Analysis and design of ship structure

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18.1 NOMENCLATURE For specific symbols, refer to the definitions contained in the various sections. ABS American Bureau of Shipping BEM Boundary Element Method BV Bureau Veritas DNV Det Norske Veritas FEA Finite Element Analysis FEM Finite Element Method IACS International Association of Classifica- tion Societies ISSC International Ship & Offshore Structures Congress ISOPE International Offshore and Polar Engi- neering Conference ISUM Idealized Structural Unit method NKK Nippon Kaiji Kyokai PRADS Practical Design of Ships and Mobile Units, RINA Registro Italiano Navale SNAME Society of naval Architects and marine Engineers SSC Ship Structure Committee. a acceleration Aarea Bbreadth of the ship Cwave coefficient (Table 18.I) C B hull block coefficient Ddepth of the ship ggravity acceleration m(x) longitudinal distribution of mass I(x) geometric moment of inertia (beam sec- tion x) L length of the ship M(x) bending moment at section x of a beam M T (x) torque moment at section x of a beam ppressure q(x) resultant of sectional force acting on a beam Tdraft of the ship V(x) shear at section x of a beam s,w (low case) still water, wave induced component v,h (low case) vertical, horizontal component w(x) longitudinal distribution of weight θ roll angle ρ density ω angular frequency 18.2 INTRODUCTION The purpose of this chapter is to present the fundamentals of direct ship structure analysis based on mechanics and strength of materials. Such analysis allows a rationally based design that is practical, efficient, and versatile, and that has already been implemented in a computer program, tested, and proven. 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 be- tween performing a design and completing an analysis. 18-1 Chapter 18 Analysis and Design of Ship Structure Philippe Rigo and Enrico Rizzuto MASTER SET SDC 18.qxd Page 18-1 4/28/03 1:30 PM 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. Results of this comparison as well as the objective functions (weight, cost, etc.) will show if updated (improved) scantlings are required. Design for structure refers to the process followed to se- lect the initial structural scantlings and to update these scant- lings from the early design stage (bidding) to the detailed design stage (construction). To perform analysis, initial de- sign is needed and analysis is required to design. This ex- plains why design and analysis are intimately linked, but are absolutely different. Of course design also relates to topology and layout definition. The organization and framework of this chapter are based on the previous edition of the Ship Design and Construction (1) and on the Chapter IV of Principles of Naval Architec- ture (2). Standard materials such as beam model, twisting, shear lag, etc. that are still valid in 2002 are partly duplicated from these 2 books. Other major references used to write this chapter are Ship Structural Design (3) also published by SNAME and the DNV 99-0394 Technical Report (4). The present chapter is intimately linked with Chapter 11 – Parametric Design, Chapter 17 – Structural Arrange- ment and Component Design and with Chapter 19 – Reli- ability-Based Structural Design. References to these chapters will be made in order to avoid duplications. In ad- dition, as Chapter 8 deals with classification societies, the present chapter will focus mainly on the direct analysis methods available to perform a rationally based structural design, even if mention is made to standard formulations from Rules to quantify design loads. In the following sections of this chapter, steps of a global analysis are presented. Section 18.3 concerns the loads that are necessary to perform a structure analysis. Then, Sections 18.4, 18.5 and 18.6 concern, respectively, the stresses and deflections (basic ship responses), the limit states, and the fail- ures modes and associated structural capacity. A review of the available Numerical Analysis for Structural Design is per- formed in Section 18.7. Finally Design Criteria (Section 18.8) and Design Procedures (Section 18.9) are discussed. Structural modeling is discussed in Subsection 18.2.2 and more extensively in Subsection 18.7.2 for finite element analy- sis. Optimization is treated in Subsections 18.7.6 and 18.9.4. Ship structural design is a challenging activity. Hence Hughes (3) states: The complexities of modern ships and the demand for greater reliability, efficiency, and economy require a sci- entific, powerful, and versatile method for their structural design But, even with the development of numerical techniques, design still remains based on the designer’s experience and on previous designs. There are many designs that satisfy the strength criteria, but there is only one that is the optimum solution (least cost, weight, etc.). Ship structural analysis and design is a matter of com- promises: • 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 de- sign analyses efficient. The results from complex analy- ses 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.), and •builder optimum design may be different from the owner optimum design. 