ShipRight. Structural Design Assessment. Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships. Guidance on direct calculations

Transcription

1 ShipRight Design and construction Structural Design Assessment Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships Guidance on direct calculations May 2004

2 ABCD Lloyd s Register Marine Business Stream 71 Fenchurch Street London EC3M 4BS Telephone Telex LR LON G Fax Document History Document Date: November 2001 Notes: Intranet user review version July 2002 Notice 1 October 2002 May 2004 New procedure Revisions as identified in History of Development up to January Revisions as identified in Structural Design Assessment Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships, Changes incorporated in May 2004 version. 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

3 Contents Contents Chapter 1 Introduction 1 Section 1 Introduction 2 Symbols 3 Direct calculation procedures report Direct calculation procedure 5 Section 1 Objectives 5 2 Structural modelling 6 3 Boundary conditions Introduction 3.2 Symmetric boundary conditions for global loads 3.3 Symmetric boundary conditions for local loads 3.4 Asymmetric boundary conditions for transverse loads 4 Loading conditions Introduction 4.2 Subload cases 4.3 Procedure to derive subload cases 5 Permissible stresses 42 6 Buckling acceptance criteria 44 Appendix A Modelling of supports and chocks Section A1 Modelling of supports and chocks 47 Appendix B Procedure to apply transverse asymmetric loads to a half-breadth FE model Section B1 Procedure to apply transverse asymmetric loads to a half-breadth FE model 48 LLOYD'S REGISTER

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5 Chapter 1 SECTION 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) procedures are mandatory for LPG ships fitted with Independent Type A cargo tanks, as defined by Lloyd's Register s Rules for Ships for Liquefied Gases. 1.2 The Rules and Regulations for the Construction and Classification of Ships for the Carriage of Liquefied Gases in Bulk incorporating the IMO International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk (IGC Code) is referred to in this document as Lloyd s Register s Rules for Ships for Liquefied Gases. References to the IGC Code in this procedure are equivalent to references to the Rules for Ships for Liquefied Gases. 1.3 For compliance with the ShipRight SDA procedure, direct calculations are to be adopted for the determination and verification of the stress level and buckling capability of the ship primary structural members, the cargo tank, including the structure supporting the cargo tanks as specified in Lloyd s Register s Rules for Ships for Liquefied Gases. 1.4 The minimum requirements specified in this procedure, in addition to the requirements in Lloyd s Register s Rules and Regulations for the Classification of Ships (hereinafter referred to as the Rules for Ships) are to be complied with. 1.5 The SDA procedure requires the following: A detailed analysis of the cargo tank support systems and hull and tank structure in way, as specified in Lloyd s Register s Rules for Ships for Liquefied Gases. This involves a detailed finite element analysis to assess the suitability of the support systems and structure in way under applied static and dynamic loads. A detailed analysis of the structural response of the ship under applied static and dynamic loads using finite element analysis. Other direct calculations as applicable. 1.6 In general, the direct calculations are to be based on a three-dimensional finite element analysis (3-D FEA) carried out in accordance with this procedure. Where alternative procedures are proposed, these are to be agreed with Lloyd s Register before commencement. LLOYD'S REGISTER 1

6 Chapter 1 SECTION A detailed report of the calculations is to be submitted and must include the information detailed in 3.1. The report must show compliance with the specified structural design criteria given in Sections 5 and 6 of. 1.8 If the computer programs employed are not recognised by Lloyd s Register, full particulars of the program will also require to be submitted, see Pt 3, Ch 1, 3.1 of the Rules for Ships. 1.9 Lloyd s Register may require the submission of computer input and output to further verify the adequacy of the calculations carried out Ships, which have novel features or unusual structural or tank configurations, may need special consideration and additional load cases may be required It is recommended that the designer consults with Lloyd s Register on the SDA analysis requirements early on in the design cycle. 2 LLOYD S REGISTER

7 Chapter 1 SECTION 2 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 k L, k = higher tensile steel factor, see Pt 3, Ch 2,1.2 of the Rules for Ships SWBM = still water bending moment VWBM = design vertical wave water bending moment M W = design vertical wave bending moment, including hog and sag factor, f 2, and ship service factor, f 1, see Pt 3, Ch 4,5 of the Rules for Ships M WO = 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 Μ S = Rule permissible still water bending moment, see Pt 3, Ch 4,5 of the Rules for Ships M s = Design still water bending moment, see Pt 3, Ch 4,5 of the Rules for Ships M SW = The still water bending moment distribution envelope to be applied to the FE models for stress and buckling assessments. The values of M sw are to be greater than Ms and less or equal to Μ S. M sw are to be incorporated into the ship s Loading Manual and loading instrument as the assigned permissible still water bending moment values. M sw is hereinafter referred as the permissible still water bending moment. T sc = scantling draught, in metres θ = roll angle C b = 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 ρ c = density of cargo P o = design vapour pressure, as defined in Ch 4, 2.6.of the Rules for Ships for Liquefied Gases A x, A y, A z = maximum dimensionless acceleration factors (i.e. relative to the acceleration of gravity) in the longitudinal, transverse and vertical directions respectively h x, h y, h z = local head for pressure evaluation measured from the tank reference point in the longitudinal, transverse and vertical directions respectively t = thickness of plating t c = thickness deduction for corrosion σ cr = critical buckling stress corrected for plasticity effects σ c = elastic critical buckling stress σ o = specified minimum yield stress of material (special consideration will be given to steel where σ N/mm 2, see Pt 3, Ch 2,1 of the Rules for Ships) 235 σ L = k L λ = factor against elastic buckling σ actual = equivalent applied stress σ e = von Mises equivalent stress, given by σ e = σ + σ σ σ + 3τ σ x σ y x y x y xy = direct stress in element x direction = direct stress in element y direction τ xy = shear stress in element xy plane 2.2 Consistent units to be used throughout all parts of the analysis. Results presentation in Newton and mm preferred. 2.3 All Rule equations are to use units as defined in the Rules for Ships. LLOYD'S REGISTER 3

