ShipRight Design and Construction

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1 ShipRight Design and Construction Structural Design Assessment Procedure for Primary Structure of Ore Carriers September 2016 Working together for a safer world

2 Lloyd's Register Group Limited All rights reserved. Except as permitted under current legislation no part of this work may be photocopied, stored in a retrieval system, published, performed in public, adapted, broadcast, transmitted, recorded or reproduced in any form or by any means, without the prior permission of the copyright owner. Enquiries should be addressed to Lloyd's Register Group Limited, 71 Fenchurch Street, London, EC3M 4BS.

3 CHAPTER 1 INTRODUCTION SECTION 1 APPLICATION SECTION 2 SYMBOLS SECTION 3 DIRECT CALCULATIONS CHAPTER 2 STRUCTURAL DESIGN ASSESSMENT PROCEDURE FOR PRIMARY STRUCTURES CHAPTER 3 APPENDIX A ORE LOADS CHAPTER 4 APPENDIX B BALLAST LOADS CHAPTER 5 APPENDIX C EXTERNAL HYDROSTATIC AND HYDRODYNAMIC PRESSURES CHAPTER 6 APPENDIX D ADJUSTMENT OF HULL GIRDER BENDING MOMENTS AND SHEAR FORCES 2 Lloyd's Register

4 Introduction Chapter 1 Section 1 Section 1 Application 2 Symbols 3 Direct Calculations n Section 1 Application 1.1 Application The ShipRight Structural Design Assessment (SDA) procedure is mandatory for ore carriers equal to and greater than 150 m in Rule length and for other ore carriers of abnormal hull form, or of unusual structural configuration or complexity For ore carriers, other than those defined in Ch 1, 1.1 Application 1.1.1, the SDA and CM procedures may be applied on a voluntary basis When applied on a mandatory basis, the SDA procedure must be utilised in conjunction with ShipRight Fatigue Design Assessment (FDA) and Construction Monitoring (CM) procedures. The application of the procedures in this way ensures that: The critical areas are identified early in the design phase. The structural details are designed to minimise the inclusion of stress concentrations. The steelweight distribution is better targeted to the important structural areas. Appropriate construction tolerances are applied to critical areas during construction which reflect the increased diligence and care taken during the design stage. The Shipowner s commitment to safety is demonstrated 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 The SDA procedure requires: A detailed analysis of the ship s structural response to applied static and dynamic loads, using three-dimensional (3-D) finite element analysis. Other direct calculations, as applicable The structural model and load cases, detailed in Ch 2, will enable the following structural responses to be investigated: Stresses in longitudinal primary members Stresses in transverse primary members including transverse bulkheads Buckling capability of plate panels of primary structures This document details the SDA procedure for carrying out a 3-D model finite element analysis of the primary structures of cargo holds A detailed report of the SDA analysis is to be submitted and must include information detailed in Ch 1, 3 Direct Calculations. The report must show compliance with the specified acceptance criteria given in Ch 2, 5 Stress acceptance criteria and Ch 2, 6 Buckling acceptance criteria If the computer programs employed are not recognised by Lloyd s Register, then full particulars of the programs are to be submitted. See Pt 3, Ch 1, 3.1 of the Rules for Ships Lloyd s Register may, in certain circumstances, require submission of the computer input and output in a suitable electronic format to verify further the adequacy of the calculations carried out Where alternative procedures are proposed, these are to be agreed with Lloyd s Register before commencement Ore carriers of unusual form or structural arrangements may need special consideration and additional calculations to those shown in this SDA procedure. Lloyd's Register 3

5 Introduction Chapter 1 Section It is recommended that the designer consult with Lloyd s Register on the structural analysis requirements of the SDA procedure at an early stage in the design cycle. n Section 2 Symbols 2.1 Symbols The symbols used in the SDA procedure, in Ch 2, are defined as follows: L = Rule length, in metres, as defined in Pt 3, Ch 1, 6 of the Rules for Ships B = moulded breadth, in metres, as defined in Pt 3, Ch 1, 6 of the Rules for Ships D = depth, in metres, as defined in Pt 3, Ch 1, 6 of the Rules for Ships T S = scantling draught T BD = deepest draught in relevant ballast conditions envisaged T HS_S = shallowest draught at the mid-hold position of the assessed cargo hold envisaged in harbour conditions, with one cargo hold fully loaded, taking into account the ship s trim. T HS_S is not to be taken as greater than 0,55T S T HS_A = shallowest draught at the mid-hold position of the assessed cargo hold envisaged in harbour conditions, with two adjacent cargo holds fully loaded, taking into account the ship s trim. T HS_A is not to be taken as greater than 0,75T S T HD = deepest draught at the mid-hold position of the assessed cargo hold in harbour conditions, taking into account the ship s trim. T HD is not to be taken as less than 0,85T S M s = still water bending moment of loading condition M SH = permissible sea-going hogging (positive) still water bending moment M SS = permissible sea-going sagging (negative) still water bending moment M SH(har) = permissible harbour hogging (positive) still water bending moment M SS(har) = permissible harbour sagging (negative) still water bending moment M WH = design hogging (positive) wave bending moment calculated in accordance with Pt 3, Ch 4, 5.2 of the Rules for Ships M WS = design sagging (negative) wave bending moment calculated in accordance with Pt 3, Ch 4, 5.2 of the Rules for Ships Q SP = permissible sea-going positive still water shear force Q SN = permissible sea-going negative still water shear force Q SP(har) = permissible harbour positive still water shear force Q SN(har) = permissible harbour negative still water shear force Q WP = design positive wave shear force Q WN = design negative wave shear force M = mass of ore intended to be carried in the hold, as specified in the ship s loading manual ΔM = margin of the cargo mass, to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, ΔM is not to be taken as less than 0,05M W C = wave pressure distribution on hull surface in wave crest, see Ch 5 Appendix C External Hydrostatic and Hydrodynamic Pressures 4 Lloyd's Register

6 Introduction Chapter 1 Section 3 W T = wave pressure distribution on hull surface in wave trough, see Ch 5 Appendix C External Hydrostatic and Hydrodynamic Pressures g = acceleration of gravity, to be taken as 9,81 m/s 2 or equivalent, consistent with the units in the analysis ρ w = density of sea-water (specific gravity to be taken as 1,025) ρ c = density of cargo κ L = higher tensile steel factor, see Pt 3, Ch 2, 1.2 of the Rules for Ships σ o = specified minimum yield stress, see Pt 3, Ch 2, 1.2 of the Rules for Ships. Special consideration will be given to the steel of σ o 355 N/mm 2 σ e = Von Mises equivalent stresswhere = σx 2 + σy 2 σx σ y + 3τ xy 2 where σ x = normal stress in element x direction σ y = normal stress in element y direction τ xy = shear stress in element xy plane δ x, δ y, δ z = translation displacement in global X, Y and Z directions θ x, θ y, θ z = rotational displacement about global X, Y and Z axes λ = factor of safety of plate panel buckling λ = σ cr /σ a σ cr = critical equivalent buckling stress σ a = equivalent applied buckling stress Consistent units are to be used throughout all parts of the analysis. Results presentation in N and mm are preferred All Rule equations are to use units as defined in the Rules for Ships. n Section 3 Direct Calculations 3.1 Direct calculation reports A report is to be submitted to Lloyd s Register for approval of the primary structures in the cargo region and is to contain the following items: 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 Shear Force (SF) and Bending Moment (BM) distributions. Details of applied loads and confirmation that individual and total loads are correct. Plots and results that demonstrate correct behaviour of the structural model to applied loads. Summaries and plots of deflections. Summaries and sufficient plots of Von Mises, directional and shear stresses to demonstrate that the acceptance criteria are not exceeded in any member. Plate panel buckling calculations and results. Tabulated results showing compliance with the acceptance criteria. Lloyd's Register 5