18.2.1 Rationally Based Structural Design versus Rules-Based Design There are basically two schools to perform analysis and de- sign 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 (3) states: In the past, ship structural design has been largely empir- ical, based on accumulated experience and ship perform- ance, and expressed in the form of structural design codes or rules published by the various ship classification soci- eties. These rules concern the loads, the strength and the design criteria and provide simplified and easy-to-use for- mulas 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, (3) further states: 18-2 Ship Design & Construction, Volume 1 MASTER SET SDC 18.qxd Page 18-2 4/28/03 1:30 PM 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 un- known; thus one cannot distinguish between structural ad- equacy and over-adequacy. Second, and most important, these formulas involve a number of simplifying assump- tions 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. Even if direct calculation has always been performed, design based on direct analysis only became popular when numerical analysis methods became available and were cer- tified. Direct analysis has become the standard procedure in aerospace, civil engineering and partly in offshore in- dustries. In ship design, classification societies preferred to offer updated rules resulting from numerical analysis cali- bration. For the designer, even if the rules were continuously changing, the design remained rule-based. There really were two different methodologies. Hopefully, in 2002 this is no longer true. The advantages of direct analysis are so obvious that classification societies include, usually as an alternative, a direct analysis procedure (numerical packages based on the finite element method, see Table 18.VIII, Subsection 18.7.5.2). In addition, for new vessel types or non-standard dimension, such direct proce- dure is the only way to assess the structural safety. There- fore 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 struc- tures compared with other types of structures. They are sub- ject 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. A notable example is the fact that the efforts of a ma- jority of specialists together with rapid advances in com- puter and software technology have now made it possible to analyze complex ship structures in a practical manner using structural analysis techniques centering on FEM analysis. 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 re- quirements, 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 evalua- tion. In addition, in order to make this a practical and ef- fective method of analysis, it is necessary to give careful consideration to more rational and accurate methods of di- rect strength analysis. Based on recognition of this need, extensive research has been conducted and a careful examination made, re- garding the strength evaluation of hull structures. The re- sults of this work have been presented in papers and reports regarding direct strength evaluation of hull structures (4,5). The flow chart given in Figure 18.1 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, con- straints…) must be made before the design starts. This is a major difficulty of this approach. 18.2.2 Modeling and Analysis General guidance on the modeling necessary for the struc- tural analysis is that the structural model shall provide re- sults suitable for performing buckling, yield, fatigue and Chapter 18: Analysis and Design of Ship Structure 18-3 Figure 18.1 Direct Structural Analysis Flow Chart Direct Load Analysis Design Load Study on Ocean Waves Effect on operation Wave Load Response Response function of wave load Structural analysis by whole ship model Stress response function Short term estimation Long term estimation Design Sea State Design wave Wave impact load Structural response analysis Strength Assessment Yield strength Nonlinear influence in large waves Investigation on corrosion Buckling strength Ultimate strength Fatigue strength Modeling technique Direct structural analysis Stress Response in Waves Long term estimation Short term estimation MASTER SET SDC 18.qxd Page 18-3 4/28/03 1:30 PM vibration assessment of the relevant parts of the vessel. This is done by using a 3D model of the whole ship, supported by one or more levels of sub models. Several approaches may be applied such as a detailed 3D model of the entire ship or coarse meshed 3D model sup- ported by finer meshed sub models. Coarse mesh can be used for determining