8 Chapter 1 SECTION 1 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 for all components including all support chocks; details of displacement boundary conditions; details of all still water and dynamic loading conditions reviewed with calculated shear force and bending moment distributions; details of the calculations for waterlines used in the dynamic loading conditions; details of the acceleration factors for each loading condition; details of applied loadings and confirmation that individual and total applied loads are correct; details of boundary support forces and moments; details of the derived tank support chock loadings and loads on other anti-rolling, anti-pitch, etc., chocks, including gap element forces (if used) and spring forces; plots and results that demonstrate the correct behaviour of the ship and tank structural models 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. 4 LLOYD S REGISTER

9 SECTION 1 Direct Calculation Procedure 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 1: Objectives 1.1 The objectives of the structural analysis is to verify that the stress level and buckling capability of primary hull structure, the cargo tank as well as the cargo support systems under the applied static and dynamic loads are within the acceptable limits. 1.2 The analysis and applied loading is to be sufficient to evaluate the loads and responses of all primary structural items including: (a) Ship s primary structure including: inner bottom and bottom shell plating, double bottom floors and girders, hopper tank floors and plating. all other structure in way of tank supports and chocks (b) Cargo tank structure including: cargo tank primary members. (c) Cargo tank support systems including: distribution of tank support loads, distribution of anti-roll and anti-pitch chock forces, distribution of anti-flotation chock forces, local stresses in way of supports and chock seatings, stresses in topside tank and deck transverses in way of anti-flotation chocks. 1.3 Adequacy of hull structure supporting the cargo containment system is to be investigated either by incorporation of fine mesh areas or by use of separate fine mesh models. 1.4 The calculated load on each tank support assumes perfect fit and alignment of all supports and structural members. Additionally, no account is taken of misalignment caused by contraction of the tank s structure during cooldown, construction tolerances or any other factors in the preparation of the finite element models. Recognition of these limitations is to be made in the assessment of the chock and support arrangements and guidance for this is given in LLOYD'S REGISTER 5

10 SECTION 2 Section 2: Structural modelling 2.1 The 3-D finite element (FE) model is to cover the central and forward cargo tank regions. This is to enable the effects of changes in ship structural arrangements, due to hull shape, and the higher vertical accelerations in Tank No.1, to be analysed. 2.2 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. 2.3 The minimum length that the FE model is to represent is from the bow to the after bulkhead of the midship cargo hold or the mid-length of the hold aft of midships. In the former case, the bulkhead at the ends of the model is to be included. The full depth of the ship is to be modelled. 2.4 This length of the FE model should enable the ship s structure and cargo tank support systems over the full cargo hold region to be assessed. If the ship s structure or cargo tank support system in the after hold(s) is significantly different from the midships hold arrangements, then a full ship FE model is required. 2.5 The procedures specified within this document are based on the assumption that the minimum recommended length FE model is acceptable. 2.6 Unless there is asymmetry of the ship or cargo tank primary structure about the ship s centreline, then only one side of the ship needs to be modelled with appropriate boundary conditions imposed at the centreline. However, it is recommended that both sides of the ship be modelled, as this will simplify the loading and analysis of the asymmetric transverse loading condition. 2.7 The FE model of the ship structure is to adopt 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 2.8 Typical arrangements representing a Type A Tank LPG ship are shown in Figs to The proposed scantlings, excluding owner s extras and any additional thicknesses to comply with the optional ShipRight ES Procedure, are to be used throughout the model. The selected size and type of elements are to provide a satisfactory representation of the deflection and stress distributions within the structure. 2.9 In general, the plate element mesh is to follow the primary stiffening arrangement for both the structure of the ship and cargo tanks. The minimum mesh size requirements are: transversely, one element between every second longitudinal or stiffener; longitudinally, one element between double bottom floors; vertically, one element between decks, stringers or every second stiffener; and three or more elements over the depth of double bottom girders, floors and side transverses in way of areas which are to be analysed in detail with adjacent structure modelled to suit. Due regard is to be paid to maintaining an adequate aspect ratio. 6 LLOYD S REGISTER

11 SECTION Where the mesh size of the 3-D finite element model is insufficiently detailed to represent areas of high stress concentrations, then these areas are to be investigated by incorporating local fine meshed zones into the main model. Alternatively, separate local fine mesh models with boundary conditions derived from the main model may be used. Clear of areas to be analysed in detail, a coarse mesh arrangement may be adopted. The areas to be sub-modelled or subject to finer meshing are to be discussed with Lloyd s Register at an early opportunity Areas where a fine mesh is needed include: selected critical cargo tank supports and the tank and ship structure in way; selected critical anti-roll chocks and the tank and ship structure in way; selected critical anti-flotation chocks and the tank and ship structure in way; the anti-pitch chocks and the anti-collision chocks and the ship structure in way; the inner bottom to hopper tank connection detail at mid-hold length. A typical fine mesh model is illustrated in Figs to The bow of the ship is to be modelled. But, it is not necessary to include all the structure within the bow region. It is sufficient to model most longitudinal plating, stringers and continuous stiffeners, together with sufficient transverse structure to support the modelled longitudinal material A typical example of a fine mesh model is shown in Figs to In general, the element size in fine mesh areas is not to be greater than 15t x 15t or 150 x 150 mm, whichever is lesser, where t is the main plate thickness. The mesh size is not to be less than t x t 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 plating and stiffener inertia (grouped as appropriate) Main frames and tank primary members including plating, deep webs and girders are to be modelled using plate elements Face plates and plate panel stiffeners of primary members are to be represented by line elements (rods or bars) with the cross sectional area modified where appropriate, in accordance with Table and Fig In general, the use of triangular plate elements is to be kept to a minimum. Where possible, they are to be avoided in areas where there are likely to be high stresses or a high stress gradient. These include areas: in way of tank support items; in way of lightening/access holes; and adjacent to brackets, knuckles or structural discontinuities Lightening holes, access openings, etc. in primary structure are to be represented in areas of interest, e.g. in 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 effects of the opening by deleting the appropriate element Lightening holes, access openings, etc., away from areas of interest referred to in 2.18, may be modelled by deleting the appropriate elements or by applying a correction factor to the resulting shear stresses, see Section The modelling of cargo tank supports and chocks is described in Appendix A. LLOYD'S REGISTER 7