7 Introduction Chapter 1 Section 3 Proposed amendments to the structure, where necessary, including re-assessment of stress level and buckling capability. 6 Lloyd's Register

8 Contents CHAPTER 1 INTRODUCTION CHAPTER 2 STRUCTURAL DESIGN ASSESSMENT PROCEDURE FOR PRIMARY STRUCTURES SECTION 1 OBJECTIVES SECTION 2 STRUCTURAL MODELLING SECTION 3 BOUNDARY CONDITIONS SECTION 4 LOADING CONDITIONS SECTION 5 STRESS ACCEPTANCE CRITERIA SECTION 6 BUCKLING ACCEPTANCE CRITERIA SECTION 7 HOLD MASS CURVES CHAPTER 3 APPENDIX A ORE LOADS CHAPTER 4 APPENDIX B BALLAST LOADS CHAPTER 5 APPENDIX C EXTERNAL HYDROSTATIC AND HYDRODYNAMIC PRESSURES CHAPTER 6 APPENDIX D ADJUSTMENT OF HULL GIRDER BENDING MOMENTS AND SHEAR FORCES Lloyd's Register 7

9 Section 1 Section 1 Objectives 2 Structural modelling 3 Boundary conditions 4 Loading conditions 5 Stress acceptance criteria 6 Buckling acceptance criteria 7 Hold mass curves n Section 1 Objectives 1.1 Objectives The objectives of the structural design assessment procedure are to ensure the stress level and buckling capability of primary structures under the applied static and dynamic loads are within acceptable limits. n Section 2 Structural modelling 2.1 Structural modelling The appropriate length of the Finite Element (FE) model depends on the cargo hold arrangements and is to be agreed with Lloyd s Register at an early stage The extent of the FE model is to be such that the scantlings and arrangements in way of the cargo holds, including bulkheads, are adequately represented In general, the requirements of Ch 2, 2.1 Structural modelling will be satisfied by using a 3-D finite plate element model of three cargo hold lengths (i.e. one hold + one hold + one hold). A typical FE model is shown in Figure D Finite Element Model Typical SDA model and Figure D Finite Element Model Internal structures The ends of the three cargo hold length model are to be located at the fore and aft end transverse bulkheads, including stools if fitted. The ends of the model are to form a vertical plane to suit the application of the boundary conditions and this may require additional transverse web sections, see Ch 2, 3 Boundary conditions In general, only one side of the ship needs to be modelled with appropriate boundary conditions imposed at the centreline. In cases where the ship structure is asymmetrical about the ship s centreline, a full breadth model will be required. The full depth of the ship is to be modelled. The transverse cross-section of the FE model may be prismatic over the model length and the geometry based on the midship section geometry The number of three cargo hold FE models required to be analysed depends upon the structural arrangement of cargo holds. If there is a significant difference in the structural arrangements, in particular, where the transverse bulkhead lower stool is not symmetrical and/or has different fore and aft extent, the separate cargo hold FE models representing different cargo hold structural arrangements may be required to be analysed The FE model is to be based upon 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. 8 Lloyd's Register

10 Section The gross thickness of proposed scantlings, excluding Owner s extras or any additional thickness for the ShipRight Enhanced Scantlings (ES) procedure, is to be used throughout the FE model The selected size and type of plate elements are to provide a satisfactory representation of the deflections and stress distributions within the cargo hold structure In general, the plate element mesh is to follow the stiffening arrangements of the structure. Standard mesh size is to be as follows: Transversely, one element for every longitudinal stiffener spacing. Longitudinally, at least three elements for every double bottom floor spacing. Vertically, one element for every longitudinal stiffener spacing Transverse ring webs in side tanks should be modelled using at least three or more plate elements in the depth. See Figure D Finite Element Model Typical transverse section Double bottom girders and floors should be defined by at least three or more plate elements over the depth, see Figure D Finite Element Model Typical transverse bulkhead with horizontal stringers and Figure D Finite Element Model Typical longitudinal section Corrugated bulkheads should be modelled using one plate element for each flange and web panel of the corrugation. Plate elements are to be defined with membrane and bending properties. Plate elements in the bulkhead near the lower stool and adjacent elements of the stool plating should have an aspect ratio of approximately one. A typical mesh arrangement of a transverse bulkhead is shown in Figure D Finite Element Model Typical transverse bulkhead with horizontal stringers Secondary stiffening members are to be modelled using line elements (bars) positioned in the plane of the plating, having axial and bending properties. The bar elements are to have: A cross-sectional area, representing the stiffener area excluding the area of attached plating; and Bending properties, representing the combined effects of the attached plating and stiffener 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 such a case, the stress at the mid-plane of the plate elements should be used for comparing against the permissible stress criteria 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. Such areas include: In way of lightening/access holes. At the connection of corrugated bulkhead, lower stool and shelf plate. Adjacent to knuckles or structural discontinuities Face plates and plate stiffeners of primary members are to be represented by line elements with the cross-sectional area modified, where appropriate, in accordance with Table Line element effective cross-section area and Figure Effective area of face bars Where the mesh size of the 3-D FE model is insufficiently detailed to represent areas of localised higher stresses, it will generally require to be investigated by means of fine mesh analysis. The fine mesh analysis can be carried out by means of separate local fine mesh models with boundary conditions derived from the main model or with local fine mesh regions imbedded in the main model For ore carriers of conventional structural arrangements, i.e., primary structure configuration and spacing as envisaged by the Rules for Ships, the following high stress areas will normally require to be investigated by fine mesh modelling: Connection of double bottom floors to longitudinal bulkhead and adjacent inner bottom. Connection of longitudinal girder to lower stool and adjacent inner bottom. Other locations where the mesh size of the 3-D FE model is insufficiently detailed to represent areas of high stress concentrations. If it can be demonstrated by the previous FE investigation or from application of the structural details reflected in relevant parts of the ShipRight FDA Level 1 procedure that the arrangements proposed are acceptable, then fine mesh models will not be required For ore carriers with non-conventional structural arrangements, e.g., wide primary structure spacing or where very large openings are incorporated in high stress areas, the scope of fine mesh modelling, in addition to those specified in Ch 2, 2.1 Lloyd's Register 9

