Tài liệu Scantling optimization ropax ship

UNIVERSITY OF LIÈGE ANTWERP MARITIME ACADEMY FACULTY OF APPLIED SCIENCE HOGERE ZEEVAART SCHOOL DEPARTMENT OF ARGENCO – ANAST MASTER THESIS SCANTLING OPTIMIZATION ROPAX SHIP Tri Dung NGUYEN Promoter: Prof. Dr. Philippe RIGO Academic year 2009 – 2010. Acknowledgements First of all, I would like to express my warmest appreciation to Prof. Philippe RIGO and Prof. Michel HOGGE, Dean of the faculty of Applied Science who granted me a scholarship for this study of Naval architechture in ANAST, university of Liège. Furthermore, I would be grateful to Prof. Philippe RIGO for his instruction and encouragement during my study. I also would like to especially thank Dr. Adrian CONSTANTINESCU and Dr. Eugen PIRCALABU who provided me various advice and helpful comments at the most difficult time of my working for this thesis. Additionally, I would like deeply thank all Professors and Professor Assistants of university of Liège and ANAST who gave me a lot of knowledge and many interesting lectures. During one year of studying in university of Liège, Belgium, I have greatly benefited from the friendship and association with many classmates. I would like to thank all students in my class for their support in various aspects. I always keep in my mind the beautiful memories about them. Finally, I would like to express my whole-hearted gratitude to my family for all their loves and support for my life. Liège, May 16th 2009 i Summary The usual method of structural design is an indirect trial – and – error approach (rules – based design). The designers intuitively choose the dimensions and then determine if the design satisfying the constraints. The designs are revised repeatedly while still satisfying the constraints. Such an approach does not necessarily yield the most economical or least weight design. In order to obtain a best design, the structural engineers have to recur to structural optimization methods. Structural design is always defined during the earliest phases of a project. It is thus not difficult to understand why a preliminary design stage optimization tool is attactive. The problem in this moment is to minimize a predetermined utility function, such as the cost or the weight under the constraints that the failure probability of the structure will not exceed several certain allowable values. Ship scantling always poses numerous problems to designers. Floating structures are indeed complex, generally composed of strongly stiffened plates, deck plates, bottom plates and sometimes intermediate decks, frames, bulkheads, etc. The stiffening system is also particularly sophisticated. Therefore an optimization tool at preliminary stage featuring flexibility, modeling speed and user-friendliness may provide precious help to designers. They can start directly with an automatic search for optimum scantling. As the above statements, the principal mission of this study is to utilize LBR-5, the optimization software to obtain the optimum scantlings of ROPAX ship with the initial scantlings as follows: - Verify the dimesions of model in input data, Modelize the frames in double bottom, Calculate the internal loads – wheeled loads following the BV rules, Verify the load cases for ROPAX ship with hull girder loads and local loads, Determine the structural constraints from BV rules as well as geometrical and equality constraints, Structural analysis the stresses of initial scantling, Run the LBR-5 to obtain the optimum scantling with respect of construction cost or structural weight. Estimate the optimal solution and propose the recommended scantling. Concerning the above tasks, this report is presented within four chapters - Chapter 1 “The background of ship structure design”, Chapter 2 “Scantling optimization and LBR-5 software for stiffened structures”, Chapter 3 “Scantling optimization of the Ropax ship”, Chapter 4 “Conclusion”. ii Table of Contents Chapter 1 THE BACKGROUND OF SHIP STRUCTURE DESIGN ........................ 1 1.1. Introduction ................................................................................................................... 1 1.1.1. Rationally based structural design versus rules-based design ..................................... 1 1.1.2. Preliminary design versus detailed design .................................................................. 2 1.2. Loads acting on a ship structure .................................................................................. 4 1.2.1 Time duration .............................................................................................................. 4 1.2.2. Local and global loads................................................................................................. 4 1.2.3. Hull girder loads calculation ....................................................................................... 5 1.2.4. Local loads calculation ................................................................................................ 8 1.2.5. Load cases ................................................................................................................. 14 1.2.6. Ship Motions and Accelerations ............................................................................... 16 1.3. Stresses and checking criteria .................................................................................... 18 1.3.1. Introduction ............................................................................................................... 