12 Fig D Finite element model of a Type A tank LPG ship

13 Fig D Finite element model showing external and internal ship structure

14 SECTION 2 Fig D Finite element model showing internal ship and tank structure at end of tank Fig D Finite element model showing tank web frame and structure at end of tank 10 LLOYD S REGISTER

15 Primary Hull and Cargo Structure of Type A Tank LPG Ships, May 2004 SECTION 2 Fig D Finite element model showing tank and ship structure in way of tank swash bulkhead Fig D Fine mesh finite element model showing the cargo tank supports LLOYD'S REGISTER 11

16 SECTION 2 Fig D Fine mesh finite element model showing the cargo tank supports Fig D Fine mesh finite element model showing the cargo tank structure 12 LLOYD S REGISTER

17 Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships, July 2002 SECTION 2 Effective Area of Face Bars 1,0 Effective area of face bars = b f t f 0,9 0,8 0,7 R b f t f 0,6 0,5 0,4 0,3 0,2 0,1 0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 1,0 0,9 0,5b f Rt f Effective area of symmetrical face bars Effective area of face bars = R b f t f 0,8 0,7 b f t f 0,6 0,5 0,4 0,3 0,2 0,1 0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 b f Rt f Effective area of asymmetric face bars moss227 Fig Effective area of face bars LLOYD'S REGISTER 13

18 SECTION 2 Table Line element effective cross-section area Structure represented by line element Effective area, A e Primary member face bars Symmetrical Asymmetrical A e = 100% A n A e = 100% A n Curved bracket face bars (continuous) Symmetrical Asymmetrical From Fig Straight bracket face bars (discontinuous) Symmetrical Asymmetrical A e = 100% A n A e = 60% A n Straight bracket face bars (continuous around toe curvature) Straight portion Curved portion Symmetrical Asymmetrical Symmetrical Asymmetrical A e = 100% A n A e = 60% A n From Fig Flat bars A e = 25% stiffener area Web stiffeners - sniped both ends Other sections A e = A Y + r A P Web stiffeners - sniped one end, connected other end Flat bars Other sections Symbols A e = 75% stiffener area A e A = Y r 2 A p A = cross-section area of stiffener and associated plating A n = average face bar area over length of line element A p = cross-section area of associated plating I = moment of inertia of stiffener and associated plating Y o = distance of neutral axis of stiffener and associated plating from median plane of plate r = radius of gyration = I A 14 LLOYD S REGISTER

19 Section 3: Boundary conditions Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships, May 2004 SECTION Introduction 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 for symmetric, asymmetric and antisymmetric load cases The boundary conditions described in this section include the different requirements for full-breadth and halfbreadth FE ship models Where anti-pitch chocks for the aft tank are not located within the modelled length, then the tank may need to be constrained in the longitudinal direction, see The boundary conditions suitable for each individual subload case are shown in Table The boundary conditions described in this section are preferred. However, alternative equivalent boundary conditions may be used. 3.2 Symmetric boundary conditions for global loads Symmetric boundary conditions for the analysis of global loads are shown in Fig These boundary conditions allow the FE model to deflect globally under the action of hull girder vertical shear forces and bending moments. 3.3 Symmetric boundary conditions for local loads Symmetric boundary conditions for the analysis of local loads are shown in Fig These boundary conditions remove the effects of hull girder bending from the FE model and are therefore only suitable for calculating stresses resulting from local loads. 3.4 Asymmetric boundary conditions for transverse loads For a full-breadth model, only one load case needs to be considered, as the complete asymmetric load scenario can be applied to the FE model. The boundary conditions suitable for the analysis of the full-breadth are shown in Fig For a half-breadth model, two load cases need to be considered where the symmetric and anti-symmetric load components are applied separately. These separated load components are then applied to the FE model with symmetric and anti-symmetric boundary conditions respectively The anti-symmetric boundary conditions suitable for a half-breadth FE model are shown in Fig The symmetric boundary conditions suitable for a half-breadth FE model are the same as those specified for global loads described in 3.2 and shown in Fig LLOYD'S REGISTER 15

20 Longitudinal material, including tank structure rigidly linked to independent point in δ x, θ y and θ z degrees of freedom Longitudinal material of side shell, δ z =0 WTB WTB WTB δ y =0 (Only applicable to a full-breadth model) WTB Centreline plane Symmetry constraints: δ y = θ x = θ z = 0 (Only applicable to a half- breadth model) Independent point constrained in all degrees of freedom NOTE For a full-breadth model, the boundary conditions at the end plane are to be applied to both port and starboard sides. No symmetry constraints are to be applied to the centreline plane. A node on the centreline at the keel, at the aft end of the model, is to be constrained in the y-direction. Fig Boundary conditions for the application of symmetric global loads (To be used for the subload cases A to G, I, J s, J w and M for a full-breadth or a half-breadth model, also for the symmetric load components of load case H 1 and H 2 for a half-breadth model.)