11 Section 2 Structural modelling , will depend on the analysis of stress result from the main model. In such cases, proposals for additional fine mesh analysis should be agreed with Lloyd s Register The mesh size adopted should be such that the structural geometry can be adequately represented and the stress concentrations can be adequately determined. In general, the minimum required mesh size in fine mesh areas is not to be greater than 15t x 15t or 150 x 150 mm, whichever is the lesser, where t is the main plating thickness. In some locations, a finer mesh may be necessary to represent the structural geometry. The mesh size need not be less than t x t unless adequate representation of the structural geometry requires a finer mesh. Triangular plate elements are to be avoided Lightening holes, access openings, etc., in primary members may be represented in areas of interest and may be modelled by removing the appropriate elements. Openings in double bottom floors adjacent to the longitudinal bulkhead should be included in the FE model, using a mesh adequate to represent the stress behaviour around the openings if they are: of unusual size, i.e., in excess of the Rule minimum requirement on the percentage of web depth (50 per cent of double bottom depth and without edge reinforcement); of unusual proportion; or in close proximity to other openings. However, no specific modelling of the openings is required if they are of standard form, even in close proximity to slots for longitudinal stiffeners, provided that collar (or filler) plates or equivalent are fitted For openings, such as lightening holes, access openings and slots for longitudinal stiffener without collar plates, which are not represented in the model, the effect of openings is to be taken into account by applying a correction to the resulting shear stresses, see Ch 2, 5.1 Stress acceptance criteria Figure D Finite Element Model Typical SDA model 10 Lloyd's Register

12 Section 2 Figure D Finite Element Model Internal structures Lloyd's Register 11

13 Section 2 Figure D Finite Element Model Typical transverse section 12 Lloyd's Register

14 Section 2 Figure D Finite Element Model Typical transverse bulkhead with horizontal stringers Figure D Finite Element Model Typical longitudinal section Lloyd's Register 13

15 Section 2 Figure Effective area of face bars 14 Lloyd's Register

16 Section 3 Table Line element effective cross-section area Structure represented Effective area, A e Primary member face bars Symmetrical A e = 100% A n Asymmetrical A e = 100% A n Curved bracket face bars (continuous) Symmetrical Asymmetrical See Figure Effective area of face bars 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 See Figure Effective area of face bars Web stiffeners sniped both ends Web stiffeners sniped one end,connected other end Flat bars Other sections Flat bars Other sections A e = 25% stiffener area e = 2 P 0 + A e = 75% stiffener area e = 2 P Symbols 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 0 = distance of neutral axis of stiffener and associated plating from median plane of plate r = radius of gyration = n Section 3 Boundary conditions 3.1 General This Section describes the boundary conditions which are to be applied to the three cargo hold length model as described in Ch 2, 2 Structural modelling. The boundary conditions are shown in Table Boundary conditions Results derived in the region of 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 structural response, see Ch 2, 5.1 Stress acceptance criteria. Lloyd's Register 15

17 Section Boundary conditions at centreline Where a half-breadth FE model is used, 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 as follows: Displacement in the transverse direction is fixed, i.e. δ y = 0. Rotation about the longitudinal axis is fixed, i.e. θ x = 0. Rotation about the vertical axis is fixed, i.e. θ z = Structural members on the centreline plane are to be modelled using half the plate thickness. 3.3 Boundary conditions at ends Longitudinal translation displacement, δ x, of all the longitudinal members is to be rigidly linked to an independent point located at the neutral axis on the centreline at the fore and aft ends of the model Hull girder bending moments are applied to the model through the independent points at the fore and aft ends To take suitably into account the relative deflection between the side shell and longitudinal bulkheads, the model is to be supported at the ends in the vertical direction by grounded springs arranged at the side shell, longitudinal bulkheads, hopper slope plates and the connected double bottom side girders. In addition, the deck and bottom shell at the ends of the model are to be supported by grounded springs in the transverse direction. The overall stiffness, k i, may be calculated as follows: i = 1 + υ wi hd where E = modulus of elasticity of material, to be taken as 2,06 x 10 5 N/mm 2 for steel υ = Poisson s ratio to be taken as 0,3 A wi = projected shear area of side shell, longitudinal bulkheads, hopper slope plates, double bottom girders, deck or bottom shell on vertical or horizontal plane, as appropriate L hd = length of the middle cargo hold of the FE model. The overall stiffness, k i, may be distributed to each grid point in the side shell, longitudinal bulkheads, hopper slope plates, double bottom girders, deck and bottom shell in proportion to the projected distance between the grid points in such a way that the sum of spring stiffness is equal to the overall stiffness. Table Boundary conditions (a) Symmetry boundary conditions at centreline for half breath FE model Translational Rotational δ x δ y δ z θ x θ y θ z Centreline plane Fixed Fixed Fixed (b) Boundary conditions at model ends Translational Rotational δ x δ y δ z θ x θ y θz All longitudinal members RL RL RL Aft end Side shell,longitudinal bulkheads, hopper plates and side girders Deck,hopper plates and bottom shell Supported by springs Supported by springs Independent point Fixed M aft 16 Lloyd's Register

18 Section 4 All longitudinal members RL RL RL Fore end Side shell, longitudinal bulkheads, hopper plates and side girders Deck,hopper plates and bottom shell Supported by springs Supported by springs Independent point M fore Symbols RL = M aft, M fore = rigidly linked to the independent point hull girder bending moment applied at the independent points at the aft and fore ends of the model, see Ch 6 Appendix D Adjustment of Hull Girder Bending Moments and Shear Forces. Where bending moment is not applied, the independent points are to remain free. n Section 4 Loading conditions 4.1 General The loading conditions which are likely to impose the most onerous regimes are to be investigated in the structural analysis. The standard load cases to be investigated are specified in Ch 2, 4.1 General 4.1.2, Ch 2, 4.1 General and Ch 2, 4.1 General The following bending moment load cases are to be analysed. These load cases are intended for assessing the overall strength of the structure: Homogeneous fully loaded conditions: see Table Bending moment load cases Fully loaded homogeneous loading conditions Ballast conditions: see Table Bending moment load cases Ballast conditions Harbour loading and unloading conditions: see Table Bending moment load cases Harbour loading/unloading conditions The following tank testing load cases are to be analysed: Tank test conditions: see Table Tank test conditions The following shear force load cases are to be analysed. These load cases are intended for assessing the shear strength of longitudinal hull girder members in way of the transverse bulkheads and connections to transverse bulkhead horizontal stringers: Harbour loading and unloading conditions: see Table Shear force load cases Harbour loading/unloading conditions For ships that are intended to operate with multiport loading patterns as specified in the ship s loading manual, the load cases for the assessment of multi-port sea-going conditions will be specially considered, based on the actual loading conditions specified in the ship s loading manual. The load cases for this assessment are to be agreed with Lloyd s Register before commencement Additional loading conditions to those specified in Ch 2, 4.1 General 4.1.2, Ch 2, 4.1 General and Ch 2, 4.1 General may be required in consideration with the proposed structural arrangements Where specified loading conditions are agreed between the Shipbuilder and the Shipowner which are not covered by the loading conditions specified in Ch 2, 4.1 General 4.1.2, Ch 2, 4.1 General and Ch 2, 4.1 General 4.1.4, these loading conditions are to be included in the SDA analysis Full details of all proposed design loading conditions are to be submitted to Lloyd s Register at an early stage for agreement of the scope of the SDA analysis Lloyd's Register 17