stress results suited for yielding and buckling control but also to obtain the displacements to apply as boundary conditions for sub models with the purpose of determining the stress level in more detail. Strength analysis covers yield (allowable stress), buck- ling strength and ultimate strength checks of the ship. In ad- dition, specific analyses are requested for fatigue (Subsection 18.6.6), collision and grounding (Subsection 18.6.7) and vibration (Subsection 18.6.8). The hydrodynamic load model must give a good representation of the wetted sur- face of the ship, both with respect to geometry description and with respect to hydrodynamic requirements. The mass model, which is part of the hydrodynamic load model, must ensure a proper description of local and global moments of inertia around the global ship axes. Ultimate hydrodynamic loads from the hydrodynamic analysis should be combined with static loads in order to form the basis for the yield, buckling and ultimate strength checks. All the relevant load conditions should be examined to ensure that all dimensioning loads are correctly included. A flow chart of strength analysis of global model and sub models is shown in Figure 18.2. 18.2.3 Preliminary Design versus Detailed Design For a ship structure, structural design consists of two dis- tinct levels: the Preliminary Design and the Detailed De- sign about which Hughes (3) states: The preliminary determines the location, spacing, and scant- lings of the principal structural members. The detailed de- sign 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 de- sign is less important than preliminary design. Each level is equally important for obtaining an efficient, safe and re- liable ship. During the detailed design there also are many bene- fits to be gained by applying modern methods of engi- neering 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 de- tail 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 in- efficient to attempt to design all of them from first princi- ples. Instead it is generally more efficient to use design codes and standard designs that have been proven by ex- perience. 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. 18.3 LOADS Loads acting on a ship structure are quite varied and pecu- liar, in comparison to those of static structures and also of other vehicles. In the following an attempt will be made to review the main typologies of loads: physical origins, gen- eral interpretation schemes, available quantification proce- 18-4 Ship Design & Construction, Volume 1 Figure 18.2 Strength Analysis Flow Chart (4) Structural model including necessary load definitions Hydrodynamic/static loads Load transfer to structural model Verified structural model Sub-models to be used in structural analysis Structural analysis Verification of response Verification of model/ loads Yes No Transfer of displacements/forces to sub-model? Verification of load transfer Structural drawings, mass description and loading conditions. MASTER SET SDC 18.qxd Page 18-4 4/28/03 1:30 PM dures and practical methods for their evaluation will be sum- marized. 18.3.1 Classification of Loads 18.3.1.1 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 con- dition, they have little and very slow variations during a voyage (mainly due to changes in the distribution of con- sumables 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 in- duced by waves, but also those generated in the same fre- quency range by motions of the ship (inertial forces). These loads can be termed quasi-static because the structural re- sponse is studied with static models. Dynamic loads: When studying responses with fre- quency 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 (spring- ing) or by mechanical excitation (main engine, propeller). Also transient impulsive loads that excite free structural vi- brations (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 (> 10-20 Hz) also are present on ships: this kind of excitation, however, involves more the study of noise propagation on board than structural design. Other loads:All other loads that do not fall in the above mentioned categories and need specific models can be gen- erally grouped in this class. Among them are thermal and accidental loads. A large part of ship design is performed on the basis of static and quasi-static loads, whose prediction procedures are quite well established, having been investigated for a long time. However, specific and imposing requirements can arise for particular ships due to the other load cate- gories. 18.3.1.2 Local and global loads Another traditional classification of loads is based on the structural scheme adopted to study the response. 