21 ss F: Vertical forces distributed to the side shell nodes at WTBs to eliminate reactions at the vertical constraints. The forces remove the vertical imbalance of the model caused by the applied buoyancy. End plane Longitudinal material, including tank structure rigidly linked to independent point in δ x, θ y and θ z degrees of freedom δ z = 0 δ z = 0 F δ z = 0 F F WTB WTB WTB δ y =0 (Only applicable to a full-breadth model) WTB Independent point constrained in all degrees of freedom Centreline plane Symmetry constraints: δ y = θ x = θ z = 0 (Only applicable for a half- breadth model) NOTE For a full-breadth model, the boundary conditions at the end plane and the vertical forces F at the side shell are to be applied to both port and starboard sides. No symmetry constraints are to be applied to the centreline plane. A node on the centreline at the keel, at the aft end of the model, is to be constrained in the y-direction. Fig Boundary conditions for the application of symmetric local loads (To be used for the subload cases K, L and N for a full-breadth or a half-breadth model)

22 Longitudinal material of side shell plating rigidly linked to the independent point in δ z degree of freedom δ y = 0 δ y = 0 δ y = 0 Longitudinal material of side shell, δ z =0 δ y = 0 WTB WTB WTB independent point constrained in all degrees of freedom WTB longitudinal material, including tank structure rigidly linked to independent point in δ x, θ y and θ z degrees of freedom Fig Boundary conditions for the application of the asymmetric loads (To be used for the subload cases H for a full breadth model)

23 ss Longitudinal material of side shell plating rigidly linked to the independent point in δ x, θ y, δ z degrees of freedom End plane Longitudinal material, including tank structure rigidly linked to independent point in δ x, θ y and θ z degrees of freedom δ y = 0 δ y = 0 δ y = 0 δ y = 0 WTB WTB δ y = 0 δ y =0 (Only applicable to a full-breadth model) WTB Independent point constrained in all degrees of freedom WTB Centreline plane Anti-symmetry constraints: δ x = δ z = θ y = 0 (Only applicable for a half- breadth model) NOTE For a half-breadth model, the applied loads are to be separated into symmetric and anti symmetric components and model run for each of these load components with the relevant boundary condition set. See Fig for the boundary condition set for the symmetric load component. For a full-breadth model, the boundary conditions at the end plane are to be applied to both port and starboard sides. No anti-symmetry constraints are to be applied to the centreline plane. The nodes of the elements at the side shell and innerskin at the end of the model are to be constrained in the z-direction. Fig Boundary conditions for the application of the asymmetric loads (To be used for asymmetric subload cases H 1 and H 2 for a full breadth model, also for anti-symmetric load components of subload cases H 1 and H 2 for a full breadth model)

24 SECTION 4 Section 4: Loading conditions 4.1 Introduction Table gives the standard load cases for stress and buckling assessment, which are to be considered in the assessment. These include components arising from static, dynamic and flooding effects Some of the standard load conditions in Table may not need to be examined if the ship is not to operate in such loading conditions. A note is to be included in the Loading Manual stating that these loading conditions are not permitted. The load cases to be analysed should be discussed and agreed with Lloyd s Register at the earliest opportunity Additional load cases may need to be examined if the ship is in an unusual configuration or is to be operated in conditions which would give rise to higher stresses, such as intermediate conditions associated with ballast water exchange at sea utilising sequential emptying and filling These standard load cases are to be generated by combining the subload cases summarised in Table and illustrated in Fig These subload cases form the loading conditions to be applied to the structural model and are summarised in The fully loaded conditions are defined on the basis that the ship s scantling draught is not significantly different from the operation draught. If this is not so, then special consideration will be given. 4.2 Subload cases Still water and Rule vertical bending moment These subload cases correspond to the specified operating conditions and only include static load components. The actual draughts and all deadweight and lightweight items are to be included. These loading conditions are likely to generate the highest still water loadings on the ship The assigned permissible design wave vertical bending moment and permissible vertical still water bending moment envelopes are to be applied. Explanatory notes for the application of vertical bending moments is given in Vertical dynamic These subload cases are to be evaluated using quasi-static techniques. The maximum downward vertical acceleration is applied to all deadweight and lightweight items and the resulting dynamic condition is balanced on a trimmed waterline The dynamic loading condition and quasi-static trimmed waterline are derived using a still water loads program. No wave profile is to be added to the trimmed waterline The following loads are to be applied to the FE model: External hydrostatic pressures due to the quasi-static trimmed waterline. Cargo pressure loads acting on the cargo tank structure. These loads are to include static pressure and dynamic pressure due to vertical and longitudinal accelerations. Inertia load of structural mass and other deadweight items are to include vertical acceleration factor. Rules design vertical wave bending moment envelope, see Assigned permissible still water bending moment, see LLOYD S REGISTER

25 SECTION The generated loading condition reflects the ship at: maximum downward heave; maximum bow down pitch and hence deep draught forward; maximum downwards inertial acceleration over the forward end; and high hogging bending moments If the ship structure aft of amidships is also to be analysed, then bow pitched up vertical dynamic load cases are also to be considered Explanatory notes for the application of the dynamic vertical load cases are given in to Transverse dynamic All loading conditions are to be reviewed to determine which gives the greatest acceleration components in each of the loaded tanks. If the ship is intended to operate with one or more cargo tanks empty, it is necessary to consider alternate or single tank loading cases These subload cases are to be based on the following two loading conditions: condition that results in greatest transverse acceleration of number one cargo tank including its contents; and condition that results in greatest transverse acceleration of number two cargo tank including its contents If the structure supporting the other cargo tanks is significantly different from that of numbers one and two tanks, then further load cases may be required to verify the scantlings of this structure (see 2.3) To simulate the dynamic transverse loads on the cargo tanks structure, the cargo tanks structure and its contents are to be subjected to a transverse acceleration, equal to A y g, and a vertical acceleration, equal to g. These accelerations are relative to the ship s axes and include the effect of gravity. The value of A y is not to be taken as less than 0,58, see These subload cases are to be evaluated using quasi-static techniques. The resulting dynamic condition is to be balanced on a trimmed waterline using a still water loads program and the resultant external hydrostatic pressures are to be based on the ship heeled to at an angle, θ, where θ is to be taken as the greater of tan -1 A y or No wave profile is to be added to the trimmed waterline. The heeled waterline need not be taken beyond the upper deck at side, provided that the heel angle, θ, is not less than Normally a positive heel angle is considered to be to port. Hence, transverse acceleration will be positive in the port (positive y) direction The following loads are to be applied to the FE model: External hydrostatic pressures due to the heeled and trimmed waterline. The pressure head distribution is given in Fig Cargo pressure due to the transverse and vertical accelerations described in Transverse and vertical components of the ship's structural weight and other items of deadweight in the heeled condition. 60% of Rule design vertical wave bending moment envelope, see Assigned permissible vertical still water bending moment envelope, see Explanatory notes for application of the dynamic transverse load case are given in to LLOYD'S REGISTER 21

