in Table 2.6.2. 6.10 For the asymmetrical loading conditions specified in Fig. 2.4.2 for tankers with two oiltight longitudinal bulkheads and a cross-tie arrangement in the centre tanks, a minimum factor against buckling of not less than 1,0 is acceptable providing these conditions are not intended to be used in sheltered water or sea-going conditions. For operations in sheltered water and sea-going conditions, the buckling criteria in Table 2.6.2 are to be satisfied. See 4.2.


Chapter 2 SECTION 6

Lloyd’s Register 41

Table 2.6.1 Standard thickness deductions, to be used to derive design applied and critical buckling stresses

Position Thickness deduction, mm

Deck and shell plating 1,0

Longitudinal bulkhead and inner hull 2,0 Within 1,5 m of weather deck Internal structure including transverse bulkheads

See Note 1

2,0

Shell plating 1,0

Longitudinal bulkhead and inner hull 1,0 Elsewhere

Internal structure including transverse bulkheads

See Note 1

1,0

NOTES 1. In uncoated tanks for refined oils where an inert gas system is not fitted the thickness deduction is to be

increased by 1,0 mm. 2. A mean value is to be taken for tanks in which the contents vary and for internal plating which separates regions

having different thickness deductions.


Chapter 2 SECTION 6


Table 2.6.2 Plate panel buckling: Required factor against buckling, λ

Structural Item Applied stresses Factor against buckling λ

Longitudinal girder in double hull (a) Local stress only

(b) Local stress and hull girder stress, see Note 3

1,2

1,0

Longitudinal girder in single hull Local stress and hull girder stress, see Note 3 1,0

Plating of deck, shell, inner hull, longitudinal and transverse bulkheads

Local stresses and hull girder stress, see Note 3 1,0

Web plating of transverse structure including midship web frame and bulkhead horizontal and vertical webs

All local stresses 1,1

Symbols

λ =Calculated critical buckling stress

Applied stress

NOTES

1. Local stresses are to be derived from the finite plate element calculation increased in direct proportion to plate thickness to account for stresses after standard thickness deduction.

2. Critical buckling stress is to be calculated using the net plate thickness taking account of the standard thickness deduction.

3. Local stress and hull girder stress combination

3.1 For all cargo and ballast conditions, the combined hull girder still water and wave bending stresses are to be added to the local stresses for buckling capability check.

3.2 For tank testing conditions, the hull girder bending stress may be based on the maximum permissible still water bending moment only, see 4.5.

3.3 For the cargo loaded conditions specified in Fig. 3.4.1 (a) 3, (b) 3 and (c) 1, in addition to Note 3.1, the global stresses arising from the application of combined still water and wave shear forces are to be added to the local stresses for buckling capability check. Thickness deduction for the global stress component is not required.

4. Still water hull girder bending stress is to correspond to the maximum permissible still water bending moment and the scantlings without applying the thickness deduction, see 4.4.1.

5. Wave hull girder bending stress is to be derived as for the still water stress using the Rule wave bending moment, see 4.4.1.

6. Combined still water and wave shear force is to correspond to the Rule design wave shear force and maximum permissible still water shear force, see 4.4.2.

7. Hogging and sagging bending moments and positive and negative shear forces are to be considered for the combination of local stresses to give maximum total stresses for buckling checks.


Chapter 2 SECTION 7

Lloyd’s Register 43

■ Section 7: Deflection of primary members 7.1 Where the relative deflection between adjacent primary transverse members exceeds the values given below, particular attention is to be paid to the design of the end connections of the longitudinals and stiffeners in way (see also 2.9): (a) For deck and bottom transverse, floors and transverse bulkhead girders:

dS2180

=δ mm for asymmetrical longitudinals and stiffeners

dS2205

=δ mm for symmetrical longitudinals and stiffener

(b) For side transverses and vertical webs of longitudinal bulkheads:

dS2160

=δ mm for asymmetrical longitudinals and stiffeners

dS2185

=δ mm for symmetrical longitudinals and stiffener

where d = depth of longitudinal, in mm S = spacing of transverse, in metres δ = maximum permitted relative deflection of primary members without special consideration being given to the end connections of the longitudinals and stiffeners in way, in mm 7.2 The critical regions are normally between transverse or swash bulkheads and the adjacent transverse frame or between the deck or bottom structure and the adjacent transverse bulkhead horizontal girder. 7.3 In addition to the relative deflection criteria given in 7.1, the maximum deflection of an individual primary member δm, is not in general to exceed the following values: (a) For deck and bottom transverses, floors and transverse bulkhead girders:

δm = 1,3 l mm (b) For side transverses and vertical webs of longitudinal bulkheads:

δm = 1,0 l mm where: l = overall length of the primary member, in metres, as defined in Pt 3, Ch 3,3.2.1 of the Rules for Ships. In the case of side transverses and the vertical webs of the longitudinal bulkheads, cross ties are to be neglected in determining l δm = maximum deflection of the primary member, in mm, measured relative to a straight line joining the ends of the overall length.

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