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 (see Subsection 18.4.3). Loads, defined in order to be applied to limited struc- tural 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 terms of a bi-dimensional distribution of pres- sures 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 analy- ses, 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. 18.3.1.3 Characteristic values for loads Structural verifications are always based on a limit state equation and on a design operational time. Main aspects of reliability-based structural design and analysis are (see Chapter 19): • the state of the structure is identified by state variables associated to loads and structural capacity, • state variables are stochastically distributed as a func- tion of time, and • the probability of exceeding the limit state surface in the design time (probability of crisis) is the element subject to evaluation. The situation to be considered is in principle the worst combination of state variables that occurs within the design time. The probability that such situation corresponds to an out crossing of the limit state surface is compared to a (low) target probability to assess the safety of the structure. This general time-variant problem is simplified into a time-invariant one. This is done by taking into account in the analysis the worst situations as regards loads, and, sep- arately, as regards capacity (reduced because of corrosion and other degradation effects). The simplification lies in considering these two situations as contemporary, which in general is not the case. When dealing with strength analysis, the worst load sit- uation corresponds to the highest load cycle and is charac- terized through the probability associated to the extreme value in the reference (design) time. In fatigue phenomena, in principle all stress cycles con- tribute (to a different extent, depending on the range) to Chapter 18: Analysis and Design of Ship Structure 18-5 MASTER SET SDC 18.qxd Page 18-5 4/28/03 1:30 PM damage accumulation. The analysis, therefore, does not re- gard the magnitude of a single extreme load application, but the number of cycles and the shape of the probability dis- tribution of all stress ranges in the design time. A further step towards the problem simplification is rep- resented by the adoption of characteristic load values in place of statistical distributions. This usually is done, for example, when calibrating a Partial Safety Factor format for structural checks. Such adoption implies the definition of a single reference load value as representative of a whole probability distribution. This step is often performed by as- signing an exceeding probability (or a return period) to each variable and selecting the correspondent value from the sta- tistical distribution. The exceeding probability for a stochastic variable has the meaning of probability for the variable to overcome a given value, while the return period indicates the mean time to the first occurrence. Characteristic values for ultimate state analysis are typ- ically represented by loads associated to an exceeding prob- ability of 10 –8 . This corresponds to a wave load occurring, on the average, once every 10 8 cycles, that is, with a return period of the same order of the ship lifetime. In first yield- ing analyses, characteristic loads are associated to a higher exceeding probability, usually in the range 10 –4 to 10 –6 . In fatigue analyses (see Subsection 18.6.6.2), reference loads are often set with an exceeding probability in the range 10 –3 to 10 –5 , corresponding to load cycles which, by effect of both amplitude and frequency of occurrence, contribute more to the accumulation of fatigue damage in the structure. On the basis of this, all design loads for structural analy- ses are explicitly or implicitly related to a low exceeding probability. 18.3.2 Definition of Global Hull Girder Loads The global structural response of the ship is studied with reference to a beam scheme (hull girder), that is, a mono- dimensional structural element with sectional characteris- tics distributed along a longitudinal axis. Actions on the beam are described, as usual with this scheme, only in terms of forces and moments acting in the transverse sections and applied on the longitudinal axis. Three components act on each section (Figure 18.3): a resultant force along the vertical axis of the section (con- tained in the plane of symmetry), indicated as vertical re- sultant force q V ; another force in the normal direction, (local horizontal axis), termed horizontal resultant force q H and a moment m T about the x axis. All these actions are distrib- uted along the longitudinal axis x. Five main load components are accordingly generated along the beam, related to sectional forces and moment through equation 1 to 5: [1] [2] [3] [4] [5] Due to total equilibrium, for a beam in free-free condi- tions (no constraints at ends) all load characteristics have zero values at ends (equations 6). These conditions impose constraints on the distributions of q V ,q H and m T . [6] Global loads for the verification of the hull girder are ob- tained with a linear superimposition of still water and wave- induced global loads. They are used, with different characteristic values, in different types of analyses, such as ultimate state, first yield- ing, and fatigue. 