26 SECTION If only half the breadth of the ship has been modelled, then these subload cases need to be derived by combining the symmetric and anti-symmetric load components, see and Appendix B Local wave effects The effects of local wave pressure are included by assuming a constant wave head along the full length of the FE model, see Separate subload cases are required for the wave crest and trough conditions, see subload cases N and P in Table These results are to be combined with results from other subload cases as specified in Table before carrying out stress and buckling checks Flotation load case This load case has been greatly simplified to include only the forces acting on the anti-flotation chocks when they are seated on top of the cargo tanks. A load case to study each tank individually may be required Tank test conditions These case(s) are to consider the ship in the actual loading conditions when the tank test procedures are undertaken. It may be necessary to analyse load cases for the testing of each cargo tank separately. All loads, including still water bending moment and shear force, are to be applied. The pressures in the tanks are to correspond to the test values Collision load case This load case is to consider the transverse bulkheads capability to withstand the collision load on the model surface corresponding to one half the weight of the cargo in the forward direction and one quarter the weight of the tank and cargo in the aft direction according to Lloyd s Register s Rules for Ships for Liquefied Gases The transverse swash bulkheads, where fitted, should be able to withstand half the collision load as described in However the transverse wash bulkheads need not be considered in the analysis if the scantlings are half of the end transverse bulkheads All static load components and external hydrostatic pressures due to the static waterline for these conditions are to be applied. 4.3 Procedure to derive subload cases General All components of a loading condition are to be included in the analysis. The lightship is to be included by adjusting the selfweight of the model to equal the required lightweight Buoyancy loads are to be applied as pressures, ρgh, to wetted shell elements, where h is the vertical distance from the waterline to the centre of the element Cargo loads, static and dynamic loads due to additional acceleration factors, are to be applied as pressures directly to the elements representing the tank plating. The following equations are to be used to determine the pressure values, see also Figs , and Appendix B. For still water: P = ρcghz + P0 22 LLOYD S REGISTER

27 SECTION 4 For vertical dynamic: ( 1+ 0, Az ) + ρcghx Ax P0 ( + Az ) 0 P = ρcghz 9 +, for load case V1, V3 and V5 P = ρcghz 1 + P, for load case V2, V4 and V6 For transverse dynamic: where P = P sym + P asym P sym is the symmetric component, P sym = ρcghz + P0 P asym is the anti-symmetric component, Pasym = ρcghy Ay To apply the asymmetric load cases to a half-breadth model, it is necessary to combine the two separate symmetric and antisymmetric load cases as follows: P asym = Psym + Pantisym where Psym = ρcgbt Ay b P = ρ t antisym cgay hy 2 b t is the tank breadth The pressure heads in the above expressions are measured as follows: h x forward from the after end of the tank, for pitching bow down accelerations, h y transversely from the starboard tank side plating vertically down from the highest point of the tank. h z Selection of maximum acceleration factors All cargoes specified in the class notation are to be investigated to determine which loading conditions generate the maximum cargo tank loadings by virtue of either high density and/or maximum acceleration factors. This analysis is required to establish the design pressure envelope for each cargo tank in accordance with the IGC Code The longitudinal and transverse acceleration factors may be derived using the guidance formula in the Rules for Ships for Liquefied Gases, Chapter 4, The vertical acceleration factors for the vertical dynamic subload cases are to be derived in accordance with The block coefficient at the full load draught is to be used for all load conditions ShipRight program No 20601, LNG/LPG Acceleration Heads may be used to calculate the longitudinal and transverse accelerations at the centre of each cargo tank and also at the selected positions along the ship length In order to comply with the IGC Code requirement that tank structures must be able to sustain a 30 degrees static heel condition, the transverse acceleration factor, A y, to be applied to the transverse dynamic subload cases is not to be taken as less than 0,58. It is necessary to increase the transverse acceleration factor to 0,58 if the calculated value is found to be less. LLOYD'S REGISTER 23