19 Section Application of loads The following local loads, where required, are to be applied to the FE model: Steel weight, the weight of hatch covers may be excluded. Static ore loads. Static ballast water pressures in tanks. External hydrostatic and hydrodynamic pressures Static ore loads, where required, are to be applied to the boundaries of the cargo holds in accordance with Ch 3 Appendix A Ore Loads Static ballast water pressure, where required, is to be applied to the boundaries of water ballast water tanks in accordance with Ch 4 Appendix B Ballast Loads External hydrostatic and hydrodynamic pressures, where required, are to be calculated in accordance with Ch 5 Appendix C External Hydrostatic and Hydrodynamic Pressures and applied to the hull surface For the bending moment load cases in Ch 2, 4.1 General 4.1.2, the hull girder bending moment in the FE model is to reach the values specified from Table Bending moment load cases Fully loaded homogeneous loading conditions to Table Tank test conditionswithin the middle hold of the FE model. Where the hull girder bending moment resulting from the application of local loads is different from the specified value, the level of bending moment is to be adjusted by the method described in Ch 6, 1.1 General For the shear force load cases in Ch 2, 4.1 General 4.1.4, the hull girder shear force in the FE model at the middle hold s fore and aft bulkhead positions is to reach the values specified in Table Shear force load cases Harbour loading/ unloading conditions. The hull girder bending moment is also to reach the values specified in the Table within the middle hold of the FE model. Where the hull girder shear forces and bending moment are different from the specified values, the method described in Ch 6, 2.1 General is to be used to adjust the shear force and bending moment levels Where ballast water exchange at sea utilising the flow-through method is agreed between the Owner and the Shipbuilder as a design basis, additional loading conditions may require to be analysed, assuming that the ballast water exchange is carried out at calm sea. The analysis may be based on hydrostatic external pressures, static ballast water pressures, static ore loads, harbour permissible still water bending moments and shear forces In case of ore carriers that are designed for operation in an asymmetrical loading condition, or large ore carriers with B 40 m or b/w 2,2, the wave loads should take account of hydrodynamic torque in oblique sea, where B = see Ch 1, 2.1 Symbols b = breadth of the deck hatch openings, in metres w = width of the cross-deck strip between hatchways, in metres. Table Bending moment load cases Fully loaded homogeneous loading conditions Load case Local loads Global loads Loads in holds and ballast water in tanks External pressure Hull bending 18 Lloyd's Register

20 Section 4 (a) All holds carry maximum mass of light ore, including a margin ( M) specified in the Note with a density of (M + M)/V h (a) Scantling draught (a) Maximum hogging or minimum sagging still water bending moment given in the ship s loading manual for homogeneous loading conditions (M S ) (b) All ballast tanks empty (b) Wave crest (b) Rule wave bending moment (hogging) Static ore pressures T S +W C M S +M WH Homo.1 Illustration of load case Homo.1 (a) All holds carry maximum mass of light ore, including a margin ( M) specified in the Note with a density of (M + M)/V h (a) Scantling draught (a) Permissible still water bending moment (sagging) (b) All ballast tanks empty (b) Wave trough (b) Rule wave bending moment (sagging) Static ore pressures T S W T M SS +M WS Homo.2 Illustration of load case Homo.2 Lloyd's Register 19

21 Section 4 (a) All holds carry maximum mass of heavy ore, including a margin ( M) specified in the Note with a specific gravity of 3,0 (a) Scantling draught (a) Maximum hogging or minimum sagging still water bending moment given in the ship s loading manual for homogeneous loading conditions (M S ) (b) All ballast tanks empty (b) Wave crest (b) Rule wave bending moment (hogging) Static ore pressures T S +W C M S +M WH Homo.3 Illustration of load case Homo.3 (a) All holds carry maximum mass of heavy ore, including a margin ( M) specified in the Note with a specific gravity of 3,0 (a) Scantling draught (a) Permissible still water bending moment (sagging) (b) All ballast tanks empty (b) Wave trough (b) Rule wave bending moment (sagging) Static ore pressures T S W T M SS +M WS Homo.4 Illustration of load case Homo.4 Note 1. M is to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, M is not to be taken as less than 0,05M. 20 Lloyd's Register

22 Section 4 Table Bending moment load cases Ballast conditions Load case Local loads Global loads Loads in holds and ballast water in (a) All holds empty tanks External pressure (a) Deepest draught in ballast conditions Hull bending (a) Maximum hogging or minimum sagging still water bending moment given in the ship s loading manual for ballast conditions (M S ) (b) All ballast tanks full (b) Wave crest (b) Rule wave bending moment (hogging) Static ballast pressures T BD +W C M S +M WH Bal. 1 Illustration of load case Bal. 1 Table Bending moment load cases Harbour loading/unloading conditions Load case Local loads Global loads Loads in holds and ballast water in tanks (a) Mid-hold carries maximum mass of light ore, including a margin ( M) specified in Note 1 with a density of (M + M)/V h and other holds empty (b) Ballast tanks in way of mid-hold empty and other ballast tanks full External pressure (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s Hull bending (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.1a Illustration of load case Har.1a (see Note 2) Lloyd's Register 21

23 Section 4 (a) Mid-hold carries maximum mass of (a) Shallowest draught in harbour light ore, including a margin ( M), other conditions holds carry half the maximum mass of T HS_S light ore, Including a margin ( M). The density of the cargo is to be taken as not to be taken greater than 0,55Ts (M+ M)/V h and ( M), according to Note 1 (a) Permissible still water bending moment in harbour (sagging) M SS(har) (b) Ballast tank empty Har.1b Illustration of load case Har.1b (see Note 3) (a) Mid-hold carries maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 and other holds empty (b) Ballast tanks in way of mid-hold empty and other ballast tanks full (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s Illustration of load case Har.2a (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.2a (see Note 2) 22 Lloyd's Register

24 Section 4 (a) Mid-hold carries maximum mass of heavy ore,including a margin ( M), other holds carry half the maximum mass of heavy ore, including a margin ( M). The cargo specific gravity is to be taken as 3,0 and ( M), according to Note 1 (b) Ballast tanks empty (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.2b Illustration of load case Har.2b (see Note 3) (a) Aft and mid-holds carry maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 and fore hold empty (b) Ballast tanks in way of aft and midholds empty and other ballast tanks full (a) Shallowest draught in harbour conditions T HS_A not to be taken greater than 0,75T s Illustration of load case Har.3a_1 (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.3a_1 (see Note 2) Lloyd's Register 23