18.3.3 Still Water Global Loads Still water loads act on the ship floating in calm water, usu- ally with the plane of symmetry normal to the still water surface. In this condition, only a symmetric distribution of hydrostatic pressure acts on each section, together with ver- tical gravitational forces. If the latter ones are not symmetric, a sectional torque m Tg (x) is generated (Figure 18.4), in addition to the verti- V (0) V (L) M (0) M (L) 0 V (0) V (L) M (0) M (L) 0 M (0) M (L) 0 VV V V HH H H TT == = = == = = == M (x) m ( ) d TT 0 x = ∫ ξξ M (x) V ( ) d HH 0 x = ∫ ξξ V (x) q ) d HH 0 x = ∫ (ξξ M (x) V ( ) d VV 0 x = ∫ ξξ V (x) q ( ) d VV 0 x = ∫ ξξ 18-6 Ship Design & Construction, Volume 1 Figure 18.3 Sectional Forces and Moment MASTER SET SDC 18.qxd Page 18-6 4/28/03 1:30 PM cal load q SV (x), obtained as a difference between buoyancy b(x) and weight w(x), as shown in equation 7 (2). [7] where A I = transversal immersed area. Components of vertical shear and vertical bending can be derived according to equations 1 and 2. There are no hor- izontal components of sectional forces in equation 3 and ac- cordingly no components of horizontal shear and bending moment. As regards equation 5, only m Tg , if present, is to be accounted for, to obtain the torque. 18.3.3.1 Standard still water bending moments 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, cal- ibrated on similar ships, are often used in the design de- velopment to provide an approximate quantification of weight items and their longitudinal distribution on board. The resulting approximated weight distribution, together with the buoyancy distribution, allows computing shear and bending moment. q (x) b(x) w(x) gA (x) m(x)g SV I =− = − At an even earlier stage of design, parametric formula- tions can be used to derive directly reference values for still water hull girder loads. Common reference values for still water bending mo- ment at mid-ship are provided by the major Classification Societies (equation 8). [8] where C = wave parameter (Table 18.I). The formulations in equation 8 are sometimes explicitly reported in Rules, but they can anyway be indirectly de- rived from prescriptions contained in (6, 7). The first re- quirement (6) regards the minimum longitudinal strength modulus and provides implicitly a value for the total bend- ing moment; the second one (7), regards the wave induced component of bending moment. Longitudinal distributions, depending on the ship type, are provided also. They can slightly differ among Class So- cieties, (Figure 18.5). 18.3.3.2 Direct evaluation of still water global loads Classification Societies require in general a direct analysis of these types of load in the main loading conditions of the ship, such as homogenous loading condition at maximum draft, ballast conditions, docking conditions afloat, plus all other conditions that are relevant to the specific ship (non- homogeneous loading at maximum draft, light load at less than maximum draft, short voyage or harbor condition, bal- last exchange at sea, etc.). The direct evaluation procedure requires, for a given loading condition, a derivation, section by section, of ver- tical resultants of gravitational (weight) and buoyancy forces, applied along the longitudinal axis x of the beam. To obtain the weight distribution w(x), the ship length is subdivided into portions: for each of them, the total weight and center of gravity is determined summing up contributions from all items present on board between the two bounding sections. The distribution for w(x) is then usually approxi- mated by a linear (trapezoidal) curve obtained by imposing MN m C L B 122.5 15 C (hogging) C L B 45.5 65 C (sagging) s 2 B 2 B ⋅ − ( ) + [] = ( ) Chapter 18: Analysis and Design of Ship Structure 18-7 Figure 18.4 Sectional Resultant Forces in Still Water Figure 18.5 Examples of Reference Still Water Bending Moment Distribution (10). (a) oil tankers, bulk carriers, ore carriers, and (b) other ship types TABLE 18.I Wave Coefficient Versus Length Ship Length L Wave Coefficient C 90 ≤ L <300 m 10.75 – [(300 – L)/100] 3/2 300 ≤ L <350 m 10.75 350 ≤ L 10.75 – [(300 – L)/150] 3/2 (a) (b) MASTER SET SDC 18.qxd Page 18-7 4/28/03 1:30 PM the correspondence of area and barycenter of the trapezoid respectively to the total weight and center of gravity of the considered ship portion. The procedure is usually applied separately for differ- ent types of weight items, grouping together the weights of the ship in lightweight conditions (always present on board) and those (cargo, ballast, consumables) typical of a load- ing condition (Figure 18.6). 