18 1.3.2. Stress and deflection components ............................................................................. 18 1.3.3. Stress calculation ....................................................................................................... 21 1.3.4. Checking criteria ....................................................................................................... 26 Chapter 2 SCANTLING OPTIMIZATION AND LBR-5 SOFTWARE FOR STIFFENED STRUCTURES..................................................................................................... 28 2.1. Introduction ................................................................................................................. 28 2.2. Scantling optimization procedure .............................................................................. 28 2.3. Failure modes classification........................................................................................ 31 2.3.1. Stiffened panel failure modes .................................................................................... 33 2.3.2. Frame failure modes .................................................................................................. 33 2.3.3. Hull girder collapse modes ........................................................................................ 34 2.4. Introduction of LBR-5 ................................................................................................ 34 2.4.1. The OPTI module ...................................................................................................... 36 2.4.2. The COST module .................................................................................................... 36 2.4.3. The CONSTRAINT module ..................................................................................... 37 Chapter 3 SCANTLING OPTIMIZATION OF ROPAX SHIP. ................................ 38 3.1. Main specification of the ROPAX ship ..................................................................... 38 3.2. Modelize the midship section ..................................................................................... 38 3.3. Loads acting on Ropax structure ............................................................................... 46 3.3.1. The hull girder global loads ...................................................................................... 46 3.3.2. The local loads .......................................................................................................... 47 3.4. The constraints of optimization ................................................................................. 56 3.5. Cost and productivity data ......................................................................................... 60 iii 3.6. The results of scantling optimization ......................................................................... 61 Chapter 4 CONCLUSIONS............................................................................................ 86 REFERENCES ............................................................................................................................ 88 APPENDICES ................................................................................................................................ i Appendix 1: General arrangement and amidship drawing of Ropax ship ........................... i Appendix 2: Longitudinal stress calculation .......................................................................... ii Appendix 3: Phenomena of each load case ............................................................................iii Appendix 4: Non-uniform pressures on decks due to wheeled loads .................................. ix Appendix 5: Equivalent angle to bulb profile stiffeners ........................................................ x iv Table of Figures Figure 1 – Direct structural analysis flow chart. ............................................................................. 3 Figure 2 – Sign conventions for shear forces Q and bending moments M. .................................... 5 Figure 3 – Distribution factor FQ..................................................................................................... 8 Figure 4 – Still water pressure......................................................................................................... 9 Figure 5 – Wave pressure for each load cases according to BV [5]. ............................................ 11 Figure 6 – Wheeled loads – Distribution of vehicles on a primary supporting member [5]. ........ 13 Figure 7 – Wheeled loads distance between two consecutive axles [5]........................................ 13 Figure 8 – Wheeled loads distance between axles of two consecutive vehecles [5]. ................... 13 Figure 9 – Wave loads in load case “a”, “b”, “c” and “d” according to BV [5].. ......................... 15 Figure 10 – Definition of stress components. ............................................................................... 19 Figure 11 – Primary, secondary and tertiary structural response. ................................................. 20 Figure 12 – A standard stiffened panel. ........................................................................................ 20 Figure 13 – Behavior of an elastic beam under shear force and bending moment. ...................... 22 Figure 14 – Element of plate structure and components of bending stress resultants. ................. 24 Figure 15 – Torsional shear flow. ................................................................................................. 