25 Section 4 (a) Aft and mid-holds carry maximum mass of heavy ore, including a margin ( M), fore hold carries half the maximum mass of heavy ore, including a margin ( M). The cargo specific gravity is to be taken as 3,0 and ( M), according to Note 1 (b) Ballast tanks empty (a) Shallowest draught in harbour conditions T HS_A not to be taken greater than 0,75T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.3b_1 Illustration of load case Har.3b_1 (see Note 3) (a) Fore and mid-holds carry maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 and aft hold empty (b) Ballast tanks in way of fore and midholds empty and other ballast tanks full (a) Shallowest draught in harbour conditions T HS_A not to be taken greater than 0,75T s Illustration of load case Har.3a_2 (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.3a_2 (see Note 2) 24 Lloyd's Register

26 Section 4 (a) Fore and mid-holds carry maximum mass of heavy ore, including a margin ( M), aft hold carries half the maximum mass of heavy ore, including a margin ( M). The cargo specific gravity is to be taken as 3,0 and ( M), according to Note 1 (b) Ballast tanks empty (a) Shallowest draught in harbour conditions T HS_A not to be taken greater than 0,75T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Har.3b_2 Illustration of load case Har.3b_2 (see Note 3) (a) Mid-hold empty and other holds carry maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (b) Ballast tanks in way of mid-hold full and other ballast tanks empty (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s (a) Permissible still water bending moment in harbour (hogging) M SH(har) Har.4a Illustration of load case Har.4a (see Note 2) Lloyd's Register 25

27 Section 4 (a) Mid-hold empty and other holds carry half the maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (b) Ballast tanks in way of mid-hold full and other ballast tanks empty (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s Illustration of load case Har.4b (a) Permissible still water bending moment in harbour (hogging) M SH(har) Har.4b (see Note 3) (a) Mid- and aft holds empty and fore hold carries maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (b) Ballast tanks in way of aft and midholds full and other ballast tanks empty (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s Illustration of load case Har.5a_1 (a) Permissible still water bending moment in harbour (hogging) M SH(har) Har.5a_1 (see Note 2) 26 Lloyd's Register

28 Section 4 (a) Mid- and aft holds empty and fore hold carries half the maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (b) Ballast tanks in way of aft and midholds full and other ballast tanks empty (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s (a) Permissible still water bending moment in harbour (hogging) M SH(har) Har.5b_1 Illustration of load case Har.5b_1 (see Note 3) (a) Fore and mid-holds empty and aft hold carries maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (b) Ballast tanks in way of fore and midholds full and other ballast tanks empty (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s Illustration of load case Har.5a_2 (a) Permissible still water bending moment in harbour (hogging) M SH(har) Har.5a_2 (see Note 2) Lloyd's Register 27

29 Section 4 (a) Fore and mid-holds empty and aft hold carries half the maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85T s (a) Permissible still water bending moment in harbour (hogging) M SH(har) (b) Ballast tanks in way of fore and midholds full and other ballast tanks empty Har.5b_2 Illustration of load case Har.5b_2 (see Note 3) Note 1. M is to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, M is not to be taken as less than 0,05M. Note 2. This load case is applicable to ore carriers with a deadweight over tonnes, ore carriers with a deadweight less than or equal to tonnes where single pass loading is required or ore carriers required to operate in multi-port loading conditions. Note 3. This load case is applicable to ore carriers with a deadweight less than or equal to tonnes where single pass loading is not required,and required to operate only in homogeneous loading conditions. Note 4. Where the ballast tanks in way of the empty holds are required to be empty in harbour loading and unloading conditions, these loading conditions are to be analysed. 28 Lloyd's Register

30 Section 4 Table Tank test conditions Load case Local loads Global loads Loads in holds and ballast water in tanks External pressure Hull bending (a) All holds empty (b) Ballast tanks in way of mid-hold full, with additional head of 2,45 m above the top of the tank and other ballast tanks empty (a) 25% of ship depth 0,25D Illustration of load case Test 1 Bending moment due to local loads. No further bending moment adjustment is required Test 1 (a) All holds empty (b) Ballast tanks in way of the model ends full,with additional head of 2,45 m above the top of the tank and other ballast tanks empty (a) 25% of ship depth 0,25D Illustration of load case Test 2 Bending moment due to local loads. No further bending moment adjustment is required Test 2 (see Note 1) Note 1. Load case Test 2 is to be assessed where ballast tanks fitted do not extend to the full length of the cargo hold. Table Shear force load cases Harbour loading/unloading conditions Load case Local loads Global loads Loads in holds and ballast water in tanks External pressure Hull bending Hull shearing Lloyd's Register 29

31 Section 4 (a) Mid-hold carries maximum mass of light ore, including a margin ( M) specified in Note 1 with density of (M + M)/V h and other holds empty (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (negative) Q SN(har) (b) Ballast tanks in way of mid-hold empty and other ballast tanks full Fore transverse bulkhead (a) Permissible still water shear force in harbour (positive) Har.1a (see Note 2) Illustration of load case Har.1a Q SP(har) (a) Mid-hold carries maximum mass of light ore, including a margin ( M), other holds carry half the maximum mass of light ore,including a margin ( M). The density of the cargo is to be taken as (M+ M)/V h and( M), according to Note 1 (b) Ballast tanks empty (a)shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55Ts (a) Permissible still water bending moment in harbour (sagging) M SS(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (negative) Q SN(har) Fore transverse bulkhead (a) Permissible still water shear force in harbour (positive) Har.1b (see Note 3) Illustration of load case Har.1b Q SP(har) 30 Lloyd's Register

32 Section 4 (a) Mid-hold carries maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 and other holds empty (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (negative) Q SN(har) (b) Ballast tanks in way of mid-hold empty and other ballast tanks full Fore transverse bulkhead (a) Permissible still water shear force in harbour (positive) Har.2a (see Note 2) Illustration of load case Har.2a Q SP(har) Lloyd's Register 31

33 Section 4 (a) Mid-hold carries maximum mass of heavy ore, including a margin ( M), other holds carry half of the maximum mass of heavy ore, including a margin ( M). The cargo specific gravity is to be taken as 3,0 and ( M), according to Note 1 (b) Ballast tanks empty (a) Shallowest draught in harbour conditions T HS_S not to be taken greater than 0,55T s (a) Permissible still water bending moment in harbour (sagging) M SS(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (negative) Q SN(har) Fore transverse bulkhead (a) Permissible still water shear force in harbour (positive) Q SP(har) Har.2b Illustration of load case Har.2b (see Note 3) (a) Mid-hold empty and other holds carry maximum mass of heavy ore, including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (a)deepest draught in harbour conditions T HD not to be taken less than 0,85T s (a) Permissible still water bending moment in harbour (hogging) M SH(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (positive) Q SP(har) (b) Ballast tanks in way of mid-hold full and other ballast tanks empty Fore transverse bulkhead (a) Permissible still water shear force in harbour (negative) Har.4a (see Note 2) Illustration of load case Har.4a Q SN(har) 32 Lloyd's Register