18.3.3.3 Uncertainties in the evaluation A significant contribution to uncertainties in the evaluation of still water loads comes from the inputs to the procedure, in particular those related to quantification and location on board of weight items. This lack of precision regards the weight distribution for the ship in lightweight condition (hull structure, machin- ery, outfitting) but also the distribution of the various com- ponents of the deadweight (cargo, ballast, consumables). Ship types like bulk carriers are more exposed to uncer- tainties on the actual distribution of cargo weight than, for example, container ships, where actual weights of single containers are kept under close control during operation. In addition, model uncertainties arise from neglecting the longitudinal components of the hydrostatic pressure (Fig- ure 18.7), which generate an axial compressive force on the hull girder. As the resultant of such components is generally below the neutral axis of the hull girder, it leads also to an addi- tional hogging moment, which can reach up to 10% of the total bending moment. On the other hand, in some vessels (in particular tankers) such action can be locally counter- balanced by internal axial pressures, causing hull sagging moments. All these compression and bending effects are neglected in the hull beam model, which accounts only for forces and moments acting in the transverse plane. This represents a source of uncertainties. Another approximation is represented by the fact that buoyancy and weight are assumed in a direction normal to the horizontal longitudinal axis, while they are actually ori- ented along the true vertical. This implies neglecting the static trim angle and to consider an approximate equilibrium position, which often creates the need for a few iterative corrections to the load curve q sv (x) in order to satisfy boundary conditions at ends (equations 6). 18.3.3.4 Other still water global loads In a vessel with a multihull configuration, in addition to conventional still water loads acting on each hull consid- ered as a single longitudinal beam, also loads in the trans- versal direction can be significant, giving rise to shear, bending and torque in a transversal direction (see the sim- plified scheme of Figure 18.8, where S, B, and Q stand for shear, bending and torque; and L, T apply respectively to longitudinal and transversal beams). 18.3.4 Wave Induced Global Loads The prediction of the behaviour of the ship in waves repre- sents a key point in the quantification of both global and local loads acting on the ship. The solution of the seakeep- ing problem yields the loads directly generated by external pressures, but also provides ship motions and accelerations. The latter are directly connected to the quantification of in- ertial loads and provide inputs for the evaluation of other types of loads, like slamming and sloshing. 18-8 Ship Design & Construction, Volume 1 Figure 18.6 Weight Distribution Breakdown for Full Load Condition Figure 18.7 Longitudinal Component of Pressure Figure 18.8 Multi-hull Additional Still Water Loads (sketch) MASTER SET SDC 18.qxd Page 18-8 4/28/03 1:30 PM In particular, as regards global effects, the action of waves modifies the pressure distribution along the wet hull sur- face; the differential pressure between the situation in waves and in still water generates, on the transverse section, ver- tical and horizontal resultant forces (b WV and b WH ) and a moment component m Tb . Analogous components come from the sectional result- ants of inertial forces and moments induced on the section by ship’s motions (Figure 18.9). The total vertical and horizontal wave induced forces on the section, as well as the total torsional component, are found summing up the components in the same direction (equations 9). [9] where I R (x) is the rotational inertia of section x. The longitudinal distributions along the hull girder of hor- izontal and vertical components of shear, bending moment and torque can then be derived by integration (equations 1 to 5). Such results are in principle obtained for each instanta- neous 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 com- ponents are larger for oblique wave systems. 