25 Figure 16 – The moment – curvature curve (M - Φ)..................................................................... 30 Figure 17 – Structural modeling of the structure and its components. ......................................... 31 Figure 18 – Modes of failures by buckling of a stiffened panel. .................................................. 32 Figure 19 – Basic configuration of the LBR-5 model and database presentation......................... 35 Figure 20 – General organisation flow chart of a structure optimization process. ....................... 35 Figure 21 – Chart of the LBR-5 model with CONSTRAINT, COST and OPTI modules. .......... 37 Figure 22 – The double bottom of a common Ropax ship (web frame – every 2800 mm). ......... 39 Figure 23 – The modelled frame in double bottom. ...................................................................... 39 Figure 24 – Equivalent angle profile. ............................................................................................ 40 Figure 25 – The central girder with frames on both sides. ............................................................ 40 Figure 26 – The midship section and the double bottom model in LBR5. ................................... 43 Figure 27 – The partial 3D model. ................................................................................................ 45 Figure 28 – The partial model in LBR5. ....................................................................................... 45 Figure 29 – The wheeled loads in load case “a“ and “c“. ............................................................. 51 Figure 30 – The wheeled loads in load case “b“. .......................................................................... 51 Figure 31 – The wheeled loads in load case “d“. .......................................................................... 52 Figure 32 – The equivalent pressure. ............................................................................................ 53 Figure 33 – The test of the transformation between uniform and non-uniform pressure. ............ 54 Figure 34 – The stresses in plate at x = 8.4 (m) by uniform pressure. .......................................... 55 Figure 35 – The stresses in plate at x = 8.4 (m) by non-uniform pressure. ................................... 55 Figure 36 – The stresses in plate at x = L/2 = 16.8 (m) by uniform pressure. .............................. 55 Figure 37 – The stresses in plate at x = L/2 = 16.8 (m) by non-uniform pressure. ....................... 56 Figure 38 – The Von Mises stress in plate from structural analysis. ............................................ 62 Figure 39 – The Von Mises stress in frames at WFJ from structural analysis. ............................. 64 Figure 40 – Objective curve of cost optimization. ........................................................................ 65 Figure 41 – Objective curve of weight optimization..................................................................... 66 v Figure 42 – Objective curve of cost optimization with the frames on panel 10, 23 and 14 are high tensile steel. ................................................................................................................................... 67 Figure 43 – Objective curve of weight optimization with the frames on panel 10, 23 and 14 are high tensile steel. ........................................................................................................................... 68 Figure 44 – Flow chart of one step optimization procedure. ........................................................ 72 Figure 45 – Flow chart of multi-steps optimization procedure. .................................................... 72 Figure 46 – Optimum plate thickness in cost multi step optimization. ......................................... 77 Figure 47 – Optimum frame web height in cost multi step optimization. .................................... 78 Figure 48 – Optimum stiffener spacing in cost multi step optimization. ...................................... 79 Figure 49 – Optimum stiffener web height in cost multi step optimization. ................................ 80 Figure 50 – Optimum plate thickness in weight multi step optimization. .................................... 82 Figure 51 – Optimum frame web height in weight multi step optimization. ................................ 83 Figure 52 – Optimum stiffener spacing in weight multi step optimization. ................................. 84 Figure 53 – Optimum stiffener web height in weight multi step optimization. ............................ 85 vi Chapter 1 The background of ship structure desgin Chapter 1 THE BACKGROUND OF SHIP STRUCTURE DESIGN 1.1. Introduction Analysis and Design are two words that are very often associated. Sometimes they are used indifferently one for the other even if there are some important differences between performing a design and completing an analysis. Analysis refers to stress and strength assessment of the structure. Analysis requires information on loads and needs an initial structural scantling design. Output of the structural analysis is the structural response defined in terms of stresses, deflections and strength. Then, the estimated response is compared to the design criteria Design for structure refers to the process followed to select the initial structural scantlings and to update these scantlings from the early design stage (bidding) to the detailed design stage (construction). To perform analysis, initial design is needed and analysis is