28 SECTION In general, it will be found that loading conditions with one or more of the following factors impose the highest loads on the tank structure: alternate or single empty hold loading; high density cargo; high metacentric height Alternatively, direct calculation procedures using appropriate ship motion program may be used to derive the acceleration factors after consultation with Lloyd s Register Procedure to derive the quasi-static waterline for dynamic load case This procedure is to be used to calculate the dynamic loads acting on all deadweight and lightweight items and to determine the resulting quasi-static external pressure distribution acting on the shell plating The longitudinal weight distribution is to be broken down into convenient longitudinal sections for all lightweight and deadweight items in a similar way to that required for a still water loads analysis A vertical acceleration factor (relative to g) at the longitudinal centre of gravity of each compartment is to be calculated in accordance with and added the static gravity of g Each section of lightweight and deadweight is to be multiplied by its corresponding vertical acceleration factor to give the combined static and dynamic weight distribution, and this is to be balanced on a suitable waterline using a still water loads program. This waterline should not include any added wave profile. Values of vertical bending moment and shear force are to be calculated at positions corresponding to the end of the finite element model and over the central 0,4L to 0,7L region of the ship The resulting quasi-static trimmed waterline is to be used to apply the external hydrostatic pressures to shell plating elements. For the dynamic transverse subload cases, the external hydrostatic pressure is to be based on the ship heeled to an angle of θ degrees, see Calculation of vertical acceleration factor along the length of the ship For the vertical dynamic subload case, the vertical acceleration factor is to be derived in accordance with this Section. The effect of gravity is not included in this vertical acceleration factor The guidance vertical acceleration formula given in the Rules for Ships for Liquefied Gases is modified, as shown below, to maintain a consistent acceleration curve over the model length. This modification takes account of the fact that the pitch motion in the aft end of the ship results in a vertical acceleration component acting in the opposite direction to that at the forward end of the ship Formula for vertical acceleration factor: For x L: A z , 45 x = A + L L + 06, , 005, C For x < L x Az = A 45 + L L + 06, , 005, Cb , b 24 LLOYD S REGISTER

29 SECTION 4 where A0 = 0,2 V L L L The distribution of vertical acceleration factor is illustrated in Fig The vertical acceleration equations, given in , are based on a ship motion of heave downwards and bow pitched down Procedure to apply assigned permissible vertical still water and design vertical wave bending moments The vertical wave bending moment, αm W, and the permissible vertical still water bending moment envelope are to be applied to the FE model for all subload cases, with the exception of the collision load cases O1, O2 and O3, see Tables and 2.4.2, where: M w is the Rule design vertical wave bending moment distribution as defined in Pt 3, Ch 4,5 of the Rules for Ships, including the ship service factor, f 1, and hogging/sagging factor, f 2, as appropriate. α is the required portion of the Rule design vertical bending moment to be applied, α = 0,6 for subload cases H1 and H2; α = 0,8 for subload cases E1 and E2; and α = 1,0 for other required subload cases The actual bending moment distribution that is required to be applied to the FE model to generate the assigned permissible and design vertical wave bending moment is illustrated in Fig This bending moment distribution takes account of the still water bending moment created by the subload case s loading condition. Care is to be taken in the sign convention of sagging and hogging in deriving the required bending moment distribution The vertical load distribution that requires to produce the bending moment distribution can be obtained by numerical differentiation method. The load distribution calculated is to be approximated by a series of vertical forces acting along the length of the FE model. These vertical forces are to be applied as a series of nodal forced at the side shell The distribution of the vertical forces in is such that the required bending moment distribution can be closely reproduced. It is recommended that the nodal forces be applied to every frame position Other proposed methods of applying the Rule vertical wave and assigned still water bending moment envelope will be specially considered Procedure to apply local wave crest or trough The additional wave head is to be applied over the full length of the FE model using the pressure distribution shown in Fig The ship may be assumed at its scantling draught in deriving the pressure head distribution. LLOYD'S REGISTER 25

30 SECTION Support and chock design loads For tank support chocks, an addition is to be made to the calculated loads to allow for any one support being set higher than those adjacent to it. This addition is a function of the construction tolerance and the relative flexibility of the cargo tank and double bottom. A 12 per cent increase in calculated loads is generally recommended when a 1mm tolerance is specified for the fitting gap for supports made of resin impregnated laminated wood construction. For application, see Allowance for structural misalignment between cargo tank and double bottom members can be made using a separate fine mesh model For anti-roll and anti-pitch chocks, it is generally recommended that the calculated loads are increased by 10 per cent when 1mm tolerance is specified to allow for fitting tolerances for chocks made of resin impregnated laminated wood construction. For application, see A forward longitudinal acceleration will increase loads on fore end supports and decrease them at aft end supports. Conversely for an aft acceleration. Therefore, for a parallel sided tank, the scantlings, its support and supporting hull structure should be symmetrical about the mid tank position. For the foremost and aftmost tanks, an additional bow up load case may be necessary Proposals for other than the recommended additional load factors are to be submitted for verification. The additional load factors for supports and chocks made from alternative materials are to be agreed with Lloyd s Register A preliminary investigation is to be made on the effect of misalignment between the tank supports and their seatings on the inner bottom due to a combination of thermal contraction, construction tolerances, and design gap at the anti-pitching chocks. If it is found that this misalignment could cause a significant increase to, or redistribution of, the stress levels in the support chocks or the reinforcement structure in way, this is to be examined further. The method of examination is to be discussed and agreed with the plan approval office Procedure for loading supports and chocks The longitudinal forces due to pitching are to be calculated for each tank using the longitudinal acceleration factor. Provided the coefficient of friction between the tank seat and support chock material is sufficient, then no load will be present at the anti-pitch chocks. If this is not the case, spring elements will be required to represent the anti-pitch chocks. The longitudinal forces are to be distributed as follows: Where anti-pitch chocks are not required, equal forces are to be applied at the top of each tank support chock to balance the longitudinal pitching force for this tank. An equal and opposite force is to be applied at the bottom of each tank support to the ship s structure. Where anti-pitch chocks are required, the maximum available frictional force from the tank support chocks is to be uniformly distributed to each tank support chock as above. The remaining longitudinal pitching force is to be absorbed by elastic springs representing the anti-pitch chocks between the tank and the ship structure. This force is not to be applied as an external load The procedure described in may also be applied to the transverse forces due to ship motions to determine the loads acting on the anti-roll chocks and transverse friction forces at the tank support chocks. 26 LLOYD S REGISTER