18.3.4.1 Statistical formulae for global wave loads Simplified, first approximation, formulations are available for the main wave load components, developed mainly on the basis of past experience. Ve rtical wave-induced bending moment: IACS classifi- q (x) b (x) m(x)a (x) q (x) b (x) m(x)a (x) m (x) m (x) I (x) WV WV V WH WH H TW Tb R =− =− =−θ cation societies provide a statistically based reference values for the vertical component of wave-induced bending moment M WV ,expressed as a function of main ship dimensions. Such reference values for the midlength section of a ship with unrestricted navigation are yielded by equation 10 for hog and sag cases (7) and corresponds to an extreme value with a return period of about 20 years or an exceeding prob- ability of about 10 –8 (once in the ship lifetime). [10] Horizontal Wave-induced Bending Moment: Similar for- mulations are available for reference values of horizontal wave induced bending moment, even though they are not as uniform among different Societies as for the main verti- cal component. In Table 18.II, examples are reported of reference val- ues of horizontal bending moment at mid-length for ships with unrestricted navigation. Simplified curves for the dis- tribution in the longitudinal direction are also provided. Wave-induced Torque: A few reference formulations are given also for reference wave torque at midship (see ex- amples in Table 18.III) and for the inherent longitudinal distributions. 18.3.4.2 Static Wave analysis of global wave loads A traditional analysis adopted in the past for evaluation of wave-induced loads was represented by a quasi-static wave approach. The ship is positioned on a freezed wave of given characteristics in a condition of equilibrium between weight and static buoyancy. The scheme is analogous to the one de- scribed for still water loads, with the difference that the wa- terline upper boundary of the immersed part of the hull is no longer a plane but it is a curved (cylindrical) surface. By definition, this procedure neglects all types of dynamic ef- fects. Due to its limitations, it is rarely used to quantify wave loads. Sometimes, however, the concept of equivalent static wave is adopted to associate a longitudinal distribution of MNm C L B C C L B C . (hog) (sag) WV B B ⋅ [] = −+ ( ) 190 110 0 7 2 2 Chapter 18: Analysis and Design of Ship Structure 18-9 Figure 18.9 Sectional Forces and Moments in Waves TABLE 18.II Reference Horizontal Bending Moments Class Society M WH [N ⋅ m] ABS (8) 180 C 1 L 2 DC B BV (9) RINA (10) 1600 L 2.1 TC B DNV (11) 220 L 9/4 (T + 0.3B)C B NKK (12) 320 L 2 C TL L− 35 / MASTER SET SDC 18.qxd Page 18-9 4/28/03 1:30 PM pressures to extreme wave loads, derived, for example, from long term predictions based on other methods. 18.3.4.3 Linear methods for wave loads The most popular approach to the evaluation of wave loads is represented by solutions of a linearized potential flow problem based on the so-called strip theory in the frequency domain (13). The theoretical background of this class of procedures is discussed in detail in PNA Vol. III (2). Here only the key assumptions of the method are pre- sented: • inviscid, incompressible and homogeneous fluid in irro- tational flow: Laplace equation 11 ∇ 2 Φ = 0 [11] where Φ = velocity potential • 2-dimensional solution of the problem • linearized boundary conditions: the quadratic compo- nent of velocity in the Bernoulli Equation is reformu- lated in linear terms to express boundary conditions: — on free surface: considered as a plane corresponding to still water: fluid velocity normal to the free surface equal to velocity of the surface itself (kinematic con- dition); zero pressure, — on the hull: considered as a static surface, corre- sponding to the mean position of the hull: the com- ponent of the fluid velocity normal to the hull surface is zero (impermeability condition), and • linear decomposition into additive independent compo- nents, separately solved for and later summed up (equa- tion 12). Φ = Φ s + Φ FK + Φ d + Φ r [12] where: Φ s = stationary component due to ship advancing in calm water Φ r = radiation component due to the ship motions in calm water Φ FK = excitation component, due to the incident wave (undisturbed by the presence of the ship): Froude- Krylov Φ d = diffraction component, due to disturbance in the wave potential generated by the hull This subdivision also enables the de-coupling of the ex- citation components from the response ones, thus avoiding a non-linear feedback between the two. Other key properties of linear systems that are used in the analysis are: •linear relation between the input and output amplitudes, and • superposition of effects (sum of inputs corresponds to sum of outputs). When using linear methods in the frequency domain, the input wave system is decomposed into sinusoidal com- ponents and a response is found for each of them in terms of amplitude and phase. The input to the procedure is represented by a spectral representation of the sea encountered by the ship. Responses, for a ship in a given condition, depend on the input sea char- acteristics (spectrum and spatial distribution respect to the ship course). The output consists of response spectra of point pres- sures on the hull and of the other derived responses, such as global loads and ship motions. Output spectra can be used to derive short and long-term predictions for the prob- ability distributions of