34 Section 5 (a) Mid-hold empty and other holds carry half of the maximum mass of heavy ore,including a margin ( M) specified in Note 1 with a specific gravity of 3,0 (a) Deepest draught in harbour conditions T HD not to be taken less than 0,85Ts (a) Permissible still water bending moment in harbour (hogging) M SH(har) Aft transverse bulkhead (a) Permissible still water shear force in harbour (positive) Q SP(har) (b) Ballast tanks in way of mid-hold full and other ballast tanks empty Fore transverse bulkhead (a) Permissible still water shear force in harbour (negative) Har.4b (see Note 3) Illustration of load case Har.4b Q SN(har) Note 1. M is to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, M is not to be taken as less than 0,05M. Note 2. This load case is applicable to ore carriers with a deadweight over tonnes, ore carriers with a deadweight less than or equal to tonnes where single pass loading is required or ore carriers required to operate in multi-port loading conditions. Note 3. This load case is applicable to ore carriers with a deadweight less than or equal to tonnes where single pass loading is not required and required to operate only in homogeneous loading conditions. Note 4. Where the ballast tanks in way of the empty holds are required to be empty in harbour loading and unloading conditions, these loading conditions are to be analysed. n Section 5 Stress acceptance criteria 5.1 Stress acceptance criteria All primary supporting members and hull plating within a longitudinal extent, covering the middle hold of the FE model, the mid-hold fore and aft transverse bulkheads and the regions forward and aft of the middle hold up to the extent of the transverse bulkhead stringers and cross-deck strip, are to be assessed. The extent of the FE model to be assessed is shown in Figure Extent of FE model to be assessed against acceptance criteria For the hull shear force analysis load cases, stress levels in the longitudinal hull girder shear load bearing structural members, such as side shell, longitudinal bulkheads and girders, and the immediate connected structure are to be assessed Detailed stresses resulting from the fine mesh analysis for locations required by Ch 2, 2.1 Structural modelling and Ch 2, 2.1 Structural modelling are to be assessed. Lloyd's Register 33

35 Section The maximum permissible stresses for plates given in Table Maximum permissible membrane Von Mises equivalent stresses are based on the element membrane stresses. The equivalent stresses, σ e in N/mm 2, in the primary supporting members and hull plating resulting from the load cases specified in Ch 2, 4.1 General are not to exceed the maximum permissible stresses, σ perm, given in Table Maximum permissible membrane Von Mises equivalent stresses, i.e. σ e σ perm Where openings are not represented in the primary supporting member in the FE model, the mean shear stress in way is to be increased in direct proportion to the modelled shear area divided by net shear area. The equivalent stress of the element is to be recalculated using the increased shear stress for comparison with relevant permissible value in Table Maximum permissible membrane Von Mises equivalent stresses. The net shear area in way of an opening is to be calculated in accordance with Table Net shear area The permissible stresses given in Table Maximum permissible membrane Von Mises equivalent stresses for the primary supporting members and fine mesh regions are based on the mesh size recommended in Ch 2, 2 Structural modelling. Attention is drawn to the relationship between the magnitude of calculated stress and the mesh size in areas where there is likely to be high stress and high stress gradient. Where the fine mesh size incorporated in the model is significantly finer than the recommended size in Ch 2, 2 Structural modelling, adjustment to the permissible stresses may be specially considered. Figure Extent of FE model to be assessed against acceptance criteria Table Maximum permissible membrane Von Mises equivalent stresses Structure items (a) Primary structural members and hull plating Permissible stress (N/mm 2 ) σ perm Remarks Upper deck outside line of openings and deck girder 0,92σ L See Note 1 Hatch side coaming 0,92σ L See Note 1 Bottom shell,side shell,inner bottom, longitudinal bulkhead, side stringer,if any, and double bottom girder Double bottom floor 0,92σ L See Note1 0,75σ o Primary transverse member 0,75σ o See Note 1 Face plate of primary transverse member 0,75σ o Transverse corrugated bulkhead and lower stool Transverse bulkhead in ballast tank and horizontal girder on it 0,75σ o 34 Lloyd's Register

36 Section 5 Cross deck, hatch end beam and upper stool 0,75σ o (b) Fine mesh regions Average stress σ average σ o See Notes 2 and 3 Peak stress 1,2σ average See Note 2 Symbols and definitions σ L = 235/k L, in N/mm 2 k L = higher tensile steel factor as specified in Pt 3, Ch 2, of the Rules for Ships σ o = see Ch 2, 2.1 Structural modelling Note 1. Details of hatch side coaming end brackets, backing bracket of inner bottom at longitudinal bulkhead connection and bracket toe of primary supporting members should comply with those shown in LR's ShipRight FDA Level 1.The assessment of these structural members is normally outside the scope of this SDA analysis. Note 2. Permissible stresses for fine mesh regions are based on the fine mesh size as recommended in Ch 2, 2 Structural modelling. Note 3. Average stress is to be calculated based on the element being assessed for peak stress and the elements connected to its boundary nodes. Averaging is not to be carried across structural discontinuity or abutting structure. Table Net shear area Types Net shear area Notes Minimum of the following: A w1, (A w2 +A w3 ), (A w4 +A w5 ), (A w2 +A w5 ), A w2 or A w3 is the minimum shear area between access opening and cutout for stiffener (A w3 + Aw4 ) Lloyd's Register 35

37 Section 5 Minimum of the following: A w6 (A w4 +A w5 ) and (A w4 +A w3 ) A w3 is the minimum shear area between access opening and cut-out for stiffener (A w4 +A w5 ) A w6 36 Lloyd's Register

38 Section 6 n Section 6 Buckling acceptance criteria 6.1 Buckling acceptance criteria Plate panel buckling is to be investigated for all areas of the primary structures and hull plating specified in Ch 2, 5.1 Stress acceptance criteria and Ch 2, 5.1 Stress acceptance criteria 5.1.2, but particular attention should be paid to the following areas: Transverse rings in side ballast tanks; Transverse bulkheads in side ballast tanks in line with hold transverse bulkheads; Horizontal girders on transverse bulkheads; Cross-deck (cross-deck plate, hatch end beam and upper stool plate); Double bottom floors For the hull shear force analysis load cases, plate panel buckling is to be investigated for the longitudinal hull girder shear load bearing structural members, such as side shell, longitudinal bulkheads and girders, and the immediate connected structure The combined interaction of bi-axial compressive stresses, shear stresses and in-plane bending stresses are to be taken into consideration in the plate panel buckling calculation. In general, the average stresses acting within the plate panel are to be used for the buckling calculation The buckling capability of a plate panel, i.e. critical equivalent buckling stress, is to be calculated based on corroded plate thickness, t corr, in mm t corr = t - t c where t = the gross thickness, in mm, of a plate panel excluding Owner-specified additional thickness t c = standard thickness deduction for corrosion, as defined in Table Standard thickness deduction for corrosion. Table Standard thickness deduction for corrosion Position Standard thickness Deduction, t c, in mm Water ballast tanks within 1,5 m of weather deck One side exposure to water ballast 1,0 Two sides exposed to water ballast 2,0 Elsewhere 1, In calculation of the equivalent compressive stress, local stresses calculated in the FE model are to be increased in proportion to the plate thickness in the model divided by the corroded plate thickness, but the global stresses calculated in the FE model may be maintained. The shear stresses calculated in the FE model are to be increased in proportion to the plate thickness in the model divided by the corroded plate thickness. The corrected element direct stresses and shear stress for the calculation of the equivalent buckling stress are obtained as follows: σ i = σlocal i c + σ Global i σ Global-i = M i σ Mu-i σ Local-i = σ FEM-i σ Global-i τ i = τfem i c Lloyd's Register 37