31 SECTION 4 Table List of standard load cases to be used for the assessing the structure against the permissible stresses and buckling structure Load case No. Static wave load cases Load case description Total still water bending moment Rule vertical wave bending moment Additional local wave pressures Combination of subload cases, see Table and Note 1 S1 Full load + Hogging BM M SW hogging Hogging Wave crest A1 + I S2 Full load + Sagging BM M SW sagging Sagging Wave trough A2 + J S3 S4 Alternate load (odd numbered tanks full) + hogging wave Alternate load (even numbered tanks full) + sagging wave M SW hogging Hogging Wave crest B + I M SW sagging Sagging Wave trough C + J S5 Heavy ballast + Hogging wave M SW hogging Hogging Wave crest D + I Vertical dynamic load cases V1 V2 V3 V4 V5 V6 Full load vertical dynamic + Hogging BM Vertical and longitudinal accelerations Full load vertical dynamic + Hogging BM Vertical accelerations Alternate load vertical dynamic (odd numbered tanks full) + Hogging BM Vertical and longitudinal accelerations Alternate load vertical dynamic (odd numbered tanks full) + Hogging BM Vertical accelerations only Alternate load vertical dynamic (even numbered tanks full) + Sagging BM Vertical and longitudinal accelerations Alternate load vertical dynamic (even numbered tanks full) + Sagging BM Vertical accelerations only Transverse dynamic load cases T1 T2 Transverse dynamic maximum acceleration in No. 1 cargo tank + Hogging BM, (see Notes 2 & 5) Transverse dynamic maximum acceleration in No. 2 cargo tank + Hogging BM, (see Notes 2 & 5) Special load cases M SW hogging 80% Hogging none E1 M SW hogging 80% Hogging none E2 M SW hogging Hogging none F1 M SW hogging Hogging none F2 M SW sagging Sagging none G1 M SW sagging Sagging none G2 M SW hogging 60% Hogging none H1 M SW hogging 60% Hogging none H2 O1 Collision load in forward direction, (see Note 2) Actual none none K1 O2 Collision load in afterwards direction, (see Note 2) Actual none none K2 O3 Collision load in forward direction on the transverse swash bulkhead, (see Note 2) Actual none none K3 O4 Tank test condition, (see Note 3) Actual none none L O5 Flotation case, (see Notes 2 & 4) none none none M NOTES 1. Permissible still water bending moment, M SW, see Ch 1,2. 2. These conditions need not be run if an acceptable alternative method is used to estimate anti-roll chock and anti-flotation chock forces and a substantial margin is allowed in the design of chocks and supporting structure. 3. These cases need not be run if it can be shown that the tank test conditions are unlikely to cause excessive stresses in the double bottom structure and that the test pressures are within the design pressure envelope for the cargo tank. 4. If the anti-flotation chock arrangement is such that this method of evaluating the anti-flotation chock forces is not valid, then an alternative method of determining these forces will be required. 5. Maximum transverse acceleration is usually achieved in a single tank loading condition. LLOYD'S REGISTER 27

32 SECTION 4 Table List of subload cases (see continuation) Subload case Condition Boundary conditions Still water and bending moment subload cases A1 A2 B C D Full load + hogging All cargo tanks full Full load + sagging All cargo tanks full Alternate load odd numbered tanks full (hog) + hogging BM Nos. 1 & 3 (& 5) tanks full Alternate loaded even numbered tanks full (hog) Nos. 2 & 4 tanks full Heavy ballast + hogging BM Dynamic subload cases E1 E2 Full load vertical dynamic condition + hogging BM All cargo tanks full Bow pitched down Vertical and longitudinal accelerations Full load vertical dynamic condition + hogging BM All cargo tanks full Bow pitched down Vertical accelerations only Symmetric global See Fig As subload case A1 Symmetric global See Fig See Note 1 in Table Symmetric global See Fig See Note 1 in Table Symmetric global See Fig Symmetric global See Fig As subload case E1 Notes A loading condition with all cargo tanks filled and at full load draught, see Note 1. All still water load items are to be applied. External hydrostatic pressures due to the still waterline are to be applied Rule hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. As subload case A1 except as follows: Rule sagging vertical design wave bending moment and assigned permissible sagging still water bending moment envelopes are to be applied. Alternately loaded condition with all odd numbered tanks full and even numbered tanks empty, see Note 1. Ballast and fuel tanks are to be arranged to maximise the hogging vertical bending moment Rule Hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. Boundary conditions and other load application is similar to subload case A1. Alternately loaded condition with all even numbered tanks full and odd numbered tanks empty, see Note 1. Ballast and fuel tanks are to be arranged to maximise the hogging vertical bending moment. Rule Hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. Boundary conditions and other load application is similar to subload case A1. A deep draught loading condition with most water ballast tanks filled Rule hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. Boundary conditions and load application is similar to subload case A1. A loading condition with bow pitched down, all cargo tanks filled and at full load draught. The loading condition, which generates maximum inertial pressures in Nos. 1 and 2 tanks, is to be chosen. All still water deadweight and lightweight items are to be applied and are to include the vertical acceleration factor, see and Cargo pressures are to include the longitudinal acceleration factors, see External hydrostatic pressures due to the quasi-static trimmed waterline are to be applied, see % Rule hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. As subload case E1 except as follows: Cargo pressures are not to include any longitudinal acceleration factor. 28 LLOYD S REGISTER