the responses and of their extreme values (see Subsection 18.3.4.5). Despite the numerous and demanding simplifications at the basis of the procedure, strip theory methods, developed since the early 60s, have been validated over time in sev- eral contexts and are extensively used for predictions of wave loads. In principle, the base assumptions of the method are 18-10 Ship Design & Construction, Volume 1 TABLE 18.III Examples of Reference Values for Wave Torque Class Society Q w [N . m] (at mid-ship) ABS (bulk carrier) (e = vertical position of shear center) BV RINA 190 8 13 250 0 7 125 2 2 3 LB C . .L W − −           2700 0 5 0 1 0 13 014 2 2 05 LB T C . . . e D . T W . − ( ) + [] −           MASTER SET SDC 18.qxd Page 18-10 4/28/03 1:30 PM [...]... solution of Reynolds Averaged Navier Stokes (RANS) equations in the time domain These methods represent the most recent trend in the field of ship motions and loads prediction and their use is limited to a few research groups MASTER SET SDC 18.qxd Page 18-21 4/28/03 1:30 PM Chapter 18: Analysis and Design of Ship Structure 18.4 STRESSES AND DEFLECTIONS The reactions of structural components of the ship. .. MASTER SET SDC 18.qxd Page 18-31 4/28/03 1:30 PM Chapter 18: Analysis and Design of Ship Structure and normal loading, deflection and stress over the length and width dimensions of a stiffened panel Remember that the primary response involves the determination of only the in-plane load, deflection, and stress as they vary over the length of the ship The secondary response, therefore, is seen to be a two-dimensional... 18.6.6) is often found to play an important role in the initiation and early growth of such originating cracks The prevention of brittle fracture is largely a matter of material selection and proper attention to the design of structural details in order to avoid stress concentrations The control of brittle fracture involves a combination of design and inspection standards aimed toward the prevention of stress... parameters: amplitude and velocity of ship motions relative to water, local angle formed at impact between 18-15 the flat part of the hull and the water free surface, presence and extension of air trapped between fluid and ship bottom and structural dynamic behavior (18,19) While slamming probability of occurrence can be studied on the basis only of predictions of ship relative motions (which should... primary bending and torsional strength analyses are based upon the assumption of no distortion of the cross section Thus, we MASTER SET SDC 18.qxd Page 18-33 4/28/03 1:30 PM Chapter 18: Analysis and Design of Ship Structure see that there is an inherent relationship between transverse strength and both longitudinal and torsional strength Certain structural members, including transverse bulkheads and deep... Chapter 18: Analysis and Design of Ship Structure valid only for small wave excitations, small motion responses and low speed of the ship In practice, the field of successful applications extends far beyond the limits suggested by the preservation of realism in the base assumptions: the method is actually used extensively to study even extreme loads and for fast vessels 18.3.4.4 Limits of linear methods... being related to a number of effects, such as: local shape and velocity of the free surface, air trapping in the fluid and response of the structure A complete model of the phenomenon would require a very detailed two-phase scheme for the fluid and a dynamic model for the structure including hydro-elasticity effects Simplified distributions of sloshing and/ or impact pressures are often provided by Classification... strength deck of the ship If its sides are coplanar with the ship s sides it is referred to as a superstructure If its width is less than that of the ship, it is called a deckhouse The prediction of the structural behavior of a superstructure constructed above the strength deck of the hull has facets involving both the general bending response and important localized effects Two opposing schools of thought... 18.qxd Page 18-16 4/28/03 1:30 PM 18-16 Ship Design & Construction, Volume 1 draft, local structural checks based on an additional external pressure Such additional pressure is formulated as a function of ship main characteristics, of local geometry of the ship (width of flat bottom, local draft) and, in some cases, of the first natural frequency of flexural vibration of the hull girder The influence on global... Chapter 18: Analysis and Design of Ship Structure tion at rest The amplitude of heave and roll motions and accelerations governs the magnitude of hull girder loads Contrary to end launch, trajectory and loads cannot be studied as a sequence of quasi-static equilibrium positions, but need to be investigated with a dynamic analysis The problem is similar to the one regarding ship motions in waves, (Subsection