required to design. This explains why design and analysis are intimately linked, but are absolutely different. Design also relates to topology and layout definition. Ship structural design is a challenging activity. Hence Hughes states: “The complexities of modern ships and the demand for greater reliability, efficiency, and economy require a scientific, powerful, and versatile method for their structural design.” Ship structural analysis and design is a matter of compromises: - Compromise between accuracy and the available time to perform the design. This is particularly challenging at the preliminary design stage. A 3D Finite Element Method (FEM) analysis would be welcome but the time is not available. For that reason, rule-based design or simplified numerical analysis has to be performed. - To limit uncertainty and reduce conservatism in design, it is important that the design methods are accurate. On the other hand, simplicity is necessary to make repeated design analyses efficient. The results from complex analyses should be verified by simplified methods to avoid errors and misinterpretation of results (checks and balances). - Compromise between weight and cost or compromise between least construction cost, and global owner live cycle cost (including operational cost, maintenance, etc.). 1.1.1. Rationally based structural design versus rules-based design There are two kinds of school to perform analysis and design of ship structure. The first one, the oldest, is called rule-based design. It is mainly based on the rules defined by the classification societies. Hughes states that: “In the past, ship structural design has been largely empirical, based on accumulated experience and ship performance, and expressed in the form of structural design codes or rules 1 Chapter 1 The background of ship structure desgin published by the various ship classification societies. These rules concern the loads, the strength and the design criteria and provide simplified and easy-to-use formulas for the structural dimensions, or “scantlings” of a ship. This approach saves time in the design office and, since the ship must obtain the approval of a classification society, it also saves time in the approval process.” The second school is the Rationally Based Structural Design; it is based on direct analysis. Hughes, who could be considered as a father of this methodology, further states: “There are several disadvantages to a completely “rulebook” approach to design. First, the modes of structural failure are numerous, complex, and interdependent. With such simplified formulas the margin against failure remains unknown; thus one cannot distinguish between structural adequacy and over-adequacy. Second, and most important, these formulas involve a number of simplifying assumptions and can be used only within certain limits. Outside of this range they may be inaccurate. For these reasons there is a general trend toward direct structural analysis.” In ship design, classification societies preferred to offer updated rules resulting from numerical analysis calibration. In addition, for new vessel types or non-standard dimension, direct procedure is the only way to assess the structural safety. Therefore it seems that the two schools have started a long merging procedure. Classification societies are now encouraging and contributing greatly to the development of direct analysis and rationally based methods. Ships are very complex structures compared with other types of structures. They are subject to a very wide range of loads in the harsh environment of the sea. Progress in technologies related to ship design and construction is being made daily, at an unprecedented pace. The majority of ship designers strive to develop rational and optimal designs based on direct strength analysis methods using the latest technologies in order to realize the shipowner’s requirements in the best possible way. When carrying out direct strength analysis in order to verify the equivalence of structural strength with rule requirements, it is necessary for the classification society to clarify the strength that a hull structure should have with respect to each of the various steps taken in the analysis process, from load estimation through to strength evaluation. In addition, in order to make this a practical and effective method of analysis, it is necessary to give careful consideration to more rational and accurate methods of direct strength analysis. The flow chart given in figure 1 gives an overview of the analysis as defined by a major classification society. Note that a rationally based design procedure requires that all design decisions (objectives, criteria, priorities, constraints…) must be made before the design starts. This is a major difficulty of this approach. 