33 Table List of subload cases (see continuation) Subload case Condition Dynamic subload cases F1 F2 G1 G2 H1 H2 Vertical dynamic odd numbered tanks full (hog) Nos. 1 & 3 (& 5) tanks full Bow pitched down Vertical and longitudinal accelerations Vertical dynamic odd numbered tanks full Nos. 1 & 3 (& 5) tanks full Bow pitched down Vertical accelerations only Vertical dynamic even numbered tanks full (hog) Nos. 2 & 4 tanks full Bow pitched down Vertical and longitudinal accelerations Vertical dynamic even numbered tanks full (hog) Nos. 2 & 4 tanks full Bow pitched down Vertical accelerations only Transverse dynamic maximum acceleration in No. 1 cargo tank + hogging BM Transverse dynamic maximum acceleration in No. 2 cargo tank + hogging BM Local wave pressure subload cases Boundary conditions Symmetric global See Fig As subload case F1 Symmetric global See Fig As subload case G1 Asymmetric case see Fig and Fig As subload case H1 I Local wave crest Symmetric local See Fig Primary Hull and Cargo Tank Structure of Type A Tank LPG Ships, May 2004 Notes SECTION 4 As subload case A1 except as follows: Alternately loaded condition with bow pitched down, all odd numbered tanks full and even numbered tanks empty The loading condition, which generates maximum pressures in Nos. 1 & 3 tank, is to be chosen. As subload case F1 except as follows: Cargo pressures are not to include any longitudinal acceleration factor. As subload case A1 except as follows: Alternately loaded condition with bow pitched down, all even numbered tanks full and odd numbered tanks empty The loading condition, which generates maximum pressures in Nos. 2 & 4 tank, is to be chosen. As subload case G1 except as follows: Cargo pressures are not to include any longitudinal acceleration factor. The loading condition, which generates maximum transverse acceleration in No.1 cargo tank and its contents, is to be chosen. This is usually a single tank loading condition. The subload case is to be based on the ship heeled at an angle of θ, see All still water deadweight and lightweight items are to be applied. Cargo tank structure and its contents are to be subjected to the transverse and vertical accelerations specified in These accelerations include the effect of gravity. Cargo pressures are to include effect of the transverse and vertical acceleration factors, see Loads on anti-roll chocks see External hydrodynamic pressures due to the quasi-static trimmed waterline are to be applied, see Fig % Rule hogging vertical design wave bending moment and assigned permissible hogging still water bending moment envelopes are to be applied. The loading condition, which generates maximum transverse acceleration in No.2 cargo tank and its contents, is to be chosen. This is usually a single tank loading condition. The subload case is to be based on the ship heeled at an angle of θ, see The load application is similar to subload case H1 Only the pressure due to a local wave crest is to be applied, see It is to be assumed that the wave crest acts over the full length of the FE model. The ship may be assumed at its scantling draught in deriving the pressure head distribution. J Local wave trough As subload case I Only the pressure due to a local wave through is to be applied, see It is to be assumed that the wave through acts over the full length of the FE model. The ship may be assumed at its scantling draught in deriving the pressure head distribution. LLOYD'S REGISTER 29

34 SECTION 4 Table List of subload cases (conclusion) Subload case Condition Boundary conditions Notes Collision subload cases K1 Forward collision Full load condition K2 Aft collision Full load condition Symmetric global see Fig , except that dx constraint is to be removed from the end plane and added to a point at the forward of the bow. As subload case K1 A fully loaded condition with all cargo tanks filled and at full load draught. All still water load items to be applied External hydrostatic pressures due to the static waterline to be applied A forward acceleration of 0,5g is to be applied in the longitudinal direction to all cargo and tank structure and the selfweight of the model. As subload case K1 except as follows: An aft acceleration of 0,25g is to be applied in the longitudinal direction to all cargo and tank structure and the selfweight of the model. K3 Forward collision assessment of the swash bulkheads Special subload cases As subload case K1 L Tank test conditions Symmetric global see Fig M Flotation case Symmetric local see Fig All still water load items to be applied. External hydrostatic pressures due to the static waterline to be applied A loading condition with the cargo tank aft of the swash bulkhead filled and at full load draught. A forward acceleration of 0,5g is to be applied in the longitudinal direction to the swash bulkhead structure and the selfweight of the model. The actual ship conditions proposed for the tests of cargo tanks 1 and 2 must be used together with the lightest draughts chosen for each condition. The cargo pressures in each tank are to represent the test pressure. All still water load items are to be applied. External hydrostatic pressures due to the still waterline are to be applied. Only the void space between the inside of the hold and the outside of the cargo tank boundaries is assumed to be flooded up to the scantling draught. Cargo tanks are to be empty. External buoyancy, deadweight and lightweight items and all other loads are not to be applied. See Note 2 and 3 NOTE 1. The still water load condition to be selected is that which generates the maximum static plus dynamic pressures in the forward loaded cargo tank 2. This load case is not based on an actual loading condition. 3. If damage stability calculations are available then the depth of flooding from the damage stability calculations may be used in lieu of the scantling draught. 30 LLOYD S REGISTER

35 Area modelled S1 Full load static + hogging wave Loading condition Fully loaded Subload cases External Hydrostatic due to static waterline (A1) Cargo pressure Cargo pressure due to gravity Additional applied BM SWBM: M SW hogging - actual VWBM: Rule hogging External Local wave crest (to be applied to full length of FE model) (I) Area modelled S2 Full load static + sagging BM Loading condition Fully loaded Subload cases External Hydrostatic due to static waterline (A2) Cargo pressure Cargo pressure due to gravity Additional applied BM SWBM: M SW sagging - actual VWBM: Rule sagging External Local wave trough (to be applied to full length of FE model) (J) Area modelled S3 Alternate load (odd numbered tanks full) + hogging wave Loading condition Alternate load, Nos. 1 & 3 (&5) tanks full Subload cases External Hydrostatic due to static waterline (B) Cargo pressure Cargo pressure due to gravity Additional applied BM SWBM: M SW hogging - actual VWBM: Rule hogging External Fig Illustration of load cases Part 1 (static wave load cases) The relevant subload cases are indicated in ( ). The factors for the subload cases are given in Table Local wave crest (to be applied to full length of FE model) (I)