39 Section 6 where σ i = the corrected direct stress of element i, in the element x or y direction. Note that both components of direct stresses are to be corrected σ Local-i = the direct stress of element i, in the element x or y direction, due to local loads σ Global-i = the direct stress of element i, in the element x or y direction, due to global hull girder bending moment M i = the vertical hull girder bending moment at the longitudinal position of element i σ Mu-i = the direct stress of element i, in the element x or y direction, due to application of a couple of unit bending moments at the ends of the FE model σ FEM-i = the direct stress of element i, in the element x or y direction, obtained from the finite element analysis of the load case τ i = the corrected shear stress of element i τ FEM-i = the shear stress of element i obtained from the finite element analysis of the load case t, t c = see Ch 2, 6.1 Buckling acceptance criteria The panel edge restraint factor c, as defined in Pt 3, Ch 4, 7 of the Rules for Ships, may be taken into account in the calculation of the critical elastic buckling stress of a plate panel subjected to compressive stress working on the long edge of the panel. A mean c value may be used for a plate panel, one edge of which is restrained by a plated structure such as a girder and the other edge by a stiffener. No edge restraint factor is to be taken into account for compressive loading on the short edge When the critical equivalent elastic buckling stress exceeds 50 per cent of the specified minimum yield stress, the critical buckling stress is to be adjusted for the effects of plasticity, using the Johnson-Ostenfeld formula. The critical equivalent buckling stress σ cr is calculated as follows: σ cr = σc for σ c σ 0 2 σ cr = σo 1 σ 0 for σ 4σ c > σ 0 c 2 where σ 0 = specified minimum yield stress σ c = critical equivalent elastic buckling stress The plate panel buckling calculation can be carried out using the software Lloyd s Register ShipRight Software s buckling module, which can automatically calculate the buckling factors of safety of the panels in an FE model, or Buckling of flat rectangular plate panels (ShipRight program No ), or equivalent. The effect of plasticity described in Ch 2, 6.1 Buckling acceptance criteria is applied within Lloyd s Register s software The equivalent compressive stress in a plate panel calculated under each of the load cases specified in Ch 2, 4.1 General is compared with the critical equivalent buckling stress for assessment of the buckling capability of the plate panel. The factor of safety of plate panel buckling, λ, is defined as follows: λ = σ cr σ a where σ cr = equivalent critical buckling stress calculated in Ch 2, 6.1 Buckling acceptance criteria σ a = equivalent applied buckling stress The required factor of safety of plate panel buckling λ R is given in Table Required minimum buckling factor of safety, λ R, of plate panel for each structure item. The factor of safety calculated in Ch 2, 6.1 Buckling acceptance criteria is to be equal to or greater than the required factor of safety, i.e.: 38 Lloyd's Register

40 Section 7 λ λ R Table Required minimum buckling factor of safety, λ R, of plate panel Structure items λ R Upper deck outside line of openings Deck girders Bottom shell,side shell,inner bottom and longitudinal bulkhead 1,0 Double bottom girders and side stringers, if any Transverse corrugated bulkhead and lower stool in cargo hold Transverse bulkhead in ballast tank and horizontal girders on it Double bottom floor Primary transverse member 1,0 1,1 Cross-deck,hatch end beam and upper stool 1,2 n Section 7 Hold mass curves 7.1 General Pt 3, Ch 4, 8.3 of the Rules for Ships requires a set of hold mass curves to be included in the ship s loading manual and the ship s loading instrument for ore carriers with a Rule length greater than or over 150 m. These hold mass curves are to show the maximum allowable and minimum allowable cargo masses as a function of the ship s draught, in sea-going, harbour loading and unloading conditions. The hold mass curves for each single hold and any two adjacent holds are to be included The hold mass curves are derived, based on the sea-going and harbour load cases given from Table Bending moment load cases Fully loaded homogeneous loading conditions to Table Shear force load cases Harbour loading/ unloading conditions. For draught conditions other than those specified Table Bending moment load cases Fully loaded homogeneous loading conditions to Table Shear force load cases Harbour loading/unloading conditions, the maximum and minimum allowable cargo masses are, in general, determined by adjusting the cargo mass such that the net load acting on the double bottom structure, i.e., the difference between cargo weight and buoyancy, is maintained as in the analysed load cases. 7.2 Hold mass curves The maximum and minimum allowable mass, m, in a single cargo hold is to be obtained as follows: M + ΔM ρ w 1 + α Δ h ρ w ref h c > 1 α Δ where h ref h c T = the local draught, in metres, at the mid-hold position of the cargo hold under consideration T ref = is the draught, in metres, of the reference load case as given in Table Reference load cases and α factors for hold mass curves Lloyd's Register 39

41 Section 7 m = the mass of the cargo in the hold, in tonnes, at draught T. m is not to be taken greater than M or less than zero M = see Ch 1, 2.1 Symbols ΔM = see Ch 1, 2.1 Symbols V h = the volume of the cargo hold excluding the volume enclosed by hatch coaming, in m 3 h c = the vertical distance from the inner bottom to the deck at centre, in metres ρ w = the density of sea-water, 1,025 tonnes/m 3 α = factor as defined in Table Reference load cases and α factors for hold mass curves The maximum and minimum allowable total mass in two adjacent cargo holds is to be obtained as follows: Σ hi Σ i + Σ Δ i ρ w ref 1 2 Σ h ci Σ i Σ Δ i 1 + Σ i Σ hi w ref 1 2 Σh ci Σ i > Σ Δ i 1 α Σ i where T = the average of the local draughts at the midhold positions of the two adjacent cargo holds under consideration, in metres T ref = the draught, in metres, of the reference load case as given in Table Reference load cases and α factors for hold mass curves Σm i = the total cargo mass in the two adjacent holds at draught T, in tonnes. The mass, m i, in each cargo hold is not to be taken greater than maximum allowable mass in the hold, M i, or less than zero ΣM i = the total cargo mass, in tonnes, intended to be carried in the two adjacent holds, as specified in the ship s loading manual for the loading condition considered ΣΔM i = the combined margin of the cargo mass of the two adjacent holds, in tonnes ΣV hi = the combined volume of the two adjacent cargo holds, excluding the volume enclosed by hatch coaming, in m 3 1 / 2 Σh ci = the average of the maximum vertical distances from the inner bottom to the deck at centre of the two adjacent holds, in metres α = factor as defined in Table Reference load cases and α factors for hold mass curves See Ch 2, 7.2 Hold mass curves for definition of other symbols Where two adjacent cargo holds are loaded, the criteria given by the hold mass curves for both the single hold and two adjacent cargo holds are to be satisfied Typical hold mass curves are illustrated in Figure Typical hold mass curves. 40 Lloyd's Register