1.1.2. Preliminary design versus detailed design For a ship structure, structural design consists of two distinct levels: the Preliminary Design and the Detailed Design about which Hughes states: 2 Chapter 1 The background of ship structure desgin Figure 1 – Direct structural analysis flow chart. “The preliminary determines the location, spacing, and scantlings of the principal structural members. The detailed design determines the geometry and scantlings of local structure (brackets, connections, cutouts, reinforcements, etc.). Preliminary design has the greatest influence on the structure design and hence is the phase that offers very large potential savings. This does not mean that detail design is less important than preliminary design. Each level is equally important for obtaining an efficient, safe and reliable ship. During the detailed design there also are many benefits to be gained by applying modern methods of engineering science, but the applications are different from preliminary design and the benefits are likewise different. Since the items being designed are much smaller it is possible to perform full-scale testing, and since they are more repetitive it is possible to obtain the benefits of mass production, standardization and so on. In fact, production aspects are of primary importance in detail design. Also, most of the structural items that come under detail design are similar from ship to ship, and so in-service experience provides a sound basis for their design. In fact, because of the large number of such items it would be inefficient to attempt to design all of them from first principles. Instead it is generally more efficient to use design codes and standard designs that have been 3 Chapter 1 The background of ship structure desgin proven by experience. In other words, detail design is an area where a rule-based approach is very appropriate, and the rules that are published by the various ship classification societies contain a great deal of useful information on the design of local structure, structural connections, and other structural details.” 1.2. Loads acting on a ship structure There are basically two aspects of loads applying on ship structure. One considered in the time duration of forces and the other based on the structural scheme. 1.2.1 Time duration - Static loads: These are the loads experienced by the ship in still water. They act with time duration well above the range of sea wave periods. Being related to a specific load condition, they have little and very slow variations during a voyage (mainly due to changes in the distribution of consumables on board) and they vary significantly only during loading and unloading operations. - Quasi-static loads: A second class of loads includes those with a period corresponding to wave actions (~3 to 15 seconds). Falling in this category are loads directly induced by waves, but also those generated in the same frequency range by motions of the ship (inertial forces). These loads can be termed quasi-static because the structural response is studied with static models. - Dynamic loads: When studying responses with frequency components close to the first structural resonance modes, the dynamic properties of the structure have to be considered. This applies to a few types of periodic loads, generated by wave actions in particular situations (springing) or by mechanical excitation (main engine, propeller). Also transient impulsive loads that excite free structural vibrations (slamming, and in some cases sloshing loads) can be classified in the same category. - High frequency loads: Loads at frequencies higher than the first resonance modes (> 1020 Hz) also are present on ships: this kind of excitation, however, involves more the study of noise propagation on board than structural design. According to time duration of loads, they are devided as follows - Still water loads are those acting on the ship at rest in calm water. Wave loads are those due to wave pressures and ship motions, which can be assumed to have the same wave encounter period. Dynamic loads are those that have a duration much shorter than the period of the wave loads. 1.2.2. Local and global loads Loads acting on the ship as a whole, considered as a beam (hull girder), are named global or primary loads and the ship structural response is accordingly termed global or primary response. Loads, defined in order to be applied to limited structural models (stiffened panels, single beams, plate panels), generally are termed local loads. The distinction is purely formal, as the same external forces can in fact be interpreted as global or local loads. For instance, wave dynamic actions on a portion of the hull, if described in 4 Chapter 1 The background of ship structure desgin terms of a bi-dimensional distribution of pressures over the wet surface, represent a local load for the hull panel, while, if integrated over the same surface, represent a contribution to the bending moment acting on the hull girder. This terminology is typical of simplified structural analyses, in which responses of the two classes of components are evaluated separately and later summed up to provide the total stress in selected positions of the structure. In a complete 3D model of the whole ship, forces on the structure are applied directly in their actual position and the result is a total stress distribution, which does not need to be decomposed. The local and global loads are once again traditionally divided into static and dynamic loads, referred respectively to the situation in still water and in a seaway. So there are some categories as follows - - Hull girder loads are (still water, wave and dynamic) forces and moments which result as effects of local loads acting on the ship as a whole and considered as a beam. Still water local loads are constituted by the hydrostatic external sea pressures and the static pressures and forces induced by the weights carried in the ship spaces. Wave local loads are constituted by the external sea pressures due to waves and the inertial pressures and forces induced by the ship accelerations applied to the weights carried in the ship spaces. These loads are well known as wave dynamic loads Dynamic local loads are constituted by the slaming and sloshing pressures (dynamic transient loads). 1.2.3. Hull girder loads calculation 1.2.3.1. Still water global loads For all ships, the longitudinal distributions of still water bending moment and shear force are to be calculated, for each of the loading conditions, on the basis of realistic data related to the amount of cargo, ballast, fuel, lubricating oil and fresh water. The actual hull lines and lightweight distribution are to be taken into account in the calculations. Figure 2 – Sign conventions for shear forces Q and bending moments M. While buoyancy distribution is known from an early stage of the ship design, weight distribution is completely defined only at the end of construction. Statistical formulations, calibrated on similar ships, are often used in the design development to provide an approximate quantification of weight items and their longitudinal distribution on board. The resulting 5 Chapter 1 The background of ship structure desgin approximated weight distribution, together with the buoyancy distribution, allows computing shear and bending moment. The design still water bending moments MSW,H and MSW,S at any hull transverse section are the maximum still water bending moments calculated, in kN.m, in hogging and sagging conditions, respectively. MSWM,H = 175n1CL2B(CB+0.7)10-3 – MWV,H (hogging) (1) MSWM,S = 175n1CL2B(CB + 0.7)10-3 + MWV,S (sagging) (2) where C: wave parameter. For 90m ≤ L ≤ 300m, 10.75 300 100 . n: navigation coefficients. For unrestricted navigation, n=1, CB: block coefficience. For Ropax ship, CB = 0.514. 1.2.3.2. Wave induced global loads The action of waves modifies the pressure distribution along the wet hull surface; the differential pressure between the situation in waves and in still water generates, on the transverse section, vertical and horizontal resultant forces and moment component. The longitudinal distributions along the hull girder of horizontal and vertical components of shear, bending moment and torque can then be in principle obtained for each instantaneous wave pressure distribution, depending therefore, on time, on type and direction of sea encountered and on the ship geometrical and operational characteristics. In regular (sinusoidal) waves, vertical bending moments tend to be maximized in head waves with length close to the ship length, while horizontal bending and torque components are larger for oblique wave systems. Simplified, first approximation, formulations are available for the main wave load components, developed mainly on the basis of past experience. The vertical wave bending moments at any hull transverse section are obtained, in kN.m, from the following formulae MWV,H = 190 FM n C L2 B CB 10-3 (hogging) (3) MWV,S = - 110 FM n C L2 B (CB + 0,7) 10-3 (sagging) (4) where FM: distribution factor, 6 Chapter 1 The background of ship structure desgin Hull transverse section location Distribution factor FM  0 ≤ x   0.4L 2.5 0.4 ≤ x ≤ 0.65L x L 1 0.65L   x ≤ L 2.86 1 x   L Table 1 – Distribution factor FM. The horizontal wave bending moment at any hull transverse section is obtained, in kN.m, from the following formula: MWH = 0,42 FM n H L2 T CB (5) The wave torque at any hull transverse section is to be calculated considering the ship in two different conditions: - Condition 1: ship direction forming an angle of 60o with the prevailing sea direction, Condition 2: ship direction forming an angle of 120o with the prevailing sea direction. The values of the wave torques in these conditions, calculated with respect to the section centre of torsion, are obtained, in kN.m, from the following formula: (6) where FTM, FTQ: distribution factors, CM: wave torque coefficient, CM = 0.45B2CW2 CQ: horizontal wave shear coefficient, CQ = 5T.CB CW: waterplane coefficient, d: vertical distance, in m, from the centre of torsion to a point located 0.6T above baseline. Ship condition  Distribution factor FTM Distribution factor FTQ  1 2 1 1 cos cos 2πx L 2π L x L sin sin 2πx   L 2π L x   L Table 2 – Distribution factor FTM and FTQ. 7 Chapter 1 The background of ship structure desgin The vertical wave shear force at any hull transverse section is obtained, in kN, from the following formula: QWV = 30 FQ n C L B (CB + 0,7) 10-2 (7) where FQ: distribution factor, Figure 3 – Distribution factor FQ. 1.2.4. Local loads calculation As above stated, the local loads are instituted by the external pressure on the wet surface of hull and the internal pressure due to the weights carried in the ship spaces. Local loads are to be calculated on the basis of the ship's draught T1 corresponding to the cargo or ballast distribution that well known as loading condition (distribution of weights carried in the ship spaces arranged for their storage). The ship draught is to be taken as the distance measured vertically on the hull transverse section at the middle of the length L, from the moulded base line to the waterline in: Full load condition, when: - one or more cargo compartments (e.g. oil tank, dry cargo hold, vehicle space, passenger space) are considered as being loaded and the ballast tanks are considered as being empty. the still water and wave external pressures are considered as acting alone without any counteraction from the ship's interior. Light ballast condition, when one or more ballast tanks are considered as being loaded and the cargo compartments are considered as being empty. In general, TB = 0,03 L ≤ 7,5 m 1.2.4.1. External loads – sea pressures Static and dynamic pressures generated on the wet surface of the hull belong to external loads. They act as local transverse loads for the hull plating and supporting