42 Section 7 Table Reference load cases and α factors for hold mass curves Description α Tref (m) Loadcases Homogeneous loading condition Single hold Sea-going Upper limit 0,5 (1) Homo.1, Homo.2, Homo.3 T s 0,0 (2) and Homo.4 Lower limit 1,0 T BD Bal.1 Homogeneous loading condition Two adjacent holds Sea-going Upper limit 0,5 (1) Homo.1, Homo.2, Homo.3 T s 0,0 (2) and Homo.4 Lower limit 1,0 T BD Bal.1 Harbour loading/ unloading (3) Single hold Harbour Harbour loading/ unloading (4) Single hold Harbour Upper limit 1,0 T HS_S Har.1a, Har.2a Lower limit 1,0 T HD Har.4a Upper limit 1,0 T HS_S Har.1b, Har.2b Lower limit 1,0 T HD Har.4b Harbour loading/ unloading (3) Two adjacent holds Harbour Upper limit 1,0 T HS_A Har.3a_1, Har.3a_2 Lower limit 1,0 T HD Har.5a_1, Har.5a_2 Harbour loading/ unloading (4) Two adjacent holds Harbour Upper limit 1,0 T HS_A Har.3b_1, Har.3b_2 Lower limit 1,0 T HD Har.5b_1, Har.5b_2 Note 1. Applicable to ore carriers with a deadweight over tonnes and ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. Note 2. Applicable to ore carriers with a deadweight less than or equal to tonnes where single pass loading is not required. Note 3. Applicable to ore carriers with a deadweight over tonnes and ore carriers with a deadweight less than or equal to tonnes where single pass loading or multi-port loading is required. Note 4. Applicable to ore carriers with a deadweight less than or equal to tonnes where single pass loading is not required and which carry cargo in homogeneous loading conditions. Lloyd's Register 41

43 Section 7 Figure Typical hold mass curves 42 Lloyd's Register

44 Contents Chapter 3 CHAPTER 1 INTRODUCTION CHAPTER 2 STRUCTURAL DESIGN ASSESSMENT PROCEDURE FOR PRIMARY STRUCTURES CHAPTER 3 APPENDIX A ORE LOADS SECTION 1 ORE LOADS CHAPTER 4 APPENDIX B BALLAST LOADS CHAPTER 5 APPENDIX C EXTERNAL HYDROSTATIC AND HYDRODYNAMIC PRESSURES CHAPTER 6 APPENDIX D ADJUSTMENT OF HULL GIRDER BENDING MOMENTS AND SHEAR FORCES Lloyd's Register 43

45 Appendix A Ore Loads Chapter 3 Section 1 Section 1 Ore Loads n Section 1 Ore Loads 1.1 General For the purpose of the structural assessment, ore cargoes are classified into light ore and heavy ore The angle of repose, ψ is to be taken as 35º for both light and heavy ore cargoes. 1.2 Ore profile in hold Light ore is assumed to be fully filled in the cargo hold up to the upper deck level, excluding the hatchway. The cargo height, h c, is to be measured from the inner bottom to upper deck, as shown in Figure Profile of light ore in hold. The density of light ore, ρ c, in tonnes/m 3, is calculated as follows: ρ c = + Δ h where M = is the mass of light ore, in tonnes, intended to be carried in the hold as specified in the ship s loading manual ΔM = margin of the mass of light ore, ΔM is to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, ΔM is not to be taken as less than 0,05M V h = is the volume, in m 3, of the cargo hold, excluding the volume enclosed by hatch coaming For heavy ore, the cargo surface is assumed to be parabolic in the transverse section and this parabolic surface is maintained constant in the longitudinal direction. The angle of intersection of the cargo surface with the longitudinal bulkhead is taken as the angle of repose of the cargo The local height of heavy ore is to be determined such that the volume under the prismatic parabolic surface is identical to the volume of heavy ore carried in the hold. The transverse parabolic cargo profile is shown in Figure Profile of heavy ore in hold. The local height, h c, in metres, is calculated as follows: where h = h y + h 2 h y = the local height, in metres, of the parabolic surface = h1 1 2 c 2 h 1 = the local height, in metres, of the parabolic surface at the centreline = c 4 tan 35o 0, 175 c h 2 = the height, in metres, of the surface at the side shell or longitudinal bulkhead measured from the inner bottom. The value of h 2 can be determined, with the aid of the hold volume curve, such that: V 2 = the cargo volume, in m 3, below the level h 2 = V V 1 V = the volume, in m 3, of heavy ore in the cargo hold 44 Lloyd's Register

46 Appendix A Ore Loads Chapter 3 Section 1 = + Δ ρ c V 1 = the cargo volume, in m 3, above the level h 2 which can be estimated as follows: = 2 3 h 1 c h 0, 117 c 2 h M = the mass of heavy ore, in tonnes, intended to be carried in the hold as specified in the ship s loading manual Δ M = margin of the mass of heavy ore, ΔM is to be taken as the lesser of 3000 tonnes and 0,1M for ore carriers with a deadweight over tonnes and for ore carriers with a deadweight less than or equal to tonnes where single pass loading is required. For all ore carriers, ΔM is not to be taken as less than 0,05M ρ c = the density of heavy ore to be taken as 3,0 tonnes/m 3 B C = the breadth, in metres, of the cargo hold L h = the length of the cargo hold, in metres Figure Profile of light ore in hold Lloyd's Register 45

47 Appendix A Ore Loads Chapter 3 Section 1 Figure Profile of heavy ore in hold 1.3 Ore loads Static ore pressures acting on the periphery of the cargo hold are given by the following formulae: p cs = ρ c c + h db where p cs = the static cargo pressure, in kn/m 2 ρ c = the cargo density, see Ch 3, 1.2 Ore profile in hold and Ch 3, 1.2 Ore profile in hold h c = the local cargo height, see Ch 3, 1.2 Ore profile in hold and Ch 3, 1.2 Ore profile in hold h db = the double bottom height, in metres g = the acceleration due to gravity, see Ch 1, 2.1 Symbols z = the z co-ordinate, in metres, of the pressure acting point, measured upwards from the base line K c = coefficient for ore pressure, where = 0 for upper deck and upper stool sloped plate 46 Lloyd's Register