structures. The still water pressure at any point of the hull is obtained from the formulae in table 6 8 Chapter 1 The background of ship structure desgin Location  Still water pressure Ps, in  kN.m2 Points at and below the waterline  z ≤ T1 ρg T1 – z   Points above the waterline  z   T1 0  Table 6 – Still water pressure. where ρ: Sea water density, taken equal to 1.025 T/m3. T1: Draught associated with each cargo and ballast distribution, according to respectively the the structural analyses based on three dimensional structural models or on plate or isolated beam structural models. Figure 4 – Still water pressure. The wave pressure acting on structure depends on the ship conditions discussed in section I.5. The wave pressure at any point of the sides and bottom is obtained from the formulae in table 7 for load case "a" and "b"; table 8 for load case “c” and “d”. Location  Wave pressure Pw, in kN.m2 Crest Bottom and sides below the waterline  z ≤ T1 Sides above the waterline  z   T1 ρghe T L Trough    ρg T1   h – z   T L ρghe 0  Table 7 – Wave pressure on sides and bottom in upright ship condition “a” and “b”. 9 Chapter 1 The background of ship structure desgin Location  Wave pressure Pw, in kN.m2  y  Bottom and sides below  the waterline  z ≤ T1   CF ρg y h e BW AR ye Sides above the waterline  z   T1   ρg T 0 C y   0  T L CF ρg T L y h BW z y h e BW AR ye AR y T L T L   0  Table 8 – Wave pressure on sides and bottom in inclined ship condition “c” and “d”. where h = CF1h1, CF1: Combination factor, see table 13, BW: Moulded breadth, in m, measured at the waterline at draught T1, at the hull transverse section considered. AR: Roll amplitude. 1.2.4.2. Internal load – wheeled cargoes loads In the case of a unit cargo (container, pallet, vehicle or other) the local translational accelerations at the centre of gravity are applied to the mass to obtain a distribution of inertial forces. Such forces are transferred to the structure in different ways, depending on the number and extension of contact areas and on topology and geometry of the lashing or supporting systems. Generally, this kind of load is modelled by one or more concentrated forces or by a uniform load applied on the contact area with the structure. The latter case applies, for example, to the inertial loads transmitted by tyred vehicles when modelling the response of the deck plate between stiffeners: in this case the load is distributed uniformly on the tyre print. Remark: The reason that only wheeled load considered in this study is that the Ropax is a vessel carrying the vehicles on its decks. Furthermore, it is designed for always being in full loading condition. It means that Ropax have never spent its life on ballast loading condition. The forces transmitted through the tyres are comparable to pressure uniformly distributed on the tyre print, whose dimensions are to be indicated by the Designer together with information concerning the arrangement of wheels on axles, the load per axles and the tyre pressures. With the exception of dimensioning of plating, such forces may be considered as concentrated in the tyred print centre. 10 Chapter 1 The background of ship structure desgin     Wave pressure in load case “a”. Wave pressure in load case “b”. Wave pressure in load case “c”. Wave pressure in load case “d”. Figure 5 – Wave pressure for each load cases according to BV [5]. The still water and inertial forces transmitted to the hull structures are to be determined on the basis of the forces obtained, in kN, as specified in table 9. Ship condition Load case Still water force Fs and inertial force Fw, in kN Still water Upright (positive heave motion) Inclined (negative roll angle) Fs = Mg “a” No inertial force “b” Fw,z = αMaz1 in z direction “c” Fw,y = MCFAay2 in y direction “d” Fw,z = MCFAaz2 in y direction Table 9 – Wheeled cargoes still water and inertial forces. 11 Chapter 1 The background of ship structure desgin where α: Coefficient taken equal to 0.4, M: Mass, in T, taken equal to QA: Axle load, in T, nw: number of wheels for the axle considered, CFA: combination factor, to be taken equal to CFA = 0.7 for load case “c”, CFA = 1.0 for load case “d”. For primary supporting members subjected to wheeled loads, the uniform pressures can be considered instead of the distribution of vertical concentrated forces, when such forces are closely located. For the determination of the equivalent uniform pressures, the most unfavourable case, i.e. where the maximum number of axles is located on the same primary supporting member according to figure 6 to figure 8, is to be considered. The equivalent still water pressure and inertial pressure are indicated in table 10 Ship condition Load case Still water pressure Ps and inertial pressure Pw, in kN/m2. Still water condition Upright condition Inclined condition Ps = Peq “a” No inertial pressure “b” Pw = αPeqaz1/ g “c” The inertial pressure may be disregarded “d” Pw = αPeqaz2/ g Table 10 – Wheeled loads, equivalent uniform still water and inertial pressures. where 10 3 nV : Maximum number of vehicles possible located on the primary supporting member, X1 : Minimum distance, in m, between two consecutive axles, see figure 7 and 8, X2 : Minimum distance, in m, between axles of two consecutive vehicles, see figure 8. 12 Chapter 1 The background of ship structure desgin Figure 6 – Wheeled loads – Distribution of vehicles on a primary supporting member [5]. Figure 7 – Wheeled loads distance between two consecutive axles [5]. Figure 8 – Wheeled loads distance between axles of two consecutive vehecles [5]. 13